FROM TRIGGER TO DATA ANALYSIS: LOOKING FOR NEW PHYSICS AT THE LHC USING DEEP LEARNING TECHNIQUES By Maria Mazza A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Physics — Doctor of Philosophy Computational Mathematics, Science and Engineering — Dual Major 2024 ABSTRACT The Standard Model (SM), crowned in 2012 with the discovery of the Higgs boson, exhibits remarkable predictive power. However, several phenomena remain unexplained and evidence for physics beyond the SM continues to emerge. The Higgs boson appears at the center of many of these pressing issues, making its study one of the top priorities at the Large Hadron Collider (LHC). To extend its discovery potential, the LHC will undergo a major upgrade that will bring a ten-fold increase in integrated luminosity and increase the center-of-mass energy to 14 TeV. Extracting relevant physics in these unprecedented extreme conditions will require an upgrade of the detector and trigger system, as well as innovative analysis techniques to enhance signal-to-background discrimination. The research presented in this work followed these new directions and challenges on two parallel fronts, with the shared goal of improving our understanding of the scalar sector, and with a common focus on the development of new machine learning methods. On one front, this work contributed to a search for new heavy resonances decaying to two SM bosons (using the full Run 2 ATLAS dataset). Models that predict such particles are often interpreted in the context of two general frameworks – the Heavy Vector Triplet and the two-Higgs-doublet models – and address important open questions related to the Higgs sector: the naturalness problem and the possibility of an extended scalar sector. In particular, this work presents the development of a new multi-class deep neural network (DNN) jet tagger strategy to compete with traditional analysis techniques. The development of the tagger as a standalone tool, as well as the deployment within the analysis workflow to improve analysis sensitivity are presented. On the other front, this work made several contributions to the High-Luminosity LHC upgrade of the ATLAS hardware-based trigger. These started from the development of the software simulation framework for trigger performance studies, and proceeded to focus on the b¯bb¯b, an important signature development of new jet triggers, targeting in particular HH for the measurement of the Higgs self-coupling. This work presents the development, bench- marking, and preliminary firmware simulation of a new jet reconstruction and triggering strategy, as well as the development and performance of a new DNN for pileup mitigation, with both algorithms designed for deployment on fast FPGA hardware. → To K´evin. E quindi uscimmo a riveder le stelle. Inferno, XXXIV iii ACKNOWLEDGMENTS I would like to begin by expressing my deepest gratitude to my Ph.D. advisor, Wade Fisher. Your invaluable teachings and your patience during the thorough discussions we shared have profoundly shaped my academic journey. I am also grateful for, and have sincerely valued, the trust you placed in me: thank you for providing me with opportunities to work on inspiring projects, while giving me the freedom to explore and define my own research path; for allowing me to go from student to teacher, by giving me the opportunity to prepare lectures for your machine learning class; and for trusting me with the freedom I needed to make important life choices. Your support really made a difference and I will always be deeply grateful. I would like to sincerely thank my committee members Wolfgang Kerzendorf, Dean Lee, Saiprasad Ravishankar, and Andreas von Manteuffel, as well as Matt Hirn who left MSU before I graduated, for their support and guidance during these past few years. I would also like to extend a special thank you to Andreas and C.-P. Yuan for having been excellent professors of theoretical high energy physics. Finally, I must thank my committee member and ATLAS collaborator Daniel Hayden, for having always been available and supportive, going well beyond what was expected from him. I would like to thank the MSU postdocs that I was lucky enough to work with. In particular, Garabed Halladjian, my first mentor in particle physics and now a dear friend, and Hector de la Torre, without whom all my work on the trigger would have not been possible. Thank you both for all your teachings, support, and friendship. I would also like to thank Garrit Raynolds, the undergraduate student I mentored, for the hard work. I also want to thank my ATLAS collaborators, especially those I had the chance to work with on the analysis and trigger fronts. My work in the analysis would have not been possible without the contributions of the other analyzers and, in particular, of the analysis contact and MSU postdoc Robert Les. I would also like to thank the US ATLAS Award Committee for rewarding my thesis work with the US ATLAS Outstanding Graduate Student Award. A very nice and unexpected surprise at the end of this long journey, that I would have never thought possible when I started. Vorrei ringraziare la mia famiglia per avermi sempre supportato nelle mie decisioni che mi hanno permesso di arrivare fino a qui. Mia madre, per i sacrifici e l’amore incondizionato, e i miei fratelli Antonio, Giulia, Elisabetta e Lorenzo, per essere sempre presenti e per darmi sempre la certezza di non essere mai sola, anche se lontana. Vorrei mandare un pensiero anche a mia nonna Marisa Freni, per essere stata un modello di donna e scienziata, e vorrei iv ringraziare anche gli zii, cugini, e tutti i parenti per darmi il supporto che solo una grande famiglia sa dare. J’aimerais aussi remercier Niels et Yulia pour m’avoir accueillie dans la famille et pour m’avoir apport´e de l’innocence dans la vie. Mon K´evin, thank you for going beyond yourself to help me these past few years and for never letting me down (even when I ask you to proofread two hundred pages of experimental physics). I will forever be grateful to you for having believed in me and for having given me a chance to be the person I was supposed to be. You inspire me to better myself every day. This thesis is dedicated to you and to the beginning of a new chapter of our lives, looking at the future with hope. v TABLE OF CONTENTS LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 2 The Standard Model (SM) . . . . . . . . . . . . . . . . . . . . . . . 2.1 A quantum theory of fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Lagrangian formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Symmetries and conservation laws . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Deriving a gauge theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 The Higgs Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 The Standard Model Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 The Higgs sector . . . . . . . . . . . . . . . . . 2.8 Hints for physics beyond the Standard Model Chapter 3 The Higgs boson as a portal to new physics . . . . . . . . . . . . 3.1 The Higgs self-coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Naturalness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Heavy Vector Triplet model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 The Two-Higgs-Doublet Model Chapter 4 The LHC and the ATLAS experiment . . . . . . . . . . . . . . . . 4.1 The Large Hadron Collider (LHC) . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 The accelerator complex . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 LHC performance and operation . . . . . . . . . . . . . . . . . . . . . 4.1.4 Brief timeline of LHC operation and upgrades . . . . . . . . . . . . . 4.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 The ATLAS coordinate system . . . . . . . . . . . . . . . . . . . . . 4.2.2 The magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 The inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 The calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 The muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 The forward detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 The Level-1 trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 The High-Level Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Trigger operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 The Phase I trigger upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.5 The Phase II trigger upgrade 4.4 ATLAS Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Tracks and vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Electrons 4.4.3 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Topological clustering . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.5 Missing transverse momentum . . . . . . . . . . . . . . . . . . . . . . 4.3 The ATLAS Trigger ix 1 5 9 11 12 13 16 20 24 30 33 34 35 36 39 43 43 43 44 46 50 51 52 53 54 56 63 65 65 66 69 70 71 74 78 79 79 80 81 83 vi 4.4.6 b-tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Jets 5.2 Jet reconstruction algorithms Chapter 5 Hadron collider physics . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 From QCD to jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 The strong coupling 5.1.2 The hard-scatter cross section . . . . . . . . . . . . . . . . . . . . . . Showering and hadronization . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Soft physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.4 5.1.5 Monte Carlo event generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . Infrared-collinear safety . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 5.2.2 Cone algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 86 87 87 88 91 91 92 94 95 96 97 98 5.3 Jets in ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Jet algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Jet inputs and jet collections . . . . . . . . . . . . . . . . . . . . . . . 101 5.4 Boosted jet tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.5 Pileup suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.5.1 Area-median subtraction . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.5.2 Grooming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.5.3 Constituent-level Sequential-recombination algorithms 5.3.1 5.3.2 Chapter 6 Concepts of statistics and machine learning . . . . . . . . . . . . 111 6.1 Statistical inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.2 Neural networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.3 Hypothesis testing with profile likelihood ratio . . . . . . . . . . . . . . . . . 115 Chapter 7 Search for new heavy resonances decaying to two SM bosons in semi-leptonic final states . . . . . . . . . . . . . . . . . . . . . . . . 120 7.1 The search for new heavy resonances . . . . . . . . . . . . . . . . . . . . . . 120 7.2 Analysis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.2.1 Analysis strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.2.2 Machine learning approach . . . . . . . . . . . . . . . . . . . . . . . . 126 . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.2.3 The Multi-Class Tagger 7.3 Signal and background processes . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.4 Data taking and trigger selection . . . . . . . . . . . . . . . . . . . . . . . . 134 7.5 Object selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.6 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 7.7 Event categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 . . . . . . . . . . . . . . . . . . . . 146 7.8 Boosted jets Multi-Class Tagger (MCT) 7.8.1 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Jet requirements 0-lepton channel 1-lepton channel 2-lepton channel 7.6.1 7.6.2 7.6.3 7.6.4 vii 7.8.2 Testing performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7.9 Resolved jets MCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.9.1 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.9.2 Testing performance . . . . . . . . . . . . . . . . . . . . . . . . 176 7.10 MCT deployment in the analysis 7.10.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 7.10.2 Studies overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 7.10.3 MCT strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 7.10.4 Signal efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.10.5 Signal significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 7.10.6 Expected limit sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 184 7.11 MCT Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 . . . . . . . . . 188 7.11.1 Derivation of background normalization scale factors 7.11.2 Modeling in pre-selection regions . . . . . . . . . . . . . . . . . . . . 189 7.11.3 Modeling in top-enriched control region . . . . . . . . . . . . . . . . . 195 7.11.4 Sensitivity to systematic variations of MCT scores . . . . . . . . . . . 196 Chapter 8 Firmware algorithm development for the HL-LHC Global Trigger upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 8.1 The Global Trigger (GT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 8.2 Trigger performance studies 8.2.1 The GT software simulation framework . . . . . . . . . . . . . . . . . 205 . . . . . . . . . . . . . . . . . . . . . . . . . 207 8.2.2 Developing a jet trigger 8.3 A cone jet reconstruction algorithm . . . . . . . . . . . . . . . . . . . . . . . 210 8.3.1 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 8.3.2 Physics performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 8.3.3 Constituent-level pileup suppression . . . . . . . . . . . . . . . . . . . 223 8.3.4 Preliminary firmware simulation . . . . . . . . . . . . . . . . . . . . . 227 8.4 Pileup-jet rejection with neural networks . . . . . . . . . . . . . . . . . . . . 229 8.4.1 Pileup jet identification . . . . . . . . . . . . . . . . . . . . . . . . . . 230 8.4.2 Neural network development . . . . . . . . . . . . . . . . . . . . . . . 234 8.4.3 Training and performance evaluation . . . . . . . . . . . . . . . . . . 236 . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 8.4.4 Trigger performance Chapter 9 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . 245 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 APPENDIX A. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 APPENDIX B. Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 viii LIST OF ABBREVIATIONS 2HDM Two-Higgs-Doublet Model. 1, 39–41, 120, 122, 123, 130, 132 BC Bunch Crossing. 46, 47, 200, 201, 203 BR Branching Ratio. 121, 122, 129, 131, 139 BSM Beyond Standard Model. 1, 8, 9, 31, 32, 34, 36, 83, 87, 103, 146 CERN European Organization for Nuclear Research. 8, 43, 51, 52 CKM Cabbibo-Kobayashi-Maskawa. 29, 33 CoM Center-of-Mass. 43, 44, 50, 51, 86, 89, 92 CR Control Region. 125, 126, 128, 145 CTP Central Trigger Processor. 66–69, 77, 201, 202 DNN Deep Neural Network. 2, 146, 147, 150, 163, 245, 247 DY Drell-Yan. 127, 129, 130, 143 ECF Energy Correlation Function. 105, 148 EF Event Filter. 66, 75, 77 EL Euler-Lagrange. 11, 12 EMCal Electromagnetic Calorimeter. 79 EMEC Electromagnetic End-cap Calorimeter. 59, 60, 62 EOR Energy Overlap Removal. 217–219, 238 EWSB Electroweak Symmetry Breaking. 34, 37 FCal Forward Calorimeter. 59, 61, 62, 68, 82 FPGA Field Programmable Gate Array. 3, 69, 72, 73, 77, 199–204, 210, 212, 213, 227–229 GEP Global Event Processor. 200–204 ggF Gluon-Gluon Fusion. 127, 129, 131, 143, 206 GT Global Trigger. viii, 3, 199–208, 210–212, 215, 223, 227–232, 235 GWS Glashow-Weinberg-Salam. 8 ix HCal Hadronic Calorimeter. 58, 60, 68 HL-LHC High-Luminosity Large Hadron Collider. 1, 2, 28, 33, 34, 51, 54, 63, 71, 74, 106, 109, 199, 200, 205, 206, 221, 229, 230, 246, 247 HLS High-Level Synthesis. 203, 227, 228 HLT High-Level Trigger. 66, 67, 69–71, 76 HVT Heavy Vector Triplet. 33, 36, 38, 120, 122, 129, 131, 132, 143, 145, 162, 176, 177, 179, 182, 184 IBL Insertable B-Layer. 54, 56 ID Inner Detector. 53–56, 58, 59, 62, 68, 69, 74, 78–81, 84, 102 IP Interaction Point. 43, 44, 48, 49, 51–53, 62, 65 IRC Infrared-Collinear. 91, 96, 97, 99, 105, 107, 210 ITk Inner Tracker. 54, 74, 77 jFEX Jet Feature EXtractor. 72–74, 269 LAr Liquid Argon. 58–62, 68, 71, 72, 74, 134–136, 202, 203 MC Monte Carlo. 92–94, 100, 103, 125, 126, 131–133, 135, 162, 205–208, 221 MCT Multi-Class Tagger. 128, 145, 146, 152, 162, 163, 179–182, 184, 186, 188–191, 195– 197, 245, 246 MDTs Monitored Drift Tubes. 64, 65, 74, 77 MET Missing Energy Transverse. 83, 134, 135, 140, 142 MS Muon Spectrometer. 74, 80, 81 MSSM Minimal Supersymmetric Standard Model. 39, 122, 123 MUCTPI Muon Central Trigger Processor Interface. 67, 69, 77, 200–202 MUX Multiplexer Processor. 200–202 NN Neural Network. 127, 148, 149 PDF Parton Distribution Function. 89, 90, 92 QCD Quantum Chromodynamics. 20, 86–90, 94, 96, 103, 104, 108, 128, 132, 140, 141, 149, 162 x QED Quantum Electrodynamics. 13–15, 22, 23 RNN Recurrent Neural Network. 127, 143 ROC Receiver Operating Characteristic. 153, 154, 156–161, 167, 171–175 RoI Region of Interest. 66, 68, 69 RPC Resistive Plate Chamber. 65, 67, 74, 77 RS Randall-Sundrum. 121, 122, 129–132 SCT SemiConductor Tracker. 54, 55, 79 SF Scale Factor. 188, 191–195, 261–268 SK Soft-Killer. 109, 110, 137, 206, 223 SLR Super Logic Region. 203, 205, 228 SR Signal Region. 125, 128, 145, 179 SSB Spontaneous Symmetry Breaking. 16, 18, 19, 24–28, 38–40 TCC Track-CaloCluster. 102, 136 TDAQ Trigger & Data Acquisition. 65–67, 71, 74, 75, 209, 211, 246 TGC Thin-Gap Chamber. 65, 67, 74 TileCal Tile Calorimeter. 59, 60, 68 TOB Trigger Object. 68, 69, 72, 77, 201, 202, 215, 269 TRT Transition Radiation Tracker. 54–56 UE Underlying Event. 91, 92, 94, 106, 108 UFO Unified Flow Object. 102, 136 VBF Vector Boson Fusion. 38, 127, 129–132, 143 vev Vacuum expectation value. 24, 30, 34, 40, 41 VR Variable Radius. 102, 137, 141, 143 WP Working Point. 79, 81, 85 xi Chapter 1 Introduction × 2s− 1034cm− The Standard Model (SM) of particle physics has proven to be a remarkably successful description of nature. However, several phenomena remain unexplained and evidence for physics beyond the SM continues to emerge. The Higgs boson appears at the center of many of these pressing issues, making its study one of the top priorities at the Large Hadron Col- lider (LHC). To extend its discovery potential, the accelerator will soon undergo a major upgrade that will raise the center-of-mass energy to √s = 14 TeV and bring the instanta- 1. At the end of the High-Luminosity LHC (HL- neous luminosity up to 5 LHC), ATLAS will have ten times the amount of data collected so far. This unprecedented opportunity will open up new search channels, previously inaccessible cross-sections, and more precise tests of SM observables. At the same time, the higher luminosity will generate unprecedented levels of radiation and pileup. Extracting relevant physics in these extreme conditions will require a substantial upgrade of the detector and trigger system, as well as innovative techniques to enhance signal-to-background discrimination, both in offline anal- yses and on real-time event selection. The research presented in this thesis followed these new directions and challenges on two parallel fronts, with the shared goal of improving our understanding of the scalar sector, and with a common focus on the development of new machine learning methods. The observation of a light scalar with a mass of 125 GeV agrees with SM predictions, but necessarily leads to the naturalness problem - the Higgs mass is unstable under radiative corrections, making its observed value the result of an unnatural fine-tuning [1, 2]. This can be prevented if one postulates the existence of new heavy particles with masses around the TeV scale that couple to the Higgs boson. Several beyond-the-SM (BSM) models predict such resonances and are tested experimentally via a general Heavy Vector Triplet model [3], which assumes a simplified phenomenological Lagrangian where only the relevant couplings and mass parameters are retained. New heavy resonances at a similar mass scale are also predicted by Two-Higgs-Doublet Models (2HDMs) [4], which assume the simplest extension of the scalar sector by predicting the existence of two SU(2) complex doublets. Most of these models predict sizable couplings of the new particles to the SM Higgs and weak gauge 1 bosons, making such final states rich landscapes where to look for new physics. This thesis contributed to the ATLAS search for such new heavy resonances in final states with two SM bosons (W W , W Z, ZZ, ZH, or W H) decaying semi-leptonically. Due to the large multiplicity of the different final states considered simultaneously, standard analysis strategies using cut-based event selections had to be rethought to avoid complex overlapping of selection criteria. One of the critical tasks in the event selection of this type of search is the correct identification of the hadronically decaying jets: signal-like events are identified by the presence of jets originating from a Higgs, W , or Z boson, while jets originating from t¯t and V +jets processes characterize the primary SM backgrounds. A significant part of this work was the development of a new multi-class jet tagging algorithm for improved identification of the hadronic decay. Because the search probes mass resonances from 220 GeV to 5 TeV, the analysis is sensitive to a wide range of transverse momenta, requiring different jet reconstruction strategies: the jets are resolved as two small radius jets at low energies, while they are identified as a single large radius jet in the boosted regime. Therefore, two different 5-class deep neural networks (DNN) were trained, one for each reconstruction strategy, and with the output of each model giving the probability of the decay to be originating from a Higgs boson, a W boson, a Z boson, a top quark, or light quarks and gluons produced via the strong interaction. The work presented here covered the development of the models as standalone tools, as well as their deployment within the analysis workflow. Within the context of the analysis, their discrimination power and modelling was assessed, and a new strategy for the event categorization was designed for improved analysis sensitivity. Electroweak baryogenesis, which predicts the Higgs boson to have developed a vacuum expectation value via a first-order phase transition in the early universe, provides a possible solution to the puzzle of the observed baryon asymmetry [5]. The nature of the transition can be accessed by the yet unmeasured Higgs trilinear self-coupling, as models that predict a first-order phase transition predict large deviations from the SM prediction [6]. Measurement of the Higgs self-coupling would also be a direct test of electroweak symmetry breaking and of the shape of the Higgs potential, the latter in turn connected to questions regarding the stability of the universe. The production of two Higgs bosons can provide a direct probe of the Higgs self-coupling, making the measurement of di-Higgs (HH) production one of the major goals of the LHC programme. Because of the low production cross section, the ATLAS and CMS experiments have so far only been able to set limits [7, 8]. However, the HL-LHC is expected to reach the ultimate sensitivity [9], making di-Higgs one of the flagship signatures for the HL-LHC and one of the main drivers of the HL-LHC trigger upgrade. In fact, for reasons that will be explained later, to retain sensitivity to λHHH it is pivotal to 2 retain the low mHH events, an extremely challenging task for the trigger: in this kinematic region the decay products of the Higgs bosons are at low pT , where signal efficiency competes with pileup rejection and is critically dependent on trigger thresholds. Successful data collection has to start with the first step of the trigger chain, which in ATLAS is the Level-0 hardware-based trigger. The Global Trigger (GT) will be a new addition at Level-0 that will allow to deploy complex algorithms on fast FPGA hardware and bring the event rate from 40 MHz down to 1 MHz [10]. The GT is primarily a firmware project, with many algorithms under study. The contributions of this work to the GT upgrade included the development of the software simulation framework for the study of new firmware algorithms, the development of a new jet reconstruction and triggering strategy to make use of the new trigger capabilities, and the exploration of new machine learning algorithms for pileup mitigation targeting di-Higgs production. The jet reconstruction algorithm was optimized by considering the trade-off between reducing algorithm complexity, required to meet FPGA resources and latency limitations, and maintaining high performance to preserve the physics goals of the collaboration. The algorithm was benchmarked against target signal simulations. In particular, the channel b¯bb¯b, with four low pT b-quarks in the final state, was the prime target in the HH → development of multi-jet triggers. → As the trigger thresholds are driven by the rate of pileup jets, a new method was pro- posed to mitigate the negative effect of pileup on trigger efficiencies and further increase the b¯bb¯b events at small mHH values. Pileup-like radiation is uncorrelated acceptance of HH from the hard scatter, resulting in a more diffuse energy pattern in pileup jets than in signal jets. This is another problem of pattern recognition well suited for deep learning applica- tions. This thesis presents the development of a new neural network to identify pileup-like jets starting from topological cluster information, and the studies of its effect on the trigger performance. The content of this thesis is structured as follows. The first part of the manuscript lays the relevant background information for this work. Chap. 2 reviews the SM of particle physics, with an emphasis on the Higgs sector. After highlighting the motivation for beyond the SM physics, Chap. 3 discusses how the scalar sector could be a portal to new physics, with a focus on the aspects relevant for this thesis. The LHC and the ATLAS experiment are described in Chap. 4, being the experimental setup necessary to perform this research. Chap. 5 covers concepts of hadron collider physics, with a focus on jets, reviewing all the technical information referenced in the following chapters. Chap. 6 provides a brief summary of the concepts of statistics and machine learning applied in this work. The latter part of the manuscript discusses the research contributions: Chap. 7 presents the contributions to 3 the search for new heavy resonances, and Chap. 8 details the contributions to the HL-LHC trigger upgrade. Chap. 9 summarizes the findings and their implications for future research. 4 Chapter 2 The Standard Model (SM) Particle physics is the study of the fundamental particles of nature and their interactions. Already in 430 BC the philosopher Democritus theorized a Universe composed of fundamen- tal building blocks that he named atomos – “indivisible” in Greek. What constitutes an elementary particle has, however, evolved over time. By the first half of the last century, it was well established that atoms — the elements of the periodic table — were, in fact, divisible, composed of a tightly bound nucleus made of protons and neutrons and a cloud of electrons around it. Three fundamentally different types of interaction were also known: the very feeble force of gravity, responsible for making Newton’s apple fall from the tree and for keeping the planets in orbit around the Sun; the electromagnetic force, which seemed to govern most of the physical processes in our daily life and was described by a mature theory developed in the previous century; and a strong force that prevented the positively charged protons from tearing the nucleus apart, but whose fundamental nature remained a mystery. In the course of the last century, serendipity coupled with technological advancements led experimental physicists to observe unexpected new particles and phenomena. It was shown that protons and neutrons were not elementary, but rather composed of a new type of parti- cle called quarks coming in two flavors (up and down). Electrons and up and down quarks were observed to have sibling particles, which behaved similarly, but with heavier masses. A new form of interaction was also theorized to explain new observed phenomena, such as radioactive decays, which required the existence of new types of particles, the neutrinos. It was called the weak interaction, owing its name to being much feebler than the strong and electromagnetic forces. After a century of discoveries and a mix of failures and successes, a coherent description of what (for now) are known to be the fundamental building blocks of nature came into shape into what is called the Standard Model (SM). The SM1 is the mathematical framework of particle physics, describing the fundamental particles of nature and their electromagnetic, weak, and strong interactions (gravity is still not included, but since its strength is much weaker than any other force, its absence does not 1A more complete introduction and in-depth explanation of the topics discussed in this chapter can be found in the textbooks and reviews this chapter is based on [12–18]. 5 Figure 2.1: The Standard Model of elementary particles [11]. affect the predictive power of the model in most conditions). The particles and interactions that it describes are summarized in Fig. 2.1. All the fundamental particles that had been observed before 2012 fell into one of two categories determined by their spin quantum number: fermions with spin 1/2 and gauge bosons with spin 1. Fermions make up all ordinary matter. They interact via the fundamental forces to form nuclei, heat up the Sun, and run the electric current in our computers. Gauge bosons are the mediators of these forces. − Fermions are of two types: the leptons and the quarks. The six quarks are organized in pairs of one up-type and one down-type quark, and the pairs are arranged in three generations of increasing mass and different flavor quantum number. The up (u), charm (c), and top (t) quarks have electric charge Q = 2/3, while the down (d ), strange (s), and bottom (b) 1/3. Similarly, leptons are arranged in pairs across three generations quarks have Q = of increasing mass and different lepton quantum number. Each pair is composed of an electrically charged lepton with Q = 1 and its associated neutrino with no electric charge. These are the electron (e) and the electron-neutrino (νe), followed by the heavier muon (µ) and tau (τ ) leptons and their respective neutrinos. Each fermion particle has a corresponding anti-particle, with equal mass but opposite quantum numbers. An interesting feature of the SM is that atoms, and hence all ordinary matter, are composed only of fermions from the first generation, while the heavier siblings are unstable and are only produced for short times before decaying. All fermions with non-zero electric charge participate in the electromagnetic − 6 Standard Model of Elementary Particlesthree generations of matter(fermions)IIIIIIinteractions / force carriers(bosons)masschargespinQUARKSu≈2.2 MeV/c²⅔½upd≈4.7 MeV/c²−⅓½downc≈1.28 GeV/c²⅔½charms≈96 MeV/c²−⅓½stranget≈173.1 GeV/c²⅔½topb≈4.18 GeV/c²−⅓½bottomLEPTONSe≈0.511 MeV/c²−1½electronνe<1.0 eV/c²0½electronneutrinoµ≈105.66 MeV/c²−1½muonνµ<0.17 MeV/c²0½muonneutrinoτ≈1.7768 GeV/c²−1½tauντ<18.2 MeV/c²0½tauneutrinoGAUGE BOSONSVECTOR BOSONSg001gluonγ001photonZ≈91.19 GeV/c²01Z bosonW≈80.360 GeV/c²±11W bosonSCALAR BOSONSH≈124.97 GeV/c²00higgs interaction. In addition to the electric charge, quarks and leptons carry an isospin charge and hence participate in the weak interaction. Quarks are the only fermions that carry another quantum number, called color charge, which allows them to interact via the strong force. The fundamental forces are characterized by their strength, determined by their coupling constants, and by their range, determined by the mass of the gauge boson that mediates the interaction. The photon is the mediator of the electromagnetic interaction. Because the force is long-range, due to the photon being massless, it is the force that we interact with the most in our daily lives. The weak interaction is mediated by the W and Z bosons, which are some of the heaviest particles observed in nature, in the order of 100 GeV, making the weak interaction very short range. Nonetheless, the weak force is necessary to explain important phenomena, such as β decay. Lastly, the strong interaction is mediated by the gluon. Like the photon, the gluon is massless, making the strong interaction technically long range. However, the coupling of the strong interaction has the peculiar feature of increasing at larger distances, which has the effect of preventing individual quarks to ever be observed alone. As a consequence, the strong force is effectively mediated by the exchange of massive particles called mesons, composed of a quark and an anti-quark. The mass of the lightest 15 m, which controls the meson, the pion, gives nuclear forces an effective range of about 10− size of the atomic nucleus. − In 2012, a new type of particle, whose existence had been predicted decades earlier, was finally discovered [19]. The Higgs boson was the first fundamental particle to have been observed with zero spin. This fundamentally different nature allowed the Higgs boson to play a special role in shaping the Universe we live in, including being responsible for the mechanism that gives mass to all other particles. It is currently believed that at the time of the Big Bang the vacuum state of the Universe was symmetrical. At this time, all particles were massless and the four fundamental forces were unified into one single force. Then, shortly after the Big Bang, the potential of the Higgs field changed shape, the symmetrical position that used to be the lowest energy state became unstable, and the Universe decayed into a lower vacuum energy state that broke the symmetry. Upon the spontaneous symmetry breaking, the three weak gauge bosons and the fermions acquired mass and the original symmetry unifying the weak and electromagnetic interaction was hidden from view. The Universe we live in is currently in this broken phase. Because elementary particles are, by definition, microscopic, and can easily reach veloci- ties close to the speed of light, they have to be described by equations that obey both the laws of relativity and of quantum mechanics. Such a theory is a relativistic quantum field the- ory, where quantum mechanics is applied to dynamical systems of relativistic fields. Forces and fundamental particles are both described as fields that permeate the four-dimensional 7 space-time we are in. The particles that we detect are localized vibrations — or quanta — of the field and propagate through it like waves. As it turns out, the SM is a special type of quantum field theory, referred to as a gauge theory, where the fields are invariant under certain space-time-dependent phase transformations. In the 1960s, Glashow proposed the unification of the electromagnetic and weak inter- actions using local gauge symmetry arguments [20]. However, his model predicted massless weak gauge bosons and fermions, in disagreement with the experimental observations. In the same years, it was discovered that a local gauge symmetry could be spontaneously broken by the addition of a massless complex scalar field, which would give rise to massive gauge bosons. This phenomenon, called the Higgs mechanism, was proposed in 1964 independently by Higgs [21], and Englert and Brout [22], opening the possibility of constructing an elec- troweak gauge theory with massive particles. The Higgs mechanism was applied to Glashow’s theory of the electroweak interaction by Weinberg [23] and Salam [24]. The prediction of electroweak symmetry breaking completed the last missing piece of the SM electroweak the- ory, also known as the Glashow-Weinberg-Salam (GWS) model. In the 1970s, a non-Abelian gauge theory of the strong interaction of quarks and gluons came also to maturity, and combined with the GWS model, forms what today is known as the SM of particle physics. Glashow, Weinberg, and Salam were awarded the Nobel Prize in Physics in 1979 for “their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles.” Experimental confirmation of their predictions soon followed with the discovery of the massive W and Z gauge bosons at CERN in 19832. Lastly, as mentioned earlier, the Higgs boson was finally discovered in 2012 at CERN by the ATLAS [25] and CMS [26] Collaborations, ultimately confirming the validity of the SM, and followed shortly after by the Nobel Prize in Physics awarded to Higgs and Englert. The SM has proven to be a remarkably successful description of nature, whose structure was dictated by symmetries and guided by the experimental discoveries of the past century. However, it remains an empirical model, with several free parameters whose measured values bring to the surface a non-intuitive and unexplained structure. Several phenomena remain also unaccounted for, including gravity and evidence of dark matter. This leads physicists to regard the SM as an effective theory, valid only up to a certain energy scale. The belief that a more fundamental theory exists motivates the quest for beyond-the-SM (BSM) physics. In Secs. 2.1 through 2.4, fundamental concepts for the development of a quantum field theory are introduced. The Higgs mechanism is discussed in Sec. 2.5. The SM Lagrangian is introduced in Sec. 2.6 and a more detailed discussion of the Higgs sector in presented in 2To which also followed the Nobel Prize in Physics in 1984 to Rubbia and Var der Meer for “their decisive contributions to the large project.” 8 Sec. 2.7. The motivation for looking for BSM physics will be briefly discussed in Sec. 2.8 and it will be the topic of the next chapter. 2.1 A quantum theory of fields The concept of field was already introduced in Maxwell’s classical formulation of electro- dynamics as a way to prevent action at a distance [16]. Imagine a test charge placed in proximity of a source charge that will instantaneously feel the effect of an electric force pro- duced by the source charge. Without an intermediary — a force carrier — this seems to violate locality. The problem of action-at-a-distance was solved by the introduction of the concept of field, where a field is a function that assigns a value to every point in space and time. An electromagnetic field permeates space, so that when a source charge is placed in the field, the field responds to it locally and then propagates the effect through the field at the speed of light. When a test charge is introduced at some distance away, it feels the influence of the modified field instantaneously. The classical theory of electrodynamics was well established by the beginning of the last century (and later found to be already consis- tent with special relativity). However, shortly after these successes, the new paradigm of quantum physics started to emerge, requiring a fundamental alteration of our understanding of nature. A systematic quantum theory of fields started with Dirac’s 1927 paper [27]. The solutions to Maxwell’s equations in free space3, are transverse waves whose Fourier components behave like individual harmonic oscillator modes. Upon canonical quantization of the dynamical variables – the energy and the phase – describing each individual mode4 , Dirac showed the equivalent interpretation of the number of quanta of energy as the number of particles moving at the speed of light and satisfying Bose-Einstein statistics, i.e. the number of photons. It follows that in quantum mechanics photons are excitations of the electromagnetic field and 3Maxwells’ equations in free space can be written as (cid:32) (cid:33) 1 c2 ∂2 ∂t2 − ∂2 Aµ = 0. (2.1) Here, the field Aµ(x, t) = (V, A) is the four-vector (µ = 0, 1, 2, 3) electromagnetic field, introduced in place of A. the classical electric and magnetic fields, which can be obtained as E(x, t) = Note that E and B are the observable physical fields. For a fixed choice of the fields E and B, A and V are not unique under certain type of transformations called, as shown later, gauge transformations. and B(x, t) = ∂A ∂t ∇× −∇ − V 4Dirac defined the new operators a and a† as a linear combination of the position q and momentum p operators: a = (1/√2ω)(ωq+ip). He then showed that the Hamiltonian could be written as H = ℏω(a†a+ 1 2 ), with eigenvalues En = ℏ(n + 1 2 ), where n = 0, 1, 2, . . . can be interpreted as the number of quanta of energy, and a and a† as annihilation and creation operators of the quanta. 9 can be created and annihilated as quanta of the field. However, electrons and the other particles still obey the Schr¨odinger equation. As we will see, this picture was not complete for a quantum theory of relativistic particles. Quantum mechanics (QM) results from the quantization of a classical theory of particles described by their positions and momenta, but if one tries to write down a single particle relativistic wave equation, several issues arise. These are in part due to the fact that QM does not allow the number of particles in a system to change while, as it turns out, requiring the validity of both the laws of special relativity and of QM implies that the number of particles in a system is not conserved. An intuitive argument can be made as follows [15]. From relativity, one inherits Einstein’s equation E = mc2, according to which the mass of a particle is proportional to its energy. QM provides Heisenberg’s uncertainty principle, which can be expressed as ∆E > ℏc/∆x, stating that the more accurately one knows the position of a particle, the less accurately one will be able to know its energy. It follows that when 2mc2, enough energy is available to produce a particle-anti-particle pair. In other ∆E words, if a physical system is probed at a length scale ∆x ≲ ℏ/(2mc), the concept of a single particle breaks down, as the uncertainty in the energy is now large enough to allow for a cloud of particle-anti-particle pairs to surround the particle. A new framework is needed to describe this phenomenon. ≥ In quantum field theory (QFT), fields are introduced to describe not only the photon, but also the electron. Because any relativistic theory has to obey Einstein’s first principle of relativity (i.e. has to be Lorentz invariant), the particles are more appropriately described by four-momentum vectors pµ = (t, px, py, pz) in Minkowski space, where space and time are treated on equal footing. Space is therefore declassed from being an operator ˆx(t), as in quantum mechanics, to being a label identifying a space-time coordinate xµ = (t, x) of the field, while the operator is now the field ϕ(xµ), which acts at every point in space-time. Of particular importance in these developments was Yukawa’s paper in 1935 that demon- strated how the interaction between particles could be shown to proceed via the exchange of virtual quanta – or mediators – of the force field [16]. In QFT, the field is the object of the quantization and both particles and force carriers arise as excitations of the fields and can be created and annihilated, just like the photon in QM. For instance, the electron and its anti-particle, the positron, can be viewed as the quanta of the electron-positron field. The particle and field pictures are equivalent in describing the system, but it turns out that the fields are the natural way to describe mathematically what is happening at these small distances [15]. Many other fields associated to new particles and interactions had to be introduced to make this description complete. 10 2.2 The Lagrangian formulation Similarly to the classical approach, the equations of motion for a relativistic field can be derived from the Lagrangian L by the principle of least action. The action is expressed as (cid:90) (cid:90) S = Ldt = Ω L (ϕ(x), ∂µϕ(x)) d4x, (2.2) L where is the Lagrangian density, which from now on will be referred to simply as the Lagrangian. This substitution is useful, as the four-dimensional volume element is Lorentz invariant, making the action explicitly Lorentz invariant provided is a Lorentz scalar. Note that is considered to be a functional of the fields and their first order time and spatial derivatives only5. The principle of least action requires the variation of the action δS to be zero for small fluctuations of the fields ϕ(x) ϕ(x) + δϕ(x). Imposing this requirement brings to the Euler-Lagrange (EL) equations of motion for a field [12], → L L ∂ L ∂ϕ − ∂µ (cid:32) ∂ L ∂ (cid:0)∂µϕ(cid:1) (cid:33) = 0. (2.3) In a combined treatment of particles and fields, the Lagrangian has three terms: a free field Lagrangian, a free-particle Lagrangian, and an interaction Lagrangian which describes the interaction between particles and fields. According to which degrees of freedom are considered for the variation of the action integral, EL equations of motion of particles or fields can be derived. A similar formulation for the dynamics of the system could be obtained in terms of the Hamiltonian. However, the Lagrangian formulation is particularly well suited for QFT as the theory is manifestly relativistically covariant and its symmetry properties and associated conservation laws are directly identifiable from the Lagrangian. One could argue that the goal of particle physics is to find a model, defined by a La- grangian, that describes the fundamental laws of nature [28]. In practice, one needs to identify what the symmetries and the fields in the theory are, and how the fields transform under the symmetries. The symmetries, plus a few theoretical requirements such as locality 6 and renormalizability7, allow one to identify all the terms allowed in the Lagrangian. Once the Lagrangian is defined, the predictive power of the model can be tested against experi- 5This requirement allows one to treat space and time on equal footing and is sufficient to describe the physics observed by experiment. 6In a local theory the Lagrangian can only contain products of fields evaluated at the same space-time location. This removes the possibility of action-at-a-distance [13]. 7A theory is renormalizable if all its physical predictions remain finite and well-defined once all the cut-offs of the theory are removed [13]. 11 ment. In the following section, it will be shown why symmetries play such a fundamental role in model building due to their connection to conservation laws. 2.3 Symmetries and conservation laws The Lagrangian is said to be invariant under a transformation if, when expressed in the new transformed coordinates and fields, it preserves the same functional form as the original Lagrangian (up to a 4-divergence, as such a term does not affect the derivation of the EL equations of motion). Assume the Lagrangian is invariant under some continuous transfor- mation of the field ϕ(x) → ϕ′(x) = ϕ(x) + ϵδϕ(x) + (ϵ2), O (2.4) where ϵ is an infinitesimal parameter and δϕ(x) is some deformation of the field configuration. (ϕ′(x), ∂ϕ′(x)) and one can show that Then, (ϕ(x), ∂ϕ(x)) = L L = 0 = δ L (cid:20)∂ L ∂ϕ − ∂µ (cid:18) ∂ L ∂(∂µϕ) (cid:19)(cid:21) δϕ + ∂µ (cid:20) ∂ L ∂(∂µϕ) (cid:21) δϕ . (2.5) From the EL equations, the first term vanishes. Therefore, the system has a conserved current ∂µJµ = 0 and a corresponding conserved charge8 given by [13], Jµ = ∂ L ∂(∂µϕ) δϕ and (cid:90) Q ≡ d3xJ 0. (2.6) This result can be easily generalized to the case of transformations involving also the space- time coordinates and is known as Noether’s theorem. More formally, the theorem states that for every continuous symmetry that leaves the Lagrangian invariant there is a conserved current and a corresponding locally conserved charge. For example, the invariance of L under translations in time and space implies conservation of energy and momentum. The transformations are required to be unitary, as this ensures observable predictions to be invariant. An important class of symmetries are internal symmetries, which involve transformations of the fields themselves and act identically at every point in space-time [15]. As an example, consider the Lagrangian density describing a free Dirac fermion L0 = ¯ψ(x)(iγµ∂µ − 8The condition ∂µJµ = 0 guarantees that dQ/dt = 0. m)ψ(x). 12 (2.7) This Lagrangian is invariant under continuous rotations of the phase of ψ(x) as ψ(x) → eiαψ(x). Such rotations belong to the one-dimensional unitary group of transformations U(1), whose operators are one-dimensional unitary matrices, i.e. complex numbers of unit modulus. These transformations bring the system from one physical state to a different one with the same physical properties. According to Noether’s theorem, this invariance determines the conservation of some quantity. In general, the number of conserved quantities is equal to the number of the generators of the group of transformations. In this case, there is one conserved current jµ = ¯ψ(x)γµψ(x). This type of transformation is said to be global, to differentiate it from what are known as local gauge transformations. As an example of a local gauge transformation, consider the free field Lagrangian of quantum electrodynamics (QED) 1 4 − = L FµνF µν, (2.8) ∂νAµ. This Lagrangian is invariant where the field strength tensor is given by Fµν = ∂µAν under the symmetry Aµ(x) Aµ + ∂µf (x), for any function f (x): − → Fµ(x) → F ′µν = ∂µ(Aν + ∂νf (x)) − ∂ν(Aµ + ∂µf (x)) = Fµν. (2.9) According to Noether’s theorem, this should produce an infinite number of conserved quan- tities. However, these are not true internal symmetries, but expressions of a redundancy of degrees of freedom in the description of the system. If one tries to apply Noether’s theorem for any of these transformations, it results in the same conserved quantity as for the global transformation where f (x) = const. When this is the case, the system is more correctly described as a set of configurations related to each other by a group of transformations. This type of symmetry is called a gauge symmetry or gauge invariance, and the vector field Aµ is called a gauge field. As shown later, to remove the redundancy one can “fix the gauge” by imposing some extra condition on the vector potential. 2.4 Deriving a gauge theory The free field Lagrangian in Eq. (2.8) describes the electromagnetic theory in the absence of sources, while Eq. (2.7) describes free fermions. If one wants to build an interacting theory of light and matter, a new term has to be included, which couples Aµ to the matter fields. How to add the interaction term? = The Maxwell Lagrangian jµAµ, called in this way because its equations 1 4FµνF µν L − − 13 of motion are Maxwells’ equations, adds the interaction via the term jµAµ, where jµ is a conserved current dependent on the fermion fields. Recall that the free fermion Lagrangian is invariant under the global U(1) phase transformation. To this true internal symmetry of the theory corresponds the conserved current jµ = ¯ψ(x)γµψ(x), which can be shown to result in the conservation of the electric charge e. A good attempt at including the interaction between the matter and the field is then QED = L 1 4 − FµνF µν + ¯ψ(x)(iγµ∂µ m)ψ(x) − − e ¯ψ(x)γµAµψ(x), (2.10) where e has been introduced as the coupling constant. This is referred to as minimal inter- action. But while the original free field Lagrangian (Eq. (2.8)) was invariant under the local gauge transformation Aµ(x) → A′µ = Aµ + ∂µf (x), (2.11) the new interaction term is not. The invariance can be restored if the transformation of the vector field Aµ is coupled to the local gauge transformation of the fermion field ψ(x) ¯ψ(x) → → ψ(x)′ = eiqf (x)ψ(x), iqf (x). ¯ψ′(x) = ¯ψ(x)e− (2.12) (2.13) The Lagrangian in Eq. (2.10) is invariant under the coupled gauge transformations from Eq. (2.11) and (2.12) and is in fact the QED Lagrangian sufficient to describe the experi- mental observations. This derivation was only possible because QED had a fully developed classical counterpart in Maxwell’s equations to guide it. However, it provided a prescription to derive other gauge theories without starting from classical inputs. When this derivation was generalized for other types of interaction, the procedure was reversed. Using again QED as an example, one starts from the free particle Lagrangian and iden- tifies the global U(1) phase transformation. This invariance indicates that the phase of the field ψ(x) has no physical meaning, as one can rotate ψ(x) by an arbitrary real constant at all points in space-time and obtain the same dynamics. However, if one allows the phase to depend on the space-time coordinate x, i.e. if one applies the local gauge transformation from Eq. (2.12), the Lagrangian is no longer invariant, as now ∂µψ(x) → eiqf (x)(∂µ + iq∂µf (x))ψ(x). (2.14) 14 Thus, while the global phase of the field depends only on the chosen convention, it has to be fixed for all space-time points. This type of restriction seems unnatural and brought to the ideation of the “gauge principle”, or the requirement of local gauge invariance. In order to restore local gauge invariance, one introduces a vector field Aµ(x) that transforms in such a way as to cancel the ∂µf (x) term: Aµ(x) −→ A′µ = Aµ + ∂µf (x) Then one changes the derivative ∂µψ(x) to the covariant derivative Dµψ(x) = (cid:2)∂µ + ieAµ (cid:3) ψ(x) (2.15) (2.16) which has the property of transforming like the field itself. Note that replacing the ordi- nary derivative ∂µψ(x) with the covariant derivative Dµψ(x) is equivalent to introducing the interaction term. The gauge field Aµ appears as the mediator of the electromagnetic interaction that couples to the field ψ with coupling strength proportional to e. Note that a mass term for the gauge field 1 2 m2AµAµ is forbidden as it would break the gauge invariance of the Lagrangian. Therefore, QED predicts the photon to be massless. To allow the new vector field to propagate in space, a gauge invariant kinetic term is added, which corresponds to the free field Lagrangian in Eq. (2.8). The final QED Lagrangian QED = L 1 4 − FµνF µν + ¯ψ(x)(i /D m)ψ(x) − (2.17) is manifestly invariant under the coupled gauge transformations from Eqs. (2.11) and (2.12). QED is the simplest example of a gauge theory, where gauge fields are included in the Lagrangian to ensure local gauge invariance. The gauge field is a dynamical variable that interacts with other particles, as well as with itself. Upon quantization, the quanta of the gauge fields are called the gauge bosons. The number of gauge fields needed to restore local gauge invariance under the given gauge symmetry group is equal to the number of generators of the group. When the symmetry group is non-commutative, the theory is a non-Abelian gauge theory. The concept of a gauge theory was formalized by Yang and Mills in 1954 starting from the Abelian gauge theory of QED and extended to non-Abelian gauge theories. This for- mulation had very fruitful implications. The modern theories of the strong and electroweak interactions are both examples of non-Abelian gauge theories and form what today is called the SM, whose mathematical formulation can be derived by the requirement of local gauge U(1)Y gauge symmetry group and the addition of invariance under the SU(3)C × SU(2)L × 15 a scalar particle to drive the Higgs mechanism. 2.5 The Higgs Mechanism The Higgs mechanism occurs when spontaneous symmetry breaking (SSB) happens within a gauge theory. The phenomenon of SSB occurs when the ground state of a system is not symmetric under a symmetry of its Lagrangian. Consider a Lagrangian that possesses a given symmetry and whose ground state is degenerate, so that the ground state eigenstates transform among themselves under the symmetry of the Lagrangian. When the system settles in its ground state, one of the degenerate states is arbitrarily chosen. The ground state is then no longer invariant under the original symmetry, which is now hidden. An example of SSB is ferromagnetism. In a ferromagnet, the ground state of the system requires the spins to be aligned along some direction producing a non-zero magnetization ⃗M . The ground- state magnetization can be oriented in any direction because the system is invariant under rotation, but once the ferromagnet cools down and a choice for the direction is made, the system is not invariant under rotation anymore. Therefore, the choice of a ground state spontaneously breaks the global rotational symmetry of the system. In a field theory, the ground state is the vacuum, so SSB can only occur if the vacuum state is not unique. To preserve Lorentz and translation invariance of the vacuum state, any = 0, spinor or vector field vacuum expectation value must vanish so that in order to break the symmetry a scalar field ϕ(x) has to be introduced. V µ(x) 0 0 ⟩ | | ψ(x) 0 0 ⟩ | | ⟨ = ⟨ In the following [13], the Goldstone model is presented as a simple example of SSB in a field theory to illustrate how SSB leads to the appearance of massless particles known as Goldstone bosons. When SSB is applied to a gauge theory, however, things are a bit In the context of a gauge theory, gauge fixing allows to convert the new non- different. physical degrees of freedom of the Goldstone bosons into mass terms for the gauge vector bosons. The original gauge symmetry is broken, but its effect remains visible in the way the interactions of the massive vector bosons are constrained. Via this mechanism, called the Higgs mechanism, the gauge bosons acquire mass and a new massive scalar field remains in the theory, the Higgs boson. This will be illustrated using the simplest example of a U(1) gauge theory. The mechanism was studied and generalized to the case of a non-Abelian gauge theory by Higgs, Kibble, Guralnik, Hagen, Brout, and Englert, and was subsequently applied to the gauge theory of electroweak interactions by Weinberg and Salam. 16 The Goldstone model Consider a complex scalar field ϕ(x) = 1 √2 [ϕ1(x) + iϕ2(x)] described by the Lagrangian (x) = ∂µϕ∗(x)∂µϕ(x) µ2 2 ϕ(x) | | − ϕ(x) λ | 4, | − L invariant under the global U(1) phase transformation ϕ(x) → ϕ′(x) = eiαϕ(x), ϕ(x)∗ → ϕ∗′(x) = e− iαϕ∗(x) The potential of this Lagrangian is (2.18) (2.19) (a) (b) Figure 2.2: Potential of Eq. (2.20) with λ > 0, for (a) µ2 > 0 and (b) µ2 < 0. Adapted from Ref. [13]. V (ϕ) = µ2 2 + λ ϕ(x) | | 4, ϕ(x) | | (2.20) µ2 − 2λ eiθ for 0 with λ > 0 for it to be bounded from below. The parameter µ can take on two possible values, as shown in Fig. 2.2. For µ2 > 0, the potential has a unique absolute minimum at ϕ(x) = 0, while for µ2 < 0, the potential has a circle of absolute minima at ϕ(x) = ϕ0 = (cid:18) (cid:19)1/2 θ < 2π. The ground state ϕ0 is degenerate, as the angle θ determines ≤ an arbitrary direction in the complex plane. The choice of one particular ground state breaks the rotational U(1) symmetry of the theory. Without loss of generality, one can choose the 17 ϕ2(x)ϕ1(x)𝒱(ϕ)ϕ2(x)ϕ1(x)𝒱(ϕ) ground state ϕ0 to be at θ = 0, so that ϕ0 is on the real axis, ϕ0 = (cid:19)1/2 (cid:18) µ2 − 2λ = 1 √2 v (2.21) One can then redefine the field ϕ(x) in terms of deviations from the equilibrium ground state ϕ(x) = 1 √2 [ϕ1(x) + iϕ2(x)] ϕ(x) = −→ 1 √2 [(v + σ(x)) + i(η(x))], (2.22) where σ(x) and η(x) are two real fields. Rewriting the Lagrangian with this substitution (x) = L 1 2 ∂µσ(x)∂µσ(x) 1 2 − (2λv2)σ2(x) + 1 2 ∂µη(x)∂µη(x) λvσ(x)[σ(x)2 + η2(x)] − 1 4 − λ[σ2(x) + η2(x)]2, (2.23) (2.24) the first line can be interpreted as the free field Lagrangian, while the second line contains the interaction terms between the fields σ(x) and η(x). From the first line one can infer that σ(x) and η(x) are real Klein-Gordon fields, which, upon quantization, lead to a spin-0 σ(x) boson with mass √2λv2 and a massless spin-0 η(x) boson. Note that the massive σ(x) field describes oscillations of ϕ(x) along the radial direction of the potential, where V (ϕ) has a non-vanishing second derivative, while the massless η(x) field is associated to displacements in the tangential direction of constant V (ϕ). The η(x) boson is an example of a Goldstone boson, a massless particle that appears in a field theory as a consequence of the degeneracy of the ground state. This is formalized by the Goldstone Theorem, which states that for every spontaneously broken continuous symmetry, the theory contains massless scalar particles whose number is equal to the number of broken symmetries. The Higgs mechanism To consider the simplest example of SSB in a gauge theory, one can generalize the Gold- stone model by requiring invariance under a local U(1) phase transformation of the same Lagrangian. Following the prescription to derive a gauge theory, the covariant derivative Dµϕ(x) = [∂µ + iqAµ(x)]ϕ(x) is introduced, with the resulting Lagrangian given by (x) = [Dµϕ(x)]∗[Dµϕ(x)] L µ2 2 ϕ(x) | | − ϕ(x) λ | 4 | − − 1 4 Fµν(x)F µν(x) (2.25) The Lagrangian has the same potential and is invariant under the coupled U(1) gauge trans- , formations, similarly to Eqs. (2.11) and (2.12). Performing the same substitution into L 18 one obtains (x) = L − + 1 2 1 4 1 2 ∂µσ(x)∂µσ(x) − Fµν(x)F µν(x) + 1 2 1 2 (2λv2)σ2(x) (qv)2Aµ(x)Aµ(x) ∂µη(x)∂µη(x) + qvAµ(x)∂µη(x) + interaction terms (2.26) (2.27) (2.28) (2.29) While the result looks similar to what was obtained with the Goldstone model, the interpre- tation of the second line as a massive vector field and of the third line as a massless boson fails because of the term in the last line, which mixes derivatives of Aµ and η(x), making the two fields not independent. However, upon more careful look, one can notice that the new Lagrangian contains an extra degree of freedom. This can be removed by an appropriate choice of gauge. Specifically, in the unitary gauge, a U(1) rotation is used to transform ϕ(x) into a real field ϕ(x) = 1 [v + σ(x)]. Upon the transformation, the η(x) field disappears √2 and the Lagrangian becomes, (x) = L − − ∂µσ(x)∂µσ(x) − Fµν(x)F µν(x) + 1 2 1 4 λvσ3(x) 1 4 − 1 2 1 2 λσ4(x) + (2λv2)σ2(x) (qv)2Aµ(x)Aµ(x) 1 2 q2Aµ(x)Aµ(x)[2vσ(x) + σ2(x)]. (2.30) (2.31) (2.32) qv | The first two lines can now be interpreted as the free field Lagrangian of a scalar boson of mass √2λv2 and a vector boson with mass , respectively. Via SSB, the original Lagrangian | with a complex scalar field and a massless real vector field turned into a Lagrangian of a real scalar field and a massive real vector field. The number of degrees of freedom remained constant (fixed to 4), but one of the two degrees of freedom of the complex scalar field ϕ(x) was taken up by the vector field that has become massive. This was done via the Goldstone boson η(x), which appeared because of SSB, but was unphysical and could be eliminated by fixing the gauge. This phenomenon by which a Goldstone boson, produced as a consequence of SSB, gets “eaten” by a gauge boson that subsequently acquires mass is known as the Higgs mechanism and the massive spin-0 boson σ(x) that survives is called a Higgs boson. 19 2.6 The Standard Model Lagrangian The SM Lagrangian before spontaneous symmetry breaking describes the electromagnetic and weak interaction between quarks and leptons and the strong interaction between quarks. It contains two types of fields, the matter fields describing the spin 1/2 fermions and the spin 1 gauge bosons, which mediate the interactions and are introduced in the theory via the requirement of gauge invariance. This Lagrangian is formed from combining the U(1)Y invariant electroweak theory and the SU(3)C gauge theory of quantum SU(2)L × SU(3)C gauge invariant theory. chromodynamics (QCD), resulting in an SU(2)L × In this Lagrangian the gauge bosons and the fermions are assumed massless, as introduction of mass terms breaks the gauge invariance of the theory. The addition of the Higgs scalar field is necessary to provide a mechanism for the fermions and gauge bosons to acquire masses, while preserving gauge invariance via the process of spontaneous symmetry breaking. U(1)Y × The SM Lagrangian can be summarized by four terms = LFermion + LGauge bosons + LHiggs + LYukawa. L (2.33) The first two terms describe the fermion and gauge fields and their interactions, while the last two terms appear after the introduction of the Higgs doublet and represent the Higgs sector, discussed in the next section. Fermions The fermion fields are the quarks and leptons, whose free field Lagrangian is given by f 0 = i ¯ψf (x)γµ∂µψf (x), L (2.34) where f runs over each fermion type. It is useful to separate each spinor into its left-handed and right-handed components, according to how they transform under the helicity projection operators. For massless particles, or for massive particles in the high energy limit, the left- handed and right-handed charged lepton fields are defined as, ψL l (x) ψR l (x) ≡ ≡ PLψl(x) = PRψl(x) = 1 2 1 2 (1 γ5)ψl(x), − (1 + γ5)ψl(x). (2.35) (2.36) This is a useful distinction, because only left-handed fermions experience the weak force. In fact, the left-handed fields transform under the SU(2) symmetry group of the weak interac- 20 tion as isospin doublets, while the right-handed components transform as singlets. In the SM neutrinos are assumed to be massless, so that only left-handed neutrinos and right-handed anti-neutrinos couple to SM interactions. The matter particles can then be summarized as: (cid:32) L1 = (cid:32) L2 = (cid:33) (cid:33) , , , νe e− νµ µ− ντ τ − (cid:32) (cid:33) L3 = (cid:124) lR1 = e−R Q1 = lR2 = µ−R Q2 = (cid:32) (cid:33) u d (cid:32) c s (cid:32) lR3 = τ −R (cid:125) Q3 = (cid:124) (cid:123)(cid:122) Leptons , uR1 = uR, dR1 = dR L (cid:33) , , L (cid:33) L uR2 = cR, dR2 = sR (2.37) = tR, uR3 (cid:123)(cid:122) Quarks dR3 = bR (cid:125) t b The leptons and quarks are grouped in the three generations and the left-handed com- ponents are combined into SU(2) doublets. U(1)Y electroweak theory, gauge invariance determines the conservation of the weak hypercharge Y and of the weak isospin I, while spontaneous symmetry breaking of SU(2)L × U(1)EM brings to the conservation of the electric charge Q. The three are related by the relationship In the SU(2)L × U(1)Y → Y = 2Q 2I3, − (2.38) where I3 is the third component of the weak isospin and Q is in units of the proton charge e. All isospin singlets have IR i = 0, indicating that they do not partake in the weak interaction. The isospin doublets have IL 2 τi, where τi are the Pauli spin matrices, so that all upper (lower) components of an isospin doublet have IL 1/2). This leads to a hypercharge of Y L 2 for the right-handed singlets. Similarly, l = l = Q = 1 Y L 1 for left-handed leptons, and Y R − u = 4 2 3 , Y R 3 for quarks. In terms of left and right-handed fields, Eq. (2.34) can be rewritten as 3 and Y R 3 = 1/2 ( i = 1 d = − − − f 0 = ¯LiiDµγµLi + ¯eRiiDµγµeRi + ¯QiiDµγµQi + ¯uRiiDµγµuRi + ¯dRiiDµγµdRi. (2.39) L The fact that left-handed and right-handed components transform differently under SU(2) prevents fermion mass terms to be added explicitly in the Lagrangian, as mass terms mix left and right-handed components, which violates SU(2) gauge invariance: me ¯ψeψe = − me ¯ψe − (cid:18) 1 2 (1 − γ5) + 1 2 (cid:19) (1 + γ5) ψe = me( ¯ψe − RψL e + ¯ψe LψR e ). (2.40) 21 In addition to participating in the electroweak interaction, the quark fields Qi, uR i , and uR i (i = 1, 2, 3) carry a color charge associated to the SU(3) symmetry of the strong interaction. Any quark can exist in one of three different color states, denoted as red, green, and blue, and transform from one color state to another under the SU(3)C group as triplets, qi =    ,    qr i qg i qb i (2.41) with C = r, g, b representing the color charge. Only color singlet combinations are observed in nature, as baryons and mesons, B = 1 √6 ϵαβγ qαqβqγ | ⟩ , M = 1 √3 δαβ qαqβ⟩ | . (2.42) This is known as color confinement: quarks are confined within color-singlet bound states. Gauge fields The introduction of force mediators in the theory can be obtained via gauge symmetry arguments. The free-fermion Lagrangian of Eq. (2.39) is invariant under global U(1)Y , SU(2)L, and SU(3)C transformations, which determines the conservation of hypercharge, weak isospin, and color charge, respectively. × Analogously to QED, the operators of the U(1) group are complex numbers of unitary module. The elements of the SU(2) group are 2 2 unitary matrices with determinant one. The generators of the group are T a = 1 2 τ a, where τ a(a = 1, 2, 3) are the Pauli spin matrices. The group is non-Abelian as the operators do not commute: [T a, T b] = iϵabcTc, where ϵabc is the anti-symmetric tensor. Similarly, the elements of the fundamental representation of the 3 matrices with determinant one, and the generators SU(3)C group are the set of unitary 3 of the algebra are the matrices T a = 1 2λa(a = 1, 2, . . . , 8), where λa are the Gell-Mann matrices. The matrices T a satisfy the commutation relations [T a, T b] = if abcTc, where f abc are the SU(3) structure constants, which are real and totally antisymmetric. × In the context of electroweak theory, under the local SU(2)L × tions, the fermion fields transform as U(1)Y gauge transforma- L(x) R(x) → → L′(x) = eiαa(x)T a+iβ(x)Y L(x), R′(x) = eiβ(x)Y R(x). (2.43) (2.44) 22 Similarly, in color space the fermion fields transform as ψ′q(x) = eiαa(x) λa 2 . ψq(x) → (2.45) Following the prescription to derive a gauge theory, invariance under the local U(1) trans- formation requires the addition of one field, denoted as Bµ, similarly to the Aµ field in QED. Similarly, three gauge fields W i µ are included to preserve SU(2) gauge invariance, cor- responding to the three generators of SU(2). Lastly, to the eight generators of the SU(3) group corresponds the octet of gluon fields, Gi µ. The new fields, with their appropriate coupled gauge transformations, are introduced via the covariant derivative, (cid:18) Dµψ = ∂µ igsTaGa µ − ig2TaW a µ − − (cid:19) Bµ ψ. ig1 Yq 2 (2.46) with gs, g2, and g1 the coupling constants of SU(3)C , SU(2)L and U(1)Y , respectively. Gauge invariant terms describing the free fields in the absence of fermions need to also be included. The final Lagrangian describing the free fermion and gauge boson fields, together with their interactions, is given by = L (cid:88) ¯Ψj LiγµDL µ Ψj L + (cid:88) ¯ψj RσiγµDR µ ψj Rσ j − 1 4 µνGµν Ga a − 1 4 j,σ µνW µν W a a − 1 4 BµνBµν, where the gauge invariant field strength tensors are given by, Ga W a Ga µν = ∂µGa ν − µν = ∂µW a ν − µν = ∂µBν ∂νGa ∂νW a ∂νBµ. − µGc µ + gsf abcGb ν, µW c µ + g2ϵabcW b ν , (2.47) (2.48) (2.49) (2.50) (2.51) Note that the richer structure of Gµν and Wµν is due to the non-Abelian nature of the corresponding groups. These terms are responsible for self-interaction vertices of the weak gauge bosons and of the gluons. Note also that the theory presented so far predicts massless gauge bosons. While the photon is indeed massless, the W and Z bosons are known not to be. Adding ad hoc mass terms for the W and Z bosons, such as m2 W W †µ(x)W µ(x) + 1 Z Zµ(x)Zµ(x), breaks gauge invariance. To include mass terms and preserve gauge in- 2m2 variance a new mechanism is necessary. After the discovery of the Higgs boson, this was confirmed to be the Higgs mechanism. 23 2.7 The Higgs sector U(1)Y gauge symmetry The electroweak SM Lagrangian is invariant under the SU(2)L × group, with three generators associated to the SU(2) symmetry and one to U(1), for a total of four generators. Via the Higgs mechanism, one would like three of the vector bosons to acquire mass and one of them, the photon, to remain massless. In order to have SSB a scalar field with a non-vanishing vacuum expectation value invariant under some symmetry of the Lagrangian has to be introduced. To break the symmetries associated to three generators, at least three degrees of freedom are needed for the scalar field. The simplest choice (providing four degrees of freedom) is to add a complex scalar field ϕ(x) that is an isospin doublet of SU(2) with hypercharge Yϕ = +1, Φ = (cid:33) (cid:32) ϕ+(x) ϕ0(x) (2.52) − where ϕ+(x) and ϕ (x) are scalars under Lorentz transformations. Note that, according to Eq. (2.38), this choice of hypercharge makes the upper (lower) component of the doublet have Q = 1 (Q = 0). The simplest way of including the new field in the electroweak Lagrangian LEW term is already SU(2) U(1) invariant, while LEW is by letting the Lagrangian Lϕ describing the scalar field can be made invariant by introducing the EW covariant derivative from Eq. (2.46) and is given by, Lϕ. The LEW + × = L LΦ = (DµΦ(x))†[DµΦ(x)] − µ2Φ(x)†Φ(x) − λ(Φ†(x)Φ(x))2. (2.53) The scalar field has a very similar potential as in the Higgs model. For µ2 < 0, the vacuum state Φ0, which occurs at the minimum of the potential, is degenerate and occurs whenever µ2 2λ . Upon the choice of a particular vacuum expectation value (vev) for the ground Φ†0Φ0 = − state U(1) transformations anymore, so the ⟩0, the system is not invariant under SU(2) Φ ⟨ symmetry is spontaneously broken. Without loss of generality, the value of the vev is chosen so that Φ develops a vev only in the lower component of the doublet, × Φ0 = (cid:33) (cid:32) 0 v √2 , with v = (cid:18) µ2 λ − (cid:19)1/2 . (2.54) One can parametrize the scalar field in terms of its deviations from the vacuum state Φ0 24 and move to the unitary gauge, Φ(x) = (cid:32) 1 √2 (cid:33) η1(x) + iη2(x) v + σ(x) + iη3(x) 1 √2 −→ (cid:32) (cid:33) 0 v + σ(x) (2.55) As observed with the Higgs model, the extra degrees of freedom of the massless η(x) bosons are unphysical. These extra degrees of freedom are “rotated away” by moving to the unitary gauge, through a gauge transformation that combines first an SU(2) rotation which converts the isospinor into a down-isospinor, followed by a U(1) transformation which makes the down isospinor real. All other fields in the Lagrangian transform accordingly, but being the SM Lagrangian SU(2) U(1) invariant, this does not affect the equations of motion. In the following the fields are assumed to have been rotated and the same notation for the fields is kept. × Note that, because SSB occurs in the component of the isospinor that is electrically neu- tral, electric charge is conserved in the vacuum state, meaning that one symmetry survives. More precisely, under a global SU(2) U(1) transformation the Higgs doublet transforms as Φ(x) Φ′(x) = exp[i(αiτi/2 + βY )]Ψ(x). For the choice of α1 = α2 = 0 and α3 = 2β, one finds a gauge transformation that leaves the vacuum field invariant: → × ϕ0 → ϕ0 = exp[i(2IW 3 + Y )β]ϕ0 = 1 ϕ0. · (2.56) × 2 Y . SU(2)L × Before SSB the SM is an SU(3) One can identify this new U(1) gauge transformation as the electromagnetic interaction and the conserved charge as the electric charge Q = IW 3 + 1 U(1)Y gauge invariant theory. After SSB U(1)Y symmetry is broken, but a new U(1)EM symmetry appears. The the SU(2)L × SU(3) symmetry stays unbroken because the Higgs field is not charged under SU(3). In the following the scalar sector Lagrangian will be analyzed after SSB and rotation to the unitary gauge. From the covariant derivative term, it will be shown that the degrees of freedom of the Goldstone bosons have been eaten by three gauge bosons, which acquired a mass. These will be identified as being the W +, W −, and Z bosons. The photon, on the other hand, will remain massless thanks to the surviving U(1)EM symmetry. Analysis of the term related to the Higgs potential will show that a new massive scalar boson appeared, the Higgs boson σ(x). From now on, σ(x) will be referred to as H. Lastly, it will be shown that the addition of a scalar field in the theory allows to introduce new gauge invariant terms to the SM Lagrangian to provide fermion masses. 25 The covariant term Writing out the covariant term after SSB in the unitary gauge one obtains, (cid:19) 2 (cid:12) (cid:12) Φ (cid:12) (cid:12) DµΦ | 2 = | (cid:18) (cid:12) (cid:12) (cid:12) (cid:12) ∂µ − ig2 Bµ 1 2 ig1 W a τa µ − 2 i 2 (g2W 3 µ + g1Bµ) ig2 µ + iW 2 2 (W 1 µ) 1 2(v + H)2 g2 8 W 1 | − (cid:32) ∂µ (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) − (∂µH)2 + = = 1 2 1 2 iW 2 µ) g1Bµ) 1g2 2 (W 1 µ − − ∂µ + i 2 (g2W 3 µ − 1 2 + µ + iW 2 (v + H)2 µ| 8 (2.57) (2.58) (cid:33) (cid:32) 0 v + H 2 (cid:33)(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) g2W 3 | µ − g1Bµ 2. | (2.59) The first term in the last line is the kinetic term for the Higgs field. The other terms can be divided into two groups, according to whether they pick out the v2 term from the factor (v + H)2 or not. In the following, it will be shown that the former group produces bilinear terms in the gauge fields that can be interpreted as mass terms for the gauge bosons. The second group provides interaction terms between the gauge bosons and the Higgs boson. In order to obtain explicit mass terms the fields can be redefined as: W ±µ = 1 √2 (W 1 µ ∓ iW 2 µ), Zµ = g1Bµ g2W 3 µ − (cid:113) g2 2 + g2 1 , Aµ = g2W 3 µ + g1Bµ (cid:113) g2 2 + g2 1 , (2.60) where two vector bosons W ±µ with electric charge 1 are obtained from linear combinations of the first two components of the Wµ field, and two electrically neutral fields Zµ and Aµ are written as linear combinations of the field Bµ and the third field component W 3 µ. The fields Zµ and Aµ are orthogonal to each other and are related to the original fields via the rotation matrix, ± Bµ(x) = W 3 sin θW Zµ(x) + cos θW Aµ(x) − µ(x) = cos θW Zµ(x) + sin θW Aµ(x). The Lagrangian with the terms containing v2 can then be rewritten as 1 8 ( LΦ ⊃ → 2 + W 1 | vg2)2W + µ + iW 2 µ| µ + µ W − 2v2 g2 1 2 1 2 1 8 1 2 ( v2 g2W 3 | (cid:113) µ − 2 + g2 g2 g1Bµ 2 | 1)2ZµZµ. v The mass terms can then be read off directly as, MW = 1 2 vg2 and MZ = (cid:113) 2 + g2 g2 1, 1 2 v 26 (2.61) (2.62) (2.63) (2.64) (2.65) while the Aµ boson remains massless. One recognizes the W +, W −, and Z bosons as the massive weak vector bosons, and the Aµ boson as the massless photon. The angle θW is the weak mixing angle (or Weinberg angle), which specifies the mixture of the electromagnetic and weak interaction. The Higgs potential The remaining part of the Higgs Lagrangian involves the potential V (Φ) = µ2Φ†Φ+λ(Φ†Φ)2. Plugging in the Higgs doublet after SSB one gets, V = µ2 2 (v + H)2 + (v + H)4. λ 4 (2.66) Including the kinetic term obtained from the covariant derivative and with the substitu- tion µ2 = − λv2 the Higgs Lagrangian is given by LH = 1 2 (∂µH)2 − λv2H2 λvH3 − λ 4 − H4. (2.67) As expected, a new massive scalar boson, the Higgs boson, appeared in the theory with mass, MH = (cid:112) 2λv2. The remaining terms represent the Higgs self-interactions with couplings9 gHHH = (3!)iλv = 3i gHHHH = (4!)i λ 4 = 3i , M 2 H v M 2 H v2 . (2.68) (2.69) (2.70) The vacuum expectation value is fixed by the value of the W boson mass (measured via muon decay) through the relation in Eq. 2.65 and was measured to be v = 246.22 GeV. The Higgs boson mass is a free parameter in the SM, dependent only on the unknown parameter λ. The most precise measurement to date of the Higgs boson mass is mH = 125.11 0.11 GeV [29]. The Higgs self-coupling is instead still unmeasured, although increasingly stringent limits are being set on its allowed value. Measurement of the Higgs self-coupling is one of the most pressing experimental goals and one of the physics motivation for the High-Luminosity LHC ± 9According to the Feynman rules, the couplings are given by the coupling term from the Lagrangian i and by a factor n!, where n is the number of identical particles interacting at multiplied by a factor of the vertex [17]. − 27 (HL-LHC) upgrade (see Sec. 3.1). The Yukawa interactions Fermion mass terms cannot be included ad hoc in the Lagrangian, as they would violate gauge invariance, and neither do they appear via the Higgs mechanism, like the gauge boson masses do. The introduction of a scalar field in the theory turns out to again be useful, as it provides a new way to add mass terms via new couplings. The fermions and Higgs fields are coupled through gauge invariant interactions, called Yukawa interactions. These occur with terms of the form ¯ψ(x)ϕ(x)ψ(x). The SM Lagrangian is augmented with the Yukawa Lagrangian given by LY ukawa = − (Yl)ij ¯Li LΦlj R − (Yd)ij ¯Qi LΦdj R − (Yu)ij ¯Qi L ˜Φuj R + h.c. (2.71) where ˜Φ = iτ2Φ∗ is the isodoublet with hypercharge Y = 1, the indices i and j run over each quark or lepton generation, and the matrices Yf (f = u, d, l) are general complex-valued matrices introduced to realize the couplings between the scalar and the fermion fields. − In the following, the new interactions are analyzed for the quarks, while generalization to the lepton case is straightforward. The following notation is used: Qi L = (cid:35) (cid:34) ui L di L = (cid:32)(cid:34) uL dL (cid:35)(cid:33) (cid:35) (cid:34) , (cid:35) (cid:34) , tL bL cL sL (2.72) For a fixed choice of quark flavor i and j, after SSB and rotation to the unitary gauge, the following terms appear: LY ukawa,q = yij d Ldj ¯di R(v + H) + yij u ¯ui Luj R(v + H). (2.73) These look like candidates for fermion mass terms and fermion coupling terms to the Higgs field. However, the matrices Y are not diagonal, as there is no symmetry principle that = j that can mix requires them to be. This means that there are non-zero terms with i fermion generations. Hence, the Yukawa interactions break the flavor symmetry of the Lagrangian. In order to obtain the physical masses and couplings observed in the laboratory, the matrices have to be diagonalized. This can be obtained via bi-unitary transformations of the form, M q diag = V q †L M qV q R, where mij = yij v √2 . (2.74) Upon diagonalization only the terms ˆyij with i = j survive. Looking at the case for i = j = 3, 28 ̸ corresponding to the up-type top quark and the down-type bottom quark, LYukawa, tb = − = − (cid:124) 1 √2 v √2 ˆyb (ˆyb ¯bLbR + ˆyt¯tLtR)(v + H) v √2 ˆyt ¯bLbR − (cid:123)(cid:122) Mass terms tLtR (cid:125) − ˆyb (cid:124) 1 √2 1 √2 ˆyt ¯bLbR − (cid:123)(cid:122) Higgs couplings (2.75) (2.76) , tLtR (cid:125) mass terms and new couplings between the fermions and the Higgs boson appear of the form, mf = ˆyf v √2 and gHf f = i mf v . (2.77) However, because the weak interaction mixes up- and down-fermions, the fermion cou- plings to the W boson, arising from the EW covariant derivative term, now contain off- diagonal elements: ¯Ψ /DΨ g2 √2 ⊃ ¯uLiγµdLW µ −→ g2 √2 ¯uLiγµ(V u L V d †L )dLW µ (2.78) The three matrices M u, M d, and VCKM ≡ VuLV †dL cannot be diagonalized simultaneously, resulting in quark flavor violating interactions. The matrix VCKM is the CKM matrix, 3 matrix named after Cabibbo [30], and Kobayashi and Maskawa [31]. It is a unitary 3 parametrized by four parameters: three mixing angles θi and one phase δ. The phase δ is responsible for all CP-violating phenomena in the SM. Experimentally, the magnitude of all CKM has been found to be [32] × VCKM | | =    Vud| | Vcd| | Vtd| | Vus | Vcs | Vts | | | |     =   0.97 0.22 0.004 0.04 0.97 0.22 0.009 0.04 0.999    Vub| | Vcb| | Vtb| | (2.79) consistent with the unitary assumption of the SM and with the interesting feature of being almost diagonal. The Higgs couplings The couplings of the Higgs boson with the fermions and vector bosons are obtained from the 29 interaction terms in the Lagrangian and are given by, gHf f = i mf v , gHV V = 2i − gHHV V = − gµν, M 2 V v M 2 V v2 gµν 2i (2.80) (2.81) (2.82) The tree level couplings of the Higgs boson to fermion mass eigenstates are flavor diagonal, CP conserving, and proportional to the mass of the fermion, making the coupling to the top-quark by far the largest. The couplings to the vector bosons are instead proportional to the square of the vector boson masses. Note that the Higgs boson does not couple at tree- level to the massless photon, nor to the gluon, as it does not carry color charge. However, these couplings appear at higher orders via loop corrections, where top-quark-induced loops provide the largest cross sections because of the larger gHtt coupling. All tree level couplings of the Higgs boson to SM particles are functions of only two parameters, either λ and µ, or v and mH . Measurement of the couplings is therefore a direct test of the mechanism of spontaneous symmetry breaking. As shown in Fig. 2.3, the measurements of the fermions and gauge couplings have so far agreed extremely well with the predictions of the SM. Although all fermion masses appear via the same mechanism of Yukawa interactions and their physics scale is set by the vev value of v = 246 GeV, the observed masses span six orders of magnitude, from the top quark mass of mt 175 GeV down to the up-quark 0.5 MeV. Given that the mass of mu structure of fermion masses originates solely from the Yukawa couplings, which are added as free parameters in the SM, the origin of their hierarchical structure is one of the most fundamental questions today. 5 MeV and to the electron mass of me ≈ ≈ ≈ − 2 2.8 Hints for physics beyond the Standard Model The SM has proven to be a remarkably successful description of nature, whose structure was dictated by symmetries and guided by the experimental discoveries of the past century. However, symmetry arguments alone are not sufficient to explain the complex structure that experiments have brought to light, such as the non-general hierarchical structure in the Yukawa couplings and the naturalness problem, which will be discussed in the next section. Important phenomena are also not accounted for, the foremost example being gravity, one of the four fundamental forces of nature. This makes physicists regard the SM as an 30 Figure 2.3: Reduced Higgs boson coupling strength modifiers and their uncertainties [33]. effective low energy theory, valid only up to a certain energy scale. This scale is generally 1019 GeV, where the strength of expected to be smaller than the Planck energy scale MP ∼ the gravitational interaction is predicted to become comparable to the other forces. Astrophysical observations, including galactic rotation speeds [34] and gravitational lens- ing (the curvature of space-time near gravitating mass) [35], indicate the existence of massive matter that seems not to interact electromagnetically with the SM particles. Because it can- not be detected directly, the presence of this dark matter is inferred from its gravitational pull on ordinary matter. Dark matter is estimated to represent 80% of all matter in the Universe, but its origin and nature remain unknown. ∼ While the SM assumes massless neutrinos, the observation of neutrino oscillations [36, 37] has proven that neutrinos must have mass, albeit a very small one. While being six orders of magnitude lighter than the electron and 1012 lighter than the top quark, the masses of the three neutrino flavors display themselves a significant hierarchy and their origin is still unknown. Whether neutrino mixing arises from a different mechanism, whether they are Majorana or Dirac particles, or whether they couple to some non SM interaction, their mass points to some BSM physics. 31 4−103−102−101−101vev Vm Vκ or vev Fm Fκ Run 2ATLASµcτbWZttκ = cκ is a free parametercκSM prediction1−10110210Particle mass [GeV]0.811.21.4Vκ or FκeνµντνuctLeptonsQuarkseµτdsbgγZWHForce carriersHiggs boson Lastly, some tensions with the SM predictions have started to arise, including the most recent B-physics anomalies [38] and the measurement of the anomalous magnetic moment of the muon (Muon g 2) [39]. All these questions call for BSM physics. Thanks to its special role in the theory, the Higgs boson is at the center of many of these questions. In the next section, the importance of the Higgs sector for BSM physics scenarios will be discussed, with particular focus for the topics relevant for this thesis. − 32 Chapter 3 The Higgs boson as a portal to new physics The fundamental role of the Higgs boson in the SM model makes many consider it the key to explain several open questions in particle physics. Most of the observed unexplained structure brought to light by experimental observations is in fact connected to the Higgs sector. While “a SM” has the structure described in the previous section, “the SM” is an empirical model with 19 free parameters 1, whose values are set by experimental measurements [28]. Of these, four parameters – three gauge couplings and the weak mixing angle – arise from the gauge sector of the theory, while the remaining fifteen parameters – six and three from the Yukawa couplings of quarks and charged leptons, four from the CKM matrix, and two from the Higgs potential – arise from the Higgs sector. The scalar sector of the SM remains greatly unexplored experimentally, as the Higgs self-coupling and the shape of the Higgs potential have still not been measured. These have important implications for some fundamental questions in cosmology. Sensitivity to di-Higgs production with the HL-LHC might help shed light on these open questions, as discussed further in Chap. 8 in relation to the HL-LHC trigger upgrade. Additionally, there is much that is not well understood about the Higgs boson itself. One issue related to the Higgs boson is the naturalness problem, which sees unnatural mathe- matical cancellations arise in the theory due to its scalar nature. In order to remove this naturalness, some models predict the existence of new gauge vector bosons. These models are often studied via the generalized Heavy Vector Triplet (HVT) framework. The question remains also of whether there is only one Higgs boson or if there might be an extended scalar sector. An important theoretical framework used to study these questions is the Two-Higgs-Doublet Model. These models are relevant for the analysis discussed in Chap. 7. 1Assuming three generations and massless neutrinos 33 3.1 The Higgs self-coupling The Higgs potential is fundamentally connected to the origin of electroweak symmetry break- ing (EWSB), but while the vev and the Higgs boson mass have been measured with high precision, the Higgs self-coupling λ remains unmeasured. Measurement of the Higgs self- coupling would help shed light on the shape of the potential, which makes it relevant for several open questions in cosmology, including the stability of the Universe and the observed baryon asymmetry. Quantum corrections are observed to affect the shape of the Higgs potential [40]. The measured values of the Higgs and top quark masses indicate that, when running the Higgs 1010 GeV [41]. self-coupling to high renormalization scales, λ turns negative at a scale Λ This indicates that the vacuum state of our Universe is not the absolute minimum and that a non-zero probability exists for quantum fluctuations to cause the decay of the Universe into a lower energy state. While the lifetime of the Universe is orders of magnitude greater than its current age, making its metastability not an issue for the survival of humanity, it is nonetheless puzzling. Is the puzzlement only due to our anthropocentric view or is there some BSM physics missing in the theory that would stabilize the vacuum? ∼ The Higgs self-coupling is related to another important question concerning the origin of the matter-antimatter asymmetry in the Universe. In order for the Big Bang nucleosynthesis to have occurred the matter-antimatter composition of the Universe had to be already asym- metric to prevent annihilation between nucleons and antinucleons. Models of electroweak baryogenesis [5] provide a mechanism for the observed baryon asymmetry that would have occurred during the electroweak phase transition, which is the process by which the Higgs field acquired a vev. The Universe after the Big Bang is thought to have started in the un- broken phase, where the SU(2)L × U(1)Y gauge invariance was manifest. As the temperature cooled down below T ≲ 100 GeV, the Higgs field settled into one of the absolute minima of the potential, spontaneously breaking the original symmetry. Electroweak baryogenesis is predicted to have taken place during this phase transition. However, for baryon creation to take place successfully, the transition has to be first order, where the departure from thermal equilibrium is violent, while the SM predicts the electroweak phase transition to be of second order, with a smooth crossover between the two phases as the temperature decreases. Any model of electroweak baryogenesis requires therefore physics beyond the SM to make the transition first order. Probing the Higgs self-coupling would help shed light on these fundamental questions. The only direct probe at colliders is the measurement of di-Higgs production (indirect con- straints can be obtained from single-Higgs production). The HL-LHC is expected to provide 34 sufficient sensitivity for the ATLAS and CMS Collaborations to measure SM di-Higgs produc- tion and the Higgs self-coupling. The experimental challenges related to this measurement will be discussed in more detail in Chap. 8. 3.2 Naturalness The inability to include a gauge theory of gravity makes physicists regard the SM as an effective low energy theory valid up to the Planck scale. However, some theoretical reasons exist to believe that the SM might break down at much lower energies, related to the presence in the theory of a fundamental scalar particle. In a quantum field theory, any scalar particle inevitably leads to ultraviolet divergences in the radiative corrections to its mass. The Feynman diagrams contributing to the one loop corrections to the Higgs boson mass are shown in Fig. 3.1. The divergent integrals can be Figure 3.1: Feynman diagrams contributing to the one-loop corrections to the Higgs boson mass in the SM. regularized by cutting off the loop integral momenta at a scale Λ. The theory can then be renormalized by expressing the mass of the physical particle in terms of the mass of the bare particle, so that the infinities only appear in the relation between the physical and bare mass, but the physical observable remains finite. Keeping only the dominant contributions, the resulting physical Higgs boson mass in the renormalized theory is given by: m2 H = (m0 H )2 + H + 2M 2 W + M 2 4m2 t ], (3.1) Z − 3Λ2 3π2v2 [M 2 where m0 H is the bare mass from the unrenormalized Lagrangian. The quadratic, rather than logarithmic, divergence as a function of Λ in the counter-term is unique in the SM and it is due to the Higgs boson being a scalar field. If the theory is considered valid up to the Planck scale Λ H term and the counter-term proportional to Λ2 would be necessary to obtain the observed renormalized mass square m2 102 GeV)2 [41]. This type of cancellation is considered unnatural and is referred to as the naturalness problem. This raises the question of whether there is 1019 GeV, a finely-tuned cancellation of 34 digits between the m0 H of ( ∼ ∼ 35 HfHHHW,Z,HHW,Z,HH some larger symmetry or some new dynamics at work to protect the Higgs from these large radiative corrections. One way in which the fine-tuning would be removed or reduced is if new particles existed with masses around the TeV scale and coupling to the Higgs boson. Several BSM models, partly motivated by naturalness arguments, predict the existence of such new heavy resonances and are often studied within the framework of the HVT model. 3.3 The Heavy Vector Triplet model New vector bosons are a common element of BSM models with an extended gauge symmetry group, where they appear as the gauge bosons of the new broken symmetries. Requirement U(1)Y in the non-broken phase strongly SUL(2) of gauge invariance under the SM SU(3)C × constraints the quantum numbers and allowed interactions of the new vector bosons. Isospin triplets are particularly interesting as, experimentally, they can give rise to sizable resonant signals [42, 43] and, from a theoretical point of view, they appear in well-known extensions of the SM, including Little Higgs [44] models and composite Higgs models [45, 46]. × While these models are theoretically consistent, it is hard to pin down specific observ- able predictions that would differentiate one model from another. Within a given model framework, different assumptions can also determine different phenomenologies. Tailoring a search for each model is unfeasible. However, resonant searches are generally not sensitive to all the free parameters of a model, but only to the mass and couplings of the predicted new particles, which determine the available decay channels, and the strength and location of the mass resonance. The HVT [3, 42] model provides a simplified framework with which one can test only the relevant phenomenological parameters: the experimental search determines the likelihood between the data and the general model; the phenomenological parameters can then be expressed analytically in terms of the parameters of the explicit theory. Note that the model assumes on-shell resonance production and decay. The HVT model is based on a simplified Lagrangian, which, in addition to the SM fields, µ (a = 1, 2, 3) charged under SU(2)L and with zero hypercharge, includes a new real vector V a with the charge eigenstates V ±µ = iV 2 µ V 1 µ ∓ √2 , µ = V 3 V 0 µ . (3.2) 36 The Lagrangian describing the new fields and their interactions with SM particles is, LV = − D[µV a 1 4 + igV cH V a ν]D[µV ν]a + m2 V 2 µ H†τ a←→D µH + µ V µa V 1 cF V a g2 gV ν D[µV ν]c + g2 µ J µa F + gV 2 cV V V ϵabcV a µ V b V CV V HH V a µ V µaH†H (3.3) (3.4) g 2 − cV V W ϵabcW µνaV b µ V c ν . (3.5) where ϵabc is the Levi-Civita symbol. The first line contains the kinetic and mass terms of the new V bosons, plus trilinear and quadrilinear interactions with the SM vector bosons arising from the covariant derivatives, D[µV a ν] = DµV a ν − D[νV a µ , DµV a ν = ∂µV a ν + gϵabcW b µW c ν (3.6) where g is the SU(2)L gauge coupling. The second line of the equation contains the interac- tions of V with the Higgs boson and with the SM left-handed fermions, iH†τ a←→D µH = iH†τ aDµH iDµH†τ aH, − J µ,a F = (cid:88) f ¯fLγµτ afL, (3.7) where τ a = σa/2 and σa are the Pauli matrices. The last line contains vertices representing bosonic interactions. However, to first approximation, these interactions do not contribute to LHC phenomenology [3], so can be disregarded. All couplings are weighted by a new parameter gV , which represents the typical strength of V interactions. The c coefficients are dimensionless parameters parametrizing the departure from the typical size. Upon EWSB, the components of the new vector triplet mix with the SM gauge bosons. After diagonalization of the mass matrices [3, 42], expressions for the physical masses of the SM W and Z bosons and the new charged and neutral vector bosons, referred to as W ′ and Z′, can be obtained. In order to preserve custodial symmetry and the SM tree-level value of ρ = 1, the W ′ and Z′ bosons are quasi-degenerate and their masses are assumed to be above 1 TeV. Thanks to the resulting mass hierarchy between the SM and the new gauge bosons, the mixing angles are naturally small and the SM couplings of the W and Z bosons are automatically close to the SM expectation. In general, the W ′ and Z′ bosons are assumed to be degenerate and the data is interpreted in terms of one effective resonance with mass MV . ≈ The small mixing angles simplify the couplings to fermions, which are determined by cF . The parameter cF controls therefore Drell-Yan the parameter combination gF = g2 gV 37 production and the fermionic decays of the new bosons. Here the coupling to fermions is assumed universal, but it could in principle be split into different couplings for leptons, and light and heavy quarks. The coupling to the SM bosons is more subtle. Because of the small mixing angles, the couplings involving transversely polarized SM vectors are suppressed. However, via a different choice of gauge it can be shown [3] that direct couplings to the longitudinal components of the gauge bosons exist. After the change of basis, the couplings are given by, gV cH 2 π L ⊃ µ (∂µhπa V a − h∂µπa + ϵabcπb∂µπc) (3.8) ± where π and π0 are the Goldstone bosons that reappear in this basis and that, by the Equivalence Theorem, correspond to the longitudinal W ± and Z bosons. Note that all the couplings are controlled by the same parameter combination gV cH . Therefore, cH controls both the interaction with the Higgs boson and with the SM weak bosons and, in particular, the resonance production via vector boson fusion (VBF)and the decay into bosonic channels. To a good approximation, the HVT phenomenology is completely described by the cou- pling to fermions gF = g2/gV cF , the coupling to bosons gH = gV cH , and the mass of the resonance MV . In order to test the broad phenomenological phase space, two benchmark scenarios are often studied for which the values of cH and cF are fixed, while scanning dif- ferent “benchmark points” in the phase space traced by the parameters MV and gV . The model described in Ref. [47] is taken as representative of a weakly coupled model, where the new triplet appears upon SSB of an extended gauge symmetry, and will be referred to as ≲ 3 are considered, pre- Model A. For this type of model, only relatively small values gV dicting comparable branching ratios into bosons and fermions. A generic Composite Higgs Model [48] is taken as representative of a strongly coupled model, referred to as Model B, ≳ 3 are studied. For large gV values, the coupling to fermions gF where larger values gV is suppressed by g2/gV . The coupling to bosons gH scales instead as gV . Strongly coupled models predict therefore dominant branching ratios into diboson final states, while fermionic channels are suppressed. For Model B, the total width increases with increasing gV and for 8 the resonance becomes very broad Γ/M >> 0.1. These values are therefore values gV ≥ not considered, as the model is only valid for narrow resonances. For both models A and B the dominant production mechanism is Drell-Yan production. VBF production can be enhanced by suppressing the coupling of the HVT bosons to fermions. This is done in Model C, where gF = 0 and gH = 1. 38 3.4 The Two-Higgs-Doublet Model One of the most stringent constraints on the SM are electroweak precision measurements, but while the value of the ρ parameter places stringent requirements on the scalar sector, it would in principle accommodate any number of scalar singlets and doublets in the theory [4]. Since the SM assumes the simplest possible scalar structure by introducing only one Higgs doublet, the question arises of whether the Higgs boson is not alone. Several examples of models with extended scalar sectors exist, including the Minimal Suppersymmetric Standard Model (MSSM) [49], axions models [50], and baryogenesis models [51]. In particular, one important class of models, called the Two-Higgs-Doublet Models (2HDMs) [4] studies the addition of a new scalar doublet 2. Flavor Changing Neutral Currents The introduction of two Higgs doublets in the Yukawa Lagrangian allows for flavor changing LYukawa is now: neutral currents (FCNCs) at tree level. Considering the quark terms only, LYukawa ⊃ − (cid:88) k=1,2 (Yd)ij,k ¯Qi LΦkdj R − (Yu)ij,k ¯Qi L ˜Φkuj R + h.c., (3.9) where the i and j quarks couple to a linear combination of the two scalar fields Φk(k = 1, 2). Consider the case of the down-type quarks. Upon SSB the mass terms appear as: LYukawa ⊃ − (cid:88) k=1,2 L (Yd)ij,k vk ¯di √2 (cid:125) (cid:124) (cid:123)(cid:122) M d ij dj R, M d ij = yij,1 d v1 √2 + yij,2 d v2 √2 . (3.10) Without further restrictions, the coupling matrices Y 1 not simultaneously diagonalizable, making the Yukawa couplings not flavor diagonal. d and the mass matrix M d d and Y 2 ij are FCNCs are highly constrained by experiment and, if they exist, would have to be ex- tremely small. For this reason, in the study of 2HDMs, a discrete Z2 symmetry is generally introduced ad hoc to suppress FCNCs. As formalized by the Paschos-Glashow-Weinberg theorem [52, 53], the condition that all fermions with the same quantum number (the only ones that can mix) couple to the same Higgs doublet is necessary and sufficient for the ab- sence of FCNCs at tree level. In the SM, this can be obtained in different ways. In the Type I 2HDM, all fermions couple only to one of the doublets, conventionally chosen to be Φ2. 2The MSSM is a special case of the Type II 2HDM described below, but the description given here is for the most general 2HDM following Ref. [4] 39 Φ1. In the For instance, this can be enforced by requiring the discrete symmetry Φ1 → − Type II 2HDM, all up-type quarks couple to one Higgs doublet and all down-type quarks and charged leptons couple to the other one. In the lepton specific model, the couplings to quarks are the same as in the Type I model, while the couplings to charged leptons are as in the Type II. The flipped model has the same couplings to quarks as in the Type II model, and to charged leptons as in the Type I model [54]. The potential With two scalar doublets, the most general scalar potential becomes quite complex, deter- mined by 14 parameters and with various minima with different charge and CP conservation properties. For this reason, several simplifying assumptions are usually made for phenomeno- logical studies. The most general CP-conserving potential with a softly broken Z2 symmetry of two Higgs doublet fields Φ1 and Φ2 with hypercharge +1 is given by V =m2 11Φ†1Φ1 + m2 22Φ†2Φ2 − + λ3Φ†1Φ1Φ†2Φ2 + λ4Φ†1Φ2Φ†2Φ1 + m2 12 Φ†1Φ2 + Φ†2Φ1 λ5 2 (cid:20)(cid:16) Φ†1Φ2 (cid:16) (cid:17) + (cid:16) λ1 2 Φ†1Φ1 (cid:17)2 (cid:16) + Φ†2Φ1 (cid:17)2 + (cid:17)2(cid:21) , (cid:16) λ2 2 (cid:17) Φ†2Φ2 (3.11) where all the parameters are real. Each doublet has four degrees of freedom, for a total of eight fields: (cid:32) Φa = ϕ+ a (va + ρa + iηa)/√2 (cid:33) , a = 1, 2. (3.12) Upon SSB, the neutral components of the two doublets acquire vevs, v1 and v2: Φ1⟩0 = ⟨ (cid:32) (cid:33) , 0 v1 1 √2 Φ2⟩0 = ⟨ (cid:33) . (cid:32) 0 v2 1 √2 (3.13) where the observed vev value requires v2 = v2 doublet to the observed SM vev is parametrized by the angle β, as tan β = 2 = (246 GeV)2. The contributions of each . The physical 1 + v2 v2 v1 40 mass eigenstates are obtained by the rotation matrices, (cid:33) (cid:32) G0 A = (cid:32) cos β sin β (cid:33) (cid:32) (cid:32) h H (cid:32) G± H± = (cid:33) = − (cid:32) sin α cos α cos β sin β sin β cos β − (cid:33) (cid:32) (cid:33) η1 η2 (cid:33) (cid:32) , (cid:33) cos α sin α − − sin β sin β − ρ1 ρ2 (cid:33) (cid:33) (cid:32) ϕ± ϕ± , , (3.14) (3.15) (3.16) where the angle β reappears, together with the parameter α, as the mixing angles of the mass matrices. The Higgs mechanism proceeds then as in the SM. Three Goldstone bosons (G± and G0) are “eaten” by the W ± and Z bosons, which subsequently acquire mass. The remaining five physical degrees of freedom correspond to five massive scalar fields: two are charged (H±), two are neutral and CP-even (h and H, with mh < mH ), and one is neutral and CP-odd (A). With the simplifying assumptions mentioned before, the 2HDM is fully determined by seven parameters: the masses of the five Higgs bosons and the two angles α and β. The Standard Model Higgs and the alignment limit The observed Higgs boson with a mass of 125 GeV and its measured SM couplings put strin- gent constraints on the phenomenology of the neutral scalars, requiring the mass eigenbasis of the two neutral scalars to lie very close to the Higgs basis. The Higgs basis is the basis where one of the two doublets is entirely responsible for the SM vev and is obtained with the following field redefinition: (cid:33) (cid:32) = (cid:32) H1 H2 cos sin sin cos (cid:33) (cid:32) Φ1 Φ2 (cid:33) . − From the relation tan β = In this basis, the physical neutral CP-even states are given by H1⟩0 = (v1 cos β + v2 sin β)/√2 = v and , one gets ⟨ v2 v1 H = (√2ReH0 h = (√2ReH0 1 − 1 − v) cos(β v) sin(β α) α) − − − − √2ReH0 √2ReH0 2 sin(β 2 cos(β α), α). − − (3.17) H2⟩0 = 0. ⟨ (3.18) (3.19) The angle (β exists if (√2ReH0 1 − 1 and H0 mixing between H0 α) characterizes the mixing of the neutral scalars. A SM-like Higgs boson v) is an approximate mass eigenstate. This occurs if there is negligible α) = 0 (HSM = h) or when 2 , which is the case when cos(β − − 41 − α) = 0 (HSM = H). This is called the alignment limit. Alignment of the Higgs basis sin(β with the mass basis can also be obtained in the decoupling limit, when the new Higgs fields are assumed to be all much heavier than the SM-like neutral scalar field h. As shown in Ref. [55], once the heavier particles are integrated out, the low energy effective field theory is equivalent to the SM Higgs sector with one scalar doublet. The decoupling limit implies the condition << 1. However, the latter condition is more general than the decoupling limit cos(β | (v). Therefore, alignment occurs and can be obtained even for all Higgs boson masses automatically in the decoupling limit, but it is also possible without decoupling. In the decoupling limit, the light neutral scalar h is indistinguishable from the SM Higgs boson. On the other hand, in the alignment limit, even if the tree-level couplings of h are SM-like, deviations can appear when higher order corrections are included[55]. ≤ O α) − | 42 Chapter 4 The LHC and the ATLAS experiment 4.1 The Large Hadron Collider (LHC) Accelerator development has historically been driven by particle physics research. The birth of collider physics can be traced back to 1932 when Lawrence’s cyclotron, based on the principle of resonance acceleration, was able to produce 1.25 MeV protons to disintegrate the atom [56]. Since then, the need to look at increasingly smaller distances has meant continuously finding new ways to produce higher energy beams. By the 1980s, it was shared expectation that new physics discoveries (including the observation of at least one Higgs particle, of the top-quark, and of possible new physics phenomena such as supersymmetry or new gauge bosons [57]) should appear at substantially higher energies than ever tested before, in the range up to 1 TeV, and several options were considered [58]. The first serious investigation of the possibility of a hadron collider was produced in 1987 by the Long-Range Planning Committee, setup at the European Organization for Nuclear Research (CERN) in 1985 and chaired by Carlo Rubbia, which recommended that a proton-proton collider 15 TeV should be the next major project at with a center-of-mass (CoM) energy of 13 − CERN [57, 58]. Thus, the Large Electron Positron collider (LEP) [59] tunnel at CERN was designed from the start to provide enough space to later install superconducting magnets for a large proton collider [58]. The tunnel was constructed between 1984 and 1989. The LEP project started in 1989 and in 2000 it was terminated and installation of the Large Hadron Collider (LHC) began [60]. Today, the LHC is the largest and most powerful particle accelerator in the world, where the same principle of resonant acceleration used in 1932 is used to accelerate protons to 7 TeV. 4.1.1 Overview The LHC [60, 61] is a 27 km proton-proton (pp) circular collider located at CERN, between 45 and 170 m under the surface on the border between France and Switzerland just outside of Geneva. Two counter-rotating beams collide at four interaction points (IP) where the four main experiments are located: ATLAS [62] and CMS [63], both multi-purpose experiments 43 designed to be sensitive to a wide range of SM processes and new physics searches; LHCb [64], a B-physics experiment; and ALICE [65], a heavy ion dedicated experiment for Pb-Pb operation, which will not be discussed in this work. The ring consists of eight 2.9 km long arcs with superconducting dipole magnets, alternating to eight straight sections of 210 m on either side of eight potential collision points where RF cavities are located1. Being a particle-particle collider, the beams require opposite magnetic dipole fields. For this reason, the accelerator consists of two rings with separate magnetic fields and vacuum chambers in the main arcs, and common sections in the intersection regions (IR) around the IPs, where the beams share a common beam pipe approximately 130m long. Because of the limited space in the tunnel, not enough room was available for two separate rings of magnets. For this reason, the twin-bore magnet design proposed by Blewett in 1971 [66] was adopted, which consists of two sets of coils and beam pipes within the same mechanical structure and cryostat, making the two magnets magnetically and mechanically coupled. 4.1.2 The accelerator complex The accelerator chain Before entering the LHC rings, the energy of the protons is increased by a series of smaller accelerators, each boosting the particles to the maximum allowed speed before injecting them into the next machine in the chain. The LHC accelerator chain [67] is shown in Fig. 4.1. The chain starts with a container of negative hydrogen ions (H−, a hydrogen atom with two electrons). The linear accelerator Linac 4, which replaced Linac 2 in 2020, boosts the ions to 160 MeV and strips them of their two electrons during injection into the Proton Synchrotron Booster (PSB). The protons are then accelerated to 2 GeV before entering the Proton Synchrotron (PS), which brings the beam to 26 GeV and injects it into the Super Proton Synchrotron (SPS). Here, the protons are accelerated up to 450 GeV before finally entering the LHC rings. The protons enter the LHC in bunches separated by 25 ns, taking about 4 minutes to fill the entire LHC ring. The protons are accelerated via a total of eight Radio Frequency (RF) cavities [69] per beam, each delivering 2 MV longitudinal voltage at 400 MHz. Twenty minutes later, after passing through the RF cavities 10 million times, the protons reach their maximum energy of 6.5 TeV, resulting in a CoM energy at collision point of √s = 13 TeV. After collision, the beams are reconstituted, and the process continues for approximately 10 hours until the beam is depleted of protons and is ready to be dumped. At this point, 1The number of cavities was originally designed to compensate for electron synchrotron radiation losses at LEP, 1013 times that of a proton. 44 Figure 4.1: The LHC accelerator complex layout as of 2022 [68]. protons exit the LHC rings and travel along a straight line until collision with a block of concrete and graphite. The RF system The RF cavities are straight metallic chambers containing a longitudinal electromagnetic field and housed in cryomodules to operate at 4.5 K. In order to accelerate particles along a closed path, an oscillating voltage is necessary, as a DC voltage would cancel its accelerating effect over a full turn. For a particle to always see an accelerating voltage at the gap, the frequency of the voltage oscillation fRF has to always be an integer multiple of the particle revolution frequency frev. Once the beam has reached the required energy, the ideally timed particle whose revolution frequency is identical to the RF frequency — the synchronous particle — will see a zero accelerating voltage every time it passes through the cavity. Any other particle with slightly different momenta will oscillate around the synchronous particle 45 along the longitudinal plane in what is called the synchrotron motion [70]. The result is that the particles get grouped into bunches around the synchronous particle in the bunch. The boundary of the bunch is called the RF bucket. Provided the energy deviations are not too large, the particles remain trapped in the bucket, which essentially acts as a potential well. The bunch structure is formed as soon as the RF system is on and the number of possible bunch crossings (BC) is fixed to fRF /frev. In fact, the PS and SPS are also synchrotrons, and it is the PS that first determines the 25 ns bunch spacing. The magnet system Along the LHC rings, 10,000 superconducting magnets of about 50 different types are used to send the protons along the circular path. A nominal magnetic field of 8.3 T in the 1232 main dipoles is necessary to bend the path of the charged particles traveling close to the speed of light. This field is much higher than any other superconducting accelerator ever built before, requiring superfluid Helium at 1.9 K [71]. Particles in a bunch will occupy different positions on the transverse plane perpendicu- lar to their trajectory. Displacements along the horizontal direction will simply cause the particles to follow different closed paths along the LHC circumference. The vertical plane, however, is unstable and the trajectory of particles with different initial conditions can end up spiraling towards the center. Combinations of 392 focusing and de-focusing quadrupole mag- nets are used to keep the beam stable along both horizontal and vertical axes. The resulting transverse oscillations on the horizontal and vertical planes are called betatron oscillations and the envelope function within which the particles oscillate is called the β-function [70]. The quadrupoles are also used to squeeze the beam and increase the beam luminosity. In particular, eight sets of low-β quadrupoles, called the inner triplets, are used at the inter- section regions of the four experiments to make the beams narrower before collision, going from 0.2 mm across down to 16 µm. 4.1.3 LHC performance and operation The bunch structure The proton bunches have an elongated shape of about 7.48 cm along the longitudinal direc- 16 µm in the transverse plane due to the tion due to the synchrotron motion, and of 16 betatron oscillations. The bunches are separated by 25 ns, or 7.5 m, giving a collision rate of 40 MHz and a maximum number of bunches in the ring of 3564. However, not all bunches are filled with protons, as empty bunches are necessary for, e.g., new bunch insertion when depleted bunches are dumped or for the abort gap needed to turn on the magnets to divert and dump the beam. This brings the effective number down to 2808. Each possible BC is × 46 assigned a Bunch Crossing Identifier (BCID) from 0 to 3563. According to the LHC filling scheme set at the beginning of an LHC fill, each BC can have either two bunches colliding, one bunch, or be empty of protons. Cross section The probability of a given collision event to occur is expressed by the cross section σ, which is measured in units of squared-area. Because particle physicists are generally interested in 24cm2. The rare events, σ is often more conveniently expressed in barns, where 1b = 10− cross section for pp collisions at 7 TeV is approximately 110 mb, of which 60 mb are due to inelastic processes. Other contributions come from diffractive and elastic scattering events, which do not reach high enough energies in the transverse plane to be seen by the detectors. For a given process with cross section σprocess, the event rate in an LHC collision is, dNprocess dt = LI σprocess, (4.1) 10− 1034cm− 2s− where LI is the instantaneous luminosity provided by the machine, which is LI ≈ at the LHC. The cross section for di-Higgs production at √s = 13 TeV via gluon-gluon fu- sion, which is by far the largest production mode, is 31.05 fb [9]. This means that there 5 events/second where two Higgs bosons are being produced or, in other are 31.05 words, a pair of Higgs bosons is produced every 53 minutes. This type of events is extremely rare when compared to the 11-14 orders of magnitude larger number of events that will have occurred during the same amount of time, as shown in Fig. 4.2. In order to draw statistically meaningful conclusions, it is crucial to produce enough of them. For this reason, as Eq. (4.1) shows, the most important parameter of an accelerator is the luminosity. × 1 Luminosity The luminosity is the number of collisions produced in a detector per squared-centimeter and per second, and it is dependent only on the beam parameters. Assuming two identical Gaussian beams colliding, the instantaneous luminosity is given by [60], N 2 b nbfrevγr 4πσxσy F , LI = (4.2) where: Nb is the number of particles per bunch; nb is the number of bunches per beam; γr is the relativistic gamma factor; frev is the LHC revolution frequency; σx and σy are the RMS cross-sectional size of the bunch in the x and y directions, which, in terms of the β-function √βiϵ; F is the geometric luminosity reduction factor due and emittance ϵ, are given by σi ≈ 47 Figure 4.2: Standard Model cross sections as a function of collider energy [72]. to the crossing angle at the IP2. The discovery reach of the LHC ultimately depends on the total integrated luminosity, L = (cid:82) LI dt, related to the total number of events of a given process as Nprocess = Lσprocess. 2]. A precise knowledge of the luminosity The total integrated luminosity has units of [cm− is necessary to extract the visible cross section in any detector. The luminosity is measured by the experiments with specific detector sub-systems that are calibrated during special runs called van-der-Meer beam-separation scans [73]. To increase the number of rare events produced at the LHC requires therefore increasing the beam energy and intensity [60]. The maximum beam energy that can be attained is limited by the dipole magnetic field and the collider length. The nominal field of 8.33 T corresponds to a maximum beam energy of 7 TeV. The collision rate can be maximized by optimizing other parameters in Eq. (4.2). The beam intensity depends on the number of 2The geometric luminosity reduction factor is given by (cid:32) = 1 + F (cid:18) θcσz 2σ∗ (cid:19)2(cid:33) 1/2 − , with θc the crossing angle, σz the RMS bunch length, and σ∗ the transverse RMS beam size at the IP. 48 0.111010-710-610-510-410-310-210-110010110210310410510610710810910-710-610-510-410-310-210-1100101102103104105106107108109σσσσZZσσσσWWσσσσWHσσσσVBFMH=125 GeVWJS2012σσσσjet(ETjet > 100 GeV)σσσσjet(ETjet > √√√√s/20)σσσσggHLHCTevatronevents / sec for L = 1033 cm-2s-1 σσσσbσσσσtotproton - (anti)proton cross sectionsσσσσWσσσσZσσσσtσ σ σ σ ((((nb))))√√√√s (TeV){ particles per bunch and on the size of the beam. The former is limited by several factors, such as beam-beam effects and collective beam instabilities, caused by the interaction of the protons with each other and with the vacuum chamber. The nominal and ultimate values 1011, respectively [67]. The of the number of protons per bunch are 1.15 × transverse beam dimensions can be optimized by improving the beam quality in terms of the emittance ϵ and the amplitude function β. The emittance is a measure of the spread of the beam, and the lower the emittance the closer the particles are together in distance and momentum. The emittance depends solely on the initial conditions set by the injection chain. The β-function can be adjusted during a run via the quadrupole magnets. In particular, the β∗ parameter determines the transverse beam size at the IP, and the smaller it is, the larger the luminosity. 1011 and 1.70 × Several LHC upgrades have already been performed and others are planned in the in- coming decade to bring the accelerator parameters to the ultimate design goals and beyond. However, with a higher collision rate come other challenges, including a higher probability of multiple simultaneous pp inelastic collisions, a phenomenon called pileup. Pileup The term pileup refers to the simultaneous pp inelastic collisions that accompany the hard scatter of interest. There are two types of pileup: in-time pileup refers to additional collisions occurring between protons in the same bunch crossing as the one of interest; out-of-time pileup refers to collisions occurring in bunch crossings just before or just after the one of interest, which, when the electronics integrate over more than 25 ns, can affect the signal of the collision of interest. These secondary collisions tend to be soft, but they can add hundreds to thousands of soft hadrons to the final state of the hard collision of interest, biasing and smearing the quantities reconstructed from the detector [74], as well as stressing the trigger and data acquisition systems, and increasing the radiation levels that detectors and front-end electronics have to withstand. For in-time pileup, one usually reports the average pileup multiplicity µ, which follows a Poisson distribution. As the accelerator complex continues to be upgraded, the number of pileup interactions has consistently been increasing. The average pileup multiplicity was µ = 200 at the High-Luminosity LHC (see below), largely ⟨ above the original design value. In order to provide a higher luminosity and at the same time cope with the increased levels of pileup, a series of concomitant upgrades was planned for the collider and for the experimental detectors. = 20 in Run 1 and will reach µ ⟨ ⟩ ⟩ 49 4.1.4 Brief timeline of LHC operation and upgrades Since its ideation, the LHC was planned to be built in stages, partly to spread the costs, and partly to await technological developments. The construction ended in 2008 and the collider was expected to start running at √s = 11 TeV in 2009. However, on September 19th, 2008 an incident occurred, in which a defective joint between superconducting cables caused several magnets to quench with severe collateral damage, including the loss of six tonnes of helium and pollution of the beam vacuum tubes [71]. After the incident, it was decided to operate at √s = 8 TeV until the first Long Shutdown (LS) planned for 2013. The LHC Figure 4.3: Snapshot of LHC schedule showing collision energy (upper line) and luminosity (bottom line) as of 2022 [75]. plan is shown in Fig. 4.3. Years-long periods of consecutive data-taking, called Runs, are separated by major upgrades necessary to bring the collider to its ultimate performance [76]: • Run 1 (2009-2013): The LHC was operated with 50 ns bunch spacing and √s = 7 8 TeV. − • LS1 (2013-2015): The LHC machine was consolidated to allow the increase of the CoM energy and luminosity to the design value. • Run 2 (2015-2018): The LHC was operated with 25 ns bunch spacing and √s = 13 TeV. The luminosity was progressively increased until attaining the nominal value of 50 5 to 7.5 x nominal Lumi13 TeVintegrated luminosity2 x nominal Lumi2 x nominal Luminominal Lumi75% nominal Lumicryolimitinteractionregionsinner triplet radiation limitLHCHL-LHCRun 4 - 5...Run 2Run 1DESIGN STUDYPROTOTYPESCONSTRUCTIONINSTALLATION & COMM.PHYSICSDEFINITIONEXCAVATIONHL-LHC CIVIL ENGINEERING:HL-LHC TECHNICAL EQUIPMENT:Run 3ATLAS - CMSupgrade phase 1ALICE - LHCbupgradeDiodes ConsolidationLIU InstallationCivil Eng. P1-P5experiment beam pipessplice consolidationbutton collimatorsR2E project13 - 14 TeV14 TeV7 TeV8 TeVLS1EYETSEYETSLS3ATLAS - CMSHL upgradeHL-LHC installationLS230 fb-1190 fb-1350 fb-13000 fb-14000 fb-120402027BUILDINGS × 2s− 1034 cm− 1 in June 2016. 1 2s− 1034 cm− design value of 2 β∗ value, while still keeping the nominal bunch population. In 2018 the peak luminosity reached the ultimate 1 thanks to small emittances and a smaller than design × • LS2 (2019-2022): Significant upgrades were carried out in the injector chain: the new Linac-4 accelerator (160 MeV) replaced the Linac-2 (50 MeV) as injector to the PSB, while the PSB was also upgraded resulting in a lower emittance and higher intensity beam. Other improvements included consolidation of the dipole magnets and cryogen- ics upgrade. The Phase I of the detector upgrades was installed and commissioned to adapt to the new conditions and in preparation for the High-Luminosity LHC. • Run 3 (2022-2025): The LHC CoM energy was increased to 13.6 TeV. With the current 1 by the luminosity-induced machine, the peak luminosity is limited at 2 heating of the inner triplet magnets at the IPs. However, a 60% increase in beam intensity, combined with luminosity leveling, which will allow to operate near peak luminosity for a longer fraction of the running time, will result in a year integrated luminosity above 80 fb− 1. This run is ongoing. 1034 cm− 2s− × • LS3 (2026-2028): The LHC will undergo the most extensive upgrade of its components, including low-β quadrupole triplets and new crab cavities [77] at the intersection re- gions. The Phase II upgrades of the detectors will be installed and commissioned. • High-Luminosity LHC (2029-2040’s): The LHC is expected to run at √s = 14 TeV 1 and an annual 1034 cm− 2s− and deliver a levelled instantaneous luminosity of 5 integrated luminosity of 250 fb− 1. × To further extend the physics potential of the LHC, CERN started in 2010 the High- 1, Luminosity LHC (HL-LHC) project, aiming at a peak luminosity of 5 1 of data collected after 12 years of operation, a ten-fold in- resulting in a total of 3000 fb− crease with respect to the data that will have been collected at the end of Run 3 and well beyond the original design values of the collider. 1034 cm− 2s− × 4.2 The ATLAS detector The ATLAS (A Toroidal LHC Apparatus) [62] experiment is one of the two high-luminosity general purpose experiments at CERN, together with CMS, built for the precise measure- ments of SM parameters and to search for a wide range of possible new physics phenomena. The design of the ATLAS detector was driven by the vast physics program of the experi- ment and by the experimental difficulties posed by two major challenges: the unprecedented 51 levels of pileup and the large background of QCD jet production due to the nature of pp colli- sions. Several requirements had to be satisfied to provide a wide physics reach [62]: fast and radiation-hard electronics and sensors; high detector granularity to handle the large particle fluxes and possible simultaneous hard collisions; large pseudorapidity acceptance to allow detection of forward particles, and almost full azimuthal angle coverage to allow complete event reconstruction on the transverse plane; good electromagnetic calorimetry for identifica- tion of electrons and photons, and hadronic calorimetry with full coverage for reconstruction of jets and missing transverse energy; a tracking detector to provide good charged particle momentum resolution, especially complementing at low transverse momentum the poorer calorimetry energy resolution, and good reconstruction efficiency of secondary vertices for τ -leptons and b-jets identification; good muon identification and momentum resolution, and ability to determine the charge of high pT muons; highly efficient triggering, especially on low transverse-momentum objects, to reduce the event rate, while keeping high efficiency for rare processes. These requirements set new standards for the design of particle detectors and the final result was only possible thanks to the work of several thousands of physicists, engineers, and technicians over fifteen years. The ATLAS detector is located in the experimental cavern at Point 1 at CERN. With its 25 m in height and 44 m in length, it is the largest detector at the LHC, weighting approximately 7000 tonnes. Coaxial layers of sub-detectors, each sensitive to different types of particles, surround the interaction point (IP). The detector has a cylindrical shape and was designed to be forward-backward symmetric and to provide an almost full azimuthal coverage. The detector layout is subdivided in two parts: a main cylinder coaxial to the beam line, called the barrel, and two end-cap regions closing the cylinder on both sides. The full detector system is immersed in a magnetic field for the bending of charged-particle trajectories necessary for charge-momentum measurement. This section presents a description of the detector as it was during Run 2, the period in which the data set used in this thesis was collected. 4.2.1 The ATLAS coordinate system ATLAS uses a right-handed coordinate system, as sketched in 4.4. The IP is the center of the coordinate system. The z-axis is placed along the beam direction, while the x- y plane, referred to as the transverse plane, is perpendicular to the beam trajectory. The positive x-axis points towards the center of the LHC, while the positive y-axis points upwards. Cylindrical coordinates are used, with the azimuthal angle ϕ measured on the transverse plane around the beam axis, and the polar angle θ measured on the z-y plane from the 52 Figure 4.4: ATLAS coordinate system. Background taken from Ref. [62]. − positive z-axis. The rapidity of a particle with energy E and momentum along the z direction pz is defined as y = 1/2 ln [(E + pz)/(E pz)]. Differences in rapidity are Lorentz invariant under boosts along the z (beam) direction. The ∆R distance between two objects i and j in the rapidity-azimuthal angle space is also Lorentz invariant and is defined as ∆Ri,j = (cid:113) ϕj).2 Lorentz invariance under boosts in the z-direction is important in a pp collider where, because of the complex QCD structure of protons, the four-momentum is not conserved along the z component. Related to θ is the pseudorapidity η = 1/2 ln[(p + pz)/(p along the z-axis. For a massless particle, rapidity and pseudorapidity are equal. ln tan(θ/2), with η = 0 along the y-axis, and η = yj)2 + (ϕi − (yi − pz)] = ±∞ − − 4.2.2 The magnet system The detector is fully immersed in a magnetic field provided by a system of four large super- conducting magnets [62], as shown in Fig. 4.5. The field covers approximately 12,000 m2 (22 m in diameter and 26 m in length) and has a total stored energy of 1.6 GJ. A thin super- conducting solenoid [78] aligned with the beam axis surrounds the ID cavity and provides an axial magnetic field of 2 T at the IP. The solenoid assembly was optimized to minimize 0.66 the radiative thickness between the ID and the EM calorimeter, resulting in only radiation lengths at normal incidence. Three superconducting toroids, one surrounding the barrel and two at the end-caps, produce toroidal magnetic fields of approximately 0.5 T and 1 T, respectively. The entire system is under vacuum and cooled down by the ATLAS cryo- genics system. A precise description of the magnetic field in the detector volume is necessary ≈ 53 xzyϕη=+∞η=−∞θη=0IP (a) (b) Figure 4.5: a) Sketch of the ATLAS magnet system, with the barrel and end-cap toroids, and the solenoid placed inside the Tile calorimeter volume [62]. b) Picture of the barrel toroid as installed in the underground cavern, with the barrel calorimeter and embedded solenoid visible on the other side, awaiting to be put in position. The person standing in front of the structure provides the scale [62]. for a high momentum measurement resolution. For this purpose, the ID is provided with four NMR probes located at z = 0 and equally spaced in azimuth distance, which provide a measurement with an accuracy of 0.01 mT, while the rest of the solenoid and the muon B | chambers are equipped with 3D Hall cards to measure each field component. | 4.2.3 The inner detector The Inner Detector (ID) [79, 80] is the closest sub-detector to the beam pipe and has to sustain the largest radiation dose and flux of particles. Despite the harsh environment, the ID has to provide precise momentum and vertex measurements. This is achieved through three complementary subcomponents, shown schematically in Fig. 4.6. On the inner part, the Pixel and SemiConductor Tracker (SCT) silicon detectors provide high-resolution tracking and vertex reconstruction; on the outer part, the Transition Radiation Tracker (TRT) provides straw-tube tracking with transition radiation detection capability for electron identification. The Insertable-B Layer (IBL) was added in front of the Pixel detectors before Run 2 to react to the harsher conditions. The different components are arranged as concentric cylinders in the barrel regions and as stacked disks perpendicular to the beam axis in the end-caps. The entire ID system is 2.3 m in diameter and 7 m in length. The current ID was designed for 10 years of operation at nominal LHC parameters. Albeit minor upgrades, the ID performance remained adequate even once the LHC exceeded the design values. However, in order to sustain the HL-LHC conditions, the ID will have to be fully replaced by a new tracking system, the Inner Tracker (ITk) [81, 82], which will be 54 (a) (b) Figure 4.6: a) Schematic view of the ATLAS ID [83]. b) Cross sectional view of the ID barrel region traversed by a charged track (in red) [76]. From the collision point, the track traverses the beryllium pipe, the three silicon pixel layers, four SCT barrel layers of silicon micro-strip sensors, and 36 TRT straws. ∼ installed during the Phase II upgrades. Pixel detector η | The pixel system [84] is composed of three layers in the barrel region and three disks at < 2.5. The basic building block of the detector is a each end-cap, and covers the region module composed of pixel sensors, front-end electronics, and control circuits. The nominal pixel size is of 50 µ m in the ϕ direction and 400 µ m in the z or r direction, resulting in 67 80 million readout million pixels in the barrel and 13 million in the end-caps, for a total of channels. The detector was designed to provide at least three points per charged track, with intrinsic accuracies of 10 µ m in the (R ϕ) plane and 115 µ m along the z direction. ≈ | − The SemiConductor Tracker The SCT [85] is composed of four cylindrical layers in the barrel and nine discs in each end-cap. Silicon micro-strip sensors are connected to 6.3 million readout channels. Each track crosses eight strip layers, giving four two-dimensional space points and providing an intrinsic accuracy of 17 µ m in the R ϕ plane and 580 µ m along the z or r direction. − 55 Transition Radiation Tracker | − η | The TRT [86, 87] is the outermost layer of the ID and provides continuous tracking coverage < 2 range, with an average of 36 hits per track. While the TRT provides within the ϕ measurements and has a lower accuracy of 130 µ m, it provides a larger number only R of hits and longer track lengths, complementing the precision trackers. The TRT consists of about 350,000 straw tubes, 4 mm in diameter and with a 31 µ m diameter gold-plated tungsten wire at their center. The straws are arranged parallel to the beam line in the barrel and in a wheel-like shape parallel to the transverse plane in the end-cap. A charged particle passing through a straw ionizes the gas producing some primary ionization electrons, which are accelerated by an electric field towards the wire, inducing an electron avalanche that produces a detectable signal. The straws are interleaved with transition radiation (TR) material. The amount of TR is proportional to the relativistic factor γ = E/m of the incident particle, so that a particle as light as the electron will produce significantly more TR photons than a pion or muon. In fact, an essential function of the TRT is electron identification [88]. Insertable B-Layer The first layer of the Pixel detector closest to the beam pipe was originally designed to be regularly replaced. However, changes to the detector system that became necessary during ATLAS operation made the extraction of the layer no longer possible. In order to retain a high tracking performance until the end of Run 3, it was therefore decided to add a new innermost layer, the Insertable B-Layer (IBL) [89, 90]. The IBL was installed at 3.3 cm from the beam axis, between the existing pixel detector and a smaller beam-pipe, and provides < 3. A combination of planar and 3D sensor technologies are a longitudinal coverage of 250 µm2. The new layer was installed during used and the pixel cells size is reduced to 50 × the first long shutdown (LS1) before Run 2 and has been successfully operating since 2015. η | | 4.2.4 The calorimeters Calorimeters [91, 92] are detectors used to measure the energy of incident particles via their total absorption. When particles are stopped in the detector volume, showers are initiated. The incoming high energy particle is converted into two or more lower-energy particles, which in turn produce more daughter particles. The cascade process stops when the final particles have an energy smaller than what would be needed to produce further particles. The shower evolution differs according to whether the incident particle interacts electromagnetically or hadronically, requiring different types of detectors. Calorimeters are particularly well-suited for a high-energy multipurpose experiment, as their energy resolution improves with energy as 1/√E (in contrast to, for instance, a magnetic spectrometer, whose 56 momentum resolution deteriorates linearly with increasing particle momentum), they provide sensitivity to both charged and neutral particles, and can provide indirect neutrino detection, measure the arrival time of particles, and provide fast signals for triggering. As they are typically segmented transversely and longitudinally, they also allow to measure the position of particles and discriminate between different particle types according to the shape of the shower. Triggering and particle identification are particularly relevant for this work. Electromagnetic showers ∼ An electromagnetic (EM) calorimeter measures EM showers induced by electrons and pho- tons. At energies above 100 MeV, electrons lose their energy almost exclusively via bremsstrahlung, while photons via electron-positron pair production. The depth and width of the showers can be expressed in terms of the radiation length X0 of the detector mate- rial3. An electron traveling in a material covers an average distance of x = X0 before its energy is reduced by 1/e, while a photon travels a distance x = 9/7X0. The resulting EM showers tend to be quite contained in width and length, requiring a smaller detector volume, but a higher granularity for precision measurements of the shower position. The energy of the incident particle initiating an EM shower is proportional to the energy deposited by the charged particles in the shower through ionization and excitation. Hadronic showers ≈ 35A1/3 g cm− Hadrons interact with the detector material mostly via the strong interaction and thus exhibit different shower characteristics, often expressed in terms of the interaction length λ (the mean free path). The hadronic cascade presents two types of processes. The first type results in the production of high-energy secondary hadrons, typically at the GeV scale, with 2. This is generally larger than the radiation length X0, requiring larger λ detector volumes. The second type consists in nuclear interactions with large transverse momentum transfers, such as excitation or nucleon evaporation, which produce particles in the MeV scale and broaden the shower shape. The soft spectrum of these inelastic processes is dominated by neutrons, photons, and electrons, while the energetic component is populated by pions and, in lower quantities, by kaons, nucleons, and other hadrons. One third of the pions produced are neutral pions, which quickly decay into two photons before they have a chance to interact hadronically, initiating electromagnetic sub-cascades within the hadronic 3The radiation length for a material with atomic number Z and atomic weight A is given by [92] X0(g/cm− 2) 716 g cm− 2 A ≃ Z(Z + 1) ln(287/√Z) . 57 shower. The total fraction of energy in a hadronic shower that comes from an EM shower is called the electromagnetic fraction fe. As the energy of the incident particle increases, the number of energetic hadronic interactions does as well, inducing a larger fe. A large fraction of the energy in a hadronic shower escapes detection: part of the energy is used to break up nuclear bonds; some energy goes into short-range nuclear fragments absorbed before they get to the active layers; long-lived or stable neutral particles, such as neutrons, K0 L and neutrinos can escape from the calorimeter, while muons produced by pions and kaons decays can deposit only part of their energy. The lower the electromagnetic frac- tion of the shower, the larger the fraction of this invisible energy from hadronic interactions. As this form of invisible energy fluctuates between events, it will affect the energy resolution. Because fe, and therefore the fluctuation, is energy dependent, the calorimeter response will be nonlinear with energy. Compensating calorimeters are detectors that compensate for the loss of this invisible energy. Sampling calorimeter In a sampling calorimeter the functions of particle absorption and energy measurement are performed by different components (in contrast to a homogeneous calorimeter, where only one medium is used). This allows to choose the optimal material for each task, at the expense of an increase in the fraction of unmeasured energy. Sampling calorimeters are generally built in alternating layers of heavy absorbing material, such as lead, and layers of active material. This makes them more easily segmented longitudinally and radially, resulting in better space resolution and particle identification. The shower generation starts in the absorber, while the active layer generates and measures the detectable signal. Sampling calorimeters are classified according to the type of active material, where the deposited energy can be measured by collecting either the light produced in a scintillating material or the charge produced by ionization. The ATLAS Calorimeter The ATLAS calorimeter [62, 93, 94] surrounds the ID and is a hybrid system consisting of EM < 4.9. A schematic view is shown and hadronic sampling calorimeters covering the range in Fig. 4.7. A finely segmented EM calorimeter closest to the beam-line provides precision measurements of electrons and photons. This is surrounded by a coarser granularity hadronic calorimeter (HCal), which provides sufficient resolution for jet and missing-transverse-energy measurements. A forward calorimeter in the end-cap closest to the interaction region ex- tends the detector acceptance to high η. Three cryostat systems surround the calorimeter components that use LAr technology: one cryostat houses the barrel EM (EMB) calorimeter, η | | 58 Figure 4.7: Schematic view of the ATLAS calorimeter [62]. while a cryostat at each end-cap contains the forward calorimeter (FCal), the EM end-cap (EMEC) calorimeter, and the hadronic end-cap (HEC) calorimeter. Hadronic calorimetry in the barrel is based instead on a steel-scintillator Tile calorimeter (TileCal). All cryostats are 184◦C. The barrel cryostat is a 6.8 m long vacuum insulated and maintain a temperature of cylinder with inner and outer radii of 1.15 m < r < 2.25 m, while the end-cap cryostat has length 3.17 m and a radius of 2.25 m, the same as the barrel. The superconducting solenoid is placed in the same insulation vacuum as the LAr system. − The electromagnetic calorimeter | | η | < 3.2. Each wheel is partitioned into two co-axial wheels that are joined at < The EM calorimeter is a high-granularity LAr sampling calorimeter, covering the range 3.2 and providing excellent energy and position resolution. In the barrel, the calorimeter consists of two half-cylinders joined at z = 0 and covering together the region < 1.475. In the end-cap, the EMEC consists of a 63 cm thick wheel covering the region 1.375 < = 2.5, η | matching the acceptance of the ID. The absorber plates are made of lead with a thickness of 1.1 2.2 mm, according to the η-region. These are interleaved with thin layers of LAr and readout electrodes. An accordion geometry is used in both the barrel and the end-caps, providing a uniform performance as a function of ϕ, and a fast signal readout. In the region < 2.5, where precision studies were considered possible, the EM calorimeter is segmented η | into three sampling layers, while two layers with coarser granularity are used in the end-caps. η | η | − | | | 59 Figure 4.8: Sketch of a module in the barrel EM calorimeter, showing the η for the cells and trigger towers in each layer [62]. × ϕ granularity The barrel layers have different resolutions and radiation lengths, according to the physics requirements. A sketch of a module in the barrel EM calorimeter is shown in Fig. 4.8. The first sampling layer has a finer η segmentation to optimize the discrimination of prompt photons from photons originating from π0 γγ decays. To limit the number of channels, the granularity in the ϕ direction was reduced, resulting in thin strip-shaped cells. The second layer has the greatest depth, as it is expected to collect the largest fraction of the EM shower, while the third layer is a thin layer collecting the tail of the EM shower. → The pre-samplers A LAr pre-sampler is used to provide corrections for the energy loss caused by the amount of material in front of the EM calorimeter. This consists of an 11 mm layer in front of the EM calorimeter in the barrel, and a 5 mm layer in front of the EMEC in the region up to = 1.4, η | to further recover the jet energy measurement. < 1.8. A scintillator layer is positioned also between the two cryostats, around η | | | The hadronic calorimeters The HCal surrounds the EM calorimeter. A scintillator-tile calorimeter (TileCal) covers the < 3.2. < 1.7, while LAr calorimetry is used in the end-caps for the range 1.5 < region The TileCal consists of a central barrel of 5.8 m in length covering the region up to η | η | | | 60 Dj = 0.0245Dh = 0.02537.5mm/8 = 4.69 mm(cid:13)Dh = 0.0031Dj=0.0245x4(cid:13)36.8mmx4(cid:13)=147.3mmTrigger TowerTriggerTowerDj = 0.0982Dh = 0.116X04.3X02X01500 mm470 mmhjh = 0Strip cells in Layer 1Square cells in (cid:13)Layer 21.7X0Cells in Layer 3(cid:13)Dj·(cid:0)Dh = 0.0245·(cid:0)0.05 Figure 4.9: Schematic view of the tile calorimeter showing the various components of the optical readout: tiles, fibers, and photo-multiplier tubes [62]. | | η | < 1, and two extended barrels of 2.6 m in length, up to < 1.7. It has a radial depth of η | approximately 7.4 λ. It is composed of 64 modules made of steel absorber plates and plastic scintillator tiles as the active medium. A schematic view of the optical readout is shown in Fig. 4.9. Ionizing particles that cross the tiles induce the production of ultraviolet scin- tillation light. Wavelength-shifting optical fibers, in contact with the tile edges, collect the scintillation light, convert it to a longer wavelength, and transmit it to the photo-multiplier tubes located at the outer edge of each module. The grouping of the 540,000 readout fibers into bundles provides a three-dimensional cell structure with three layers in depth, of 1.5, 4.1 and 1.8 λ thickness at η = 0, and a ∆η 0.1 in the first two layers and 0.2 ∆ϕ granularity of 0.1 0.1 in the last one. × × The hadronic end-cap calorimeter (HEC) is a LAr sampling calorimeter that uses copper as the absorber material. Each HEC is designed as two wheels, with the outer wheel built with thicker copper layers (50 mm instead of 8.5 mm). The HEC has a depth of approximately 10 λ. A granularity of 0.1 = 2.5, while for higher η values it is reduced η | to 0.2 0.1 is used up to 0.2. × | × × The forward calorimeter The FCal provides both EM and hadronic energy measurements, and extends the detector 61 PhotomultiplierWavelength-shifting fibreScintillatorSteelSourcetubes Figure 4.10: Schematic view of the FCal calorimeter inside the end-cap cryostat, showing the three FCal modules, the shielding layers, and the cryostat walls in black [62]. | η | = 4.9. The FCal is the innermost layer of the end-cap detectors, acceptance up to positioned along the beam axis at 4.7 m from the IP. The high levels of radiation in this region make this a particularly challenging detector. In order to reduce the neutron albedo in the ID cavity, the front face of the detector is moved back by about 1.2 m with respect to the EMEC edge. This is a trade-off in longitudinal length, requiring a very high density detector to integrate the full interaction length of the forward particles and preventing energy spills and pile-up contamination into the surrounding detectors. The design, as shown in Fig. 4.10, consists of three sections: the first section, closest to the IP, uses copper as the absorber to optimize detection of EM radiation; the two outer layers use tungsten for hadronic calorimetry. Calorimeter read-out The building block of the calorimeter readout is a cell, defined by the total integrated energy deposited in its volume, and by its (η, ϕ) coordinates and the sampling layer where it is 10 MeV up to 3 TeV. located. The dynamic range for the energy of the cells goes from The lower limit is set by the irreducible thermal noise in the calorimeters, also referred to as electronic noise. The other source of noise in the cell readout is pileup noise, caused both by in-time and out-of-time pileup, for a total noise given by: ∼ σtotal noise = (cid:113) (σelectronic noise )2 + (σpileup noise )2. (4.3) Prior to 2011, the total noise was driven by the electronic noise, but with the increasing luminosity the pileup term has now become the dominant source [95]. Its effect is not = 200 simulation. The homogeneous in the detector volume, as shown in Fig. 4.11 for a majority of the energy flow is absorbed by the LAr calorimeters, while the Tile calorimeter µ ⟨ ⟩ 62 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(cm)z (cm)EMECHEC(back)PumpFCal 1FCal 2FCal 3(EM)(Had)(Had)(front)HECModerator shieldingshielding plugLAr Calorimeter Figure 4.11: The total energy-equivalent cell noise at the EM scale as a function of η for the different detector sampling layers for a HL-LHC simulation with µ = 200. has little sensitivity. The energy deposited in the calorimeters is processed by the on-detector (front-end ) and off-detector (back-end ) electronics. The necessity for low electronic noise and low latencies favored the choice of a readout architecture with analog processing close to the detectors. The amplification, processing, and digitization of the analogue signals is therefore performed directly by the front-end electronics, which in turn required custom designed radiation-tolerant ASIC’s. The back-end system is instead located in the main services cavern (USA15), 70 m away from the detector, and is made of commercial components. 4.2.5 The muon spectrometer The muon spectrometer [62, 96] detects the momentum and trajectory of charged particles escaping the hadronic calorimeter. In the energy range of the LHC, muons behave like mini- mum ionizing particles. This characteristic behavior makes them easily distinguishable in the detector, making muons essential pieces in many analyses. However, this also requires their momentum to be inferred from the curvature of their trajectory, rather than from the energy deposition in a calorimeter, a measurement that degrades with increasing energies. Accurate measurement of muons was an important design goal for the experiment and significantly shaped the design of the entire detector, starting from its size. A schematic view of the ATLAS muon system is shown in Fig. 4.12. Three superconduct- ing air-core toroids provide strong bending power within a large open volume. High-precision < 2.7, while tracking chambers provide excellent muon momentum measurement within η | | 63 Figure 4.12: Schematic view of the muon spectrometer [62]. Figure 4.13: Cross-section of the muon spectrometer along a plane containing the beam axis. The straight lines represent infinite momentum muons, which traverse three muon stations [62]. < 2.4. A cross- trigger chambers with position and timing resolution cover the range sectional view of the different detector components is shown in Fig. 4.13. Accurate muon momentum reconstruction relies on the precise alignment between the muon chambers and on an accurate magnetic field reconstruction. For this purpose, a high-precision optical alignment system monitors the relative positions and possible deformations of the MDT chambers, while approximately 1800 Hall sensors monitor the magnetic field throughout the spectrometer volume. η | | The precision chambers The precision-tracking chambers are positioned in three concentric cylindrical layers in the barrel, in between the coils of the barrel toroid magnet, and in three parallel wheels in the end-caps, in front and behind the end-cap toroids. The precision measurement of muon momentum is performed by the Monitored Drift Tubes (MDTs) in almost all the spectrom- < 2.7, the innermost eter volume, covering the region layer is made of Cathode Strip Chambers (CSCs), a finer granularity detector required by the higher background rates in this region. The CSCs are multi-wire proportional cham- bers, where cathode planes made of strips are positioned in orthogonal directions to provide measurements of both coordinates. In the region 2 < < 2.7. η | η | | | The muon triggers < The precision-tracking system is complemented by fast trigger chambers in the region 2.4. The trigger chambers look for high transverse momentum muon tracks and deliver track information to the Level-1 muon trigger within a few tens of nanoseconds from the passage η | | 64 of a particle. Reconstructed tracks are required to originate from approximately the IP and to pass certain pT thresholds. Additionally, the trigger provides bunch-crossing identifica- tion and measurements of both coordinates, complementing the MDTs measurement. In 1.05), three layers of Resistive Plate Chambers (RPCs) are operated in η the barrel ( | avalanche mode. In the end-cap region (1.05 2.4), the trigger is composed of four layers of Thin-Gap Chambers (TGCs), multi-wire chambers operated in saturated mode. | ≤ | ≤ ≤ | η 4.2.6 The forward detectors | In addition to the main detector systems, ATLAS is equipped with a set of smaller sub- > 5 on both sides of the IP. Moving away η detectors located in the very forward region | from the IP, the first system is the LUCID (LUminosity measurement using Cerenkov Inte- grating Detector) detector [62]. Located at 17 m from the IP, LUCID primarily provides ± online relative luminosity monitoring. Next is the Zero-Degree Calorimeter (ZDC) [62], lo- 140 m from the IP, and whose cated at approximately zero degrees to the incident beam, > 8.3) particles. Coincidence requirements η primary purpose is to detect neutral forward ( | on the two ZDC systems are also used to suppress beam-induced backgrounds and provide some knowledge of the vertex location. The ALFA (Absolute Luminosity For ATLAS) detec- 240 m, is used to measure the absolute luminosity. The AFP (ATLAS tor [62], located at Forward Proton) detector [97] was installed in 2017 at 217 m from the IP to measure diffractive protons scattered at small angles (100 µ rad), where one or both protons remain intact. 204 m and ± ± ± ± | 4.3 The ATLAS Trigger The ATLAS Trigger [62, 98] system is responsible for the selection of the subset of events to be stored on disk and used in physics analyses. With an LHC event rate of 40 MHz and an event size of approximately 1.5 MB, the ATLAS trigger has to handle a data volume of 60 TB/s. Storing all this data is not only unfeasible, but it is also not desirable, as the events that are interesting for physics analyses are orders of magnitude rarer than the large background of QCD jet production and pileup, as shown in Fig. 4.2. The role of the TDAQ system is therefore to process the live stream of data coming from the detectors and select the most interesting events to study, while rejecting the remaining 99.9975%. As the events that are rejected are lost, this is a crucial step for the ATLAS experimental program. In order to handle the large data flow, while keeping high signal efficiency and background rejection, the ATLAS trigger is a two-level system. The first pass is a hardware-based trigger, 65 executing fast algorithms on custom electronics for a first coarser selection. The reduced event rate is then processed by the second step in the trigger chain, which can run more complex algorithms on commercial software. During Run 2, the first trigger stage was called Level-1 (L1) and the second step was called the High-Level Trigger (HLT)4. The flow of data from the detectors, through the trigger chain, up to when the data is written to disk, is controlled by the Data Acquisition (DAQ) system. The full Run 2 Trigger and Data Acquisition (TDAQ) system is shown in Fig. 4.14. The L1 trigger receives partial event data from the detector. If the event passes the L1 trigger (L1-Accept), the full event data is read-out by the front-end electronics of all the detectors and sent to the ReadOut Drivers (RODs), which perform an initial processing and pass it to the ReadOut System (ROS). The ROS buffers the data and sends it to the HLT on HLT request. Events that pass the HLT selection (HLT-Accept) are transferred to local storage, ready for offline reconstruction. 4.3.1 The Level-1 trigger The L1 trigger is a hardware-based system that reduces the LHC event rate of 40 MHz down to the maximum detector read-out rate of 100 kHz. In addition to rejecting events, the L1 ϕ to be used by the algorithms in the next trigger identifies Regions of Interest (RoI) in η stage of the trigger chain. × The 25 ns interval between collisions is too short for the processing and evaluation of the trigger decision. Therefore, while the trigger decisions are being formed, the collision data is stored in memory buffers. These memories are contained on electronics on or near the detector, where radiation is high and costs and readout reliability put constraints on the amount of time the data can be stored for. For this reason, the maximum L1 latency, defined as the time between the pp collision of interest and the moment the L1 trigger decision is made, is required to be less than 2.5 µs. Custom-built electronics are needed to satisfy these requirements. The L1 trigger receives reduced-granularity data from the calorimeter and muon detec- tors, with the two detector systems handled by separate trigger components, the L1 Muon trigger (L1Muon) and the L1 Calorimeter trigger (L1Calo). The results are passed to the L1 Topological (L1Topo) processor, which was added during the first Long-Shutdown (LS1) in order to cope with the increased event rates by providing more sophisticated topological selections. The final step in the L1 trigger chain is the Central Trigger Processor (CTP), 4During Run 1 the HLT was based on two separate farms: the Level-2 (L2) trigger requested reduced event data and provided a first coarse selection. The reduced event rate was then processed by the Event Filter (EF), which had access to the full event information and longer latency. For Run 2, the L2 and EF were merged into a single system to allow better resource sharing and simplify the hardware and software [98]. 66 Figure 4.14: The ATLAS TDAQ system in Run 2, showing the relevant L1 and HLT trigger components, as well as the detector read-out and data flow to permanent storage on L1- and HLT-Accept [99]. Note that the Fast Tracker project was canceled and should be ignored in this figure. which provides the L1 trigger decision to the TDAQ system. L1Muon The L1Muon [100] uses the hits from the RPC and the TGC muon triggers to apply coinci- dences requirements and identify high pT muon candidates. The results from L1Muon are sent to the CTP via the Muon Central Trigger Processor Interface (MUCTPI). L1Calo The L1Calo [101] receives signals from all the calorimeter detectors and uses information about the energy deposits to identify high ET objects or energy sums of interest. The input data consists in trigger towers of coarser granularity than the calorimeter cells, mostly ∆ϕ, with larger sizes in the end-caps. A tower takes up the full depth of 0.1 0.1 in ∆η × × 67 Level-1Level-1 AcceptLevel-1 MuonEndcapsector logicBarrelsector logicLevel-1 CaloCP (e,γ,τ)JEP (jet, E)Central TriggerMuon CTP Interface(MUCTPI)L1TopoCentral Trigger Processor (CTP)PreprocessorDetectorRead-OutRODFERODFE...DataFlowRead-Out System (ROS)Data Collection NetworkData StorageMuon detectorsCalorimeter detectorsHigh Level Trigger(HLT)ProcessorsRoIEventDataFast TracKer(FTK)TileCalAcceptPixel/SCTTier-0RODRODFE each EM or hadronic calorimeter. The number of cells used to form a tower varies with the granularity of the calorimeter element, and it goes from a few in the end-caps, up to 60 in the LAr EM barrel. In the TileCal, most towers are built by summing the signal from five photo-multiplier tubes. The analogue trigger-tower signals are carried from the front-end electronics of the calorimeters to the L1Calo system located fully off-detector in the USA15 cavern. The L1Calo system consists of three main sub-systems. The Pre-Processor [102] digitizes the analogue calorimeter signals, identifies the bunch-crossing they originated from, and performs a series of operations to clean and calibrate the signals. The data is then transmitted in parallel to the Cluster Processor and the Jet/Energy-sum Processor (JEP), which use sliding window algorithms to identify energy depositions of interest. See Ref. [101] for a comprehensive description of the algorithms. It operates within the region The Cluster Processor identifies clusters of energetic towers that could be associated to an electron, photon, or tau that pass a programmable ET threshold and, if desired, isolation < 2.5, corresponding to the boundary of η requirements. | high-precision data from the ID and EM calorimeter. The e/γ algorithm looks for narrow high ET deposits in the EM calorimeter. To suppress hadronic jet background, the deposits are required to be isolated in the transverse plane and to not penetrate into the HCal. The τ /hadron algorithm, looks for collimated hadronic τ decays with looser isolation requirements and allowing deposits in the HCal. | | | η | η | The JEP is similarly used to identify jets and produce total, missing, and jet transverse < 3.2, the limit of end-cap acceptance, energy sums. The jet trigger uses data up to < 4.9, including also FCal information. For the while the energy sums extend up to purposes of jet and energy sum reconstruction, a coarser granularity can be used, and the EM and hadronic calorimeters do not need to be considered separately. The JEP towers, called jet elements, are the sum of 0.2 ∆ϕ windows in the EM calorimeter and 0.2 in ∆η in the hadronic calorimeter. The jet algorithm calculates the ET sums in windows of 2 2, 3 4 jet elements and compares them to programmable thresholds specifying the minimum ET requirement and the window size. The different sizes are sensitive to different signatures: smaller windows are better suited to discriminate nearby small-radius jets, while larger sizes are more efficient for individual energetic large-radius jets. As the windows are overlapping, a jet can exceed the energy threshold in more than one window. In order to avoid double-counting of jets, a 2 2 window is required to be a local maximum compared to its eight neighboring jet elements. This is used to also define the η and ϕ coordinates of the RoI. 3, and 4 × × × × × × The Common Merged Module (CMM) merges the results from the Cluster Processor and JEP modules and sends the information to the CTP in the form of Trigger Objects (TOBs), 68 described by the ET , η and ϕ coordinates, and the isolation threshold when used. L1Topo The L1Topo [103] consists of two modules of Field Programmable Gate Arrays (FPGAs). The modules are provided with the same TOBs from the L1Calo and MUCTPI systems, and execute parallel and independent algorithms. To reduce the combinatorics, part of the computational time is dedicated to produce reduced lists of sorted TOBs. The remaining time is used to evaluate the algorithms on the reduced lists. Various algorithms are avail- able: angular separations in ∆ϕ, ∆η, and ∆R; energy thresholds of objects inside a cone; selection on invariant, transverse, or effective mass; event-hardness selections; corrections to the Emiss . L1Topo can also apply requirements on triggers from adjacent bunch crossings. T The L1Topo decisions are transmitted to the CTP after ns. ≈ Central Trigger Processor The L1 trigger decision is formed by the Central Trigger Processor (CTP) [104]. The CTP receives inputs from the L1Calo, L1Muon through the MUCTPI, and L1Topo, as well as from some detector subsystems. The trigger decision is implemented as a logical combination of the L1 outputs according to the trigger menu (see Sect. 4.3.3). The CTP is also responsible for applying pre-scales on certain menu items and for applying the deadtime, a mechanism used to prevent the detector front-end buffers from overloading by limiting the number of L1-Accepts. If an event passes any of the L1 trigger items, a L1-Accept signal is sent. On L1-Accept, L1 trigger decisions and RoIs are sent to the HLT. 4.3.2 The High-Level Trigger The HLT reduces the event rate from 100 kHz down to 1 kHz. The HLT has access to the full granularity calorimeter information, data from the muon spectrometer precision chambers, and tracking information from the ID. The processing sequence consists in a first step, in which fast algorithms provide a fast coarse rejection, followed by a finer selection using CPU-intensive algorithms similar to the ones used in offline reconstruction. The algorithms are based on the offline software Athena [105] and are run on a farm of more than 40,000 Processing Units (PUs), which are continuously replaced with newer hardware throughout operations. Some algorithms use the L1 RoIs as seeds, requiring event data only around the RoI, while others require data from the full detector. The HLT algorithms were developed to be as close as possible to their offline versions. For instance, jet reconstruction is performed using the anti-kt algorithm [106] with a radius parameter R of 0.4 or 1.0 (see Sec. 5.2). A detailed description of the HLT algorithms can be found in Ref. [98]. The HLT latency is of 69 a few hundred milliseconds. On HLT-Accept, the events are transferred to local storage and are ready for offline reconstruction. 4.3.3 Trigger operations During detector operations [99] the trigger configuration determines the active triggers. For an event to be accepted, it has to pass one L1 trigger, referred to as L1 item, and one HLT trigger. A trigger chain is defined by a combination of one L1 item and one or more HLT selections. Trigger names are usually given by the name of the trigger level (L1 or HLT), followed by the object multiplicity, the particle type (e.g. j for jet, or xe for Emiss ), and the pT threshold. Some triggers are prescaled in order to adjust the rate of accepted events: a prescale value of n means that an event that passes the given trigger is retained with a probability of 1/n. T Each chain targets a specific physics signature and will be used by a physics analysis to recover events with the desired topology. A share of the rate budget is assigned to each chain according to the physics goals of the collaboration, and the threshold requirements of the L1 and HLT triggers are set to keep the expected rate within this budget. The list of trigger chains forms the trigger menu. The most significant constraints on the trigger menu design during Run 2 were the limits on the L1 and HLT output rates of 100 kHz and 1kHz, respectively. The design of the Run 2 trigger menu was shaped by the goal of maintaining the unprescaled single-electron and single-muon trigger pT thresholds around 25 GeV, in order to preserve the trigger efficiency for events with W and Z boson leptonic decays. The trigger menu was adjusted several times during the course of Run 2 in response to changes in LHC bunch filling patterns and bunch intensities, which affected the peak luminosity and average number of pileup interactions. The physics trigger menu and operations for 2015 data-taking can be found in Ref. [98]. T Different types of triggers and trigger menus exist. The primary triggers are used to select events of interest for physics analyses and are usually unprescaled. These cover all the signatures relevant to the ATLAS physics program, such as electrons, photons, taus, muons, jets, Emiss , and b-jets, all necessary for SM measurements and BSM searches. Other exam- ples are calibration triggers, which store only partial event information while operating at high rates, and support triggers, which are used for monitoring and are usually prescaled. For trigger algorithm development and rate predictions, a special menu is used called minimum bias [107]. To estimate the rate of events that would pass any given trigger one needs an unbiased data sample, such as the one collected by a trigger that fires at random. However, most selections in ATLAS are interested in rare events with small cross sections, and require 70 some level of event activity, such as a high pT lepton or jet. To reduce the amount of data necessary to have sufficient statistics for these rare events, a minimum bias sample is used. This is obtained by using a collection of several L1 trigger items targeting various signa- ture types. The resulting sample re-introduces some bias for these harder events, while still not favoring any particular signature, and results in a mixture of soft and hard processes, with soft events dominating. Because the correlation between the triggers is preserved, a re-weighting of the events allows to recover a zero-bias sample. 4.3.4 The Phase I trigger upgrade ⟨ µ − × ⟩ ≈ 2s− The ATLAS Phase I upgrades [76, 108] were installed before the start of Run 3 in order to cope with the concomitant LHC upgrade during the second Long-Shutdown (LS2) and as a first step in preparation for the HL-LHC. The LS2 upgrades to the injection system allow for lower emittance and higher intensity bunches. The full beam intensity attainable with these upgrades will be usable only after the final upgrades for the HL-LHC, mainly because of heating limitations of the inner-triplet magnets. Nonetheless, the improvements will provide 60% more intense beams already in Run 3 and luminosity leveling will allow to remain at a 1 for up to 10 hours during an LHC fill, 1034cm− peak luminosity of approximately 2.4 increasing the average pileup to 70 [76]. In order to sustain the higher rates and 60 radiation conditions, several detector systems were upgraded, including significant upgrades to the LAr calorimeter electronics to provide finer granularity and energy resolution to the trigger system, and the New Small Wheel (NSW) muon detector that replaced the inner end-caps of the muon spectrometer. The TDAQ system had to be upgraded to adapt to the new detectors, as well as to handle the higher event rates and pileup levels, both in terms of resources and algorithm performance. In particular, the DAQ system had to handle a 30% larger event size at L1 (2.1 MB at 60), while the latency and output rate of the L1 trigger were fixed by the original specifications of the detector to 100 kHz. At the same time, the HLT system had to target an output rate to disk of 3 kHz and the DAQ system had to sustain a maximum throughput of 8 GB/s, a factor of two improvement in performance with respect to Run 2 [76]. The increased pileup levels were expected to degrade the calorimeter resolution and object isolation, which would result in a decreased trigger efficiency and higher rates, pushing the trigger thresholds up. In order to retain the physics reach in the near-threshold regime, a more refined data processing was necessary, obtained via improved trigger algorithms with access to higher granularity. The Run 3 TDAQ system is shown in Fig. 4.15. In the following, the upgrades to the L1Calo jet trigger algorithms are discussed, as these are relevant for this work. µ ⟨ ⟩ ≈ 71 Figure 4.15: Schematic view of the Trigger and Data Acquisition system at the beginning of Run 3 [76]. L1Calo × The Run 3 L1Calo system was equipped with new Feature EXtraction (FEXs) algorithms running on FPGA modules and with access to a finer granularity calorimeter information. In place of the 0.1 0.1 trigger towers of Run 1 and 2, the LAr processing system now sends the information along the trigger path in the form of Super Cells containing sums of four or eight calorimeter cells (the maximum granularity of the detector front-ends). Fig. 4.16 shows an example of a 0.1 0.1 trigger tower in the EM Barrel calorimeter, now containing ten Super Cells. Different FEX algorithms are used to reconstruct different TOBs. The electron feature extractor (eFEX) module performs e/γ and hadronic τ identification, with < 2.5. The jet feature extractor (jFEX) coverage limited to the tracking acceptance of 4.9, hadronic τ decays in system identifies small and large-radius jets in the region 2.5, and electrons in the forward region outside the eFEX acceptance. It the region also computes energy sums and applies pileup and noise subtraction cuts. Lastly, the global feature extractor (gFEX) processes data from the entire calorimeter on a single module and performs full-scan algorithms to identify large-radius jets with pileup suppressed energies | ≤ | ≤ η | η | η | × | 72 Level-1 AcceptLevel-1 MuonEndcapsector logicBarrelsector logicCP (e,γ,τ)CMXJEP (jet, E)CMXCentral TriggerMUCTPIL1TopoCTPCTPCORECTPOUTPre-processornMCMDetectorRead-OutRODFERODFE...Read-Out System(ROS / Software ROD)Data Collection NetworkData StorageMuon detectors (including NSW)Calorimeter detectorsHigh Level Trigger(HLT)ProcessorsRoIEventDataTileCalAcceptTier-0Level-1 CaloLevel-1 TriggerTREXCMXe/j/g FEXLArTileCalvia TREXFELIXFELHC collision rate & event size40 MHz3.0 MBLevel-1 accept rate100 kHz300 GB/sHLT output to storage3 kHz6 GB/sDataFlow...L1TopoLegacy Figure 4.16: Example of an EM barrel 0.1 × 0.1 trigger tower containing ten Super Cells [76]. T and global observables, such as Emiss . The full Super Cell granularity is available only to the eFEX algorithms, while the jFEX and gFEX systems have access to 0.1 0.1 towers, 0.2 resolution of the jet elements in Run 2. A still an improvement with respect to the 0.2 × brief summary of the jFEX small-R jet algorithm is given next, while a detailed description of all the FEX algorithms can be found in Ref. [76]. × The jFEX small-radius jet algorithm | 0.1 trigger towers in the region The calorimeter inputs to the jFEX algorithm are 0.1 < 2.5, with slightly coarser granularity in the end-cap and forward regions. Each jFEX η | module covers an η slice of the calorimeter while providing full ϕ coverage. Each of the ϕ, with overlap areas between FPGAs to four FPGAs in a module is assigned a slice in η correctly handle objects located on the edges. × × × 5 trigger towers (0.5 The jFEX small-radius jet algorithm is a sliding-window algorithm, with the main steps ϕ). shown in Fig. 4.17. The search window consists in 5 The seeds are constructed as the sum of 3 3 tower blocks centered on each tower in the search window. Comparative operators, which take care of the possibility of comparing equal digital values, are used to find the seed with the maximum energy in the search window. The tower at the center of the maximum energy seed is chosen as the center of the jet. The already computed energy sum inside the seed (shown in red in Fig. 4.17) is added to the energy ring including all the towers within a radius of 0.2 R < 0.4 (shown in purple). The final jet consists of 45 towers forming an approximately round shape of R = 0.4. 0.5 in η × × ≤ × 73 0.10.1 Figure 4.17: The jFEX small-radius jet algorithm. From left to right: the seed finding process with identification of local maxima; comparative operators used to identify a local maxima; the final small-R jet centered on the trigger tower at the center of the maximum energy seed and built with all the towers within R < 0.4 [76]. 4.3.5 The Phase II trigger upgrade × 10− 2s− 34cm− 1and is The HL-LHC will run at a peak instantaneous luminosity of 5 to 7.5 1 of data, ten times the entire data set collected expected to collect between 3000 to 4000 fb− up until Run 3. This will allow the ATLAS experiment to substantially extend its physics program, by opening up the possibility of high precision measurements of SM observables and giving access to previously prohibitively small cross sections. At the same time, the increase in luminosity will result in unprecedented levels of radiation and pileup, with up to 200 simultaneous pp interactions per bunch crossing. This extreme environment will pose new constraints on the ATLAS detector and TDAQ systems and will require extensive upgrades that will be installed during the LS3, referred to as Phase II upgrades. The main = 4.0 (compared to the current detector upgrades will be described here briefly, but one is referred to the corresponding Technical Design Reports for more information. The current ID will be fully replaced by the = 2.5). A η ITk, which will extend the η-coverage up to | | new detector, the High-Granularity Timing Detector [109], will be added between the ITk and the LAr end-cap calorimeter to provide precision hit-timing information to aid with pileup mitigation and luminosity measurement. The LAr [110] and tile calorimeters readout electronics will be upgraded to improve the current limitations on the L1 trigger latency. Similarly, the MDTs front-end electronics will be replaced to handle the higher rates and provide MDTs hit information to the first step of the trigger chain. The rest of the MS upgrade will focus on upgrading the electronics of the RPC and TGC trigger chambers and adding new RPC detectors to increase the solid angle coverage. η | | The Phase II TDAQ upgrade [10] is required to adjust to the new detector systems and to the harsher data taking conditions. Without an upgrade of the TDAQ system, the high 74 levels of pileup would significantly degrade the performance of the current trigger algorithms. The larger backgrounds would also result in higher trigger thresholds to keep the rates under control, which would reduce the sensitivity of physics analyses, as discussed more in detail in Chap. 8. An upgrade of the trigger is necessary to retain ATLAS physics goals, which are summarized in Fig. 4.18, together with the triggers and hardware systems required to achieve these goals. For instance, the Global Trigger (see below) is necessary for improved multi-jet b¯bb¯b. The architecture of the triggers needed to achieve sensitivity to non-resonant HH → Figure 4.18: Diagram showing the relationship between ATLAS physics goals, required trig- gers, to the related trigger components of the Phase II trigger system [10]. Phase II TDAQ system is shown in Fig. 4.19. The trigger will still be a two-level system, with a first hardware-based trigger, now called Level-0 (L0), and a second software-based trigger, now named Event Filter (EF). The DAQ system will handle the data flow from the detector electronics, through the trigger chain, up to permanent storage. The L0 trigger will still receive data at the LHC event rate of 40 MHz, but the new detector readout electronics 75 will allow a L0 output rate of 1 MHz (from the 100 kHz of Run 3). The HLT will also have an increased output rate of 10 kHz (from the 3 kHz of Run 3). With a predicted event size of 6 MB, the total output bandwidth will be 60 GB/ s. Figure 4.19: Design of the Phase II TDAQ system with its three main systems: L0 Trigger, DAQ system, and Event Filter. The black dotted lines indicate the data flow at 40 MHz from the detectors to the L0 trigger system, which must produce a trigger decision within 10µ s. The red dashed arrow indicate the flow of the L0 trigger decision. The solid black arrows represent the detector and trigger data being transmitted through the DAQ system at 1 MHz. The EF makes the second level trigger decision reducing the event rate to 10 kHz. On EF-Accept events are transferred to permanent storage [111]. 76 Inner TrackerCalorimetersMuon SystemL0CaloGlobal TriggerCTPEvent FilterProcessor FarmData HandlersDataflowEventAggregatorPermanentStorageFELIXOutput data (10 kHz)Readout data (1 MHz)L0 accept signalL0 trigger data (40 MHz)eFEXfFEXL0MuonBarrel Sector LogicEndcapSector LogicMUCTPINSW TriggerProcessorStorageHandlerEventBuilderEF accept signaljFEXgFEXMDT TriggerProcessorEventProcessor The Level-0 Trigger The L0 trigger will be composed of the L0Calo, L0Muon, MUCTPI, and the CTP, inherited from the current trigger system, and a new addition, the Global Trigger. The L0Calo and L0Muon sub-systems will receive reduced granularity information at 40 MHz from the calorimeter and muon detectors, respectively. They will be mostly similar to their Phase I predecessors. The L0Calo will run the FEX algorithms described in the previous section, with the addition of a forward FEX (fFEX) for reconstruction of forward electromagnetic (jet) objects in the region 2.5 < < 4.9). The L0Muon sub-systems will receive inputs from all the muon detector systems and the Tile calorimeter. New additions will be the inclusion in the trigger decision of precision MDTs momentum measurements and signals from the RPC inner stations. The MUCTPI will calculate multi- plicities of high energy muons, check for double-counting of muon candidates, and interface the L0Muon with the Global Trigger (GT) and the CTP. < 4.9 (3.2 < η | η | | | The GT will be an entirely new addition to the trigger system that will bring EF-like capabilities to the L0 trigger by running offline-like algorithms on custom FPGA hardware. The GT will have access to full granularity calorimeter data, as well as TOBs from the L0Calo and L0Muon. The refined TOBs produced by the GT will be available as input to topological algorithms, as the GT will replace and extend the functionalities of the L1Topo system. The new TOBs and trigger conditions will be sent to the CTP for evaluation of the final trigger decision. The development of firmware algorithms for the GT is a major part of the work presented in this thesis, so the GT will be discussed in detail in Sec. 8.1. The Event Filter The EF system will still consist in a large CPU-based processing farm running offline-like reconstruction algorithms. Most importantly, the EF will have access to tracking informa- tion, which will allow to perform track reconstruction and implement vertex-finding and particle-flow-like algorithms to significantly reduce the rates by improving pileup mitigation, the identification of b-jets, and the Emiss calculation. A first fast initial rejection will be provided by regional tracking based on TOBs received from the L0 trigger. The reduced event rate will then be input to a global tracking performed over the full ITk detector. Note that the plan for the EF tracking Phase II upgrade has evolved since the original Technical Design Report [10], which was superseded by Ref. [111]. T 77 4.4 ATLAS Event reconstruction The reconstructed final state of a collision in ATLAS includes electrons, photons, muons, τ -leptons, jets, and missing transverse energy. Except for muons, reconstruction of all the other objects requires calorimeter information. Fig. 4.20 shows the paths that different types of particles follow in the detector systems. Charged particles, such as electrons, protons, and muons, leave curved tracks in the inner detector (ID). Thanks to the solenoidal magnetic field, the particles are bent and the direction and radius of curvature of the tracks provides charge and momentum information. Neutral particles, like photons and neutrons, do not interact with the ID. Electromagnetic interacting particles, like electrons and photons, are stopped in the electromagnetic calorimeter, while hadronically decaying particles deposit most of their energy in the hadronic calorimeter, where they are stopped after a longer and wider shower. Muons interact with the ID but, behaving as minimum ionizing particles, usually escape the calorimeters and leave tracks in the muon spectrometer bent by the toroidal magnetic field. Neutrinos escape the detector volume undetected, but their presence in the event is inferred from a momentum imbalance on the transverse plane. In the following, the Figure 4.20: Cross-section of the ATLAS detector with simulated particles trajectories [112]. reconstruction of the physics objects relevant for this thesis is briefly reviewed. Jets will be treated separately and more extensively in the next chapter. The algorithms discussed here 78 are developed by the ATLAS Combined Performance groups, which provide working points (WPs), calibrations, and general recommendations for all physics analyses. 4.4.1 Tracks and vertices The track reconstruction [113] algorithm reconstructs the trajectory of charged particles from the electronic signals, or hits, left in the ID. Tracking is a pattern recognition task made more difficult by the busy environment of the ID, including in-time and out-of-time pileup, and the possibility of collimated tracks. Track reconstruction starts from seeds made of tracks with three hits recorded in the Pixel or the SCT detectors. The seeds are then extended to include further hits to create track candidates. An ambiguity resolution step removes overlaps or wrongly assigned hits. Finally, a χ2-based track fit is performed and only tracks with pT > 400 MeV and passing quality selection criteria are retained. The final track is specified by the collection of hits assigned to it and the associated parameters describing the particle’s trajectory: the transverse and longitudinal impact parameters d0 and z0, the azimuthal and polar angle ϕ and θ, and the charge to momentum ratio q p . The tracks are also used to reconstruct the primary vertices [114], by iteratively associ- ating the reconstructed tracks with pT > 500 MeV. Primary vertex candidates are required to have at least two reconstructed tracks with pT > 500 MeV and to be compatible with the interaction region. The hard-scatter vertex is the vertex with the highest p2 T sum of the tracks associated to it. The other primary vertices are assumed to be produced by in-time pileup. Different track and track-vertex-association quality criteria WPs are provided. 4.4.2 Electrons Several analyses, including the one discussed in this thesis, rely on the efficient identification of prompt electrons originating from decays of W and Z bosons, from electrons produced by photon conversions, misidentified hadrons, and non-isolated electrons from heavy-flavor decays. Electrons and photons travel through the ID, where only electrons leave tracks, and are then stopped in the EM calorimeter (EMCal). Almost 40% of photons convert to electron- positron pairs (converted photons). An electron can lose energy through bremsstrahlung radiation due to the interaction with the different detector materials, with the radiated photon also possibly decaying to an electron-positron pair. These interactions can occur already in the beam pipe or in the ID, producing multiple tracks in the ID, or they can occur in the EMCal, where they are contained in the EM shower. A schematic view of the path of an electron traveling through the detector is shown in Fig. 4.21. 79 Figure 4.21: Illustration of the trajectory of an electron through the detector (solid red), with a photon emitted via bremsstrahlung radiation (dashed red) [115]. In 2015 and 2016 electrons and photons were reconstructed using a sliding window algo- rithm seeded by calorimeter towers [115]. A new algorithm [116, 117] based on topological clusters was introduced in 2016. The variable-size topoclusters, as opposed to fixed-size tow- ers, are better fit to capture the dynamic shape of the EM shower, subject to bremsstrahlung photon emission and photon conversions. The algorithm starts by selecting the subset of the 4-2-0 topoclusters (as described in Sec. 4.4.4) that are primarily generated by showers in the EM calorimeter, by requiring the EM fraction fEM > 0.5. A set of the EM clusters is selected as seeds of possible electrons and photons, and superclusters are formed by associat- ing nearby EM clusters that originate from the same vertex, in the case of an electron and a bremsstrahlung photon, or that originate from a displaced vertex, in the case of a converted photon. In general, an electron is defined as a supercluster in the calorimeter matched to a track in the ID; a converted photon as a supercluster in the calorimeter matched to a con- version vertex; and an unconverted photon as a supercluster matched to neither a track nor a vertex. The reconstructed electrons are further cleaned via quality criteria based on a like- lihood discriminant. Four sets of electron identification criteria with increasing background rejection power are provided: VeryLoose, Loose, Medium, and Tight. Isolation requirements are also defined to suppress background from hadrons faking electrons. 4.4.3 Muons Muon reconstruction [118] is based on detector information from the muon spectrometer (MS), the inner detector (ID), and the calorimeter. The primary reconstruction strategy looks for reconstructed tracks in the MS, which are then matched to ID tracks. A combined fit of the MS and ID tracks, which takes into account the energy loss in the calorimeter, gives 80 second layerfirst layer (strips)presamplerthird layerhadronic calorimeterTRT (73 layers)SCTpixelsinsertable B-layerbeam spotbeam axisd0ηφ∆η×∆φ = 0.0031×0.098∆η×∆φ = 0.025×0.0245∆η×∆φ = 0.05×0.0245electromagnetic calorimeter | the final combined muon. Other reconstruction strategies are available to retain efficiency. Inside-out muons are reconstructed from extrapolating ID tracks into the MS, where they are required to match with three MS hits included in the final fit. This allows to recover efficiency in regions of low MS acceptance or for low pT muons. Muon spectrometer extrapolated tracks are reconstructed from only MS tracks and are used to extend the acceptance outside the < 2.5 region covered by the ID. Segment-tagged muons are reconstructed from ID tracks η | that satisfy tight matching requirements on hits in the MS, but only the ID information is used to obtain the muon parameters. Lastly, calorimeter-tagged muons are reconstructed by matching ID tracks to energy depositions in the calorimeter consistent with a minimum- 0 gap region. ionizing particle signature, and compensate for the MS inefficiency in the After reconstruction, identification criteria are applied to select the highest quality tracks. Muon candidates are separated into prompt muons originating from the interaction vertex, and non-prompt muons originating from secondary decays. The WPs used in ATLAS are, in order of decreasing efficiency and increasing purity of prompt muon selection: Loose, Medium, and Tight. Special WPs are provided for analyses targeting more exotic regions of phase space. These are the Low – pT and High - pT WPs, respectively. | ∼ η | 4.4.4 Topological clustering Topological clusters, or topoclusters, are clusters of topologically connected calorimeter cells that are used for the reconstruction of isolated hadrons, jets, and Emiss . Each topocluster is three-dimensional, thanks to the longitudinal segmentation of the sampling layers, and can contain the full or partial response to one or multiple signal particles. The topoclustering algorithm [95] starts by evaluating the significance of each cell, T = S EEM cell σEM cell noise , (4.4) where σcell noise is estimated for each run according to Eq. (4.3). Both the cell energy and noise are evaluated at the EM energy scale, which is the scale at which photon and electron energy depositions are reconstructed correctly. The algorithm proceeds by identifying the > 4. Each seed cell represents a protocluster, seed cells, defined as those cells with which is progressively grown in volume. For each protocluster, the algorithm finds all the neighboring cells (cells adjacent to the seed either in the same sampling layer, or in adjacent > 2. These cells are added to the layers and overlapping in the (η, ϕ) plane) with > 2 adjacent to the protocluster protocluster and the step is repeated until no cells with |S| > 2 is assigned to two protoclusters, the protoclusters are merged. are left. If a cell with |S| |S| |S| 81 > 0 is added. Lastly, an outer layer of cells adjacent to the protocluster and satisfying The resulting clusters have a high core, which differentiates them from background noise, while the softer outer layer allows to retain signals that are closer to the noise level. A representative simulation of the three stages of the clustering process is shown in Fig. 4.22. |S| S Figure 4.22: Stages of topological clustering in the first FCal layer for a simulated di-jet event with at least one jet entering the FCal and no pileup. From left to right: all seed cells > 2 are added recursively with > 0 are included. Topocluster fragments to the protocluster; all neighboring cells with not associated to a seed are seeded in a surrounding calorimeter layer [95]. > 4 starting a protocluster; all neighboring cells with |S| |S| |S| Due to the shaping of the calorimeter signal, it is possible for calorimeter cells to have negative energy signals if induced by out-of-time pileup that occurred 100 ns before the event. Out-of-time pileup can also cause positive energy signals, when this comes from collisions It is therefore desirable to include negative energy cells in the in closer bunch crossings. clustering process for these positive and negative noise fluctuations to cancel each other out, providing an implicit noise suppression. However, this can result in negative energy clusters, especially when the seed itself was a large negative energy cell. Negative energy clusters are not used as input to jet reconstruction, as they represent pileup-induced energy fluctuations with no real correlation with the particle that is being reconstructed. The kinematics of the final clusters are obtained from a sum of the four-vectors of the associated cells. Including the negative energy cells would distort the calculation, to the point of projecting clusters to the opposite side of the detector, while not including them would result in a bias from the positive fluctuations. A special recombination scheme is therefore used that includes all cells, but avoids biasing in either direction and is described in Ref. [95]. Once the basic kinematic variables (ηclus, ϕclus, EEM clus ) are calculated, the final four-vector is obtained by interpreting the topocluster as a massless pseudo-particle. At this point the energy of the topoclusters is still at the EM scale, which does not account for the non-compensating calorimeter response to hadrons. The topoclusters need therefore to be calibrated to properly represent the hadronic energy scale. The calibration signal clusters because of compensates also for the inefficiency due to the loss of low S 82 φ cos ×|θ|tan-0.0500.05φ sin ×|θ|tan-0.0500.05210310410510E [MeV]ATLAS simulation 2010Pythia 6.425dijet eventφ cos ×|θ|tan-0.0500.05φ sin ×|θ|tan-0.0500.05210310410510E [MeV]ATLAS simulation 2010Pythia 6.425dijet eventφ cos ×|θ|tan-0.0500.05φ sin ×|θ|tan-0.0500.05210310410510E [MeV]ATLAS simulation 2010Pythia 6.425dijet event the pileup-dependent clustering strategy. The calibration is referred to as Local hadronic Cell Weighting (LCW). It consists in a series of corrections to iteratively reweight the cells energy, and is performed using simulation of neutral and charged pions, representative of electromagnetic and hadronic showers, respectively. The final calibrated cluster energy is typically ELCW clus ≥ EEM clus. 4.4.5 Missing transverse momentum T Missing transverse momentum (Emiss or MET) [119] is an important proxy to identify the production in the hard scatter of stable weakly interacting particles, which escape the experimental volume without leaving any detectable signal and include neutrinos, as well as possible new BSM particles. Indicating the contributions from all the observable electrons, photons, taus, muons, and jets, and the non-observable (invisible) particles, the vectorial sum of the transverse momenta of all the objects emerging from the hard scatter pHS is calculated as, T 0 = pHS T = (cid:88) pe T + (cid:88) (cid:124) (cid:88) pγ T + (cid:88) pτ T + (cid:123)(cid:122) pobs T (observable) (cid:88) pµ T + + pjet T (cid:125) (cid:88) pν T . (cid:124) (cid:123)(cid:122) (cid:125) pinv T (not observable) (4.5) T By conservation of momentum in the transverse plane, any significant deviation from zero indicates the presence of a particle that eluded detection with transverse momentum pinv T = pobs T . In practice, due to limitations of the detector acceptance and experimental ineffi- − ciencies in the reconstruction of the hard objects, only a proxy of pobs can be measured, referred to as Ehard and which includes only the reconstructed objects that pass kinematic selection and reconstruction quality criteria. In general Ehard T . To partially recover this loss, an additional soft-term psoft is included, built from reconstructed charged-particle tracks coming from the hard-scatter vertex, but not associated to any hard object5. As the hard objects are reconstructed and calibrated independently, it is possible that different objects share energy contributions, such as a topocluster contributing both to a jet and to an electron. For this reason, a signal ambiguity resolution procedure is implemented. The missing transverse momentum observable Emiss ) is then calculated as, < pobs T T T T = (Emiss x , Emiss y Emiss T = − (phard T + psoft T ), (4.6) 5A less commonly used definition calculates the soft-term from the unmatched topoclusters in the calorimeter, which includes neutral particles, but suffers from a large residual dependence on pileup. 83 with magnitude and azimuthal angle, Emiss T = (cid:113) (Emiss x )2 + (Emiss y )2, 1 ϕmiss = tan− (cid:32) (cid:33) . Emiss y Emiss x (4.7) Important quantities used to estimate the event hadronic activity are (cid:80) ET , the scalar sum of the transverse momenta of all the hard and soft contributions to the Emiss calculation, and HT , the scalar sum of the transverse momenta of all the hard objects only. T T In practice fake Emiss can arise due to limited detector acceptance, signal fluctuations in the detector response, and fluctuations in pileup contribution. The level of agreement between the observed non-zero Emiss is given by the significance . This is calculated with respect to the event activity as, value and the hypothesis of true Emiss T T S Emiss T √HT = S or = S Emiss T (cid:112)(cid:80) ET . (4.8) Another more recent object-based definition [120] calculates the significance as a likelihood ratio to test the hypothesis pinv = 0, and is the one used in the analysis discussed in this thesis to select events with true neutrinos. T = 0 and pinv T 4.4.6 b-tagging The identification of jets6 containing b-hadrons is an important step in ATLAS physics [121, 122], as top quark and Higgs boson decays proceed almost exclusively via bottom quarks. Jets originating from b-quarks can be identified by exploiting the distinct features of such decays. A b-quark hadronizes into a B meson – a meson composed of a b-quark and a u-, d-, s-, or c-quark. The lifetime of a B-meson is of the order of 1.5 ps ( 4.5 mm), which cτ ⟨ = γβcτ before decaying. At LHC energies, this is of corresponds to a mean flight length of the order of a centimeter [123],a sizable distance observable in the ID as a displaced vertex: a certain number of tracks points to a secondary vertex, with large longitudinal and transverse impact parameters. The decay of the B-meson is well described by the decay of the b-quark inside the hadron (spectator model), which proceeds predominantly via b cW −, with the virtual W decaying either leptonically into l¯ν, or into a pair of quarks, which then hadronizes. The transition b c is favored for the hadronic decay path by the CKM matrix, so that hadronic decays of B-mesons typically produce at least one c-flavoured hadron (a D meson), which then decays further, also with an appreciable lifetime, resulting in a characteristic topological configuration with two secondary vertices. ⟩ ∼ l ⟨ → → ⟩ 6Jets are discussed in detail in Chap. 5 84 ̸ The tagging of b-jets in ATLAS relies on the track reconstruction of the displaced B- meson decay and is a two-stage approach. In the first step, a series of low-level algo- rithms [124] exploits the characteristic features of the decay: the IP2D and IP3D track- based impact parameter taggers; the SV1 secondary vertex reconstruction algorithm; and JetFitter algorithm for a topological reconstruction of the full b- and c-hadron decay chain. The discriminating variables produced by these algorithms provide complementary informa- tion and are used in the second stage as inputs to the DL1r[122] algorithm7 , a high-level tagger which includes as input also the output probabilities from the RNNIP algorithm [125]. The algorithm output is multidimensional and provides the probability of the jet to be a b-jet (pb), a c-jet (pc), or a light-flavor jet (plight), with the final b-tagging discriminant (cid:32) DDL1r = ln pb pc + (1 fc · fc) · − plight (cid:33) , (4.9) where fc gives the percentage of c-jets in the background hypothesis and can be optimized at the physics analysis level. Different WPs at fixed signal efficiency are provided. 7Historically, two high-level taggers were available: the MV2 boosted decision tree classifier, and the DL1 artificial neural network. The DL1 algorithm was introduced for Run 2 and has now evolved into the DL1r. The latter achieves the best tagging performance and is the current recommendation for physics analyses. 85 Chapter 5 Hadron collider physics Thanks to the unprecedented center-of-mass (CoM) energies of the LHC, the ATLAS and CMS experiments can probe the SM over scales ranging from 10 GeV up to 10 TeV. The vast experimental reach relies on two fundamental principles of collider physics [126]: i) the higher the energy, the smaller the length scale one can probe, according to de Broglie relation λ = h p ; and ii) particles interacting at high energies should enable the production of heavier particles, according to Einstein’s equation E = mc2. At the same time, understanding the final states of these high-energy collisions is challenging both theoretically and experimentally. In particular, the evolution of hadron-hadron collisions is tightly connected to the nature of the QCD interaction and its running coupling. When two protons collide, a hard scattering event — an event with a large momentum transfer — will involve only one parton from each proton. At the energy scale of the hard scatter, QCD can be treated as a perturbative quantum field theory and the matrix element for any hard process can be calculated systematically at fixed order using the standard Feynman diagrammatic techniques. The hard process results in the production of a few energetic or heavy particles — whether quarks, leptons, or bosons — and, if these are short- lived, their resonant decays. These particles usually represent the process of interest that one would like to study. However, on top of this hard process several effects related to QCD have to be taken into account. The primary partons from the hard scatter will have a non-zero probability to split further into mostly soft and collinear gluons and quarks, resulting in a parton shower. The evolution produces progressively softer and smaller angles partons, down to a scale where QCD becomes non-perturbative. At this point, when the momentum transfers are small and the QCD running coupling is large, hadronization occurs: the connected partons combine into color singlet states, with unstable hadrons decaying further. The final stable hadrons (with lifetimes τ > 10 ps) are the physical particles that interact with the detector. These neutral and charged hadrons are stopped in the hadronic calorimeter, leaving a cone like energy deposition that is reconstructed as a jet. For an experimentalist, jets are one of the main means to gain insight into what happened in the hard scatter. As such, they are part 86 of almost any physics analysis and are fundamental for the study of the SM, as well as for the search of new BSM phenomena. For a theorist, jets offer a rich playground where to test QCD predictions at high energies. Additional soft physics arising from interactions between the colliding proton remnants, as well as pileup radiation, can contribute to the final state, making the reconstruction of the event more difficult. The partons confined in the incoming protons, as well as the hadronization of the final state partons, occur at a much lower scale than the hard scattering process, of the order of 1 GeV, where the validity of QCD as a perturbative theory comes short. These processes cannot be calculated theoretically, and have to be modelled and fit to data. Additionally, the final state of such collisions typically involves hundreds of particles. The high final state multiplicities make matrix element computations in the perturbative regime often too complex to be calculated exactly. Despite these difficulties, theoretical predictions can still be obtained thanks to the factorization of the contributions from the different scales and the use of Monte Carlo methods. 5.1 From QCD to jets 5.1.1 The strong coupling The strong coupling αs = g2 s 4π is the fundamental parameter governing QCD interactions. The strong coupling “runs”, meaning that the effective strength of the strong interaction changes with the physics scale Q of the process in question. The running of the strong coupling is governed by the renormalization group equation (RGE), Q2 ∂αs ∂Q2 = β(αs) = α2 s(b0 + b1αs + b2α2 s + . . .), − (5.1) − where b0 = (33 2nf )(12π) and nf is the number of quark flavors relevant at the given scale. The RGE allows to take the known value of the coupling at a given scale and find the value at any other scale. Numerically, this is often done with respect to the known value αs(M 2 Z ) = 0.12, so that Eq. (5.1) is solved as αs = αs(M 2 Z ) 1 + b0αs(M 2 1 Z )ln Q2 M 2 Z . (α2 s) + O (5.2) 87 Figure 5.1: Measurements of αs as a function of the energy scale Q. The order in perturbative QCD used in the extraction of αs is indicated in parentheses [123]. The negative sign in Eq. (5.2) causes the coupling to decrease with increasing energy, as shown in Fig. 5.1. For large momentum transfers, or small distances, QCD becomes almost a free theory, a phenomenon known as asymptotic freedom. 1 and perturbation theory is valid. Conversely, at small momentum transfers, or large distances, the ⪅ 200 MeV, QCD becomes non-perturbative. The coupling diverges and, at the scale ΛQCD fact that the coupling diverges at large distances prevents quarks from ever being observed alone, but only as color singlet bound-states, mesons or baryons. This phenomenon is called confinement. In the context of LHC physics, confinement plays a fundamental role in the evolution from the free quarks and gluons produced in the hard scatter to the hadrons actually observed in the detector. In this regime, αs ≪ 5.1.2 The hard-scatter cross section While high energy proton collisions involve, by definition, high momentum transfers, the partons confined in the incoming protons interact at a much lower scale – of the order of 1 GeV – where QCD is non perturbative1. It follows that in an LHC collision there are two scales at play: one is the soft long-distance physics of the proton structure, and the other 1The proton can be described as a sea of strongly interacting quarks and gluons, where q ¯q pairs and gluons carrying a small fraction x of the proton’s momentum are constantly being produced and absorbed. The three quarks that define the hadron type (two up-quarks and a down-quark in the case of a proton) are the valence quarks, which can be described, at first approximation, as the quarks whose net number is non-zero. 88 is the high energy short-distance physics of the hard process. While the latter is calculable in perturbative QCD, the former is too low for perturbative methods to work. This issue is resolved by the factorization theorem, which theorizes the independence of the short and long f can be expressed as [127], distance physics. The total cross section for the process pp → σpp → f = (cid:90) (cid:88) i,j dx1dx2fi(x1, µ2 F )fj(x2, µ2 F )ˆσij f (x1p1, x2p2, µ2 F ), → (5.3) where p1 and p2 are the colliding protons, ˆσij f is the parton-level cross section for the production of the final state f through the initial partons i and j, and the functions fi(xn, µ2 F ) are the PDFs. The PDFs represent (at first approximation) the number density of partons of type i carrying a fraction xn of the momentum of the proton pn, when the proton is probed at the factorization scale µF . → Parton distribution functions The factorization theorem can be intuitively understood by the fact that the hard interaction occurs over a much shorter timescale than the fluctuations inside the proton structure, so that from the point of view of the hard scatter, the quark sea appears frozen [128]. The PDFs are in fact decoupled from the short distance physics and their shape can be treated as universal, or process-independent. Therefore, although not calculable from first principles, the PDF shape as a function of x can be modelled and constrained by fitting cross sections to experimental data. Once this is performed at a given µF , the result can be derived for a different scale by renormalization group evolution 2. Fig. 5.2 shows the PDFs behavior of gluons and sea-quarks inside the proton as a function of x, for Q = 10 GeV and Q = 100 GeV, where µF is taken to be equal to Q. While the valence up and down quarks carry a significant portion of the proton momentum, at high Q the sea-quarks and gluon contributions become enhanced, even if with smaller x values. The strong enhancement of gluon PDFs towards low x at increasing Q is particularly relevant for LHC physics: as can be observed in Fig. 4.2, cross sections for gluon-initiated processes have a steeper slope of increase with increasing CoM energy than quark-initiated ones [126]. It should be noted that different collaborations use different functional forms for the PDFs and may also constraint the fit using different datasets. In the context of ATLAS physics, PDF modelling contributes to the systematic uncertainties of many analyses. Cross section The cross section of an interaction is calculated using two main ingredients: the matrix 2Specifically, the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) renormalization group equations. 89 Figure 5.2: Parton distribution functions obtained by NNLO NNPDF3.0 global analysis illustrating the gluon and quark flavor contributions to the proton composition as a function of x at Q = µF = 10GeV (a) and Q = µF = 100 GeV (b). Note that a factor of 0.1 is applied to the gluon PDF [32]. → M element and the phase space integral. The matrix element represents the probability amplitude for the transition from an initial state i to a final state f to occur. The phase space integral represents the kinematics available to the participating particles for the interaction to occur. In practice, the parton-level cross-section ˆσi f is obtained by taking the absolute value squared of the matrix element, summing over all possible polarizations and color states, and integrating over the phase space. The cross section can be calculated at fixed order in perturbation theory, where one approximates the series up to a given order n in the strong coupling αn s , with the assumption that the contribution from the omitted higher orders should be small. Each power of αs corresponds to the addition of new diagrams including an extra real or virtual emission, starting from the leading order (LO) diagram with no emissions. The cross section calculated at next-to-leading (NLO) accuracy contains the contribution from diagrams with one emission or one loop. These diagrams introduce different types of divergences, which have to be regulated to preserve unitarity. Diagrams with loop corrections introduce ultraviolet (UV) divergences. Because QCD is a renormalizable theory, these divergences can be treated by first regularizing and then renormalizing the theory, i.e. the divergences can be absorbed in the redefinition of the parameters. Both virtual and real-emission diagrams exhibit infrared and collinear (IRC) divergences when the emitted gluon is soft or collinear. However, according to the Kinoshita-Lee- Nauenberg (KLN) theorem, order-by-order unitarity implies that the singularities coming from integration over unresolved real emissions must cancel, order by order, with the equal but opposite sign singularities generated by integrating over the virtual loop corrections. As 90 long as both contributions are included, the calculation of the nth order is finite [128]. In principle, the energy and spatial resolution of the detector acts as a regularizer, by making these corners of phase space not detectable and therefore not contributing to the total ob- servable cross section. However, it is desirable not to have theoretical calculations based on experiment-dependent parameters [127]. It is therefore preferable to study observables for which the KLN theorem holds, called IRC-safe observables. 5.1.3 Showering and hadronization The scattering of any charged particle leads to the emission of radiation, called bremsstrahlung. This occurs both in QED and QCD, with photon and gluon emission respectively. Unlike photons, however, gluons carry themselves color charge and will give rise to further gluon radiation and parton multiplication [129]. A parton produced in the hard scatter will start at the scale of the hard process and move towards a lower scale, with predominantly soft and collinear emissions. This process is called fragmentation and continues until the par- tons are resolved at a scale of Qhad ∼ 1 GeV. At this point, confinement requires these particles to undergo some transition from free colored partons to color singlet hadrons. This non-perturbative process is called hadronization. Although the quark and gluon emissions occur in the perturbative regime, the high parton multiplicities would require matrix element calculations to very high orders, a task in most cases not solvable analytically. At the same time, the hadronization process is non-perturbative and not very well understood theoretically. Event generator packages use therefore an alternative approach, where the perturbative emissions are treated as a prob- abilistic process, referred to as parton shower. A shower of soft and collinear quarks and gluons is simulated to accompany the partons participating in the hard scatter, in practice providing approximations of the higher-order real-emission corrections [130]. Matrix element calculations provide an exact solution at fixed order for hard wide-angle emissions, but can only handle a few for the problem to be analytically solvable. On the other hand, parton showers describe well regions of the phase space dominated by soft and collinear gluon emissions, but fail to model hard wide-angle gluon emissions. In order to simulate pp collisions, both methods are typically combined, as discussed later. 5.1.4 Soft physics The Underlying Event UE describes any process that accompanies a hard inelastic scatter. Due to the composite nature of protons, each pp collision can contain several few-GeV collisions between secondary partons from the same colliding protons, referred to as multi- 91 parton interactions (MPIs). In addition, each colliding proton may also leave behind a beam remnant, which does not take part in the initial state radiation or hard-scattering process, but still remains color connected to the rest of the event. The contribution of the UE to the final state is understood only phenomenologically from data due to its non-perturbative nature. In particular, the UE is related to the pedestal effect: kinematic distributions of hard jets display a constant ET plateau that is significantly higher than what is observed for a minimum bias event3. The larger activity is explained by a trigger-induced bias. The trigger selection of a hard jet biases the event selection towards more central collisions, associated to a larger number of MPIs and increased event activity [129]. 5.1.5 Monte Carlo event generators Monte Carlo (MC) simulations are an essential part of the ATLAS physics program, as they allow to develop new analysis methods, isolate specific physics signatures with targeted phase space selections, perform calibrations between data and MC, and provide the distri- butions for the background-only hypothesis in any statistical fit. A MC sample is a set of events representing a given process. Each event represents the same hard interaction, but the kinematics of the final state objects varies event-by-event according to the true probability distributions. The MC generation path is generally composed of independent steps carried out by different MC simulation programs. The objects output at each of these steps are said to be at the parton level, hadron-level, or reco level. In the context of ATLAS perfor- mance studies, reconstruction algorithms can be fed input objects from any of these stages, according to the need. Parton-level Matrix element generators are used to simulate pp collision events at the parton-level. One of the most widely used is MadGraph. In the first step, MadGraph calculates the matrix element, which provides the mathematical description of the interaction and is a function of the momenta of the final state particles. This is usually performed to the highest possible order, although this often remains the LO. The result is then convoluted with the chosen PDF set describing the partonic structure evaluated at the LHC CoM energy. Short-lived particles produced in the hard-scatter are decayed. When referring to the parton-level, one refers to the particles output by the matrix element calculation. The phase space integral is 3Minimum bias refers to a data sample collected by an experiment using a “minimum bias trigger” (see Sec. 4.3.3). The resulting sample includes a mixture of soft and hard processes, with a prevalence of soft events. While the processes that make up the UE are similar to the soft interactions that dominate a Minimum Bias sample, the two are not the same, as the definition of the UE requires a hard scatter to have occurred, resulting in increased event activity. 92 then computed using numerical integration to obtain real predictions for the cross section. The result is a statistically representative sample of parton-level events for the given process. The parton level gives a good description of the momenta of the outgoing particles. However, fragmentation and hadronization have to be simulated in order to correctly reconstruct the interaction with the detector. Hadron-level Common event generators are Pythia, Herwig, and Sherpa, which can be used to sim- ulate the parton shower, the decay of unstable particles, the formation of hadrons, and multiple pp interactions. The packages differ in the type of algorithm used for showering and hadronization. For instance, Pythia showering algorithm is based on the Lund string model, where quarks are thought of as strings and quark confinement is represented as a string potential. As the quarks at the endpoints of the string move apart, the potential energy increases until enough energy is available for a new q ¯q pair to be created, breaking the string into two separate color singlet pieces. At the end of this fragmentation process the color connected partons are combined to create hadrons. The most common method to simulate pp collisions is to combine LO matrix element predictions with parton showers. Another possibility is to start from NLO (or higher) matrix element calculations before interfacing with a parton shower generator. Such approaches are used by MC@NLO and Powheg. This is advantageous, as one can benefit from the higher accuracy and smaller normalization uncertainty of NLO predictions. However, when combining NLO matrix element calculations with parton showering, special care has to be taken to avoid double counting in overlapping regions of phase space, a process called merging. The stable hadrons at this point are referred to as the hadron-level or particle-level of the MC simulation. A particle is considered stable if its lifetime is long enough for it to interact with the detector. Although the actual lifetime cutoff is somewhat arbitrary, the convention used by ATLAS in MC simulation is τ > 10 ps. Reco-level The stable particles output by the event generators are passed through the detector simu- lation GEANT4 [131], which simulates their interaction with the different detector materials. Next, a digitization step reproduces the detector’s response and readout. At this point, the simulated events are in the same format as any real data event recorded during oper- ations. The only difference is that the MC simulation retains the truth information about the hard process, including particle types, four-momenta, and decay chains [126]. The same 93 object reconstruction algorithms are run on data and MC events. The objects output by the reconstruction step are said to be at the reco-level or detector-level. 5.1.6 Jets A jet is a collimated spray of particles resulting from the showering and hadronization of high-energy quarks and gluons. As discussed in the previous section, the hadronic final state of a hard scatter can be described on three levels: the final state partons of the hard process (parton-level ), the final stable hadrons before interaction with the detector systems (hadron-level ), and the observable energy depositions in the detector (reco-level ). A jet algorithm takes a list of input objects — at the level of particles, hadrons, or energy deposits — and returns a list of new objects called jets. The processes that relate these three levels are complex and result in jets whose composition — in terms of type, multiplicity, and momenta of the particles associated to each jet — varies between events. Nonetheless, the direction of the jet, built from the four-momentum sum of its constituents, is generally a good representation of the original direction of the parent parton [13]. In principle, therefore, there is a close correspondence between these three levels of description, as represented in Fig. 5.3. This makes jets important proxies to study the partonic dynamics of the collision and ubiquitous tools in collider physics. However, in practice soft non-perturbative physics, such as pileup and UE, as well as additional hard QCD emissions, can blur the picture, making the task of a jet algorithm more complicated. As an example, consider a simple di- jet event, where two quarks are produced in the hard scatter accompanied only by soft and collinear emissions. The event will have two cone-shaped energy depositions in the detector associated to the two quarks and can be reconstructed in a straightforward way. In contrast, consider an event where one quark emitted a hard wide-angle gluon. There is somewhat an ambiguity on whether this should be considered a single jet or two jets. The decision of when an emission is deemed hard enough for it to be considered a separate jet depends on what physics question one wishes to study and is made via the choice of a jet algorithm [127]. The presence of extra radiation in the final state, including pileup, can also affect jet physics, as it can modify jet properties. The subject of jet reconstruction and identification and of pileup suppression are relevant for this work and will be discussed in detail in the following sections. 94 Figure 5.3: Illustration of the correspondence between a jet and the possible types of objects associated to it: the partons produced in the final state, the hadrons resulting from show- ering and hadronization, and the energy depositions in the calorimeter. Reproduced with permission from Springer Nature from Ref. [130], Fig. 5.2. 5.2 Jet reconstruction algorithms The reconstruction of jets depends on the jet definition and the algorithm inputs. The input particles are described by their four-vectors and can be partons, hadrons, or energy deposits. The jet definition is determined by the jet algorithm, or the rules used to combine particles into groups of objects, and by the recombination scheme, the rules used to combine the momenta of the grouped objects into the momentum of the final jet. The standard scheme, where the four-vector of the jet is given by the recombination scheme is the E − 95 sum of the components of the four-vectors of its constituents. All jet algorithms can be classified according to two broad categories [127]: • Cone algorithms rely on an event-level (top-down) approach where the jets are viewed as dominant directions of energy flow. • Sequential-recombination algorithms have a bottom-up approach, where the closest particles – according to some predefined metric – are recombined iteratively, as if reproducing in reverse the fragmentation process. The choice of which algorithm to use is based on physics and practical considerations, in- cluding the requirement of infrared-collinear (IRC) safety, the dependence of the boundary of the jets on soft emissions, and the computational time. Until the first years of LHC op- eration, cone algorithms were favored despite being IRC unsafe, because of the well-defined circular shape of the output jets, less sensitive to non-perturbative effects and easier to cal- ibrate. This changed, however, with the development of the anti-kT algorithm [106], as it provided both an IRC safe and soft-resilient shape option, making it the current standard of jet reconstruction. 5.2.1 Infrared-collinear safety Ideally the set of hard jets reconstructed in an event should be insensitive to the random soft and collinear emissions characterizing the showering process. Experimentally, the de- tectors’ resolution acts already as a regularizer, as below a certain scale one has no way of distinguishing a parton from a parton plus a collinear or soft emission. However, this is detector-dependent and can make it difficult to connect the experimental measurement to theoretical predictions. From the theoretical side, as discussed in the previous sections, fixed- order perturbative QCD calculations used to make these predictions remain finite thanks to the cancellation of divergent contributions from real and virtual emission diagrams. Observ- ables where this cancellation is guaranteed are said to be IRC-safe. In general, an observable is IRC-safe if its value remains unchanged under any number of soft or collinear splittings. In other words, if ⃗pi is the momentum of any particle entering the definition of an observ- ⃗pk able, the observable must be invariant under the branching ⃗pi → (collinear) or ⃗pj → ⃗pj + ⃗pk, whenever ⃗pj ∥ IRC-safety for jet algorithms is necessary for any QCD precision studies. The preferred IRC safe algorithm for jet reconstructions in ATLAS is currently the anti-kT algorithm, while for jet substructure the kT or Cambridge/Aachen are generally used, as they are more sensitive to QCD branching. Nonetheless, non-IRC safe jet algorithms can still give good 0 (soft) [127]. 96 and not necessarily worse predictions. Most cone jet algorithms used up until recently fall into this category. 5.2.2 Cone algorithms Cone algorithms rely on the idea that soft and collinear emissions will not modify the main features of an event and define jets as angular cones around dominant directions of energy flow [127]. In order to reduce the computational time, cone algorithms are typically seeded. A proto-jet is built around the seed, whose constituents are selected by drawing a cone of radius R around it4. The four-momentum of the jet is calculated from the constituents according to the recombination scheme used. Iterative procedures are usually implemented to select stable cones: a cone is stable when the axis (usually given by the four-vector sum of its constituents) points in the same direction as its seed. Typical issues with these algorithms are the problem of overlapping cones and IRC un- safety. The overlap of two cones is an issue for the reason that energy is being double-counted. Cone algorithms can be subdivided into two classes according to how they deal with this. Some algorithms, including the old ATLAS iterative cone with split-merge (IC-SM) algo- rithm, implement a split-merge approach: if two overlapping jets share more than a fraction f of their energy, the jets are merged, otherwise the constituents are split among the two jets. Other algorithms build the cones starting from the hardest seed, and once the stable cone is found, its constituents are removed from the event before moving on to the next seed. This results in hard jets always being perfectly circular. An example of this type is the old CMS iterative cone with progressive removal (IC-PR) algorithm. The problem of IRC-unsafety typically arises from the seeding procedure: the selection of seeds according to their hardness is problematic, as particles pT ’s are not collinear safe quantities. If a hard particle, which under the no-emission scenario would result in a hard seed, undergoes a resolvable collinear splitting, the result will be two lower energy seeds. This can result in different seed choices and hence in different jets. An attempt at avoiding selecting seeds according to their hardness was made by building all the possible stable cones to then select the hardest ones. However, this was shown to be unsafe under soft emissions. Consider two hard particles at a distance R < ∆R < 2R, where the cones built on them do not overlap. If a soft emission occurs at a distance R between the two, it will produce a cone including both jets that could be harder than the two jets alone. In 2007 an IRC-safe cone 4As defined in Sec. 4.2.1, the angular distance between two objects i and j in the detector is given by ϕj )2. Drawing a cone of radius R around the seed means selecting all the (cid:113) yj )2 + ∆(ϕi − ∆Ri,j = ∆(yi − objects with ∆Rseed,object < R. 97 algorithm was developed called SISCone (Seedless Infrared Safe Cone) [132]. However, this option loses one of the advantages of cone algorithms, as it produces irregular jet boundaries due to soft radiation. For a comprehensive list of cone algorithms see Ref. [133]. 5.2.3 Sequential-recombination algorithms The most widely used sequential-recombination algorithms today belong to the family of the kt algorithms. These algorithms introduce a new distance metric between particles and iteratively combine the closest pair of particles until not particles are left. The inter-particle distance is given by, dij = min(k2p ti , k2p tj ) ∆R2 ij R2 , diB = k2p ti , (5.4) where kti is the transverse momentum of particle i, ∆Rij is the distance in the rapidity and azimuth plane between particle i and j, R is the radius parameter of the algorithm, and p is an input parameter. The algorithms differ in the value of the parameter p, which determines the momentum weighting: p = 2 for the kt algorithm [134, 135], which combines soft and collinear particles first; p = 0 for the Cambridge/Aachen algorithm [136, 137], which clusters particles together only based on angular proximity; and p = 2 for the anti-kt algorithm [106], which preferentially combines hard particles. − The recombination is an iterative procedure: 1. Start with a list of input objects 2. For each particle i, calculate the distances dij from every other particle and the distance diB of the particle from the beam. 3. Find the minimum distance dminin the set of , combine particles i and j into a new particle, remove them from the list of input objects, and , call particle i a jet and remove it add the new particle to the list. If dmin ∈ { from the list of inputs. . If dmin ∈ { dij} ∪ { diB} diB} dij} { 4. Repeat from step 2. Originally these algorithms were considered very slow, as naively the algorithmic complexity scales like N 3: one has to calculate N 2 distances and repeat for N iterations. However, it was later shown that the speed can be greatly improved with geometrical arguments [138]. First, one can prove that the dij distance in step 2 does not need to be computed for every pair of particles i and j, but only for particle i and its nearest neighbor, so the total complexity 98 is reduced to O(N 2). This can be further improved by making the finding of the nearest neighbor more efficient. Using the Voronoi diagram technique from computational geometry one can reach an algorithm complexity of O(N lnN ). This class of algorithms is usually trivially made IRC safe. Consider the case of the anti-kt algorithm and assume a new soft particle i is produced in the event. If diB is the minimum distance, this will produce a new jet with pT → 0. If instead the particle is closest to another particle j, the dij distance will be dominated by the 1/k2 ti term, so that dij → ∞ and the soft particle will be clustered last. Similarly, a particle originating from a collinear emission will have ∆Rij → 0, so it will cluster first to the hard jet and not change its coordinates. Either way, the addition of a soft or collinear particle has no effect on the hard jets found in the event. These algorithms implicitly produce a clustering sequence for the event. In the case of the kt algorithm, this is closely related to the probabilistic emissions in the parton shower: the pair that recombines first is the one with the highest probability of having been produced by the same splitting. For this reason, the kt algorithm is often used for substructure studies of hadronic decays of boosted massive particles, such as top-quark and Higgs, W , and Z bosons. A draw back of the kt algorithm is that the shape of the resulting jets is sensitive to soft radiation, resulting in irregular boundaries. This is caused by the fact that soft particles are clustered together first, so the presence of a soft jet around the boundary can affect whether close-by particles get assigned to the jet or not. Similar conclusions hold for the Cambridge/Aachen algorithm. Conversely, the anti-kt algorithm clusters first hard objects that are close together, which ensures that the jet grows around a hard core, but does not bring information about the substructure. As new particles are added to the proto-jet, the jet axis can move slightly but, in the absence of other nearby hard particles, the final shape will be a perfect cone of radius R. The result is that of an ideal stable cone algorithm, making it the most accurate algorithm to resolve jets. Anti-kt also automatically takes care of the potential issue of two hard particles at a distance ∆R that is R < ∆R < 2R, a situation that would produce overlapping cone jets. Considering the two extreme situations: • If kt1 >> kt2, the jet around particle 1 will be conical, while the second jet will lose some of its constituents. • If kt1 = kt2, the boundary will be a straight line equidistant between the two jets. 99 5.3 Jets in ATLAS Being a pp collider, jets are ubiquitous in LHC physics and are essential components to many SM measurements and searches for new phenomena. On average, two-thirds of the visible jet energy is contributed to by charged particles, predominantly by charged pions, a quarter is composed of photons from neutral hadron decays, and the remainder consists in neutral hadrons [139]. Jets interact therefore with the inner detector (ID), before being stopped in the calorimeter, where they leave a cone-like energy deposition. The standard for jet reconstruction in ATLAS is the anti-kt algorithm with radius pa- rameter R = 0.4 for small-R jets, and R = 1.0 for large-R jets, the latter used in the reconstruction of boosted hadronic decays of massive particles. The inputs to the jet algo- rithm consist in a list of four-vectors, which can describe charged particle tracks from the ID or energy deposits in the calorimeter, or a combination of the two. Stable particles from MC generators at the parton- or hadron-level can also be used for MC studies. Jets produced with different inputs are referred to as jet collections. Jets built from detector inputs have to be calibrated to compensate for several factors, including detectors inefficiencies (particularly the non-compensating nature of the hadronic calorimeter) and electronic and pileup noise. The calibration chain is different for small-R [140] and large-R [141] jets, and is performed independently for any given jet collection. As large-R jets are used to reconstruct decays of boosted massive particles, where the jet mass is well-defined, their calibration includes both energy and mass corrections. Different techniques for pileup mitigation can also be used, both directly on the set of objects input to the jet algorithm, and on the reconstructed jets. Lastly, an essential step in most physics analyses is the identification of the true particle from which a given jet originated, a procedure called jet tagging. Several algorithms have been developed in ATLAS in the context of heavy flavor (see Sec. 4.4.6) and boosted large-R jet identification. In the following, the steps of the ATLAS jet reconstruction process most relevant for this thesis are discussed, including jet collections and methods for boosted jet tagging. The topic of pileup suppression is discussed in the next section. 5.3.1 Jet algorithm In ATLAS, jets are reconstructed using the anti-kt jet algorithm, as implemented in the FASTJET package [142]. The standard radius parameter for jet reconstruction is R = 0.4. These are referred to as small-R jets and are used to reconstruct jets originating from individual partons, such as a hard quark produced via the strong interaction or the two b-quarks from a resolvable Higgs boson decay. The average transverse distance between two 100 particles coming from the decay of a particle of mass m and transverse momentum pT is approximately [126], ∆R ≈ 2m pT . (5.5) For example, a Higgs boson with pT = 250(500) GeV produces a jet contained on average within a cone of radius 1.0 (0.5). In other words, the larger the transverse momentum of a particle, the more its decay products are collimated. For large boosts, the decay products can be sufficiently collimated that they are not resolvable as separated jets anymore. Large- R jets with R = 1.0 were introduced to recover efficiency in the reconstruction of boosted decays of massive particles such as top-quark and W , Z, and Higgs bosons. 5.3.2 Jet inputs and jet collections EMTopo and LCTopo During Run 2, the standard inputs for jet reconstruction were topological clusters (see Sec. 4.4.4). According to whether the topoclusters are input at the EM scale or are LCW calibrated, the corresponding jet collection is referred to as EMTopo or LCTopo. This was possible thanks to the excellent ATLAS calorimetry, which provides clusters with high energy resolution. However, in the increasingly dense environments of the LHC, several improve- ments can be gained with a particle flow approach that makes use of both calorimeter and track information. Two such reconstruction strategies were developed at the end of Run 2. Particle Flow The Particle Flow (PFlow) algorithm [139] relies on tracking information to improve the performance of the reconstruction of low pT charged particles. Tracks provide a superior momentum resolution for low pT particles, and better angular resolution that allows to recover low pT charged particles swept outside the jet cone by the magnetic field before reaching the calorimeter. They also allow to reject charged pileup particles not originating from the primary vertex. The algorithm associates individual well-reconstructed tracks to single topoclusters in the calorimeter and then finds the best position and energy measure- ment for each track-cluster system according to which detector has a better resolution in the given energy regime. Different processing steps account for the possibility of overlapping showers or of a track contributing to more than one cluster. The final input objects (PFOs) consist of tracks, the remaining modified clusters, and the clusters not matched to any track that are considered originating from neutral particles. The resulting PFlow jets show a su- perior performance at low pT . Originally, the tracking resolution deteriorated at higher pT , 101 but more recent developments obtained a resolution compatible to EMTopo jets [140]. Track-CaloClusters The Track-CaloClusters (TCCs) [143] algorithm focuses on combining the spatial information of the tracker and the energy measurement of the calorimeter at high pT . This method also improves the identification of substructure in large-R jets, as it can resolve distinct particles associated to a single topocluster. However, TCC jets suffer from pileup instabilities and their performance is typically worse than the standard jets at low pT . Unified Flow Objects In 2021 a new input definition called Unified Flow Objects (UFOs) was developed [144], which combines the desirable aspects of PFlow and TCC reconstruction for an optimal overall performance across the full pT regime. The resulting jet collection is referred to as UFO jets, and has a superior performance to TCC jets at high pT , while retaining a similar performance to PFlow jets at low pT . Track jets Track jets are built from ID tracks. These jets are primarily used in the context of b- tagging of subjets contained in large-R jets. At the beginning of Run 2, the standard radius parameter for track jets was R = 0.2. This was later changed to a variable radius parameter R(pT ) = 30GeV , inversely proportional to the pT of the jet, which better describes the pT - pT dependence of the angular spread of a jet according to Eq. (5.5). The algorithm [145] has two additional parameters, Rmin and Rmax, to set the lower and upper limits on the jet size. The resulting jets are referred to as variable-radius (VR) track jets. Truth jets Truth jets take as input hadron level stable particles (see Sec. 5.1.5). Truth jets can only be reconstructed in simulation, but are essential for performance studies, such as algorithm development or calibration. In this context, it is often important to know the true generator- level parton from which a reconstructed jet originated. This is typically found via truth matching: the reconstructed jet is matched to the closest truth jet, and the truth jet is matched to the closest stable particle, where matching generally consists in a minimum ∆R requirement. The label of the reconstructed jet will be the type of the matched particle. 102 5.4 Boosted jet tagging A tagger attempts to identify the true particle from which a jet originated. Several BSM models predict new heavy resonances with masses around 1 TeV and with significant decay branching ratios into highly Lorentz boosted SM bosons (see Chap. 3). Since in more than 60% of the cases W , Z, and Higgs bosons decay hadronically into a pair of quarks, boosted jet tagging plays an essential role in these searches, including the one discussed in this thesis (see Chap. 7). Most forms of jet tagging are a form of supervised learning, so that a method needs to be established to provide true labels for the jets. For boosted heavy particles, such as top-quark and W , Z, and Higgs (H) bosons, the radiation pattern is generally isolated from the rest of the event, although some ambiguity remains related to whether the full radiation originating from the particle is contained in the jet. This is more complicated for jets originating from colored particles, for which a formal separation of the decay from the rest of the event is not possible [146]. The labeling of the training samples typically involves truth-matching together with some containment criteria based on the truth information from the parton-level of the MC simulation. Defining the true particle type as signal, and the rest as background, the performance of a tagging algorithm is quantified in terms of the signal efficiency ϵs — the probability of correctly tagging a signal jet — and of the background efficiency or mis-tag rate ϵb — the probability of incorrectly identifying a background jet as signal. One often quotes also the background rejection factor, defined as 1/ϵb 5. The reconstructed mass of a jet is one of the most important discriminants between jets of different origin. For a jet originating from a heavy particle, the jet mass has a scale associated to the mass of the particle, while for a q/g-induced jet, the mass scales as the product of the jet pT and radius. Important information about a large-R jet is contained also in its internal structure, as different particle origins will determine different multiplicities and kinematic distributions of the jet constituents. Jet substructure [146, 147] is a field that aims at exploiting the radiation pattern inside jets as a tool for boosted jet-tagging, as well as to perform precision tests of QCD. An important feature that is usually exploited by jet substructure techniques is the number of prongs in the jet. For instance, H/W/Z boson hadronic decays typically display a two-prong structure, with two subjets evenly sharing the momentum of the mother particle. Similarly, a large-R jet fully containing a hadronic top-quark decay will have a three-prong structure. On the other hand, a q/g-initiated jet is generally one-pronged and, in the case of a real emission, the second prong is usually In fact, several substructure observables rely on the identification of significantly softer. 5In other fields background rejection is more commonly defined as 1 ϵb. − 103 dominant directions of energy flow inside the jet. Some techniques look explicitly for hard subjets contained in the jet. These include N-subjettines observables, which rely on the identification of explicit axes associated to N-prong decays, and declustering techniques, such as kt splitting scales, which identify the subjets by walking in reverse the jet clustering history. Other jet-shapes methods, such as energy correlation functions and Fox-Wolfram moments [148], quantify the energy dispersion of the jet constituents in an axis-independent way. In the following, a subset of these substructure observables and boosted jet tagging methods relevant for this thesis are discussed. kt splitting scales The kt splitting scales [149] are obtained by reclustering the jet constituents using the kt algorithm, which clusters harder constituents last, and then look at the kt distance at a given step of the clustering history. The splitting scale variable dij is defined as, (cid:113) dij = min(pT,i, pT,j × ∆Rij). (5.6) In particular, the √d12 variable refers to the splitting scale at the last clustering step for the two hardest subjets. Similarly, √d23 is given by the second-to-last clustering step for the second and third hardest subjets. The variables √d12 and √d23 are helpful in identifying the two- and three-prong decays of heavy particles, which show a more symmetric energy sharing between the subjets than the splittings in q/g-jets. N -subjettiness The N -subjettiness [150] observables τN are also obtained by reclustering the jet constituents using the kt algorithm to identify the N hardest subjets. The variable τN is calculated as, τN = 1 d0 (cid:88) k ∆R1,k, ∆R2,k, . . . , ∆RN,k} pT,kmin { , (5.7) where d0 is the normalization factor d0 = (cid:80) k pT,kR0 and the sum runs over the k jet constituents. The result can be interpreted as a metric of how good is the hypothesis that the jet has N hard subjets. For a jet with N or fewer true subjets, τN ≈ 0, as all the jet constituents are aligned with one of the N directions. On the other hand, jets with more than N true subjets, will have τN ≫ 0, as a larger number of constituents will be at a larger distance from the identified axes. For instance, a jet originating from a W decay, with two subjets, will have τ1 ≫ 0. A QCD jet containing two hard quarks can in principle have τ2 ≈ 0. However, such a QCD jet is accompanied by significantly 0 and τ2 ≈ 104 more wide-angle radiation, determining a correlation between τ2 and τ1. For this reason, the N -subjettiness ratio τ21 = τ2/τ1 has a greater discrimination power to identify two-hard- prongs decays from a q/g-initiated jet. Similarly, the ratio τ32 = τ3/τ2 is used to identify three-pronged top-decays. Energy correlation functions Energy correlation functions (ECFs) are used to identify N -prong substructure in a similar manner to N -subjettiness ratios, with the main difference being that ECFs do not require finding subjets. For a hadron collider, the N-point ECF is defined as ECF(N, β) = (cid:88) J i1 0. Different ECFs are useful according to the application. In practice, if a jet J has N subjets, then ECF (N + 1) ECF (N ). It follows that the ratio rN = ECF (N + 1)/ECF (N ) behaves very similarly to the N -subjettiness observable behave like N -subjettiness ratios. Two τN , while the energy correlation double ratios important dimensionless ratios of ECFs (proposed in Refs. [151] and [152], respectively) are, rN rN ≪ − 1 Cβ 2 = Dβ 2 = ECF (3, β)ECF (1, β) ECF (2, β)2 ECF (3, β)ECF (1, β)3 ECF (2, β)3 , . (5.12) (5.13) These are useful for the identification of 2-pronged substructure and are used for boosted W/Z/H vs. q/g jet discrimination, with the former signatures having predominantly lower values of C2 and D2. 105 Grooming algorithms Grooming techniques aim at cleaning the jet of soft and wide-angle radiation in order to enhance the hard radiation pattern inside the jet, with the overall effect of also reducing the sensitivity to radiation that does not originate from the final state, such as pileup and the UE. In the context of jet tagging, grooming has proven a useful tool in identifying jet substructure, and it is often used in combination, or as input, to jet tagging algorithms. The main difference between a groomer and a tagger is that a tagger provides a classification of the true jet origin and is optimized to increase the signal-to-background ratio, while a groomer returns the cleaned (groomed) jet and is optimized in order to improve the resolution of the jet kinematics and properties [74]. Several grooming algorithms are used in ATLAS. All share the common idea of reclustering the jet constituents using the kt or C/A algorithms and then use the output clustering history to remove soft components. Here, the soft drop algorithm [153] is described, as it is the one relevant for this work. In the first step, the anti-kt R = 1.0 jets are reclustered with the C/A algorithm. The angular-ordered clustering sequence history is then reversed. The last stage of C/A clustering pi + pj is undone by breaking the jet pi+j into two subjets pi and pj. The soft drop pi+j → condition is then evaluated: min(pT,i, pT,j) pT,i + pT,j > zcut (cid:18)∆Rij R0 (cid:19)β , (5.14) where R0 is the jet radius and β and zcut are parameters to be optimized for the algorithm. If the condition is satisfied, the declustering is stopped and the jet i + j is taken as the final jet, otherwise only the subjet with larger pT is kept and the procedure is repeated. The parameter zcut determines the choice of what emissions should be deemed soft and excluded, while the angular exponent β weights the soft threshold according to the angular separation between the two subjets. In ATLAS the current recommendation is β = 1.0 and zcut = 0.1. 5.5 Pileup suppression Pileup6 refers to the simultaneous pp collisions that occur per bunch-crossing (see Sec. 4.1.3). The average pileup multiplicity was already < N >= 20 in Run 1, < N >= 50 at the end of Run 2, and is expected to go up to < N >= 200 at the HL-LHC. As every pileup collision adds tens of soft hadrons to the final state, the net effect is that of adding hundreds to thousands of soft particles on top of the decay products of a hard collision of interest [74]. 6The material in this section is based primarily on Ref. [74] 106 Mitigating the effect of this extra radiation is one of the main challenges for trigger and data analysis at the LHC. In the context of jet reconstruction, pileup contamination has two main consequences: a bias and a smearing of measured kinematic quantities. Consider the pileup contribution at any given (η, ϕ) location as sampled from a Gaussian of mean ρ and standard deviation σ. The mean represents the average positive bias induced by the increased hadronic activity on the quantities measured. For example, the transverse momentum of a jet increases with increasing pileup proportionally to the jet area. The variation σ parametrizes the fluctuations in the pileup-induced bias ρ per event and across the detector volume. The fluctuations are a form of noise that blurs the reconstructed quantities reducing their resolution. One third effect is the impact of the particles originating from pileup interactions on the jet clustering procedure itself, as jets built with and without pileup will look slightly different due to different clustering histories. However, this effect is generally negligible. All pileup mitigation techniques aim at reducing these effects, but the approaches differ according to which object is “corrected”. Historically, the standard methods included event- by-event and jet-by-jet algorithms. However, to address the new challenges posed by the increasing levels of pileup, new approaches have been developed based on the correction of the jet algorithm inputs. In this section, some of the most common techniques of pileup suppression are discussed, with a focus on those that are most relevant for this thesis. 5.5.1 Area-median subtraction The most widely used event-level scheme is the area-median subtraction approach. This was the standard in ATLAS during Run 1, and it was still extensively used during Run 2. The algorithm is based on the fact that, if one draws a grid on the y ϕ plane for a given event, most patches will not contain any particle from the hard scatter, so that their momentum flow pT /Apatch is a good estimate of the pileup transverse momentum density in the event ρ. The algorithm is therefore split in two steps. In the first step, one finds an estimate of ρ by breaking the event into patches of similar areas and taking the median pT,i/Ai of all patches. The use of the median instead of the average makes ρ less sensitive to outliers, such as very hard jets. The second step is to subtract from the kinematic distribution of each jet the correction ρAjet, where Ajet is the catchment area of the jet7. Computing ρ event- − 7The catchment area of a jet is defined as the area in y ϕ space where the jet would contain infinitely soft particles. For pileup subtraction, the active area is generally used, obtained by running the jet clustering algorithm on all the particles in the event plus a dense coverage of ghost particles (particles with infinitely small momentum) distributed evenly in y ϕ space. Assuming an IRC-safe algorithm, the addition of these soft particles does not affect the momentum of the output jets. Moreover, for the anti-kt algorithm, the boundary of the jets will always be circular and approximately independent of the initial set of ghosts. If − − 107 by-event and A jet-by-jet results in jets with better resolution compared to other methods that subtract the average pileup contamination per-vertex or per-event, as averaging usually introduces extra resolution degradation. The area-median subtraction approach has proven to be a robust method, that leaves on average an unbiased transverse momentum of the jet. However, it also leaves a residual pT resolution degradation from pileup fluctuations (σ) across the detector for a given event. The smearing was sufficiently small during Run 1 and 2 not to be an issue. However, as the levels of pileup keep increasing, these effects will become non-negligible, particularly on low pT jets essential for certain measurements, such as di-Higgs production. 5.5.2 Grooming Pileup mitigation techniques at the jet level usually focus on large-R jets, as the larger area makes them more sensitive to pileup or the UE. In this context, grooming techniques (discussed in the previous section) can be a useful tool. A fundamental difference exists between groomers and an approach like the area-median subtraction method. The latter aims at reducing the positive bias due to the pileup contribution independently of the hard In the case of the measurement of the mass of a boosted top large-R jet, this process. approach will apply the same correction to a top jet and a QCD jet, reproducing on average the correct top mass, but including a smearing effect coming from pileup fluctuations. A groomer, on the other hand, aims at reducing the smearing as much as possible to improve the jet kinematics resolution. This is at the expense of always introducing a negative bias, as the output jet is always pruned of some of its constituents even in the absence of pileup. In the case of a top-quark decay, a groomer would therefore retain the three hard prongs of the decay, while cleaning the jet of the extra radiation, resulting in a sharply peaked mass distribution, with little bias from pileup. For a QCD jet, on the other hand, a groomer would remove a significant portion of the soft radiation in the jet, hence strongly reducing the jet mass. While this represents a large negative bias, it is desirable in this case, as it allows to identify the QCD jet as background. The study of the interplay between grooming, pileup removal, and jet tagging algorithms is an active area of study. 5.5.3 Constituent-level More recent approaches attempt to explicitly remove pileup contributions in a noise suppres- sion fashion: the inputs to the jet algorithm themselves are pileup suppressed, by being re- the number of ghosts per unit area is νg and g(J) is the number of ghosts contained in jet, then the scalar active area of the jet is given by A(J) = N N g(J) νg [74]. 108 moved or by having their energy adjusted, thereby automatically improving jet observables, independently of the jet clustering algorithm. Different algorithms have been developed, including Soft-Killer (SK) [154] used by ATLAS and PUPPI [155] used by CMS. Other al- gorithms, such as Voronoi Subtraction [156] and Constituent Subtraction (CS) [157], extend the area-based subtraction method to particle-level pileup mitigation and are often used as a pre-processing step to adjust the constituents four-vectors before these are input to the former algorithms. In the following, the algorithms relevant for this work are discussed. Soft-Killer The SK algorithm relies on the idea that the most important discriminant between a particle originating from a pileup interaction and a particle coming from the hard scatter is its trans- verse momentum. The algorithm consists in calculating an event-dependent pcut threshold quantifying the hadronic activity and removing particles that have a transverse momentum below this cutoff. This is similar to the pileup suppression strategy implicit in the ATLAS topoclustering algorithm 4.4.4, where the energy cut-off on the input cells is determined by the event-dependent pileup noise, so that as pileup increases, the noise threshold increases as well. T In practice, the value pcut is found as the pT threshold that gives ρ = 0, where ρ is the transverse-momentum-flow density used in the area-median approach. In practice, the event is divided into patches of area Ai, and ρ is set to the median transverse-momentum-flow density of all the patches: T pT,i Ai ρ = median patches i ∈ (cid:26) pT,i Ai (cid:27) . (5.15) T The value pcut is found by increasing the pT threshold until exactly half of the patches contain no particles. In practice, this is fast to compute, as it is equivalent to taking the median of the pT ’s of the leading particles in each patch: pcut T = median patches i ∈ (cid:110) pmax T,i (cid:111) . (5.16) The value of pcut 2 GeV at the HL-LHC T = 200 conditions [154]. µ ⟨ ⟩ computed as a function of pileup vertices was shown be slightly above Two types of biases can arise with this method: a positive bias caused by energetic pileup particles that are above threshold and do not get removed, and a negative bias from soft true signal particles that get suppressed. The jet energy scale will not be affected only if the two biases cancel each other out. Similarly, the energy resolution will not suffer only if the 109 fluctuations in the biases are not large. When the particles in question are at the detector-level (towers or topoclusters), the issue arises that a single particle may contribute in energy to different signals, or a given signal may receive contributions from different particles. In particular, in the case of a hard particle sharing a topocluster/tower with pileup particles, the pileup contribution will never get removed. In this case, the SK algorithm can be adapted: for a tower of area A, the pT is adjusted as psub T = max(0, ptower ρA). The standard SK algorithm in Eq. (5.15) is then applied on the subtracted towers. − T Voronoi and Constituent Subtraction Voronoi (Vor) [156] and Constituent Subtraction (CS) [157] are both extensions of the area- based subtraction method to particle-level pileup mitigation. Consider the case of the particle type being topoclusters. In Voronoi subtraction each individual topocluster is assigned a Voronoi cell, defined as all the points in space that are closer to the topocluster than to any other particle. The area of each cell is called the Voronoi area AVor. Each topocluster receives a correction to its transverse momentum as pcorr AVor, where ρ is the per-event pileup density as in the jet-area correction method. T = pT − ρ · The CS subtraction method uses ghost particles with pg (η, ϕ) plane. Every particle-ghost pair i and the following correction to each particle and ghost pT is applied: − ρ uniformly covering the × k is then considered in ascending order of ∆Ri,k, T = Ag pg T,k, If pT,i ≥ pg T,k: otherwise: pT,i → pg T,k → pg T,k → pT,i → pT,i − 0 GeV pg T,k, − 0 GeV. pT,i, (5.17) Fixing the maximum ∆R values to be considered allows to tune the maximum jet area. The original method similarly provides also a mass correction, but this is not applicable when using topoclusters, as they are massless. After the energy has been corrected, different techniques can be used to remove pileup- T < 0 GeV to fed the like topoclusters, going from simply removing any topocluster with pcorr correcte topoclusters to a more sophisticated algorithm, such as SK. 110 Chapter 6 Concepts of statistics and machine learning 6.1 Statistical inference Consider1 a set of independent and identically distributed (i.i.d.) data X = (x1, ..., xn) that is assumed to be sampled from a probability density function (PDF) p(x θ), dependent on | some parameters θ. In a standard inference problem, one wants to find the estimate of θ. Frequentist vs. Bayesian Statisticians use probability to quantify uncertainties, but they do not all agree on the be an element of the sample space. The frequentist interpretation interpretation. Let views probability as a limiting relative frequency. From a frequentist point of view, A represents a possible outcome of a measurement assumed to be repeatable and, given N measurements, the probability of is given by A A P ( ) = lim n →∞ A nnumber of occurrences of outcome N A . ) represents the degree of belief that hypothesis represents a statement that can be either true or false, and From a Bayesian perspective, p( is true. Note that since the statement that “an experiment yields a given outcome a certain fraction of the time” can be regarded as a hypothesis, the framework of Bayesian probability includes the frequentist interpretation. A A A Frequentist inference The most common method of frequentist inference is based on Maximum Likelihood Esti- 1This section draws on notes taken throughout the years, particularly from Refs. [158–160]. 111 mation (MLE). Given the observed data X, one first builds the likelihood function, L(θ) = p(X θ) = | N (cid:89) i=1 p(xi; θ), (6.1) where the second equality holds because the measurements are assumed to be independent. The likelihood attains higher values for the choices of θ that are closer to the true distri- bution p(xi; θtrue). The best estimate of θ is then found by maximizing the likelihood or, equivalently, by minimizing the negative log-likelihood (NLL): ˆθM LE = arg max θ n (cid:89) i=1 θ) = arg max p(xi| n (cid:88) i=1 log p(xi| θ) = arg min n (cid:88) i=1 − log p(xi| θ). (6.2) In the frequentist framework, the true parameter θ is assumed to be fixed, but unknown. The parameter estimate ˆθM LE, on the other hand, is a function of the data and therefore is a random variable. In other words, one can define a bias and a variance for the estimator, which describe how the estimator is distributed if one repeats the experiment several times. The variance of the estimator quantifies the irreducible aleatoric uncertainty due to the inherent variability of a random variable. Note that, contrary to Bayesian inference, MLE does not offer a way to quantify possible sources of epistemic uncertainty. This has the consequence of making the MLE prone to overfitting and to be overconfident in its predictions when limited data is available. Bayesian inference When performing Bayesian inference one encodes previous knowledge (or guess) about θ in a prior distribution p(θ) and applies Bayes theorem to obtain the posterior distribution over θ, p(θ X) = | Πn i=1p(xi| (cid:82) Πn i=1p(xi| θ)p(θ) θ)p(θ)dθ , (6.3) where the numerator is the product of the likelihood and the prior. The denominator can be regarded, in most cases, as a normalization factor. From a Bayesian perspective, θ is not simply unknown, but it is itself a random variable, and the posterior distribution p(θ X) | naturally expresses both the aleatoric and epistemic uncertainty over θ. One can still obtain a point estimate by taking the maximum of the posterior (MAP), ˆθM AP = arg max θ log p(θ X) = arg max | θ logp(X θ) + logp(θ). | (6.4) 112 The objective function in Eq. 6.4 retains the log-likelihood term from MLE as in Eq. 6.2, plus what looks like a regularization term coming from the prior. As shown later, this is often related to the choice of loss function and regularization method when training a neural network. Note that in the case of unlimited training data X, the second term becomes negligible and ˆθM AP → ˆθM LE. 6.2 Neural networks In a supervised learning problem one has a training dataset D composed of input features X and input targets Y . Given x Y , the goal is to find a mapping f such X and y that y = f (x). A machine learning algorithm , which is a function of some parameters, provides an approximation ˆf = (D) of this mapping. Given a data point x, the quality of the prediction ˆy = ˆf (x) is measured by a loss function J = J(y, ˆy(x)), a metric of how close the predicted and expected target values are. The learning – or training – is then formulated as an optimization problem over the model parameters to minimize the loss function. ∈ A A ∈ Figure 6.1: Architecture of a deep neural network with N input features, 3 hidden layers of 100 neurons each, and 5 output nodes. A simple feed forward neural network architecture is defined by the number of hidden layers, the number of input, output, and hidden neurons, and the activation functions, as shown in Fig. 6.1. The output of the first hidden layer with n neurons is given by the affine transformation A(x) = W T x + b, followed by a nonlinear transformation by a monotonic activation function h(x) = s(A(x)). This operation is then cascaded over all the L hidden layers ˆf (x) = hL(...(h1(x))). The architecture is set by the choice of several hyperparameters, which are fixed before training. Thus, at the moment of training, the neural network output ˆf = N Nw depends only on the weights w2. The training then consists in finding the optimal 2From now on, the term weights will refer to both weights and biases, as one can always redefine the weight matrix to include the bias terms in the first row and append a 1 at the top of the input vector x. 113 DNNxNxN1...x2x1...n100n99n98...n3n2n1n100n99n98...n3n2n1n100n99n98...n3n2n1y5y4y3y2y1 weights. Most neural networks are trained using MLE. In order to do this, one typically specifies x, w). The cost function is taken to be the NLL of the conditional | x, w), and the optimization procedure consists in finding the parameters w | a probabilistic model p(y distribution p(y that minimize this objective function, also called the loss function, wM LE = arg min w logp(Y X, w). | − (6.5) To prevent the model from overfitting to the training data, regularization can be imple- mented. This is often achieved by introducing a prior over the weights and finding the maximum posterior probability, wM AP = arg max w logp(w D) | = arg max w logp(D w) + logp(w). | (6.6) (6.7) As mentioned before, the cost function penalizes deviations from the prior predictions. Consider the case of a regression task, where y R. To express the aleatoric uncertainty associated to a random variable, one could assume the target variable y to be given by a deterministic function f (x, w) with additive Gaussian noise, ∈ y = f (x, w) + ϵ, ϵ (0, β− 1). ∈ N (6.8) The objective of the training of a neural network would then correspond to find the mean ˆy = N Nw(x) or, equivalently, to find the Gaussian conditional probability distribution p(Y X, w, β) = | N (cid:89) n=1 (yn N N Nw(x), β− | 1). (6.9) Defining the cost function as the NLL of Eq. 6.9 and removing the terms not dependent on w, the optimal parameters are found by minimizing the following objective function: ˆw = arg min w − logp(Y X, w, β) = arg min | w β 2 N (cid:88) n=1 yn || − ˆyn(x, w) 2 || (6.10) Hence, minimizing the NLL is equivalent to minimizing the Mean Squared Error (MSE). If λ I2), it can be shown one now assumes a Gaussian prior on the weights of the form that the log-prior term in the cost function corresponds to the weight decay penalty λwT w. (w; 0, 1 N 114 In practice, the training is divided into two steps. During the forward pass, the network reads a set of inputs x, produces the outputs ˆy(x), and evaluates the cost function J(y, ˆy). In this step information flows forward through the network. During the backward pass, information from the cost function flows backward through the network to calculate the gradient. The back propagation algorithm is used to compute the gradient of the cost function with respect to the model weights. The gradient is typically estimated on a mini-batch of m examples as g = ∇ wJ(w) = 1 m∇ w m (cid:88) i=1 L(x(i), y(i), w). (6.11) Here L is the per-example loss. Stochastic gradient descent is then implemented to update the model parameters in the direction of decreasing loss as, wnew = w αg, − (6.12) where α is the learning rate, a hyperparameter fixed before training. 6.3 Hypothesis testing with profile likelihood ratio In particle physics experiments one often looks for new signal processes that have not been observed before3. In order to make conclusions regarding an excess over the background prediction, or lack thereof, a frequentist statistical test is performed, where one quantifies the level of agreement of the data with a given predicted hypothesis H. The hypothesis to be tested is generally referred to as null hypothesis H0. In order to make a statement about the viability of the null hypothesis, this is compared to an alternative hypothesis H1. In general, the null-hypothesis is the hypothesis one wants to exclude. For the purpose of claiming discovery of a new signal when a data excess is observed, the null hypothesis H0 is the background-only hypothesis. If no excess is observed, exclusion limits are set where the null-hypothesis is the signal-plus-background hypothesis to be excluded with a given confidence level. P-value and significance The concepts of significance and p-value are related and are often used in evaluating how well a given hypothesis describes the data. Suppose the background-only null-hypothesis H1), H0 and the new-physics-hypothesis H1 predict two different PDFs, f (x | H0) and f (x | 3This section is based on Ref. [161] 115 for a set of observations x = (x1, . . . , xN ). Consider the observation of n events in data, which can consist of nb events from known processes (background) and ns events from a new process (signal). The background-only hypothesis predicts n = nb, while the signal hypothesis predicts n = ns + nb. The p-value of hypothesis H0 is given by the probability, under the assumption of the hypothesis H0, to observe data with equal or of lesser compatibility with H0 than the one actually observed (note that this is not the probability that H0 is true). In their words, the p-value expresses the level of compatibility of the hypothesis H0 with the observed data, and the weaker the compatibility, the more likely it is that H0 can be rejected. The significance S of a given p-value is often defined as the number of standard deviations that a Gaussian variable would fluctuate in one direction to give the same p-value: (cid:90) p = S S = Φ− ∞ 1 √2π 1(1 − x2/2dx = 1 e− Φ(S), − p) (6.13) where Φ(S) is the inverse of the cumulative distribution of the standard Gaussian. Note that the p value is defined for a standardized Gaussian centered at 0 and with σ = 1. The tradition in particle physics is that the threshold to report evidence of a new signal is p < 0.003, or 7, or a significance of S = 5, to report a a significance of S = 3, while it is p < 2.87 × discovery. To exclude a signal hypothesis one requires a p-value of 0.05, corresponding to a 95% confidence level and a significance of S = 1.64. 10− Likelihood parameters The data is usually assumed to be a set of i.i.d. measurements x and the hypothesis is ex- pressed as a PDF, with each hypothesis predicting a different PDF f (x). Often a continuous set of hypotheses is considered f (x; µ), where each hypothesis is determined by the param- eter µ, called the parameter of interest. For instance, µ could be the signal strength that relates the true to the simulated signal cross section σs = µσMC . In particular, µ = 0 corre- sponds to the background-only hypothesis and µ = 1 to the background-plus-nominal-signal hypothesis. s Once the model is fixed, a likelihood function can be constructed L(f (x; µ)), giving 116 the probability of the data given the hypothesis f (x; µ). The value ˆµ that maximizes the likelihood is the best fit estimator of µ. Experimental and theory systematic uncertainties can affect the PDF of x, both in terms of shape and normalization. Their effect is encoded in the model via a set of nuisance parameters θ. Their values are unknown and must be estimated in the fit together with the parameter of interest µ. Binned likelihood Consider the case of one signal and one background simulated samples and a variable of interest x, e.g. the invariant mass distribution of the reconstructed signal resonance. Signal and background will have different PDFs of the variable x, fs(x; θ) and fb(x; θ). If one constructs a histogram n = (n1, n2, , nN ) with N bins of the variable x, the expectation value of the number of events in a given bin i is given by E[ni] = µsi(θ) + bi(θ), (cid:82) bin i fb(x; θb), and similarly for si. The number of entries ni in each bin where bi = btot is generally assumed to be Poisson distributed with mean νi, so that the joint likelihood function for all bins is given by the product of the Poisson probabilities in each bin. The likelihood L(µ, θ) can then be expressed as, · · · L(µ, θ) = N (cid:89) i=1 Pois (ni| µsi (θ) + bi(θ)) θ (cid:89) θk θ0 k, σk), (θk| N (6.14) where Gaussian priors are included to constraint the k nuisance parameters θ. The priors act as a penalty term in the maximum likelihood fit, as a postfit value ˆθk ̸ k decreases the likelihood. = θ0 Profile likelihood ratio test In order to test a hypothesized value of µ one needs a test statistics qµ [161]. This is often obtained from the profile likelihood ratio λ(µ), given by λ(µ) = ˆˆθ) L(µ, L(ˆµ, ˆθ) (6.15) ˆˆθ represents the ML estimate The numerator is the profile likelihood function. The quantity of θ conditional on the specified value of µ, and thus depends on µ. The denominator is the maximized unconditional likelihood function, where ˆµ and ˆθ are set to their MLE estimators. 1, with λ The denominator represents the global maximum, so that the ratio is always closer to 1 implying a better agreement between the data and the given hypothesis f (x; µ). ≤ 117 Generally one assumes that the presence of a signal could only increase the observed number of events, so one defines ˜λ(µ) =    ˆˆθ) L(µ, , L(ˆµ, ˆθ) ˆˆθ) L(µ, L(0, ˆθ(0)) 0, ˆµ ≥ , ˆµ < 0, (6.16) where it is assumed that the best level of agreement for an observed value of ˆµ < 0 occurs for µ = 0. The test statistic qµ is given by qµ = 2 ln ˜λ(µ). − The test statistic qµ depends on the data, so it is itself a random variable described by a PDF f (qµ µ) under the assumption of µ. To quantify the level of disagreement with the | data one would like to calculate the p-value of a given observed value qµ,obs, but in order to evaluate this one needs to know the PDF f (qµ µ). This can be approximated via Monte | Carlo methods, where pseudo-experiments are performed by sampling the likelihood and generating toy datasets. However, it can be shown that, under the Wald’s approximation, the PDFs assume the shape of χ2 1 functions, such that the p-value can be expressed in terms of the cumulative distribution of a standard Gaussian as pµ = (cid:90) ∞ qµ,obs f (qµ µ)dqµ = 1 | − F (qµ µ) = 1 | − Φ(√qµ). (6.17) A predefined critical threshold α = 0.05 is often chosen, so that if the p-value is found to be pµ < α, then the value of µ is excluded at a confidence level (CL) of 1 α = 95% . The upper limit on the signal strength can be found by solving for the value of µ at pµ = 0.05. For the discovery of a signal, one tests the background-only hypothesis µ = 0. In this − case, qµ=0 =    − 0, 2 ln λ(0), µ, ˆµ ≥ ˆµ < µ (6.18) where qµ is 0 if the data fluctuates downward, as an observed value ˆµ < µ is not regarded as less compatible with the background-only hypothesis. The p-value can be calculated as p0 = (cid:90) ∞ q0,obs f (q0| 0)dq0. (6.19) If no excess is observed, exclusion limits are set on the signal strength µ by excluding the 118 signal-plus-background hypothesis at a given confidence level. The test statistic is given by qµ=0 =    − 0, 2 ln λ(µ), ˆµ µ, ≤ ˆµ > µ, (6.20) where qµ is zero if the data fluctuates upward, as an observed value ˆµ > µ would not be considered less compatible with the signal-plus-background hypothesis. The corresponding p-value is pµ = (cid:90) ∞ qµ,obs f (qµ µ)dqµ. | (6.21) The upper limit on µ is given by the largest µ such that pµ for µ, one obtains ≤ α. Setting pµ = α and solving µup = ˆµ + σΦ− 1(1 α), − (6.22) where σ is the standard deviation of ˆµ and can be obtained via Monte Carlo methods or from Asimov data. 119 Chapter 7 Search for new heavy resonances decaying to two SM bosons in semi-leptonic final states The search for new heavy resonances has been the focus of intense efforts at the LHC since it began operations. If these particles are produced in an LHC collision, it should be possible to reconstruct the four-vectors of their decay products and they should appear as a narrow resonance on the invariant mass distribution of the final state particles over a smoothly falling background. However, if such collision events exist, they are very rare, making designing this type of searches a non-trivial task. In this chapter the search for new heavy resonances decaying to a pair of Standard Model bosons in semi-leptonic final states is presented, including the new deep learning techniques developed to enhance the sensitivity of this type of searches1. 7.1 The search for new heavy resonances Several well motivated extensions of the Standard Model predict the existence of new heavy resonances appearing at the TeV scale that can couple to the Higgs, W, and Z bosons and could be produced in pp collisions at the LHC. A class of these models, motivated by naturalness arguments, predicts additional vector gauge bosons and include composite Higgs [45, 46] and little Higgs [44] models. As experi- mental searches are not sensitive to all the parameters of a theory, these models are studied experimentally in the context of a general Heavy Vector Triplet (HVT) model [3], which is parametrized by a simplified Lagrangian with an additional SU (2) triplet (see Sec. 3.3). A second class of models, the two-Higgs-doublet models (2HDMs) [4], predicts the simplest ex- tension of the SM scalar sector, by including an additional scalar SU(2) doublet, resulting in 1The analysis discussed in this chapter was still ongoing at the time of this writing. Certain details might therefore evolve before the analysis is published. 120 five physical scalars (see Sec. 3.4). In addition, Randall-Sundrum (RS) models with warped extra dimensions [162] or the bulk RS model, predict new particles, including a spin-0 ra- dion and the spin-2 Kaluza-Klein excitation of the graviton, which are used as additional benchmark signatures in this type of searches. Several of these new heavy resonances are predicted to decay with significant branching ratios (BRs) to a vector boson and a Higgs boson (W H, ZH) or to pairs of vector bosons (W Z, W W , ZZ). In the following, these will be referred to as V H and V V processes, respectively. According to the decay mode of the SM bosons, the final state of these processes is referred to as fully leptonic if both bosons decay to a pair of leptons, fully hadronic if both bosons decay to two quarks, or semi-leptonic when one boson decays leptonically and one hadronically. The semi-leptonic final state is particularly advantageous, as one can benefit from the higher decay BR of the hadronic decay, while keeping a high trigger and selection efficiency thanks to the cleaner leptonic signature. 1 [164], and 139 fb− 1 [166, 167] and the 139 fb− Previous searches have been performed in ATLAS in semi-leptonic final states for VH 1 [163], and VV processes separately. The VH analyses were performed using the 3.2 fb− 1 [165] datasets. The VV searches were performed using the 36.1 fb− 1 [168] datasets. Similar searches in semi-leptonic final 36.1 fb− 1 states have been performed in CMS as well, with the latest analyses using the 137 fb− dataset being a search for a new resonance decaying to W Z/W W/W H [169] and to ZH final state [170]. ATLAS has also performed searches for the same process in other final 1 states, including two fully hadronic searches based on an integrated luminosity of 139 fb− for VH [171] and VV [172]. CMS has performed a fully-hadronic VH search [173] and a ZH search in final states with two taus and two light leptons [174] with the 35 fb− 1 dataset. Statistical combinations of the available searches for different processes and in the differ- 1 analyses [175] and the ongoing ent final states have also been performed with the 36.1 fb− 1 searches [176], which includes also decays of heavy resonances di- effort with the 136 fb− rectly into a pair of leptons. CMS has performed similar combination efforts at the beginning of Run 2 [177] and with the 35.9 fb− 1 dataset [178]. Several small excesses have been observed in the latest publications, all below a local significance of three standard deviations (σ). In the VH analysis, the largest deviations from the SM expectations in the latest publications have been observed in the search for a pseudoscalar A, where an excess was observed around a mass of 500 GeV of 2.1 (1.9) σ in the ggA (bbA) channel, primarily originating from the 2 b-tag category in the 2-lepton channel. A similar excess was observed in the Z′ search at the same 500 GeV mass. Other smaller excesses of 2 standard deviations were observed at a resonance mass of 2.2 TeV for the Z′ search and 400 GeV for the W ′ search. In the VV analysis, an excess around an RS 121 radion mass of 1.5 TeV with a local significance of 2.8 standard deviations was observed, induced by the merged HP region in the 0-lepton channel. The pseudoscalar excess is of 1 publication with a local (global) particular interest, as it was already present in the 36.1 fb− significance of 3.6 (2.4) standard deviations and a disagreement around a similar mass was 1 [179] with a local (global) also observed both in the A τ τ ATLAS significance of 3.5 (1.9), and a local excess above 2σ is observed in the A 1 [180]. It should be noted that the excess is around the threshold for search with 139 fb− top-pair production, where higher-order electroweak corrections to the SM t¯t production can become important and could induce misinterpreted distortions [? ]. Nonetheless, it is worth investigating further. t¯t CMS search with 35.9 fb− → → Fig. 7.1 shows a summary of all ATLAS searches interpreted in a benchmark scenario for the MSSM Higgs sector 7.1a and for a Type I 2HDM 7.1b, while Fig. 7.2 shows the latest ATLAS summary of the mass exclusion limits from diboson searches for new HVT and RS bosons with the full Run 2 dataset. These figures are representative of the effort that ATLAS has devoted to looking for these new particles. 7.2 Analysis overview ) → → → l± ν ¯ν, W This section presents the ongoing search for new heavy resonances decaying through VV and VH processes in the semi-leptonic final state. The leptonic decay of one vector boson ( l+l−, where l refers to a light charged lepton − proceeds as Z ν , or Z (electron or muon). The hadronic decay of vector bosons proceeds as W q ¯q, while the analysis targets only Higgs boson decays to a pair of b-quarks in order to capitalize on the large BR of the H ∼ Different signal interpretations are considered. A search for new HVT bosons W ′ and Z′ is performed in both the VV and VH final states, which motivated in part the combination of the VV and VH analyses into a single search. Specific to the VH analysis is also the search ZH. Lastly, for a new pseudoscalar A predicted by the 2HDM model in the process A specific to the VV analysis are the signal interpretations as a Kaluza-Klein Graviton and a RS radion, both of which can decay to W W and ZZ final states. b¯b decay channel ( 57% )2. qq and Z → → → → The search re-analyzes the 139 fb− 1 dataset collected up until the end of Run 2. A new analysis of this dataset was motivated by several developments, including improved b- tagging algorithm, improved jet collections, and a new optimized event selection, including 2From now on, the references to particle/anti-particle state will be omitted, e.g. the W leptonic decay will be referred to as W lν. → 122 (a) (b) Figure 7.1: Left: Regions of the [mA, tan β] phase space excluded for a type of MSSM model by direct searches for new heavy Higgs bosons and by constraints from fits of the measured production and decay rates of the observed Higgs boson. Both the data (solid lines) and the expectation for the SM Higgs sector (dashed lines) are shown. Right: Regions of the [mH , tanβ] phase space excluded for a benchmark scenario of the Type I 2HDM by direct searches, comparing observed (filled) and expected (lines) limits. [181]. 123 [GeV]Ambtan tt figg/bb H/A, H/A -1139 fbPhys. Rev. Lett. 125 (2020) 051801-1, 36.1 fbnt fi +, H+t(b) HJHEP 09 (2018) 139 bbfib(b) H/A, H/A -127.8 fbPhys. Rev. D 102 (2020) 032004-1, 139 fbnn 4l/llfi ZZ fiH Eur. Phys. J. C 81 (2021) 332-1 bb, 139 fbfi Zh, h fiA arXiv:2207.00230-1 tb, 139 fbfi +, H+t(b) HJHEP 06 (2021) 145-1, 36.1 fbnln lfi WW fiH Eur. Phys. J. C 78 (2018) 24tt/bbgg 4b/bbfi hh fiH -1126 - 139 fbATLAS-CONF-2021-052]dk, uk, Vkh couplings [-136.1 - 79.8 fbPhys. Rev. D 101 (2020) 012002-1 tt, 139 fbfittH/A, H/A ATLAS-CONF-2022-008PreliminaryATLAS hMSSM, 95% CL limits = 13 TeVsRun 2, September 202220030040010002000123451020304060ObservedExpected25140060080010001200mH[GeV]0.52.55.07.510.012.515.017.520.0tanβSeptember2022ATLASPreliminary√s=13TeV,126–139fb−195%CLlimits,cos(β−α)=+0.1,type-I2HDMObs.Exp.Obs.Exp.Obs.Exp.Hwidth>5%H→hhATLAS-CONF-2021-052A/H→ττPRL125(2020)051801A→ZharXiv:2207.00230 Figure 7.2: Summary of mass exclusion limits at 95% confidence level from ATLAS diboson searches with the full Run dataset [182]. the development of new machine learning techniques. In particular, the power of a search can be gauged by the expected significance, which can be approximated as, = S Ns (cid:112)Nb = σsϵs √σbϵb , √ L (7.1) L is the total integrated luminosity, ϵs and ϵb are the signal and background efficiencies, where and σs and σb are the predicted cross sections. By the end of Run 3, will have increased by a factor of 2. Assuming everything else constant, which means assuming that the hypothetical signal will be produced at the same rate as in Run 2, the observed Run 2 significances of √2 = 2.8, a very small increase that would still not ∼ qualify as evidence of new physics3. This value would be even lower if what was observed in Run 2 was just an upward fluctuation of the signal. It follows that in order to increase the physics reach of the search one cannot only rely on a larger dataset and methods to increase the analysis’ signal efficiency are necessary. In practice, this means developing more 2 will result in a significance of 2 × L 3The tradition in particle physics is that the threshold to report “evidence of a particle” is 3σ, and the standard to report a “discovery” is 5σ. 124 ModelChannel†Strategy*LimitReferenceExtradimensionsGaugebosonsBulkRS(kπrc=35,ΛR=3TeV)R→WW,ZZ→ννqq,ℓνqq,ℓℓqqresolved,boostedEur.Phys.J.C80(2020)11650.3-3.2TeVBulkRS(kπrc=35,ΛR=3TeV)R→WW→eνµνresolvedATLAS-CONF-2022-0660.2-1.0TeVBulkRS(kπrc=35,ΛR=3TeV)R→WW,ZZ→qqqqboostedJHEP06(2020)0421.3-3.0TeVRS1(k/MPl=0.01)GKK→γγresolvedPhys.Lett.B822(2021)1366510.5-2.2TeVU2.4-2.6TeVRS1(k/MPl=0.05)GKK→γγresolvedPhys.Lett.B822(2021)1366510.5-3.9TeVRS1(k/MPl=0.1)GKK→γγresolvedPhys.Lett.B822(2021)1366510.5-4.5TeVBulkRS(k/MPl=1.0)GKK→ZZ→ℓℓℓ′ℓ′,ννℓℓresolvedEur.Phys.J.C81(2021)3320.6-1.8TeVBulkRS(k/MPl=1.0)GKK→WW→eνµνresolvedATLAS-CONF-2022-0660.3-1.3TeVBulkRS(k/MPl=1.0)GKK→WW,ZZ→ννqq,ℓνqq,ℓℓqqresolved,boostedEur.Phys.J.C80(2020)11650.3-2.0TeVBulkRS(k/MPl=1.0)GKK→WW,ZZ→qqqqboostedJHEP06(2020)0421.3-1.8TeVHVTmodelAW′→WZ→ℓνℓ′ℓ′resolvedarXiv:2207.039250.3-2.4TeVHVTmodelAW′→WZ→ννqq,ℓνqq,ℓℓqqresolved,boostedEur.Phys.J.C80(2020)11650.3-3.9TeVHVTmodelAW′→WH→ℓνbbresolved,boostedarXiv:2207.002300.4-3.0TeVHVTmodelAW′→WZ→qqqqboostedJHEP06(2020)0421.3-3.4TeVHVTmodelAW′→WH→qqbbboostedPhys.Rev.D102(2020)1120081.5-2.9TeVHVTmodelAZ′→WW→eνµνresolvedATLAS-CONF-2022-0660.3-2.1TeVHVTmodelAZ′→WW→ℓνqqresolved,boostedEur.Phys.J.C80(2020)11650.3-3.5TeVHVTmodelAZ′→ZH→ννbb,ℓℓbbresolved,boostedarXiv:2207.002300.3-2.8TeVHVTmodelAZ′→WW→qqqqboostedJHEP06(2020)0421.3-2.9TeVHVTmodelAZ′→ZH→qqbbboostedPhys.Rev.D102(2020)1120081.5-2.2TeVHVTmodelBW′→WZ→ℓνℓ′ℓ′resolvedarXiv:2207.039250.8-2.6TeVHVTmodelBW′→WZ→ννqq,ℓνqq,ℓℓqqresolved,boostedEur.Phys.J.C80(2020)11650.8-4.3TeVHVTmodelBW′→WH→ℓνbbresolved,boostedarXiv:2207.002300.8-3.3TeVHVTmodelBW′→WZ→qqqqboostedJHEP06(2020)0421.3-3.6TeVHVTmodelBW′→WH→qqbbboostedPhys.Rev.D102(2020)1120081.5-3.2TeVHVTmodelBZ′→WW→eνµνresolvedATLAS-CONF-2022-0660.8-2.4TeVHVTmodelBZ′→WW→ℓνqqresolved,boostedEur.Phys.J.C80(2020)11650.8-3.9TeVHVTmodelBZ′→ZH→ννbb,ℓℓbbresolved,boostedarXiv:2207.002300.8-3.2TeVHVTmodelBZ′→WW→qqqqboostedJHEP06(2020)0421.3-3.1TeVHVTmodelBZ′→ZH→qqbbboostedPhys.Rev.D102(2020)1120081.5-2.7TeVHVTmodelCW′→WZ→ℓνℓ′ℓ′resolvedarXiv:2207.039250.3-0.34TeVExcludedmassrange[TeV]0.511.522.533.544.5ATLASDibosonSearches-95%CLExclusionLimitsStatus:March2023ATLASPreliminaryL=139fb−1√s=13TeVHVTmodelA:gF=−0.55,gH=−0.56HVTmodelB:gF=0.14,gH=−2.9HVTmodelC:gF=0,gH=1*small-radius(large-radius)jetsareusedinresolved(boosted)events†withℓ=µ,e sophisticated data acquisition and analysis techniques. For this reason, while waiting for the delayed Run 3 dataset, the analysis effort focused on optimizing the analysis workflow, making extensive use of deep learning techniques, and preparing the groundwork for the future. In particular, a new analysis strategy based on deep-learning algorithms has been implemented, with several possible extensions envisioned for the future. 7.2.1 Analysis strategy The analysis is conducted as a “bump search”, by looking for a localized data excess with respect to the known SM background in the distribution of the reconstructed resonance mass obtained from the selected ννqq(bb), νlqq(bb), or llqq(bb) systems. In practice, the statistical interpretation is performed as a binned maximum likelihood fit (see Sec. 6.3) of the invariant mass distribution in all the signal regions (SR) and the background-dominated control regions (CRs). The final regions of the analysis that enter the fit are defined via a series of cuts referred to as event selection. The selection is performed by applying requirements on the kinematic properties of the final state objects, or on event-level variables, to select regions of phase space close to what would be populated by the target signal. This process is dependent on the signal topology, which can be determined by the signal hypothesis, production mode, and final state. Each event topology has a specific event selection, which defines a channel. For each production mode, six channels are always defined according to the process being VV or VH, and to the number of charged leptons (0, 1, or 2) in the final state. Events in final regions can then be sorted into different categories, a process sometimes referred to as categorization. One reason to do this is to isolate particular signatures with different back- ground contributions, which helps to better constraint the given background normalization. For example, separating according to the number of b-tagged jets allows to better isolate different V+jets contributions according to the number of light and heavy flavor jets, as shown later. Different types of final regions are defined. Signal regions (SR) select events with the goal of maximizing the significance of the target signal, according to Eq. (7.1). Control regions (CR) are defined such that they target a region of phase space close to the SRs, but with negligible signal efficiency. This is usually done by using the same event selection as for the SRs, and then inverting one single cut that is expected to drastically remove signal. The use of CRs is two-fold. During the analysis optimization, when the analysis is blinded, they are used for the validation of background Monte Carlo (MC) modeling and of analysis techniques. They are then included in the final fit in order to constraint 125 background normalizations. Validation regions are defined similarly to CRs, but are used only for validation purposes and are not included in the fit. Once the final regions have been defined, the discriminant distribution in each final region for data and background are input to the fit to test the background-only hypothesis. The background is provided by the MC simulation of the SM processes that pass the event selection and whose normalizations are mostly fixed by the fit using the CRs. The data is passed through the same event selection as MC. In case of an excess, the fit outputs a p-value, or the probability that the background can produce a fluctuation greater than the excess observed in data. When the background-only hypothesis cannot be excluded, upper limits on the signal cross section times branching fraction are set. Further constraints on specific model parameters can also be provided. Once the channels have been analyzed independently, further improvements on the search sensitivity can be obtained by performing a combined fit, or a combination. For each signal hypothesis, a simultaneous analysis of the discriminants of all the channels sensitive to that hypothesis is performed. This provides several advantages. The first is an increase in the power of the search due to the fact that the total significance grows as the sum in quadrature of the significance in each bin entering the fit. Another advantage is the possibility to treat certain background contributions as correlated between different channels, which allows to better constraint their normalization and reduce the post-fit uncertainties, hence increasing the fit sensitivity. Different channels can also provide complementary information, so that a combined treatment results in an overall stronger sensitivity. This is the case, for instance, for the VH channel with 0 and 2 charged leptons, where the first provides stronger exclusion limits at high resonance masses, while the latter is more sensitive at low masses. Lastly, the inclusion of more bins also means stronger constraints on the parameters of the model under study. 7.2.2 Machine learning approach Traditional cut-based analyses place hard cuts on individual variables to increase the signal purity of the final regions. While the significance is kept high, this is often at the expense of signal efficiency, which in previous searches of this type was below 20%. This is not surprising, as the final state of an LHC pp collision contains hundreds of particles. Even when one focuses on only a handful of objects, each of these is described by a four-dimensional four vector. The event selection therefore has to be optimized in N > 16 dimensions. A more nuanced event selection can be obtained by moving to a deep-learning-based approach. Deep learning provides a way to optimally process a large number of correlated 126 inputs and find optimal decision boundaries. Consider a neural network (NN) with one out- put node that yields a probability score, serving as a classification metric. The score functions as a one-dimensional test statistic, t(x), analogous to the traditional one-dimensional cuts. However, unlike simple threshold-based methods, the NN dynamically optimizes its inter- nal weights to maximize the separation of the PDF of t(x) for the signal and background hypotheses. In doing so, the NN is capable of learning any form of correlation among the In addition, a cut on t(x) corresponds, in fact, to a non-linear decision input variables. boundary in the feature space, which can retain a higher signal efficiency and purity than a combination of hard cuts on the input variables. The strength of the NN lies therefore in its ability to map a high dimensional space onto a low dimensional output, while providing enhanced discrimination power. This motivated a more global machine learning approach in the analysis, including the development of a new multi-class NN jet classifier, one of the main contributions of this thesis. The analysis makes also use of two other multivariate algorithms inherited and repur- posed from previous publications. The vector-boson fusion (VBF) and gluon-gluon fusion (ggF)/Drell-Yan (DY) production modes are characterized by characteristic event topologies that require different final region definitions. In particular, the VBF topology has two addi- tional jets, referred to as “VBF candidates,” that tend to be well separated in pseudorapidity and to have a large di-jet invariant mass. In the previous VV search [168], the VBF and ggF/DY final regions were made orthogonal via a Recursive Neural Network (RNN) [183], which uses as inputs the four-momenta of the small-R jets in the event identified as the “VBF candidates.” The same RNN is used in the current analysis, and is applied for the first time to VH final states as well. The analysis workflow is shown in Fig. 7.3. Figure 7.3: Analysis workflow displaying where the VBF-RNN and the MCT are applied. 7.2.3 The Multi-Class Tagger A new five-class neural network was developed for the identification of the hadronic decay as coming from a Higgs boson, a W boson, a Z boson, a top-quark, or light-quarks and gluons 127 Pre-selection......VBFRNN...EventselectionCRMulti-classjetclassifierVVSRVHSRleptonsn-lepn-lepggF/DYVBFW/ZH (QCD). The identification of the hadronic decay is an essential part of the search for new heavy resonances, both in the semi-leptonic and fully-hadronic final states. On one side, the SRs are generally defined to select hadronic decays of a H/W/Z boson. On the other, the major backgrounds that mimic these decays are mis-reconstructed top-quarks or energetic QCD jets, often with specific designated CRs. Having simultaneous access to the likelihood for all these hypotheses is therefore highly desirable. The multi-class-tagger (MCT) was designed as a general tool in the context of boosted jet tagging. Individual taggers targeting specific signatures already exist in ATLAS, such as the top tagger [184] or the W/Z tagger [185], which attempt to identify a top quark or a vector boson from light jets. However, comparing scores from different taggers is potentially complicated, as the output scores are not correlated in a well understood way. The ambi- guity in the interpretation of the scores is resolved if one moves to multi-class classification. Here, the output scores are by construction correlated, allowing for simultaneous scoring, in particular via the definition of likelihood ratios, as shown in Fig. 7.4b. Because the scores are correlated, the ratios are automatically well-defined and can bring significant improvements in terms of tagger performance, thanks to their ability to capture in part the uncertainty in the network predictions. As shown in Fig. 7.4c, likelihood ratios can also be used to access a multi-class space, which can provide further discrimination power. Multi-class classification was already used in ATLAS in the context of flavor tagging (see Sec. 4.4.6), but at the time of this work it had not been explored by ATLAS for boosted jet tagging. A multi-class approach has already been used by CMS [186]. The fact that the VV and VH final states are considered simultaneously in a single analysis was a second motivation for the development of the MCT. While harmonizing the efforts permits a better optimization of the event selection in anticipation of a combination of the results, considering different channels simultaneously can increase the complexity of the analysis. In particular, standard cut-based analyses can incur in the issue of overlapping selection criteria. In the case of the V V + V H effort, the jet mass windows overlap, which requires an extra step to orthogonalize the final regions. Since the VV and VH processes differ only by the hadronic decay, the multi-class tagger provides an optimal way to solve this issue. The next sections will discuss the development of the MCT for large-R jet classification, its extension to the resolved jets topology, and its deployment in the analysis to orthogonalize the VV and VH final regions. Although not discussed in this thesis, the way the MCT was envisioned allows for a straightforward extension to aid in the definition of top- and QCD- enriched control regions. Output scores of the MCT would also be candidate high-level inputs to a possible event-level classifier. These are ideas that will be explored in the future. 128 (a) (b) (c) Figure 7.4: Example of multi-class classification showing: the raw scores for true Higgs, W, and top jets (left); the a likelihood ratio log(p(h)/p(t)) for true Higgs and top jets (center); and the simultaneous evaluation of all the likelihoods in the two-dimensional space of likelihood ratios (right). These figures were produced with true Monte Carlo data and with the merged MCT described in the following section, but with an additional cut on the pT of the large-R jet for displaying purposes. 7.3 Signal and background processes The search targets different signal interpretations, with different production modes. Both DY (or quark-antiquark annihilation) and VBF productions are considered in the search for new HVT bosons. In the search for a pseudo-scalar A, ggF and b-quark associated production are considered. For the spin-0 RS radion and the spin-2 graviton, both ggF and VBF mechanisms are studied. Representative Feynman diagrams of the different production modes are shown in Fig. 7.5 for a general new resonance X. W H, Z′ → W W , and Z′ → In the HVT (see Sec. 3.3) signal interpretation, X can be a new electrically charged W Z, W ′ or electrically neutral Z′ vector boson. The possible decay modes are W ′ → ZH. The two resonances are assumed degenerate, W ′ → which favors a common interpretation of the results. The coupling of the new particles to the SM bosons is parametrized by the combination gH = gV cH , while the couplings to fermions by gF = g2/gV cF . The parameters cH and cF are expected to be of order unity, so the parameter gV represents the typical strength of the interaction. The results are interpreted with respect to three benchmark models. Model A predicts comparable fermionic and bosonic BRs and is representative of a weakly coupled model. Model B is representative of a composite model with the couplings to fermions suppressed. Lastly, Model C is representative of a fermiophobic scenario, with gV = gH = 1 and the couplings to fermions set to zero. For Models A and B, the W ′ and Z′ bosons are produced mainly via 129 (a) (b) (c) (d) Figure 7.5: Representative Feynman diagrams for Drell-Yan (a), vector-boson fusion (b), gluon-gluon fusion (c), and b-quarks associated production (d) of a new heavy resonance X. When multiple options are possible for quark flavor or for vector boson charge, these are left unspecified. DY. For Model C this mode is vetoed, making production via VBF enhanced. This is the first time VBF production is considered in the VH analysis in ATLAS. The analysis aims at setting upper limits on the production cross-section of the new particles, which can be used to constraint the model parameters gF and gH . The search is performed in the mass range from 300 GeV to 5 TeV. Specific to the VH analysis is the search for a new pseudoscalar scalar A, one of the heavier Higgs bosons predicted by the 2HDM model (see Sec. 3.4). The resonance can decay to a ZH final state. The search is performed in the mass range between 220 GeV and 2 TeV. Higher masses are excluded by the class of models targeted by this search, as they make the Higgs potential unstable. The search aims at setting limits on the production cross section, α). The search which is then used to constrain the model parameters tan(β) and cos(β targets both ggF and b-quarks associated production (bbA). − Specific to the V V analysis are two other signal interpretations. One is the radion (R), a new neutral scalar particle predicted by certain RS models [187, 188]. The other is a neutral spin-2 graviton (GKK ) [162, 189], the first Kaluza-Klein (KK) excitation in a bulk 130 q¯qVV/HXqqVVqqVV/HXggVV/HXgg¯bbVV/HX RS model. Both are predicted to have dominant BRs to W W or ZZ final states and can be produced via ggF or VBF processes. This search is performed in the mass range between 300 GeV and 5 TeV. A summary of the decay modes and channels of interest for each signal interpretation is given in Tab. 7.1. Production Process Channels HVT bosons DY VBF ggF bbA DY VBF pp pp pp pp → → → → pp pp → → pp pp → → W W/ZH W Z/W H Z′ → W ′ → Z′jj → W ′jj → W W/ZHjj W Z/W Hjj Pseudoscalar A VV 1-lepton and VH 0/2-lepton VV 0/1/2-lepton and VH 1-lepton VV 1-lepton and VH 0/2-lepton VV 0/1/2-lepton and VH 1-lepton ZH A → Abb ZHbb → VH 0/2-lepton VH 0/2-lepton Radion/Graviton W W/ZZ VV 0/1/2-lepton W W/ZZjj VV 0/1/2-lepton R/G → R/Gjj → Table 7.1: Channels used in the searches for HVT bosons, pseudoscalar A, radion, and graviton. Several SM processes can have similar final states as the signals and act therefore as background: W and Z boson production in association with jets (V +jets); top quark pro- duction, with top-quark pair production (t¯t) as the primary contribution, but including also single-top-quark production; non-resonant diboson production (W W , W Z, or ZZ) with semi-leptonic decays; and multi-jet production. Other minor background processes for the V H topology are the production of t¯t + h, t¯t + V (V = W, Z), and the irreducible SM background V + h. All Monte Carlo (MC) samples are generated at the center-of-mass energy of √s = 13 TeV and are passed through the full Geant4-based [131] ATLAS detector simulation. All samples include the simulation of in-time and out-of-time pileup by overlaying the simulated minimum bias events on the generated event, matching the pileup conditions of the different data taking periods. The MC production undergoes the same event reconstruction as data. A multiplicative factor to the event weight of the generated events is applied to correct for differences between data and MC. These include corrections of the jet energy scale and 131 resolution, of the triggering, reconstruction, and identification efficiency of leptons, and of the jet flavor-tagging efficiencies. The HVT Z’ and W’ production via quark-antiquark annihilation was modelled at LO accuracy in QCD with MadGraph5 (MG5) [190] generator, using the NNPDF2.3LO PDF set [191], interfaced with Pythia8 [192] for modeling of the parton shower with the ATLAS A14 set of tuned parameters [193]. Different samples were generated assuming various W’ and Z’ masses ranging from 500 GeV to 5 TeV. For benchmark models A and B, only samples for model A were generated, as the differences in the final state kinematics are considered negligible once detector response effects are taken into account. Only the predicted produc- tion and decay rates differ, which are fixed at the moment of the statistical interpretation. The generated samples include decays of the Higgs boson to both b- and c quarks, where ¯c) = 0.0287, and mH = 125 GeV were assumed. the SM values of B Another set of samples is generated for model C for VBF production only. b¯b) = 0.569, → → (h (h − B The 2HDM ggA signal sample was generated with MG5 at LO accuracy in QCD with the narrow width approximation, using the 2HDM GF FeynRules model [194], and the NNPDF2.3 LO PDF set. The 2HDM bbA process was generated using the four-flavor scheme at next-to-leading order (NLO) with massive b-quarks with MadGraph5 aMC@NLO2.2.3 and the NNPDF2.3NLO PDF set. Shower modeling was performed with Pythia8 with A14 tun- ing. Resonance masses in the range between 220 GeV and 2 TeV were simulated for each signal process. Signal samples for the RS graviton and radion were produced with MG5 interfaced to Pythia8 using the NNPDF2.3LO PDF. For each interpretation, samples were produced for masses ranging from 300 GeV to 6 TeV. The QCD multi-jet background is not well-modeled by MC and it is generally derived from data. In the context of the analysis, it would appear as a mis-modelling when comparing data and MC distributions. However, the event selection of the analysis is able to select a phase space with negligible multi-jet contamination. A summary of the MC generators used to produce the other background processes is given in Tab. 7.2. 132 Process Generator Vector boson + jets Sherpa2.2.1 Sherpa2.2.1 W Z lν → ll/νν → t¯t single top W t-channel t¯t + h t¯t + V Top quark Poweheg+Pythia8 Poweheg+Pythia8 Poweheg+Pythia8 MadGraph5 aMC@NLO + Pythia8 MadGraph5 aMC@NLO + Pythia8 Diboson qg/q ¯q → qg/q ¯q gg qg/q ¯q W W → ℓνqq ℓℓqq/ννqq/ℓνq ¯q ℓℓq ¯q/ννq ¯q ℓνqq → ℓℓq ¯q/ννq ¯q ℓℓνν → W Z → ZZ W W → → → ZZ qg/q ¯q → → → Sherpa2.2.1 Sherpa2.2.1 Sherpa2.2.1 Sherpa2.2.2 Sherpa2.2.2 Sherpa2.2.2 V + SM Higgs ℓνbb → ννbb/ℓℓbb ννbb/ℓℓbb Powheg+Pythia8 Powheg+Pythia8 Powheg+Pythia8 qq W h → Zh Zh → → → → gg qq gg Table 7.2: Summary of the MC generators used to produce the various background processes. Adapted from analysis ATLAS internal note. 133 7.4 Data taking and trigger selection The analysis uses pp collision data recorded by ATLAS during the 2015, 2016, 2017, and 2018 runs at a center of mass energy of √s = 13 TeV. Only events during which all ATLAS sub-detectors were fully operational are included. The resulting total integrated luminosity 1. The breakdown of the integrated luminosity 2.4 fb− collected during this period is 139.0 per data taking period is shown in Tab. 7.3. ± Year [fb− 1] L 2015+2016 2017 2018 Total 36.2 44.3 58.5 139 Table 7.3: Integrated luminosity for each data taking period. The event selection relies on the lowest unprescaled single-lepton and Emiss (MET) trig- gers, according to the lepton channel. Different triggers were used according to the data taking period due to the evolving pileup conditions during Run 2. The full list of triggers is shown in Tab. 7.4. T T The 0-lepton channel relies on different combinations of MET triggers, which rely on different online Emiss reconstructed at the High-Level Trigger, as well as different thresholds. In particular, the online MET reconstruction does not include muon information. The MET calculation of the xe trigger uses all noise suppressed cells from the LAr and Tile calorimeters. The mht trigger uses the jet based Emiss , where the MET is calculated using all the calorimeter jets reconstructed at the HLT, which have been energy-corrected for pileup contribution. The pufit trigger uses the pufit algorithm [98], which groups topoclusters into towers of size η 0.79 that are subtracted with an event-dependent pileup correction. The latter reconstruction was found to be optimal as the pileup levels increased during Run 2. Since the Emiss values of roughly 200 GeV, the 0-lepton channel only extends down to masses of 500 GeV (which corresponds roughly to Emiss triggers reach 100% efficiency at offline Emiss 250 GeV). 0.71 × ≈ × ϕ T T T The 2-lepton channel uses single-electron and single-muon triggers, defined by different requirements on the ET of the reconstructed HLT lepton, as well as lepton identification and isolation criteria. In most periods a logical OR of different settings is used, as at higher ET values quality criteria can be relaxed to increase efficiencies, and vice versa. T ∼ 134 The 1-lepton channel uses combinations of single-electron, single-muon, and MET trig- gers. Because the MET triggers do not include muons in the calculation, they will trigger on an event with a high pT muon, hence compensating for single-muon trigger inefficiencies. After passing the trigger requirements, the data events go through a cleaning procedure. Events are removed if they are deemed corrupted due to LAr noise burst and data corruption, or incomplete events. All events are also required to only have “clean” reconstructed jets. A procedure called “jet cleaning” identifies “bad jets” built from noisy calorimeter cells or non-collision background. Because jets affect the calculation of other objects in the event, such as Emiss , events with one or more unclean jet are removed. T Data-taking period eνqq and eeqq channels HLT e24 lhmedium L1EM20 OR HLT e60 lhmedium OR HLT e120 lhloose HLT e26 lhtight nod0 ivarloose OR HLT e60 lhmedium nod0 OR HLT e140 lhloose nod0 HLT e300 etcut 2015 2016a (run < 302919) 1034 cm−2 s−1) 302919) ≥ 1034 cm−2 s−1) (L < 1.0 × 2016b (run (L < 1.7 2017 2018 × µνqq (pT (µν) < 150 GeV) and µµqq channels HLT mu20 iloose L1MU15 OR HLT mu50 µνqq (pT (µν) > 150 GeV) and ννqq channels HLT xe70 HLT mu26 ivarmedium OR HLT mu50 HLT xe90 mht L1XE50 same as above same as above same as above same as above same as above same as above HLT xe110 mht L1XE50 HLT xe110 pufit L1XE55 HLT xe110 pufit xe70 L1XE50 Table 7.4: List of triggers used in the analysis. Adapted from analysis ATLAS internal note. 7.5 Object selection The same object reconstruction and selection procedure is performed on data and simulated MC samples. A detailed description of ATLAS event reconstruction is provided in Sec. 4.4, while the focus in this section will be in the quality criteria used to select well-reconstructed objects for the analysis. Tracks Tracks are reconstructed from hits in the ID using the Primary tracking algorithm with the Tight track quality selection and the Tight track-vertex association criteria. All tracks are required to have > 2.5 and pT > 5 GeV. η | | Electrons Electrons are reconstructed from topological clusters in the electromagnetic calorimeter matched to tracks in the ID. All electron candidates are required to have pT > 7 GeV and 135 | η | < 1.52. Additionally, each electron track in required to have < 2.47, excluding the gap region between the barrel and the endcap LAr calorimeters η | | < 0.5 mm z0 sin θ 1.37 < | < 5. Two identification criteria are d0| and transverse impact parameter significance | used in the analysis. The Tight selection is used in the 1-lepton channel to select electrons eν. This relies on tight identification and isolation criteria, and requires from the decay W e+e− electrons in the electrons with pT > 30 GeV. The Loose criteria is used to select Z 2-lepton channel, with looser identification and isolation working points, and no isolation requirement for electrons with pT > 100 GeV. /σd0 → → | Muons | z0 sin θ | < 0.5 mm and Muons are reconstructed from combined tracks using information from both the ID and the < 2.5, muon spectrometer. All muon candidates are required to have pT > 7 GeV and < 3. Similarly to electrons, two identification /σd0 as well as criteria are used. The Tight selection is used in the one-lepton channel to select muons µν. This applies the medium identification working point and tight from the decay W isolation criteria, and requires muons with pT > 30 GeV. The Loose selection is used to µ+µ− decays in the 2-lepton channel, with looser identification and isolation select Z working points, and no isolation requirement for electrons with pT > 100 GeV. d0| | η | → → | Small-R jets Small-R jets are reconstructed using the anti-kt algorithm with radius parameter R = 0.4 and PFlow input objects. The topological clusters used to reconstruct the jet have been calibrated at the EM scale. Different selection criteria are used for what will be referred to as signal and forward < 2.5) and are required to jets. Signal jets are reconstructed in the central η region ( η | < 4.5) have pT > 20 GeV. Forward jets are reconstructed in the forward region (2.5 < and are required to have pT > 30 GeV. To reduce contamination from jets originating from pileup vertices, jets with pT < 60 GeV and < 2.4 are further required to pass a jet-vertex tagging [195] selection. Selected small-R jets are referred to as signal jets. η | η | | | | Large-R jets The large-R jets are built with the anti-kt algorithm with R = 1.0 using UFO input objects. As described in Sec. 5.3.2, the resulting UFO jets benefit from the optimal performance of PFlow jets at low pT and of TCC jets at high pT , and are expected to improve the perfor- mance of the analysis with respect to previous publications, which relied on the standard LCW calibrated topoclusters (see Sec. 4.4.4) as inputs. 136 Prior to jet reconstruction, the set of input objects is pre-processed with a combination of constituent-level pileup-suppression algorithms (see Sec. 5.5). The pT of each constituent is first adjusted with the Constituent Subtraction (CS) method. The Soft Killer (SK) al- 0.6, is then used to remove low pT gorithm, with a grid granularity of ∆η constituents. Further pileup suppression is obtained by applying the Soft-drop algorithm, with parameters β = 1.0 and Zcut = 0.1, on the set of reconstructed jets, removing con- stituents associated with soft and wide-angle radiation. ∆ϕ = 0.6 × × Variable radius track jets Variable radius (VR) track jets are used to identify b-tagged subjets in large-R jets (see Sec. 5.3.2). After reconstruction, they are assigned to the large-R jets in the event via ghost- association. VR track jets are built by running the anti-kt algorithm on the tracks using a pT -dependent radius parameter given by Reff(pT,i) = ρ , with ρ = 30 GeV and the upper pT,i and lower limit on the jet size set to Rmax = 0.4 and Rmin = 0.02. All VR jets are required < 2.5, and number of associated tracks nTrk > 1. Collinear track to have pT > 10 GeV, jets can occur and are problematic, as their interplay with the track-association step used by b-tagging algorithms is not well understood. In order not to expose b-tagging algorithms to these pathological cases, events with an overlap between track jets used for b-tagging (pT > 5 GeV and nTrk > 1) and VR track jets selected by the analysis are removed. η | | Flavor-tagging The DL1r flavor-tagging algorithm is used to tag signal jets and VR track jets. A cut on the DL1r score as defined in Eq. 4.9 is used to identify jets as b-tagged. The cut at the 70% b-tagging efficiency working point (WP) is used for signal jets, while the VR track jets are selected using the 85% WP. A higher efficiency WP corresponds to an increase in both signal and background acceptance. Missing transverse momentum T Different metrics exist to evaluate the presence of a large momentum imbalance in the transverse plane, which are described in Sec. 4.4. The analysis makes use of the missing transverse momentum Emiss given by the sum of a hard term and a track-based soft term to reconstruct neutrinos in the event. Additional selection requirements make use of a track- based missing transverse momentum estimation pmiss , built from the negative vectorial sum In order of the transverse momenta of all the tracks associated to the primary vertex. to decrease contributions from background with large Emiss , which can arise from mis- measurements of leptons and jets energies, the Emiss significance is also used. T T T 137 τ -leptons Hadronically decaying τ -lepton candidates are used in the ννb¯b channel to reject background with real hadronic τ -leptons. Hadronic τ candidates [196] are reconstructed using R = 0.4 calorimeter jets. They are required to have one or three associated tracks, pT > 20 GeV and < 2.5. The τ identification is performed using a multivariate technique algorithm and η | the Medium working point is used in this analysis. | Overlap removal As the different object collections are reconstructed and selected independently, it is possible that different objects are built from the same inputs. In order to avoid double counting of energy, an overlap removal procedure is implemented on the set of selected objects. First, a τ -lepton is removed if it overlaps with a muon within ∆R < 0.2, unless the muon is not a combined muon and the τ has pT > 50 GeV. Electrons are removed if they share an ID track with a muon. A small-R jet is removed if it is within ∆R = 0.2 of an electron or a muon that passed isolation requirements. In order to retain jets originating from a true b-hadron decay that included muons in the decay chain, jets are only removed if they have fewer than three associated tracks, or if more than 70% of the transverse momentum sum of the associated tracks comes from the muon. Lastly, electrons and muons are removed if they overlap with any of the remaining jets within 0.2 < ∆R < min(0.4, 0.04 + 10 GeV/pT ). 7.6 Event selection After the final state objects have been reconstructed, and events with good data collection and object reconstruction quality have been selected, the next step is to define the final regions of the analysis. The event selection goes from general requirements common to all regions, to more specific selections targeting each decay channel. The first step consists in reconstructing the leptonic decay. The events are separated into lepton channels, targeting the corresponding leptonic decays, according to the number µν in of reconstructed charged leptons: Z the 1-lepton channel; and Z νν in the 0-lepton channel; W µµ in the 2-lepton channel. → ee or Z eν or W → → The next step is to reconstruct the hadronic candidate. According to the signal hypoth- esis, this is either a Higgs boson (H), or a W or Z boson. In the former case, the region is said to be in the “VH analysis,” while in the latter it is said to be in the “VV analysis.” The hadronic reconstruction differs in terms of mass window and b-tagging requirements. According to whether the reconstruction of the hadronic decay uses small-R or large-R jets, the region is categorized as resolved or merged. This separation is not by itself orthogonal. → → 138 The two reconstruction strategies proceed in parallel, producing merged and resolved final regions, and only at the end the regions are made orthogonal by prioritizing one over the other. This is referred to as prioritization and it is performed to maximize the analysis sensi- tivity. The reconstruction of the leptonic decay is the same for VV and VH final regions, but can differ between resolved and merged, as a larger boost in the hadronic decay is generally accompanied by a more boosted leptonic system. A last set of selection cuts is specific to each lepton channel, analysis, and kinematic regime and aims at reconstructing the full resonance decay from the reconstructed final state to obtain the invariant mass distribution to feed into the statistical fit. 7.6.1 Jet requirements A set of kinematic cuts on the reconstructed jets is used to select events compatible with a H, W , or Z hadronic decay. The selections differ according to the reconstruction strategy. Resolved regime The H/W/Z candidate is reconstructed by first selecting the small-R jets that are most compatible with the given decay hypothesis, and then summing their 4-vectors. Events are first required to have the leading small-R jet pT above 45 GeV. The W/Z candidate is recon- structed from the two leading small-R jets in the event. The H candidate is reconstructed from the two leading b-tagged small-R jets or, in the case of only one b-tagged jet, from the b-tagged jet and the leading non-b-tagged jet. The use of b-tagging in the selection of the Higgs boson candidate allows to significantly reduce background contamination, which re- b¯b has a sizable BR, the use of b-tagging sults in better sensitivity. Although the decay Z was not observed to bring a significant improvement in this case. The reconstructed dijet system (jj) is then required to have a reconstructed mass consistent with the H, W , or Z hypothesis. The following mass windows are used: → • Higgs boson: 110 < mjj < 140 GeV (0/1 lepton), 100 < mjj < 145 GeV (2-lepton) • W boson: 62 < mjj < 97 GeV • Z boson: 70 < mjj < 105 GeV Merged regime The H/W/Z candidate is taken as the leading large-R jet (J) in the event. Events are required to have the leading large-R jet with pT > 250 GeV (pT > 200 GeV) in the VH (VV) analysis. In the VH analysis, the Higgs candidate is selected using a mass window 139 requirement of 75 GeV < mJ < 145 GeV. The mass windows in the merged regime of the VV analysis are defined using the pT -dependent W and Z mass cuts from the W/Z Tagger [185]. The W/Z tagger provides pT -dependent two-dimensional cuts in the large-R jet mass and D2 substructure variable to tag W or Z candidates against multi-jet background. The mass windows as a function of pT are shown in Fig. 7.6. Events passing both the mass window and D2 cuts are defined as High-Purity (HP), while events that pass the mass cut, but fail the D2 cut are classified as Low-Purity (LP). Figure 7.6: Upper and lower cut values on m(J) for the cut-based W tagger (left) and Z tagger (right) in bins of large-R jet pT [185]. 7.6.2 0-lepton channel The 0-lepton selection targets Z and Emiss multijet background. Further cuts are applied specifically to suppress this contribution: νν decays. Events are required to have no Loose leptons > 250 GeV. The largest contamination in this region comes from the QCD- → T • The object-based MET significance, as defined in Sec. 4.4.5, is required to be > 10. S • The reconstructed Emiss T π 9 , where ϕ is the angle between Emiss T is required to be isolated by requiring min[∆ϕ(jet, Emiss and the nearest small-R jet. T )] > • The track-based missing transverse momentum pmiss T is required to be above 80 GeV. → The decay of the Z boson to two neutrinos does not allow the complete reconstruction of the Z νν candidate, as the z-component of the four vector is not known. For this reason, the final discriminant is taken to be the transverse mass of the reconstructed ZH/ZZ/ZW candidate. This is obtained by summing the MET vector (Emiss , 0) with the four-vector representing the H/W/Z candidate without the longitudinal components. , Emiss x , Emiss y T 140 50010001500200025003000 [GeV]T jet pRLarge-406080100120140160180Mass [GeV]ATLASSimulation Preliminary WZfi = 13 TeV W's R=1.0 UFO Soft-Drop CS + SK jetstanti-kW tagger 50% signal efficiency| < 2.0h > 200 GeV, |TpUpper mass cut fitUpper mass cut binnedLower mass cut fitLower mass cut binned50010001500200025003000 [GeV]T jet pRLarge-406080100120140160180Mass [GeV]ATLASSimulation Preliminary WZfi = 13 TeV W's R=1.0 UFO Soft-Drop CS + SK jetstanti-kZ tagger 50% signal efficiency| < 2.0h > 200 GeV, |TpUpper mass cut fitUpper mass cut binnedLower mass cut fitLower mass cut binned 7.6.3 1-lepton channel The 1-lepton channel targets W lν decays. Events are required to have exactly one lepton satisfying the Tight criteria for either electrons or muons, and no additional Loose leptons. In order to select W decays, events are further required to have Emiss > 60(100) GeV and T the W candidate pT > 75(200) GeV in the resolved (merged) region. → The neutrino reconstruction only provides the transverse components of its four-vector. z is obtained W = In order to reconstruct the full W four-vector, the z-component of the neutrino pν by imposing a W mass constraint on the lepton-neutrino system, via the relation m2 (pl + pν)2. The result is given by, pz,ν = 1 2p2 T,l (cid:104) pz,lA + El (cid:113) A2 4(p2 T,l(Emiss T )2) − (cid:105) , (7.2) with A = m2 x + 2pl taken. If both solutions are real, the smaller one is taken. W + 2pl xEmiss yEmiss y . In case of complex solutions, the real solution is Additionally, a set of requirements are imposed to remove background contributions. The requirement min (cid:0)pT (Wlep), pT (W/Z/Hhad)(cid:1) m(V V /V H) > 0.35 (7.3) is used to select events with an even pT sharing between the hadronic and leptonic decay systems, to target signal-like two-body decays. Contamination from t¯t is further suppressed by removing events with additional b-tagged signal jets not used to reconstruct the dijet system in the resolved regime, or with b-tagged VR jets outside the large-R jet in the merged regime. In the resolved channel, several angular requirements are further applied to suppress QCD-multijet contributions. The cuts ∆ϕ(l, Emiss ) < 1.5 and ∆ϕ(j1, j2) < 1.5 select events T with well contained leptonic and hadronic decays, respectively. The cuts ∆ϕ(l, j1/j2) > 1.0 and ∆ϕ(Emiss , j1/j2) > 1.0 select events with well separated leptonic and hadronic decays. In addition, when the lepton is identified as an electron, the additional requirement Emiss /pT (W ) > 0.2 is applied in the resolved region. The contribution of QCD background T in the merged region is less significant, and no specific anti-QCD cut is implemented. T 141 7.6.4 2-lepton channel → The 2-lepton channel selects events compatible with a Z ll decay. Events are required to have exactly two isolated Loose leptons of the same flavor (electrons or muons) and either of the two leptons has to be matched to the HLT lepton that fired the trigger and its ET is required to be 5% above the trigger threshold to ensure full trigger efficiency. The leading lepton is required to have pT > 27 GeV and the sub-leading lepton is required to have pT > 20(25) GeV in the resolved (merged) regime. In the case of two muons, these are required to have opposite charge. This requirement is not imposed on electrons because of their higher rate of charge misidentification due to possible converted photons from bremsstrahlung radiation. The Z candidate is reconstructed as the four-vector sum of the two leptons. The invariant mass of the dilepton system is required to be consistent with the Z boson mass in order to suppress backgrounds without a resonant dilepton pair. Electron pairs are required to have [83, 99] GeV, while a pT,ll-dependent cut is required for muon pairs to compensate for mee the di-muon mass resolution degradation at high Z transverse momentum. The following cut was optimized in the previous VV publication to maintain approximately a constant 95% selection efficiency across resonance masses: ∈ (85.6 − 0.0117 · pT,ll) < mµµ < (94.0 + 0.0185 pT,ll) GeV · (7.4) The same pT balance requirement as in Eq. (7.3) is used in the region m(V V /V H) < 320 GeV to further suppress background: min (cid:0)pT (Zlep), pT (W/Z/Hhad)(cid:1) m(V V /V H) > 0.35 (7.5) At higher signal masses the background contamination is sufficiently low, so the cut is removed to recover signal efficiency. The VH analysis has significant contributions from the t¯t background, which is often char- acterized by the presence of a neutrino in the final state. This contamination is suppressed < 4, removing events consistent with by requiring the object-level MET significance to be the presence of Emiss S . T The signal resonance is obtained from the four-vector sum of the Z candidate from the dilepton system and the reconstructed hadronic decay. The final discriminant is given by the invariant mass of the reconstructed resonance. 142 7.7 Event categorization The event selection just described selects events with signal-like topologies and is used to define the final regions that will be input to the statistical fit. However, at this point the regions are not orthogonal, neither between resolved and merged categories, nor between different production modes of a given signal hypothesis, and further criteria have to be imposed. Final regions In a given analysis, the searches targeting ggF and DY production processes have similar event topologies, and thus they share the same final regions. The bbA production is charac- terized by the presence of two extra b-quarks in the final state, while the VBF process has two extra quarks. For the definition of VV/VH VBF-HVT final regions a recurrent neural network (RNN) is used, as mentioned earlier. The RNN was developed in the context of the previous VV search and was redeployed in this round for both VV and VH. The RNN takes as input up to two extra jets in the event and outputs the probability of the event as being VBF or not-VBF. Events are removed from any HVT final region and put in VBF-HVT final regions if they have an RNN score above 0.8. In the VH analysis, in the searches for W’ and Z’ via DY or VBF production and in the search for A via the ggF process, only events with exactly one or two b-tagged jets are considered. Events with 0-btagged jets are discarded, as the background contamination is too large to add sensitivity to the search. The bbA signal interpretation is targeted by requiring at least one extra b-tagged jet. In the resolved region, events are required to have tags), while in the merged region only events with at least three b-tagged signal jets (3 + b tag&1 + add.). additional b-tagged VR track jets outside the large-R jet are considered (2b For each lepton channel, the VH signal regions are classified according to the merged or resolved reconstruction of H b¯b decay and to the number of b-tagged jets. − − → In the VV analysis, for regions targeting Z qq decays, events with zero or one b-tagged jet are combined in the same category (0/1), while events with 2 b-tags make up a different b¯b decays. Search channels with a category to increase the significance by targeting Z hadronically decaying W are analyzed in the inclusive region. As mentioned previously, in VV merged signal regions, events are sorted into HighPurity and LowPurity according to J candidate. In summary, for each lepton channel the the quality of the reconstructed V qq VV final regions are classified according to: merged and resolved reconstruction of V qq decay; high and low purity of merged V reconstruction; 0/1 or 2 b-tagged jets in Z → → → → → 143 decays; and mass windows of Z qq or W → → qq decays. Prioritization strategy Events are separated in the resolved and merged category according to the reconstruction strategy. The wide range of masses targeted by the analysis results in a wide range of trans- verse momenta of the decay products. At low transverse momenta, the two quarks from a H/W/Z decay are well separated and can be reconstructed as individual small-R jets, called resolved reconstruction. However, as the boost of the mother particle increases, the daughter particles become increasingly collimated, until they cannot be resolved as two individual jets anymore. This causes a drop in signal efficiency, if one continues to rely on the small-R jets reconstruction strategy. The efficiency can be recovered by reconstructing the hadronic decay using a larger jet radius. This was indeed the motivation to introduce large-R jets and will be referred to as merged reconstruction. The interplay between resolved/merged reconstruction and signal efficiency is shown in Fig. 7.7 for the previous VH 2-lepton chan- nel analysis. In practice, each event is reconstructed with both strategies. Most events are Figure 7.7: Acceptance function of the resonance mass in latest VH publication [165]. efficiency in the VH 2-lepton analysis for Z′ → × Zh signal as a better reconstructed with only one of the two strategies, so that when the alternative recon- struction is used, it produces a poorly reconstructed event that is rejected by the analysis. However, for a subset of events in the intermediate kinematic region, both strategies pro- vide equivalent signal efficiencies. In this case, it is possible for an event to enter both the resolved and merged signal regions. In order to remove this overlap, a prioritization strategy is implemented. 144 10002000300040005000 [GeV]Z'm00.20.4 efficiency·Acceptance All signal regions, resolved1 b-tag, resolved2 b-tags, merged1 b-tag, merged2 b-tags SimulationATLAS-1 = 13 TeV, 139 fbs Zhfi2L channel, HVT Z' It was found that the VH analysis reaches higher sensitivity by prioritizing the resolved region, while the VV analysis performs better by prioritizing the merged region. These strategies will be referred to as PriorityResolved and PriorityMerged, respectively. For instance, the VH PriorityResolved strategy is implemented as follows: • If an event is in a Resolved SR, it is removed from any other Merged SR or CR. • Else, if an event is in a Merged SR, it is removed from any other CR. • Else if an event is in a Resolved CR, it is removed from any other Merged CR. Similarly, in VV final regions, the order of selection is as follows: Merged HP SR LP SR Merged HP CR Merged LP CR Resolved CR. Resolved SR Merged → → → → → VV and VH Orthogonality The VV and VH HVT signal regions are included in the same statistical fit for the HVT interpretation and are therefore required to be orthogonal. Because the jet mass windows overlap, this is generally not the case. The regions are made orthogonal using the Multi- Class Tagger (MCT). This will be discussed in detail in Sec. 7.10, but in general the MCT sorts the events between VV and VH final regions, according to whether the hadronic decay is deemed more likely to be coming from a W or Z boson, in the first case, or from a Higgs boson, in the second. Control regions Control regions (CRs) are used to constraint the normalization of the most dominant back- grounds in the final fit. All CRs are common to the VV and VH analyses. Mass sideband CRs are obtained by inverting the mass window requirement of the given signal region. More specifically, events are required to have mass values within 50 GeV < mjj/J < 200 GeV, but outside the VV and VH mass windows. A special control region targeting t¯t background and referred to as top-CR (TCR) is used in the 2-lepton channel. This is obtained by inverting the lepton flavor requirement, requiring leptons of opposite flavor. 145 7.8 Boosted jets Multi-Class Tagger (MCT) The merged MCTis a deep neural network (DNN) large-R jet classifier trained to identify a jet as originating from a Higgs boson, a W boson, a Z boson, a top quark, or light quarks and gluons (q/g). This section presents the training and testing performance of the MCT, while the deployment in the context of the analysis is discussed in later sections. 7.8.1 Training Jet reconstruction and selection The DNN was trained using pileup-suppressed UFO R = 1.0 jets. The specific jet collection is the same as the one used in the analysis and described in Sec. 7.5. In order to focus on the kinematic region of interest for the analysis, only large-R jets with mreco [50, 200] GeV, reco < 2.0 are selected. The VR track jets are reconstructed preco η T ∈ | | < 2.5. The DL1r algorithm η using the anti-kt algorithm on tracks with pT > 10 GeV and | is applied on each VR track jet to provide the output probabilities for the jet to be coming from a b-quark p(b), a c-quark p(c), or light-quarks and gluons p(qg). [200, 3500] GeV, and ∈ | MC samples and truth labeling The training samples were Monte Carlo generated samples. Signal samples enriched in W/Z/H/top-tagged jets are obtained from simulations of heavy BSM resonances decaying into boosted SM particles. The truth labeling relies on truth matching 4 and further recon- struction quality criteria. The QCD sample is obtained from multijet processes, where the jets are produced via the strong interaction, and represent light quark and gluon jets. To provide discrimination power over a wide range of large-R jet pT , it is important that the training samples include a large number of events up to very high pT regimes. For this reason, the di-jet samples are generated in bins of pT , so that each bin is sufficiently populated. Similarly, the BSM samples are generated for different BSM resonance masses to span a wide range of pT for the daughter particles. The effect of multiple pp interactions is also included in the simulation. HH processes, where G is a Randall- Sundrum graviton. The events are simulated using Pythia8 with the ATLAS A14 tune and the NNPDF2.3LO PDF. Only reconstructed Higgs candidates truth-matched to a true Higgs particle and with two ghost-associated b-hadrons are selected. b¯b decays are generated with G Jets from H → → 4All jets are truth matched by first dR matching the jet to a truth jet, and then dR matching the truth jet to a truth particle. 146 A sample of hadronically decaying top quarks is obtained from simulated Z′ → t¯t decays, generated with PYTHIA8 and NNPDF2.3LO PDF using the A14 tuning. The truth-labeling strategy to select well-reconstructed top-quark jets requires the two truth top quarks to be well separated with ∆R(t, ¯t) > 2.0. Inclusive top decays are selected by truth-matching the reconstructed top-jet to the generator-level top-quark using ∆R < 0.75. Only contained tops, with all the decay products contained in the large-R jet, are selected by requiring the truth jet to be truth matched also to the W boson with ∆R < 0.75. The ungroomed jet mass is required to be m > 140 GeV and at least one b-quark is required to be ghost-associated to the ungroomed truth jet. The large-R jet is also required to have Split23/1.e3 > exp[3.3 6.98e 04 · − − pT /1.e3]. (7.6) W and Z boson jets are obtained from W ′ → W Z decays, where only hadronically decaying W/Z are considered. The samples are generated with PYTHIA8 and NNPDF2.3LO PDF using the A14 tuning. To select isolated jets, the W and Z bosons are required to have ∆(W, Z) > 2.0. Reconstructed jets are required to be truth matched to the true W/Z bosons using ∆R < 0.75. The ungroomed truth jet mass is required to be above 50 GeV and to pass the following cut on the d12 kt-splitting scale: (cid:112) d12 > 55.25 (cid:20) exp · Input variables − 2.34 10− · GeV 3 (cid:21) pT . (7.7) The DNN inputs include the kinematics of the large-R jet and the kinematics and b-tagging information of the associated VR track-jet, for up to three leading track jets. The flavor tagging information is provided by the raw scores of the DL1r algorithm, which represent , or q/g-jet. The variables describing the the probability of the given track jet to be a b − kinematics of the large-R and track jets originally included the mass, transverse momentum, and (η, ϕ) coordinates, in order to allow the full four-vector reconstruction. In order to remove a potential artificial η-dependence between the true class of the jet and the boost and spin of the simulated resonance, the η variable was removed, without a significant decrease in performance. Having removed the ability to reconstruct the four-momentum of the jet, the ϕ coordinated was also removed. , c − This input information was supplemented with several substructure variables (see Sec. 5.4). These are referred to as high-level variables, as they provide pre-processed information of the low-level inputs, such as tracks or topoclusters. The expectation is that the high-level inputs provide already optimized discrimination power which can aid the classifier, while the 147 performance will improve with respect to using the individual variables thanks to the ability of the network to learn correlations between the large number of inputs. Classifiers using high-level inputs have already been shown to bring an increased performance in the context of b-tagging, with the DL1r algorithm being itself an example. The inputs were selected among an original set of 100 variables, of which the majority were substructure observables useful for one-, two-, and three-prong identification, including N-subjettiness variables and ratios, energy correlation functions (ECFs) with different β values, and their corresponding ratios. In particular, all variables that had already been seen to perform well in the context of top-tagging or W/Z tagging were included [184]. The original set was down-selected by removing variables which did not affect the network performance. This removed redundant information and allowed to keep the size of the training samples manageable. The final reduced list of inputs used for the training is shown in Tab. 7.5. Examples of input variables are shown in Figs. 7.8, ??, ??, and ??. As expected, the most powerful observable is the jet mass, which for a large-R jet originating from a heavy particle has a scale associated to the mass of the particle. (a) (b) (c) Figure 7.8: Subset of input variables to the Merged MCT describing the large-R jet. Pre-processing The list of inputs passed to the NN is fixed by definition. For cases where less than three VR track jets are associated to the large-R jet, the corresponding variables are set to 0. As the input variables have widely different scales and units, standardization was a necessary step to obtain a satisfactory model performance. For each feature x, the mean µ and standard deviation σ were obtained only from the samples in the training dataset. Then, before being passed through the network, every event had its features standardized 148 5075100125150175200Large-Rjetm[GeV]0.000.010.020.030.040.05NormalizedtounityTrueclassqgtWZh100020003000Large-RjetpT[GeV]0.000.000.000.000.000.000.000.000.00NormalizedtounityTrueclassqgtWZh020406080100Ntrk5000.000.020.040.060.08NormalizedtounityTrueclassqgtWZh Type Observable Definition Large radius jet 3 leading track jets pT m N Const N trk500 pT DL1r pb DL1r pc DL1r pu Transverse momentum Mass Constituents multiplicity Tracks multiplicities pT > 500 MeV Transverse momentum Bottom quark probability Charm quark probability Light quark probability Substructure observables τ2 τ3 τ21 τ32 C2 D2 ECF (n = 1, β = 1) ECF (n = 3, β = 1) Angularity Aplanarity PlanarFlow FoxWolfram20 ZCut12 Split12 Split23 N-subjettiness Energy correlation functions Other Table 7.5: Merged MCT input variables by applying the corresponding transformation x′ = (x µ)/σ. − (7.8) Jets corresponding to different classes show different pT distributions. In general, it is desirable to make the network’s decision independent of the pT of the jet. In particular, QCD jets tend to have a lower transverse momentum, which would bias the network to believe that a high pT jet is most likely not a qg-jet and a low pT signal jet to be most likely a qg-jet. In order to remove the dependence of the NN decision on the large-R jet pT , the training samples were reweighted to obtain a flat large-R jet pT distribution. The reweighting was performed for each class separately. In order to have the most accurate reweighting, the pT 149 (a) (b) (c) (d) (e) (f) Figure 7.9: Subset of input variables to the Merged MCT describing the large-R jet sub- structure. distribution was re-binned using the finest binning that allows to retain a statistical error below 5% in each bin. The pT density was then made flat by assigning to each event in a bin i of width b and containing n events the weight w b). Lastly, in order to have a balanced class representation, the samples were reweighted to have an equal class normalization. This adds a constant multiplicative factor wj to the weight of every event belonging to class j. After the reweighting procedure, each jet-event i true labeled, for example, as a Higgs boson is assigned a weight wi = w Flat pT i wHiggs. = 1/(n · Flat pT i · Hyperparameters and training The model was trained using Keras with TensorFlow [197] backend. The number of samples used for training and validation was 9 M and 4 M, respectively. A dataset of 5.5 M was holdout for testing. The architecture used is a fully connected DNN. A dropout layer was inserted between every hidden layer for regularization. The network was trained with the maximum number of epochs set to 500, but early stopping was implemented to interrupt 150 0.00.20.40.60.81.0τ2101234NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0τ320123456NormalizedtounityTrueclassqgtWZh0.00.10.20.30.40.5C2010203040NormalizedtounityTrueclassqgtWZh050000100000150000Split120.00.51.01.52.02.53.03.5Normalizedtounity×10−5TrueclassqgtWZh020000400006000080000Split230.0000000.0000250.0000500.0000750.0001000.0001250.0001500.000175NormalizedtounityTrueclassqgtWZh0.00.10.20.30.40.5ZCut12012345678NormalizedtounityTrueclassqgtWZh (a) (b) (c) (d) (e) (f) Figure 7.10: Subset of input variables to the Merged MCT describing the large-R jet sub- structure. the training when no further reduction in the loss was observed for more than 40 epochs. The hyperparameters were optimized using a grid search and the final choice is shown in Tab. 7.6. The training and validation accuracy of the model was found to be 0.74. Batch size Learning rate Dropout probability Hidden layers Nodes per hidden layer 1000 0.0001 0.1 3 200 Table 7.6: Merged MCT final choice of hyperparameters. 151 0246810D210−410−310−210−1100101102NormalizedtounityTrueclassqgtWZh0.00.51.01.52.02.5ECF(n=3,β=1)×10150.000.000.000.000.00NormalizedtounityTrueclassqgtWZh−0.20.00.20.40.60.81.0FoxWolfram2001234NormalizedtounityTrueclassqgtWZh0.000.020.040.060.080.10Angularity10−410−310−210−1100101102103104NormalizedtounityTrueclassqgtWZh0.00.10.20.30.40.5Aplanarity10−410−310−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0PlanarFlow0.000.501.001.502.002.503.003.504.00NormalizedtounityTrueclassqgtWZh (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 7.11: Subset of input variables to the Merged MCT describing the b-tagging DL1r scores of the three leading track jets inside the large-R jet. 7.8.2 Testing performance Fig. 7.12 shows the output probabilities for all the events in the testing dataset separated by their true class label. The score of the given true class peaks at 1, while the corresponding background classes peak at 0, indicating the MCT is performing as expected. Similarly, the 152 0.00.20.40.60.81.0trkJet1DL1rp(b)10−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet1DL1rp(c)10−310−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet1DL1rp(u)10−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet2DL1rp(b)10−1100101102NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet2DL1rp(c)10−310−210−1100101102NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet2DL1rp(u)10−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet3DL1rp(b)10−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet3DL1rp(c)10−310−210−1100101102NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0trkJet3DL1rp(u)10−1100101102103NormalizedtounityTrueclassqgtWZh plots in Fig. 7.13 show the log-likelihood ratios for different true class combinations, showing significant discrimination power. (a) (b) (c) (d) (e) Figure 7.12: Merged MCT output probabilities tagging on true class label. The confusion matrices for the testing dataset are shown in Fig. 7.14. The events are separated in bins of large-R jet pT . The matrices are highly diagonal with little pT depen- dence, except a small decrease in performance in the lowest pT bin of [200, 250] GeV. The W vs. Z discrimination is the task that causes the most confusion. However, for the purpose of this analysis, only the“vector boson” (V) class, taken as the maximum score between the W and Z scores, was considered, resulting in an average accuracy in the network predictions above 75% for all classes. The ROC (Receiver Operating Characteristic) curves, representing the signal efficiency vs. background rejection, were produced for all signal-background combinations: for a Higgs signal in Fig. 7.15, for a q/g signal in Fig. 7.16, for a top-quark signal in Fig. 7.17, for a W signal in Fig. 7.18, and for a Z signal in Fig. 7.19. Each ROC was built using the output score distribution for the specified signal class of the given true signal and true background events. For each signal-background pair, the ROC is built using events in different pT bins. Similarly 153 0.00.20.40.60.81.0p(h)10−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0p(qg)10−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0p(t)10−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0p(W)10−810−610−410−2100102NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0p(Z)10−810−610−410−2100102NormalizedtounityTrueclassqgtWZh (a) (b) (c) (d) (e) Figure 7.13: Merged MCT output log-likelihood ratios tagging on true class label. to the confusion matrices, only a minor pT dependence is observed, with degradation only in the lowest pT bin. The ROC can also be built using likelihood ratios between the signal and background class. As discussed in the introduction, this results in a better discrimination power with respect to using the raw scores, as shown in Fig. 7.20. 154 −4−2024log(p(h)/p(qg))0.00.10.20.30.40.50.6NormalizedtounityTrueclassqgtWZh−4−2024log(p(h)/p(t))0.00.10.20.30.40.50.60.7NormalizedtounityTrueclassqgtWZh−4−2024log(p(h)/p(V))0.00.10.20.30.40.50.60.70.8NormalizedtounityTrueclassqgtWZh−4−2024log(p(t)/p(qg))0.00.10.20.30.40.50.60.70.8NormalizedtounityTrueclassqgtWZh−4−2024log(p(V)/p(qg))0.00.10.20.30.40.50.60.70.8NormalizedtounityTrueclassqgtWZh (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) Figure 7.14: Merged MCT confusion matrices as a function of pT of the large-R jet. 155 qgtWZhPredictedLabelqgtWZhTrueLabel0.770.020.120.050.040.120.420.190.080.180.140.010.730.110.020.100.020.370.350.170.050.050.040.080.79TestpTbin:200-250GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.740.040.110.070.040.040.800.040.030.090.110.020.730.120.010.100.020.340.410.130.030.050.020.090.81TestpTbin:250-300GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.730.060.100.070.040.040.860.020.010.060.110.020.730.130.010.090.030.330.450.110.040.050.020.090.79TestpTbin:300-350GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.730.060.100.060.040.050.870.020.010.060.100.030.740.110.010.090.030.330.450.100.040.060.020.100.79TestpTbin:350-400GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.740.060.100.060.040.060.860.010.010.060.100.030.740.120.010.080.040.300.480.100.040.050.020.090.80TestpTbin:400-450GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.740.070.090.060.040.060.860.020.010.060.090.030.750.120.010.070.030.290.510.090.040.050.020.100.79TestpTbin:450-500GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.750.070.080.060.040.060.860.020.010.050.080.030.750.130.010.070.030.270.540.090.040.050.020.100.79TestpTbin:500-600GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.750.080.080.050.040.060.860.020.010.050.080.030.750.130.010.060.030.260.560.080.040.040.030.110.79TestpTbin:600-800GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.760.080.080.050.030.060.860.020.010.050.070.020.750.140.010.060.030.270.560.080.040.040.030.110.78TestpTbin:800-1000GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.760.080.080.050.030.070.860.010.010.040.070.020.720.180.020.060.020.280.560.080.040.030.040.110.78TestpTbin:1000-2000GeV0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.740.110.070.050.040.070.860.010.010.040.060.010.650.240.040.060.010.310.520.090.040.030.040.110.78TestpTbin:2000-3500GeV0.00.20.40.60.81.0 (a) (b) (c) (d) Figure 7.15: Merged MCT ROC curves built using the output score p(h), taking the Higgs class as signal and each of the remaining classes as background. The ROCs are shown as a function of pT of the large-R jet. 156 0.20.40.60.8)sig˛Higgs efficiency (10210310410510610)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Higgs efficiency (10210310410)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Higgs efficiency (10210310410510)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Higgs efficiency (10210310410510)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-600 (a) (b) (c) (d) Figure 7.16: Merged MCT ROC curves built using the output score p(q/g), taking the q/g class as signal and each of the remaining classes as background. The ROCs are shown as a function of pT of the large-R jet. 157 0.20.40.60.8)sig˛Multi-jet efficiency (10210310410510610)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Multi-jet efficiency (10210310410510)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Multi-jet efficiency (10210310410510610)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Multi-jet efficiency (10210310410510610)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-600 (a) (b) (c) (d) Figure 7.17: Merged MCT ROC curves built using the output score p(t), taking the top class as signal and each of the remaining classes as background. The ROCs are shown as a function of pT of the large-R jet. 158 0.20.40.60.8)sig˛top efficiency (10210310410510)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.81)sig˛top efficiency (10210310410510610)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛top efficiency (10210310410510)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛top efficiency (10210310410510)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-600 (a) (b) (c) (d) Figure 7.18: Merged MCT ROC curves built using the output score p(W ), taking the W class as signal and each of the remaining classes as background. The ROCs are shown as a function of pT of the large-R jet. 159 0.20.40.60.8)sig˛W efficiency (10210310410510)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛W efficiency (10210310410510)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛W efficiency (10210310410)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛W efficiency (10210310410)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-600 (a) (b) (c) (d) Figure 7.19: Merged MCT ROC curves built using the output score p(Z), taking the Z class as signal and each of the remaining classes as background. The ROCs are shown as a function of pT of the large-R jet. 160 0.20.40.60.8)sig˛Z efficiency (10210310410)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Z efficiency (10210310410510)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Z efficiency (10210310410)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-6000.20.40.60.8)sig˛Z efficiency (10210310410)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sampleTLarge-R jet p200-250250-300300-350350-400400-450450-500500-600 (a) (b) (c) (d) Figure 7.20: Merged MCT ROC curves for Higgs signal class. Comparison of performance when using as discriminant the output score of the signal class vs. using the log-likelihood ratio of signal and background score. 161 0.20.40.60.8)sig˛Higgs efficiency (10210310410510610)bkg˛Multi-jet rejection (1/ = 13 TeVs = [250, 3500] GeV TLarge-R jet pTruth matched sampleDiscriminantMCT score hlog( h / qg )0.20.40.60.8)sig˛Higgs efficiency (10210310410510610710)bkg˛Top rejection (1/ = 13 TeVs = [250, 3500] GeV TLarge-R jet pTruth matched sampleDiscriminantMCT score hlog( h / t )0.20.40.60.8)sig˛Higgs efficiency (210410610810)bkg˛W rejection (1/ = 13 TeVs = [250, 3500] GeV TLarge-R jet pTruth matched sampleDiscriminantMCT score hlog( h / W )0.20.40.60.8)sig˛Higgs efficiency (10210310410510610)bkg˛Z rejection (1/ = 13 TeVs = [250, 3500] GeV TLarge-R jet pTruth matched sampleDiscriminantMCT score hlog( h / Z ) 7.9 Resolved jets MCT The resolved MCT was developed to classify the hadronic decay in the resolved regime, where the relevant objects are small-R jets. The development followed closely what was done for the merged MCT. 7.9.1 Training Jet reconstruction and selection The small-R jet collection is the same as the one used in the analysis: R = 0.4 jets built by < 2.5 and to running anti-kt on PFlow inputs. All jets are required to be in the region have pT > 20 GeV, with the leading jet required to have pT > 45 GeV. η | | MC samples and truth labeling The resolved event topology is more dependent on the generating process. For this reason, the samples used for training were a subset of the Monte Carlo samples used in the analysis, as shown in Tab. 7.7. The signal classes were obtained from the respective signal samples: HVT- VH and ggA were used as sources of Higgs boson decays; HVT-VV, radion, and graviton as sources for the W and Z boson classes. The t¯t events were used as sources of top-quark decays, and the V+jets samples as sources of events with light quarks and gluons. Class Light quarks and gluons Top quark W boson Z boson Higgs boson Process V+jets t¯t HVT V’ → HVT V’ WW/WZ (W WZ (Z qq), Graviton-WW, Radion-WW → qq), Graviton-ZZ, Radion-ZZ → → HVT V’ VH, ggA → Table 7.7: MC samples used to select the training events for the Resolved MCT. Except for the QCD sample, all training samples were truth matched by first matching the truth particle to the closest truth jet, and then matching the truth jet to the closest reconstructed small-R jet, using dR = 0.35. In the case of the Higgs, W, and Z signal samples, the training events were required to have both daughters of the truth boson to be truth matched to two of the three leading jets. This removed events where one of the truth quarks was outside the η acceptance region, as well as cases of “super merged” boson decays, where the truth quarks overlap. For events with top quarks, the three leading jets 162 were required to be truth matched to the three decay products from the top quark. This was done to remove possible noise from a partial reconstruction of the top decay, similarly to what was done for the merged MCT by accepting only contained tops. In order to train on events similar to the ones passing the analysis pre-selection, the training samples were further required to pass the trigger selection for the given lepton channel, as well as to have at least two signal jets. The leading jet was required to have pT > 45 GeV and η < 2.5, while the second leading jet was required to have pT > 20 GeV and η < 2.5. In addition, if the third leading jet was found to have pT < 20 GeV or η > 2.5, since this jet would not pass the analysis selection for small-R jets, the corresponding input variables were set to 0. Lastly, in order to focus on the kinematic region of interest for the resolved regime, only events where the sum of the pT of the two leading jets was below 500 GeV was considered for training. Input variables In the resolved regime, true Higgs, W, and Z boson decays are reconstructed using two small-R jets, which usually are the leading jets in the event. Top decays produce instead three small-R jets. For this reason, the inputs to the DNN were chosen to describe the three leading small-R jets in the event: kinematic and b-tagging information, as well as some reconstructed variables, as shown in Tab. 7.8. In particular, the inputs include the dR between any possible pair of the three leading jets and the mass of the reconstructed object from any two pairs of jets and from all three jets. The distributions of the input variables for the signal samples were shown to be lepton-channel independent, which motivated the choice to train lepton-channel agnostically. Examples of distributions of input variables for the five true classes are shown in Figs. 7.22 and 7.21. Pre-processing Because of the much larger number of V+jets and t¯t Monte Carlo events with respect to signal events, the background classes were down-sampled to have a similar number of events as the signal classes per pT bin. Then, similarly to the Merged MCT, the training events were re-weighted to have a per-class flat distribution of the sum of the pT of the two leading jets. The samples were then re-weighted to have an equal class normalization. Hyperparameters and training The model was trained using Keras with TensorFlow [197] backend. The number of samples used for training and validation was 1.6 M and 411 K, respectively. A dataset of 686 K was holdout for testing. The architecture used was a fully connected DNN. A dropout layer 163 Type Observable Definition Transverse momentum Pseudorapidity Azimuthal angle Mass Bottom quark probability Charm quark probability Light quark probability 3 leading small-R jets Masses of reconstructed objects Angular separations pT η ϕ m DL1r pb DL1r pc DL1r pu mJ1+J2 mJ1+J3 mJ2+J3 mJ1+J2+J3 ∆RJ1,J2 ∆RJ1,J3 ∆RJ2,J3 Table 7.8: Resolved MCT input variables describing the three leading small-R jets. was inserted between every hidden layer for regularization. The network was trained with the maximum number of epochs set to 1000, with early stopping implemented to stop the training when no further reduction in the loss was observed for more than 40 epochs. The hyperparameters were optimized using a grid search and the final choice is shown in Tab. 7.9. The training and validation accuracy of the model was found to be 0.72. Batch size Learning rate Dropout probability Hidden layers Nodes per hidden layer 1000 0.0001 0.3 3 300 Table 7.9: Resolved MCT final choice of hyperparameters. 7.9.2 Testing performance The model performance was evaluated on the testing dataset. Fig. 7.23 shows the output probabilities for all the events in the testing dataset separated by their true class label. The score of the given true class peaks at 1, while the other classes peak at 0, as desired. Similarly, Fig. 7.24 shows the log-likelihood ratios for different class combinations, where the 164 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 7.21: Subset of input variables for the Resolved MCT tagged according to the true class representing the kinematic variables of the leading (top) and 2nd leading (middle) jets, and the b-tagging scores of the first leading jet (bottom). p(V ) score is taken as max(p(W ), p(Z)). The output probabilities show some uncertainty in the W and Z predictions. However, this is mostly resolved when looking at the likelihood ratios, when uncertainty about the other classes is taken into account. A confusion remains for a subset of events between the Higgs and V classification, which will be explained in the 165 100200300400500LeadingjetpT[GeV]0.0000.0010.0020.0030.0040.0050.0060.0070.008NormalizedtounityTrueclassqgtWZh020406080100120Leadingjetm[GeV]0.000.010.020.030.040.050.060.070.08NormalizedtounityTrueclassqgtWZh−2−1012Leadingjetη0.00.10.20.30.40.50.6NormalizedtounityTrueclassqgtWZh501001502002502ndLeadingjetpT[GeV]0.00000.00250.00500.00750.01000.01250.01500.01750.0200NormalizedtounityTrueclassqgtWZh02040602ndLeadingjetm[GeV]0.000.020.040.060.080.100.120.140.16NormalizedtounityTrueclassqgtWZh−2−10122ndLeadingjetη0.00.10.20.30.40.5NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0LeadingjetDL1rp(b)10−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0LeadingjetDL1rp(c)10−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0LeadingjetDL1rp(u)10−410−310−210−1100101102103NormalizedtounityTrueclassqgtWZh (a) (b) (c) (d) (e) (f) Figure 7.22: Subset of input variables for the Resolved MCT tagged according to the true class representing the mass and dR distances of reconstructed objects. (g) following. The confusion matrices are shown in Fig. 7.25. The events are separated in bins of the sum of the pT of the two leading small-R jets. The matrices are highly diagonal with little pT dependence, except a small decrease in performance in the two lowest pT bins. The Z class is the one that suffers the most from the confusion with both the W and the Higgs 166 123456dRj1,j2[GeV]01234NormalizedtounityTrueclassqgtWZh123456dRj1,j3[GeV]0.00.20.40.60.81.01.2NormalizedtounityTrueclassqgtWZh123456dRj2,j3[GeV]0.00.10.20.30.40.50.60.7NormalizedtounityTrueclassqgtWZh0100200300400500mj1+j2[GeV]0.000.010.020.030.040.05NormalizedtounityTrueclassqgtWZh0100200300400500mj1+j3[GeV]0.00000.00250.00500.00750.01000.01250.01500.01750.0200NormalizedtounityTrueclassqgtWZh0100200300400500mj2+j3[GeV]0.00000.00250.00500.00750.01000.01250.01500.01750.0200NormalizedtounityTrueclassqgtWZh02004006008001000mj1+j2+j3[GeV]0.00000.00250.00500.00750.01000.01250.01500.01750.0200NormalizedtounityTrueclassqgtWZh (a) (b) (c) (d) (e) Figure 7.23: Resolved MCT output probabilities tagging on true class label. class. However, part of this confusion is resolved by considering only the “vector boson” (V) class, taken as the maximum score between the W and Z scores. The resulting average accuracy in the network predictions is above 75% for all classes. The confusion matrix for true Higgs, W, and Z events was further investigated by sepa- rating the events by true sample of origin, by pT bin and by number of b-tagged three leading small-R jets, as shown in Fig. 7.26. A dependence on the number of b-tags is observed and is expected, as a W boson should in principle only populate the 0 b-tag region, a Z boson hadronically decays to two b-quarks 15% of the times, and a Higgs boson hadronically decays to two b-quarks 95% of the times. The ROC curves, representing the signal efficiency vs. background rejection, were pro- duced for all signal-background combinations: for a Higgs signal in Fig. 7.27, for a q/g signal in Fig. 7.28, for a top-quark signal in Fig. 7.29, for a W signal in Fig. 7.30, and for a Z signal in Fig. 7.31. Each ROC was built using the output score distribution for the specified signal class of the given true signal and true background events. For each signal-background pair, the ROC is built using events in different pT bins. The greatest pT dependence is observed for the q/g class and the greatest degradation on performance occurs for the lowest pT bin. 167 0.00.20.40.60.81.0p(h)10−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0p(qg)10−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.81.0p(t)10−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.8p(W)10−410−310−210−1100101102103NormalizedtounityTrueclassqgtWZh0.00.20.40.60.8p(Z)10−410−310−210−1100101102103NormalizedtounityTrueclassqgtWZh (a) (b) (c) Figure 7.24: Resolved MCT output log-likelihood ratios tagging on true class label. (d) (e) 168 −4−2024log(p(h)/p(qg))0.00.10.20.30.40.50.60.70.8NormalizedtounityTrueclassqgtWZh−4−2024log(p(h)/p(t))0.00.10.20.30.40.50.6NormalizedtounityTrueclassqgtWZh−4−2024log(p(h)/p(V))0.00.20.40.60.8NormalizedtounityTrueclassqgtWZh−4−2024log(p(t)/p(qg))0.00.10.20.30.40.5NormalizedtounityTrueclassqgtWZh−4−2024log(p(V)/p(qg))0.00.20.40.60.8NormalizedtounityTrueclassqgtWZh (a) (b) (c) (d) (e) (f) (g) (h) Figure 7.25: Resolved MCT confusion matrices as a function of the sum of the pT of the two leading small-R jets. 169 qgtWZhPredictedLabelqgtWZhTrueLabel0.570.040.180.130.090.070.760.050.040.080.120.050.660.140.030.130.040.310.360.170.090.050.010.050.81TestpTbin:65-100GeV,In-training0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.640.050.150.090.070.030.870.040.020.050.070.060.670.170.030.110.070.370.330.130.050.080.030.030.82TestpTbin:100-150GeV,In-training0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.730.050.110.070.050.030.870.030.020.040.070.050.640.200.040.070.060.350.390.130.040.070.030.050.82TestpTbin:150-200GeV,In-training0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.820.050.060.040.030.040.870.030.020.040.040.030.690.210.020.040.040.380.440.100.020.050.020.080.84TestpTbin:250-300GeV,In-training0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.840.050.050.040.020.040.890.020.020.030.040.030.690.220.020.040.030.360.490.080.020.040.010.080.85TestpTbin:300-350GeV,In-training0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.850.050.050.040.020.040.900.020.020.030.030.030.660.260.020.030.030.340.530.070.020.040.010.090.84TestpTbin:350-400GeV,In-training0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.860.050.050.030.010.040.910.010.010.030.030.020.610.310.020.030.020.290.590.070.010.040.010.090.85TestpTbin:400-450GeV,In-training0.00.20.40.60.81.0qgtWZhPredictedLabelqgtWZhTrueLabel0.860.050.050.030.010.040.920.010.010.020.030.020.640.280.030.040.020.310.570.070.010.030.010.080.87TestpTbin:450-500GeV,In-training0.00.20.40.60.81.0 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 7.26: Resolved MCT confusion matrices separated by true sample of origin and number of b-tags among the three leading small-R jets, in different bins of the sum of the pT of the two leading small-R jets. 170 qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.190.120.090.240.370.120.070.150.280.380.040.020.790.160.000.040.020.610.320.010.060.030.630.280.000.070.030.340.550.010.040.030.660.260.010.050.030.380.530.01TestpTbin:250-300GeV,0b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.050.170.020.060.700.020.140.020.080.740.040.150.620.130.060.040.160.360.260.190.060.170.440.210.120.050.180.160.350.260.030.180.440.220.130.040.170.140.370.27TestpTbin:250-300GeV,1b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.000.050.000.060.890.000.020.000.080.900.000.630.110.050.210.000.030.010.490.470.000.070.010.470.440.010.030.000.470.480.010.050.010.540.390.000.020.000.540.44TestpTbin:250-300GeV,2b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.140.110.090.260.400.130.060.090.220.510.030.010.790.170.000.030.010.580.380.010.050.020.590.320.010.050.020.290.620.010.030.020.570.370.010.040.020.290.640.01TestpTbin:350-400GeV,0b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.030.130.010.090.740.020.100.020.080.790.030.100.650.170.050.020.120.350.360.150.040.130.410.290.120.030.110.160.510.200.030.120.450.280.130.020.140.170.440.22TestpTbin:350-400GeV,1b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.000.030.000.090.870.000.020.000.090.900.050.140.290.430.100.000.020.000.690.290.000.040.020.660.280.000.020.000.670.310.010.020.010.590.370.000.030.000.620.35TestpTbin:350-400GeV,2b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.140.090.110.220.440.070.030.090.240.560.020.010.780.190.000.020.010.480.480.010.060.020.550.350.010.060.020.290.620.010.040.030.550.370.010.050.020.310.610.01TestpTbin:450-500GeV,0b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.030.090.020.100.750.010.060.020.070.850.030.060.700.160.050.010.050.410.370.150.040.060.450.310.130.040.070.210.480.190.020.090.440.300.130.040.080.180.510.19TestpTbin:450-500GeV,1b-tags0.00.20.40.60.81.0qgtWZhPredictedlabelggA-hHVT-hHVT-WHVT-ZRadion-WRadion-ZRSG-WRSG-ZTruesamplelabel0.000.020.000.080.890.000.010.000.060.920.060.120.250.440.120.010.040.020.670.270.010.010.050.630.300.010.010.010.670.300.000.030.030.640.290.000.010.010.730.24TestpTbin:450-500GeV,2b-tags0.00.20.40.60.81.0 (a) (b) (c) (d) Figure 7.27: Resolved MCT ROC curves built using the output score p(h), taking the h class as signal and each of the remaining classes as background. The ROCs are shown as a function of the sum of the pT of the two leading small-R jets. 171 0.20.40.60.81)sig˛Higgs efficiency (10210310410510)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.81)sig˛Higgs efficiency (10210310410510)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.81)sig˛Higgs efficiency (10210310410510)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛Higgs efficiency (10210310410)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score hTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-400 (a) (b) (c) (d) Figure 7.28: Resolved MCT ROC curves built using the output score p(q/g), taking the q/g class as signal and each of the remaining classes as background. The ROCs are shown as a function of the sum of the pT of the two leading small-R jets. 172 0.20.40.60.8)sig˛Multi-jet efficiency (10210310410)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛Multi-jet efficiency (10210310410)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛Multi-jet efficiency (10210310410)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛Multi-jet efficiency (10210310410)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score qgTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-400 (a) (b) (c) (d) Figure 7.29: Resolved MCT ROC curves built using the output score p(t), taking the top class as signal and each of the remaining classes as background. The ROCs are shown as a function of the sum of the pT of the two leading small-R jets. 173 0.20.40.60.81)sig˛top efficiency (10210310410510)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.81)sig˛top efficiency (10210310410510)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.81)sig˛top efficiency (10210310410510)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.81)sig˛top efficiency (10210310410)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score tTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-400 (a) (b) (c) (d) Figure 7.30: Resolved MCT ROC curves built using the output score p(W ), taking the W class as signal and each of the remaining classes as background. The ROCs are shown as a function of the sum of the pT of the two leading small-R jets. 174 0.20.40.60.81)sig˛W efficiency (10210310410510)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛W efficiency (10210310410)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.81)sig˛W efficiency (10210310410510)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛W efficiency (10210310410)bkg˛Z rejection (1/ = 13 TeVsDiscriminant: DNN score WTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-400 (a) (b) (c) (d) Figure 7.31: Resolved MCT ROC curves built using the output score p(Z), taking the Z class as signal and each of the remaining classes as background. The ROCs are shown as a function of the sum of the pT of the two leading small-R jets. 175 0.20.40.60.8)sig˛Z efficiency (10210310410)bkg˛Higgs rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛Z efficiency (10210310410)bkg˛Multi-jet rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛Z efficiency (10210310410)bkg˛top rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-4000.20.40.60.8)sig˛Z efficiency (10210310410)bkg˛W rejection (1/ = 13 TeVsDiscriminant: DNN score ZTruth matched sample [GeV]2jT + p1jTp65-100100-150150-200200-250250-300300-350350-400 7.10 MCT deployment in the analysis The VV and VH final regions have to be made orthogonal in order to perform a combined statistical fit for the HVT interpretation. The events are sorted in orthogonal regions using the two Multi-Class Tagger neural networks described in the previous sections. This strategy differs from what was done in previous combination efforts and ultimately results in a higher search sensitivity. This section discusses the motivation, development, and results of this new deep-learning-based strategy. 7.10.1 Motivation The search for a new spin-1 HVT boson (V ′) is performed in both the VV and VH channels, as a new W ′ can decay both to W h and W Z, and a new Z′ can decay to Zh and W W . In order to exploit the complementarity of the different searches, analyses assuming the same underlying model can be combined to provide more stringent limits on the model parameters and increase the statistical power of the search. However, before performing the statistical combination, one has to ensure orthogonality of the signal regions going into the fit. The main categories used to define the final regions are given by the lepton channel and by the reconstruction strategy of the hadronic decay. While in a given analysis different lepton channels are orthogonal by construction, the resolved and merged categories are not. As explained in Sec. 7.7, the resolved and merged reconstruction strategies are used to maximize the efficiency in low- and high-boost scenarios, where the hadronic decay is better reconstructed as two resolved small-R jets (jj) or as a single large-R jet (J), respectively. However, for a subset of events, both reconstruction strategies provide equivalent efficiencies and, within a given analysis, it is possible for an event to end up in both resolved and merged final regions. In these cases, a choice has to be made on which final region the event should go into, a decision called prioritization. As already discussed, these are the PriorityResolved and PriorityMerged strategies for the VH and VV analysis, respectively. After prioritization is enforced, the final regions within a given analysis are fully orthogonal. In a given lepton channel, the VV and VH SRs are not orthogonal a priori, because the jet mass windows overlap. The definitions of the mass windows were discussed in Sec. 7.6.1 and are summarized in Tab. 7.10. Recall that the VV analysis uses the pT -dependent WZTagger mass cut, where the upper Z (W) mass-cut is approximately in the range [94, 115] GeV ([106, 130] GeV). This overlap can be understood schematically as shown in Fig. 7.32. The x-axis shows the resolved mass window selections on m(jj), while the y-axis shows the selections on the large-R jet mass m(J). Note that this is approximate, as the jj di-jet 176 system is not necessarily identical between the W/Z candidate and the H candidate. All the events in the shaded regions (A, B, and C) can potentially enter both VV and VH SRs. The grey shaded regions (C) correspond to regions where the overlap is in the same kinematic region for VV and VH, while the red-saded regions (A and B) represent regions of possible mixed-overlap, where an event enters either both VH-SR-Res and VV-SR-Merg, or both VH-SR-Merg and VV-SR-Res. Analysis Channel Resolved Merged 0-lep 1-lep 2-lep W Z VH 75 ≤ m(jj) 145 ≤ 75 ≤ m(J) 145 ≤ 100 68 78 m(jj) m(jj) m(jj) 145 98 106 VV ≤ ≤ ≤ ≤ ≤ ≤ Table 7.10: Mass window definitions in VV and VH signal regions. All numbers are in units of GeV. In the VH analysis the cuts are assigned per lepton channel, while in VV they are given according to whether the final region is looking for a hadronically decaying W or Z boson. The VV m(J) window is defined using a pT -dependent cut provided by the WZTagger and shown in Fig. 7.6. Pass WZTagger WMassCut Pass WZTagger ZMassCut Figure 7.32: Schematic visualization of VV and VH resolved (x-axis) and merged (y-axis) mass windows overlap. See text for explanation. The VV and VH semi-leptonic analyses were part of previous combination efforts [175, 176] interpreted in the context of the HVT framework. In these publications, the analyses 177 68106m(jj)1456475106145m(J)100VH Res SR (Priority)VV Res SR (Secondary)VH Merg SR (Secondary)VV Merg SR (Priority)(A)(B)(C) were combined after having been optimized as standalone searches. Therefore, the orthog- onality condition between the SRs had to be imposed a posteriori. The best compromise was found to be rejecting the VV mass window in VH. This meant retaining 100% of the events in the VV SRs, at the expense of losing some events in the VH SRs. The idea being that most of the events lost in VH would end up in the VV SRs and therefore would still contribute to the combination. While this was found to be the best strategy, it is not fully efficient and resulted in a loss of sensitivity in VH at high mass, as will be shown in the following studies. Moreover, because the orthogonality cuts are applied a posteriori, some events can still be lost: an event that does not enter the VV SRs, but is within the VV mass window, will be removed from the VH analysis. Additionally, events that end up in mixed regions, do not get sorted exclusively. Considering only events in the overlap region and referring to Fig. 7.32, the effect of the mass cut used in the previous combination is the following: • Events in the shaded gray area (C) always migrate from VH to VV. • The events in the shaded red regions (A, B) remain shared between VH and VV. The latter case was tolerated because deemed negligible. However, it is still not desirable, particularly for region A where events are in the priority regions of both analyses. The number of events in the inclusive overlap region and mixed-overlap regions only, for the 36.1fb− 1 mc16a dataset is shown in Tab. 7.11 for the 2-lepton channel. Total Any SR VH SR’s VV SR’s Overlap VH & VV SR % of total % of any SR Res-VH & Merg-VV % of overlap Merg-VH & Res-VV % of overlap data 8546693 – – – 412 0.01 – 74 18.00 29 7.04 HVT-WZ HVT-ZH 287777 102940 97235 12892 7187 2.50 7.00 1057 14.71 414 5.76 326257 145928 7856 145057 6985 2.14 4.79 150 0.91 64 2.15 ttbar 24496926 57031 54612 2639 220 0.00 0.39 50 22.73 1 0.45 Wjets 764373 64 26 40 2 0.00 3.12 0 0.00 0 0.00 Zjets 39371912 1376956 814163 581859 19066 0.05 1.38 3396 17.81 1689 8.86 Table 7.11: Number of events in the 2-lepton channel for data, HVT signals, and the most important background processes. The data counts in the signal regions are not shown because the analysis was still blinded. The number of events that enter the VV and VH signal regions can be compared to the event counts in the inclusive overlap region, as well as in the mixed- overlap regions. 178 In this publication for the first time the VV and VH processes were considered in the same analysis, making it possible to implement a recycling strategy so that no event is lost and the mixed-regions can be taken care of properly. Moreover, the harmonization of the two analyses into a single effort opened up the possibility for a more efficient event categorization into the respective VV and VH signal regions. In this analysis a new orthogonalization strategy that makes use of the output scores of the MCTs was proposed. In fact, it was shown that the loss in sensitivity from the mass cut strategy was mostly due to events in the gray shaded regions, so that most of the recovering of the sensitivity will be due to the MCT. 7.10.2 Studies overview 1 (referred to as mc16a) to The studies presented here use the 2016 dataset with 36.1 fb− reduce the processing time, but it can be considered representative of the full Run 2 dataset. For these optimization studies only the HVT signal samples with DY production was used, as shown in Tab. 7.12, with the corresponding signal regions, shown in Tab. 7.13. Note that the 0-lepton channel of the VV analysis does not have a resolved signal region. 0-lep 1-lep 2-lep VH HVT Z’ VV HVT W’ → → ZH HVT W’ WZ HVT W’ WH HVT Z’ WZ HVT W’ → → → → ZH WZ Table 7.12: Signal samples used in the orthogonality studies. 0 Lepton 1 Lepton 2 Lepton VV Res - VH Res VH Merg VV Merg Merg HP GGF WZ SR Merg LP GGF WZ SR Res SR 1b Merg SR 1b0add Res SR 2b Merg SR 2b0add Res SR 1b Merg SR 1b0add Res GGF WZ SR 01b Merg HP GGF WZ SR 01b Res SR 2b Merg SR 2b0add Res GGF WZ SR 2b Merg HP GGF WZ SR 2b Merg LP GGF WZ SR 01b Merg LP GGF WZ SR 2b Merg HP GGF WZ SR Merg LP GGF WZ SR Res SR 1b Merg SR 1b0add Res SR 2b Merg SR 2b0add Res GGF WZ SR Table 7.13: VV and VH HVT signal regions (SRs) used in the orthogonality studies. An event is in a VV or VH SR, if it enters any SR in the corresponding column. The following region definitions will also be used throughout the studies: • VH-SR: an event that enters any HVT-VH SR (columns “VH Res” and “VH Merg” in Tab. 7.13). • VV-SR: an event that enters any HVT-VV SR (columns “VV Res” and “VV Merg” in Tab. 7.13). 179 • Overlap region: an event that enters both VV-SR and VH-SR. • Mixed-Overlap region: an event that enters the overlap region with VH-SR-Res and VV-SR-Merg, or VH-SR-Merg and VV-SR-Res. 7.10.3 MCT strategy The new proposed orthogonalization strategy, which will be referred to as MCT strategy, uses the p(h) and p(V ) scores of the resolved and merged MCTs to categorize the events into the VV and VH signal regions. This can be done in two ways: 1) using the MCT scores directly, before any prioritization is enforced; 2) first applying each analysis’ own resolved versus merged prioritization strategy, and then use the MCT to choose the final region. In particular, for the latter case all possible combinations of Both options were studied. prioritization strategies were reconsidered. The best option was found to be retaining the current prioritization strategy and then apply the MCT selection. In practice, the procedure to orthogonalize is the following: • Run analysis event selection to find active signal regions • Apply prioritization strategy (PriorityResolved for VH and PriorityMerged for VV) • Set MCT p(h) score to 0 if event is not in VH-SR, according to Tab. 7.13 • Set MCT p(V ) score to 0 if event is not in VV-SR, according to Tab. 7.13 • Take pmax = max(p(h), p(V )). – If pmax = p(h), turn the VV signal region off. – If pmax = p(V ), turn the VH signal region off. The orthogonalization strategy is optimized with the goal of deviating as little as possible from the sensitivity of the baseline analyses, where no orthogonality is yet imposed. The following strategies will be compared: • Baseline: no orthogonality. • MCT : use MCT strategy. • MassCut: reject the VV mass window in VH. 180 Note that the MassCut strategy is applied only to events that are in the overlap region. This removes possible inefficiencies due to a loss of events from applying the cut a posteriori. The effect of the MCT and MassCut strategy is compared in Tab. 7.14, which shows the percentage of events in the overlap region that are assigned to the VH and VV analysis using the MCT or the Mass sorting strategy. Note that, with the MCT strategy the sorting is always an OR between the VV and VH final regions, so the percentages always add up to 100%. On the other hand, the mass cut strategy cannot orthogonalize cases of Mixed- Overlap. Since an event that enters a VV SR is always sorted into VV by construction, the VH percentage gives the number of events that are still shared. In the following sections the two strategies will be compared in terms of signal efficiency as a function of jet transverse momentum 7.10.4, signal significance as a function of heavy resonance mass 7.10.5, and expected limit sensitivity 7.10.6. 0 Lepton channel MCT Mass VH(%) VV(%) VH(%) VV(%) MCT Mass VH(%) VV(%) VH(%) VV(%) MCT Mass VH(%) VV(%) VH(%) VV(%) data HVT-WZ HVT-WW HVT-ZH HVT-WH ttbar Wjets Zjets 80.34 65.52 19.66 34.48 5.73 10.87 100. 100. 21.55 78.45 1.30 100. 75.35 24.65 7.07 100. 55.01 44.99 18.91 100. 76.95 23.05 4.28 100. – – – – – – – – 1 Lepton channel data HVT-WZ HVT-WW HVT-ZH HVT-WH ttbar Wjets Zjets 86.02 83.69 13.98 16.31 14.85 19.04 100. 100. 57.49 42.51 1.68 100. 83.13 16.87 13.47 100. 84.55 15.45 18.58 – 89.17 10.83 10.44 100. 22.00 78.00 1.78 100. – – – – 2 Lepton channel data HVT-WZ HVT-WW HVT-ZH HVT-WH ttbar Wjets Zjets 76.30 67.23 23.70 32.77 20.72 21.12 100. 100. 21.89 78.11 2.49 100. 82.43 17.57 17.87 100. 74.55 25.45 17.27 100. 100. 0.00 0.00 100. – – – – – – – – Table 7.14: Percentage of events in overlap region that end up in VH or VV analysis using the MCT or Mass sorting strategy. 7.10.4 Signal efficiency The effect of the orthogonality cut on the signal efficiency is compared for the MCT and MassCut strategies. This is shown for the 2-lepton channel in Figs. 7.33 and 7.34, for 181 the merged and resolved regions respectively. The 0- and 1-lepton channels showed similar behaviors. R R is given by the ratio of the number of signal events in The events are grouped into one of four categories – resolved or merged, and VV or VH – depending on which signal region they enter, according to Tab. 7.13. The signal efficiency ϵS of a signal S in the region R . The efficiency that pass the orthogonality cut to the total number of signal events in is evaluated in bins of pT of the reconstructed hadronic decay to separate the events into decays that are kinematically similar. In the merged regions the pT corresponds to the pT of the large-R jet, while in the resolved regions is taken as the scalar sum of the pT of the two leading small-R jets. In blue are the efficiencies of the HVT-VH signal, in red of the HVT-VV signal. The dark hue represents the MCT strategy, while the light hue follows the MassCut strategy. Note that for the former, the histograms are exclusive, e.g. an event cannot enter more than one histogram, while this is not necessarily true for the MassCut strategy due to the mixed-overlap-region. The ideal cut would leave 100% of VH signal in VH SRs, and remove 100% VH signal from VV SRs, and vice versa. In the resolved SR the two strategies remove the same amount of “wrong” signal and leave most of the “correct” signal. In the merged SRs, the MassCut strategy removes most of the VV signal from VH SRs, but also a significant portion of VH signal. On the other hand, the MCT strategy does a more efficient sorting, leaving most of the correct signal in both VV and VH signal regions. This behavior is observed for all lepton channels, making the MCT strategy a more efficient event categorization strategy. 7.10.5 Signal significance Selection criteria are often optimized with respect to the expected significance S of a given signal hypothesis. The concept of the significance was discussed in Sec.6.3. In these studies, an approximation is used, where S is estimated as the number of standard deviations of the background distribution to which the signal corresponds. Consider n events where n = nb + ns. Here nb is the total number of MC events from known SM processes and ns is the number of MC generated signal events. The quantity nb is assumed to be known with an uncertainty σn, which in the following is just the statistical uncertainty in a given bin. The random variable n is assumed to be Poisson distributed, with Poisson error given by √n. The significance S is then calculated as, Si = (cid:113) ns nb + σ2 b . (7.9) 182 (a) (b) Figure 7.33: Efficiency of HVT-VH and HVT-VV signals as a function of pT of the large-R jet in merged signal regions (SRs). The events are grouped according to whether they pass a given selection, according to Tab. 7.13, into HVT-VH Merg SR (left) and HVT-VV Merg SR (right). (a) (b) Figure 7.34: Efficiency of HVT-VH and HVT-VV signals as a function of the scalar sum of the pT of the two leading small-R jets in resolved SRs. The events are grouped according to whether they pass a given selection, according to Tab. 7.13, into HVT-VH Res SR (left) and HVT-VV Res SR (right). When the data is binned, each bin i contains ni events, and a significance Si can be calculated for each bin. The total binned significance of a histogram is then obtained as, = S (cid:115)(cid:88) i 2 i . S 183 (7.10) 30010002000 [GeV]TFat jet p0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VH Merg-SRHVT-VH MCTCutHVT-VH MassCutHVT-VV MCTCutHVT-VV MassCut30010002000 [GeV]TFat jet p0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VV Merg-SRHVT-VH MCTCutHVT-VH MassCutHVT-VV MCTCutHVT-VV MassCut100200300400500 [GeV]2jT + p1jTp0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VH Res-SRHVT-VH MCTCutHVT-VH MassCutHVT-VV MCTCutHVT-VV MassCut100200300400500 [GeV]2jT + p1jTp0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VV Res-SRHVT-VH MCTCutHVT-VH MassCutHVT-VV MCTCutHVT-VV MassCut In the following, the histogram used to calculate the total binned significance is that of the final discriminant of the analysis, i.e. In a given signal region, the total significance is calculated for different signal mass points, and is shown in a significance scan as a function of the signal mass. the invariant mass distribution. The expected HVT signal significance as a function of V ′ resonance mass is shown in Figs. 7.35 and 7.36 for VH signal regions, and in Figs. 7.37 and 7.38 for VV signal regions. This is shown for the 2-lepton channel, with similar performance having been observed for the 0- and 1-lepton channels. The MassCut strategy causes a reduction in VH signal significance in the Merged VH signal regions, while the MCT strategy does not affect the significance. In the VV signal regions, the MassCut strategy gives the same result as the Baseline analysis by construction, while the MCT strategy is not observed to bring any decrease in performance. (a) (b) Figure 7.35: Significance scans as a function of Z′ resonance mass in VH merged signal regions. The baseline analysis is compared to the MCT and MassCut strategies for orthog- onalization. 7.10.6 Expected limit sensitivity The expected limit sensitivities when using the MCT and MassCut orthogonalization strate- gies are compared. The limits are calculated following the procedure described in Sec. 6.3 without including systematics. The likelihood is built using Asimov data, as the analysis has not been unblinded yet. Figs. 7.39, 7.40, and 7.41 show the limit for Z′ or W ′ signal interpre- tations calculated for the mass points [300 GeV, 500 GeV, 1 TeV, 2 TeV, 3 TeV, 4 TeV, 5 TeV] for 0-, 1-, and 2-lepton channels, respectively. As expected from the previous studies, the MCT strategy does not cause any loss in performance with respect to the Baseline analyses. 184 012Significance-1 = 13 TeV, 36.1 fbs ZhfiHVT Z' VH 2-lep Merg 1btag0add SRBaselineBaseline + MCT cutBaseline + Mass cut10002000300040005000m(VH) [GeV]0.60.811.21.4Ratio00.511.52Significance-1 = 13 TeV, 36.1 fbs ZhfiHVT Z' VH 2-lep Merg 2btag0add SRBaselineBaseline + MCT cutBaseline + Mass cut10002000300040005000m(VH) [GeV]0.60.811.21.4Ratio (a) (b) Figure 7.36: Significance scans as a function of Z′ resonance mass in VH resolved signal regions. The baseline analysis is compared to the MCT and MassCut strategies for orthog- onalization. (a) (b) Figure 7.37: Significance scans as a function of Z′ resonance mass in VV merged signal regions. The baseline analysis is compared to the MCT and MassCut strategies for orthog- onalization. On the other hand, the Mass cut strategy causes a loss of sensitivity at high mass in the 0- and 2-lepton channels. A similar loss was observed in previous combination efforts. This is due to the higher mass region being more dependent on the merged signal regions, where the cut on the mass of the large-R jet was observed to decrease the VH signal efficiency and significance. 185 00.20.40.60.8Significance-1 = 13 TeV, 36.1 fbs ZhfiHVT Z' VH 2-lep Res 1btag SRBaselineBaseline + MCT cutBaseline + Mass cut600800100012001400m(VH) [GeV]0.60.811.21.4Ratio012Significance-1 = 13 TeV, 36.1 fbs ZhfiHVT Z' VH 2-lep Res 2btag SRBaselineBaseline + MCT cutBaseline + Mass cut600800100012001400m(VH) [GeV]0.60.811.21.4Ratio0123Significance-1 = 13 TeV, 36.1 fbs WZfiHVT W' VV 2-lep MergHP GGF WZ SRBaselineBaseline + MCT cutBaseline + Mass cut10002000300040005000m(VV) [GeV]0.60.811.21.4Ratio00.511.52Significance-1 = 13 TeV, 36.1 fbs WZfiHVT W' VV 2-lep MergLP GGF WZ SRBaselineBaseline + MCT cutBaseline + Mass cut10002000300040005000m(VV) [GeV]0.60.811.21.4Ratio Figure 7.38: Significance scans as a function of Z′ resonance mass in VV resolved signal regions. The baseline analysis is compared to the MCT and MassCut strategies for orthog- onalization. (a) In conclusion, the MCT strategy does not cause any loss in sensitivity in the limits, allows to recover up to 20% loss in sensitivity at high resonance mass with respect to the Mass cut strategy, and allows to simplify the combined search for new heavy resonances. (a) (b) Figure 7.39: Expected limits in VH and VV 0-lepton channel, shown in the inclusive regions. The baseline analysis is compared to the MCT and MassCut strategies for orthogonalization. 186 00.020.040.060.08Significance-1 = 13 TeV, 36.1 fbs WZfiHVT W' VV 2-lep Res GGF WZ SRBaselineBaseline + MCT cutBaseline + Mass cut5001000m(VV) [GeV]0.60.811.21.4Ratiom [TeV]1-10110210310 Zh) [fb]fi *BR(Z's12345m [TeV]0.811.2Ratio95% CL LimitBaseline ExpBaseline + MCT cut ExpBaseline + Mass cut Exp-1=13 TeV, 36.1fbsVH 0-lep m [TeV]1-10110210310410 WZ) [fb]fi *BR(W's12345m [TeV]0.811.2Ratio95% CL LimitBaseline ExpBaseline + MCT cut ExpBaseline + Mass cut Exp-1=13 TeV, 36.1fbsVV 0-lep Merg (a) (b) Figure 7.40: Expected limits in VH and VV 1-lepton channel, shown in the inclusive regions. The baseline analysis is compared to the MCT and MassCut strategies for orthogonalization. (a) (b) Figure 7.41: Expected limits in VH and VV 2-lepton channel, shown in the inclusive regions. The baseline analysis is compared to the MCT and MassCut strategies for orthogonalization. 187 m [TeV]1-10110210310 Wh) [fb]fi *BR(W's12345m [TeV]0.811.2Ratio95% CL LimitBaseline ExpBaseline + MCT cut ExpBaseline + Mass cut Exp-1=13 TeV, 36.1fbsVH 1-lep m [TeV]1-10110210310 WZ) [fb]fi *BR(W's12345m [TeV]0.811.2Ratio95% CL LimitBaseline ExpBaseline + MCT cut ExpBaseline + Mass cut Exp-1=13 TeV, 36.1fbsVV 1-lep m [TeV]1-10110210 Zh) [fb]fi *BR(Z's12345m [TeV]0.811.2Ratio95% CL LimitBaseline ExpBaseline + MCT cut ExpBaseline + Mass cut Exp-1=13 TeV, 36.1fbsVH 2-lep m [TeV]1-10110210310 WZ) [fb]fi *BR(W's12345m [TeV]0.811.2Ratio95% CL LimitBaseline ExpBaseline + MCT cut ExpBaseline + Mass cut Exp-1=13 TeV, 36.1fbsVV 2-lep 7.11 MCT Modeling In this section, the modeling of the Multi-Class Tagger (MCT) scores is studied in the context of the analysis. As described in the previous section, the MCT is used to orthogonalize the VV and VH signal regions, with a recycling strategy that ensures that no event is cut away. Most importantly, this means that the cut on the MCT is applied only to the small subset of events that ends up in both VV and VH signal regions. As long as the MCT scores are well modeled and cuts on the MCT scores do not produce or exacerbate mis-modeling, a full calibration of the classifier is deemed not necessary. Being the analysis blinded, the modeling is studied in the pre-selection (Sec. 7.11.2) and control regions (Sec. 7.11.3). The pre-selection regions allow to have access to larger statistics and to include all the events that will end up in the signal regions, while the modeling in a top-enriched control region is studied as representative of the procedure that would be used to calibrate a top or W -tagger. In order to disentangle true mis-modeling coming from the MCT from that induced by differences in background contributions between data and Monte Carlo (MC), preliminary normalization scale factors (SFs) are derived for the background samples by fitting the reconstructed mass of the hadronic decay in the given region. This is discussed in Sec. 7.11.1. After fixing the normalizations of the backgrounds, the MCT scores look well-behaved and the SFs are close to one. One might argue that even in the case of scale factors close to unity, the scale factor itself comes with an uncertainty that has to be evaluated and included in the fit.However, because the MCT is evaluated for every event that enters the analysis, as the systematic variations are applied, the score distributions will vary accordingly. It is therefore argued that the possible sources of uncertainties are already taken into account in the way the statistical fit is performed. Nonetheless, a study is also included in Sec. 7.11.4 of the effect of an artificial systematic uncertainty in the MCT scores on the final analysis sensitivity, and no effect is observed. 7.11.1 Derivation of background normalization scale factors The number of events from a background process b in a given region is given by Nb = σb L, where σb is the theory background cross section, ϵb 0 is the nominal experimental efficiency, and L is the luminosity. The difference between observed and expected background normalization can be corrected by deriving a scale factor of the form τ = N data/N M C . ϵb 0· · The normalization scale factors of the background processes can be obtained via a binned maximum likelihood fit (see Sec. 6.3 and, specifically, Eq. (6.14)) of the predicted observable 188 of interest to the observed data. The normalization scale factor for each background sample can be included in the fit model as nuisance parameters that allow to vary the normalization of the given process. The fit outputs the maximum likelihood estimator of the scale factors. The nuisance parameters can be introduced in the fit as unconstrained nuisance param- eters, which are allowed to take on any value, or as constrained parameters with a Gaussian In the first case, the fit is fully data-driven and outputs directly the maximum- prior. likelihood-estimator of the scale factor ˆτ . Nuisance parameters of this type introduce signif- icant freedom in the optimization procedure, so they should only be used when necessary to avoid overfitting. In the case of constrained nuisance parameters, the efficiency is assumed to be sampled from a Gaussian with mean ϵb 0 and standard deviation δ. The efficiency can then be parametrized as ϵb(α) = ϵb α), where the prior for α is a normal distribution 0 · with mean 0 and standard deviation 1. The best fit finds ˆϵb(α) = ϵb ˆα). The ˆα, with uncertainty δ corresponding scale factor is given by ˆτ = 1 + δ · An uncertainty associated to the luminosity is also included in the fit as a constrained nuisance parameter with a Gaussian prior and it is applied to all non-data-driven normaliza- tion coefficients. The Gaussian prior uncertainty is obtained from the auxiliary measurement 1, which corresponds to an of the total integrated luminosity from Run 2 of (139.0 uncertainty of δL = 1.7%. 0 × ˆα. · 2.4) fb− (1 + δ (1 + δ ± · · In these studies, the normalization scale factors are derived from fitting the mass distri- bution of the hadronic decay, corresponding to the large-R jet mass in merged regions and the di-jet mass in resolved regions. The fits are performed only in unblinded regions, either pre-selection or control regions. Shape systematic uncertainties are not included, so the fits are limited by the irreducible contributions of background shape mismodeling. Nonetheless, the residual mismodelings are found to be small. 7.11.2 Modeling in pre-selection regions The modeling of the MCT scores was studied in the pre-selection regions, which provide a large statistical sample and contain the important events that will end up in the signal regions. Events in the pre-selection regions were required to pass trigger, lepton selection, and anti-QCD cuts specific to each lepton channel, as well as the MCT training selection in Tab. 7.15. The results are shown in the 2-lepton pre-selection regions, while the 0- and 1-lepton channels are provided in the Appendix 9. The V +jets (V = W, Z) MC background was separated into sub-samples according to the truth flavor of the jets - the two leading signal jets or the two leading track jets in the large-R jet, according to the region of interest. As the MCT scores are sensitive to the 189 Merged MCT mJ pJ T ∈ ∈ [50, 200] GeV p ηJ | [200, 3500] GeV < 2 p | Resolved MCT ηj1 | ηj2 | j2 T < 500 GeV j1 T > 45 GeV and j2 T > 20 GeV and j1 T + p p | | < 2.5 < 2.5 Table 7.15: MCT training cuts applied to the pre-selection region definition. different flavor contributions, this was necessary to disentangle mismodeling originating from incorrect background normalizations from mismodeling induced by the MCT. The following V +jets sub-samples were defined according to the truth flavor of the jets: • V + bb, V + cc, V + bc : The two jets are truth tagged as b/c-quarks. • V + bl, V + cl: One jet is truth tagged as a b/c-quark, while the other jet is tagged as a light-quark. • Z + l: No jet is truth-tagged as a heavy quark, and one or two jets is truth tagged as a light-quark. • V + c,V + b: Only one jet, truth tagged as a b/c-quark. • V : No signal jets. In the following studies, the last two categories are grouped into the V, V c, V b sub-sample, as they bring a negligible contribution5. When considered inclusively, the different sub-samples have a similar shape. In order to provide the fit with a handle on the different flavor contributions, each fitted region was separated into three sub-regions according to the number of b-tagged jets – either zero, one, or two. The three regions are provided to the fit model and one normalization scale factor is output for each V +jets background sub-sample, as well as for the other SM backgrounds. The following data/MC comparison plots show the MCT scores p(h) and p(V ) for the Merged (Resolved) MCT in the merged (resolved) pre-selection regions, both inclusively in Figs. 7.42 and 7.44, and in the zero, one, and two b-tagged regions in Figs. 7.43 and 7.45. The latter distributions show the different dominant contributions from the V +jets com- ponents: Z + l in the zero b-tagged region; Z + bl, Z + cl in the one b-tagged region; and Z +bb, Z +bc, Z +cc in the two b-tagged region. The corresponding normalization uncertain- ties were left unconstrained in the fit for the given region. The jet mass distribution used for 5The event selection in VH regions and VV resolved regions always requires at least two jets, so the last two categories should be empty. In VV merged regions, there is no minimal requirement on the number of track jets associated to the large-R jet, so it is possible for these regions to be populated. 190 the fit is also shown to gauge the presence of residual shape mismodeling. The uncertainties in the plots are given by the combined statistical uncertainties and the uncertainties for the normalization coefficients derived from the fit. The only noticeable mismodeling appears in the resolved p(h) score in Fig. 7.45b. However, part of the mismodeling is likely due to the residual shape mismodeling in the jet mass distribution 7.45a. In addition, once a full treatment of the systematic uncertainties is included, the fits are expected to improve and the uncertainties to increase. Overall, the MCT is therefore observed to be well-modeled in the pre-selection regions. (a) (b) (c) (d) (e) (f) Figure 7.42: Data and MC comparison in the inclusive merged pre-selection region in the 2-lepton channel. Distributions of the large-R jet mass and the raw merged MCT scores p(h) and p(V ) are shown before (top) and after (bottom) applying the derived normalization SFs. 191 02000400060008000EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510610EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC02000400060008000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 7.43: Data and MC comparison in the merged pre-selection region separated by the number of b-tagged jets in the 2-lepton channel. Distributions of the large-R jet mass and the raw merged MCT scores p(h) and p(V ) are shown after applying the normalization SFs in the 0 b-tag (top), 1 b-tag (middle), and 2 b-tag (bottom) regions. 192 02000400060008000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L0 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L0 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L0 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC05001000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L1 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410510Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L1 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L1 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC050100Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L2 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L2 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 2L2 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) Figure 7.44: Data and MC comparison in the inclusive merged pre-selection region in the 2-lepton channel. Distributions of the large-R jet mass and the raw merged MCT scores p(h) and p(V ) are shown before (top) and after (bottom) applying the normalization SFs. 193 050100150310·EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC050100150310·Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 7.45: Data and MC comparison in the resolved pre-selection regions separated by the number of b-tagged jets in the 2-lepton channel. Distributions of the di-jet mass and the raw resolved MCT scores p(h) and p(V ) are shown after applying the normalization SFs in the 0 b-tag (top), 1 b-tag (middle), and 2 b-tag (bottom) regions. 194 050100310·Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L0 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L0 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L0 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC050001000015000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L1 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L1 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L1 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC0100020003000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L2 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L2 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 2L2 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC 7.11.3 Modeling in top-enriched control region A similar study as discussed in the previous section was carried out in the top-enriched CR VV1Lep MergHP GGF WZ 01btag TCR. This was done to emulate what would be the procedure if one were to calibrate the MCT, as a top CR provides a subset of events rich in true W jets coming from non-contained top decays. In this case, there was no need to separate the V +jets background into the flavor components, as the only dominant background is t¯t. The region was fit inclusively, with only the t¯t normalization uncertainty left unconstrained. The results are shown in Fig. 7.46. As observed in the pre-selection regions, after applying the normalization SFs no differences are observed between data and MC. (a) (b) (c) (d) (e) (f) Figure 7.46: Data and MC comparison in top-enriched CR VV1Lep MergHP GGF WZ 01btag - TCR. Distributions of the large-R jet mass and the merged MCT scores p(h) and p(V ) are shown before (top) and after (bottom) applying the normalization SFs. 195 020004000EventsDatattbarstopWjetsZjetsDibosonttVttHSMVH-1 TeV, 36.1 fb13VV1Lep MergHP GGF WZ 01btag TCR80100120Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410510610EventsDatattbarstopWjetsZjetsDibosonttVttHSMVH-1 TeV, 36.1 fb13VV1Lep MergHP GGF WZ 01btag TCR00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510610EventsDatattbarstopWjetsZjetsDibosonttVttHSMVH-1 TeV, 36.1 fb13VV1Lep MergHP GGF WZ 01btag TCR00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC020004000Events * NormSFDatattbarstopWjetsZjetsDibosonttVttHSMVH-1 TeV, 36.1 fb13VV1Lep MergHP GGF WZ 01btag TCR80100120Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopWjetsZjetsDibosonttVttHSMVH-1 TeV, 36.1 fb13VV1Lep MergHP GGF WZ 01btag TCR00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopWjetsZjetsDibosonttVttHSMVH-1 TeV, 36.1 fb13VV1Lep MergHP GGF WZ 01btag TCR00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC 7.11.4 Sensitivity to systematic variations of MCT scores To conclude the MCT modeling studies, it was investigated whether an artificial upward or downward variation on the MCT scores would affect the analysis sensitivity. The expectation is that the limits would not be affected anyway because of the small subset of events to which the MCT is applied. The mismodeling was simulated as a 10% systematic effect on the resolved (merged) p(h) score, which was propagated to the resolved (merged) p(V ) score as p(V ′) = p(V ) + (p(h) p(h′)) and with the scores min-maxed-out at 0 and 1. Note that this is an unrealistic extreme scenario, as the error would most likely be propagated more evenly among all the remaining four scores. ± − 0 Lepton channel data HVT-WZ HVT-WW HVT-ZH HVT-WH ttbar Wjets Zjets 80.34 19.66 84.31 15.69 73.69 26.31 21.55 78.45 25.88 74.12 16.63 83.37 76.95 23.05 81.91 18.09 70.21 29.79 55.01 44.99 57.33 42.67 51.54 48.46 75.35 24.65 79.52 20.48 68.59 31.41 VH 65.52 VV 34.48 VH 69.03 VV 30.97 VH 60.01 VV 39.99 – – – – – – – – – – – – 1 Lepton channel data HVT-WZ HVT-WW HVT-ZH HVT-WH ttbar Wjets Zjets 86.02 13.98 89.10 10.90 79.87 20.13 57.49 42.51 63.91 36.09 49.22 50.78 22.00 78.00 26.33 73.67 17.18 82.82 89.17 10.83 91.59 8.41 85.27 14.73 84.55 15.45 87.47 12.53 80.25 19.75 83.13 16.87 86.90 13.10 77.02 22.98 VH 83.69 VV 16.31 VH 86.42 VV 13.58 VH 78.55 VV 21.45 – – – – – – 2 Lepton channel data HVT-WZ HVT-WW HVT-ZH HVT-WH ttbar Wjets Zjets 76.30 23.70 79.68 20.32 70.57 29.43 21.89 78.11 25.87 74.13 16.66 83.34 82.43 17.57 85.95 14.05 77.19 22.81 74.55 25.45 77.73 22.27 70.00 30.00 100. 0.00 100. 0.00 100. 0.00 VH 67.23 VV 32.77 VH 72.09 VV 27.91 VH 61.17 VV 38.83 – – – – – – – – – – – – Nominal p(h) ∗ 1.1 p(h) ∗ 0.9 Nominal p(h) ∗ 1.1 p(h) ∗ 0.9 Nominal p(h) ∗ 1.1 p(h) ∗ 0.9 Table 7.16: Percentage of events in overlap region that end up in VH or VV analysis using the MCT strategy, comparing the nominal scenario, and the effect of an up and down variation on the scores (see text). All values are given as percentages of the number of events in the overlap region for the given data or MC sample. 196 Tab. 7.16 shows the migration of events after the MCT sorting in the nominal, up-, and down-variation scenarios. Figs. 7.47 and 7.48 show the inclusive signal efficiencies as a function of pT , similarly to the studies presented in Sec. 7.10.4, for the three scenarios. The only significant difference is observed in the background efficiencies (defined as the efficiency of a signal in the incorrect SR). Indeed, this resulted in no difference in the limit sensitivities (not shown) and similar results were observed in the other lepton channels. The conclusion therefore is that the analysis is not sensitive to possible systematic variations of the MCT scores. (a) (b) (c) (d) Figure 7.47: Signal efficiency as a function of pT in the 2-lepton channel for VV and VH merged signal regions, after orthogonalization with the MCT strategy. The nominal result is compared with the effect of an artificial up- and down-variation on the resolved and merged p(h) scores (see text for explanation). 197 0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VH Merg-SRMCT StrategyHVT-VHp(h)*1.1p(h)*0.9100020003000 [GeV]TFat jet p0.60.811.21.4Ratio0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VH Merg-SRMCT StrategyHVT-VVp(h)*1.1p(h)*0.9100020003000 [GeV]TFat jet p0.60.811.21.4Ratio0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VV Merg-SRMCT StrategyHVT-VHp(h)*1.1p(h)*0.9100020003000 [GeV]TFat jet p0.60.811.21.4Ratio0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VV Merg-SRMCT StrategyHVT-VVp(h)*1.1p(h)*0.9100020003000 [GeV]TFat jet p0.60.811.21.4Ratio (a) (b) (c) (d) Figure 7.48: Signal efficiency as a function of pT in the 2-lepton channel VV and VH re- solved signal regions, after orthogonalization with the MCT strategy. The nominal result is compared with the effect of an artificial up- and down-variation on the resolved and merged p(h) scores (see text for explanation). 198 0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VH Res-SRMCT StrategyHVT-VHp(h)*1.1p(h)*0.9100200300400500 [GeV]2jT + p1jTp0.60.811.21.4Ratio0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VH Res-SRMCT StrategyHVT-VVp(h)*1.1p(h)*0.9100200300400500 [GeV]2jT + p1jTp0.60.811.21.4Ratio0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VV Res-SRMCT StrategyHVT-VHp(h)*1.1p(h)*0.9100200300400500 [GeV]2jT + p1jTp0.60.811.21.4Ratio0.511.5Efficiency-1 = 13 TeV, 36.1 fbsAny 2-Lep HVT-VV Res-SRMCT StrategyHVT-VVp(h)*1.1p(h)*0.9100200300400500 [GeV]2jT + p1jTp0.60.811.21.4Ratio Chapter 8 Firmware algorithm development for the HL-LHC Global Trigger upgrade The Global Trigger (GT) will be a major addition to the ATLAS Level-0 trigger system to be installed during the Phase II upgrades in preparation for the High-Luminosity LHC (HL-LHC1). In order to handle the larger event size and unprecedented pileup levels, the GT will provide a platform to run complex algorithms at the first stage of the trigger chain and bring the event rate from 40 MHz down to 1 MHz. It is important to note that there will be no legacy triggers left as back-up at the beginning of Run 4. The successful operation of the GT will be necessary for ATLAS to take data. The trigger installed during the Phase II upgrades is expected to run for more than ten years, during which physics objectives might change, possibly due to new discoveries. One of the design principles of the GT is therefore for it to be sufficiently adaptable to allow ATLAS to react as quickly as possible to such changes. For this reason, the different functions that execute the trigger algorithms will be implemented in firmware, which provides more flexibility than standard hardware triggers. The firmware will then be executed on a common hardware platform based on Field Programmable Gate Arrays (FPGAs), which in turn reduces the hardware complexity. It follows that the GT is primarily a firmware project, a very different paradigm from what historically has been the hardware-based trigger in ATLAS. Most of the work within the GT upgrade project goes into the software and firmware co-development of the new trigger algorithms. A significant contribution of this thesis was the development of the software simulation framework for GT firmware algorithm development, as well as the development of a new jet reconstruction and triggering strategy. Every trigger is designed to target a specific physics signature. For instance, events including hadronic decays of heavy particles are often characterized by the presence of at least one energetic small-R jet. In order to record this type of events, a one-jet trigger selects events where the leading small-R jet has a transverse momentum (pT ) above a given threshold. In practice, of the forty million events that the Level-0 trigger receives per second, 1See Sec. 4.3.5 for an overview of the Phase II trigger upgrade. 199 only one million of them can be accepted. This 1 MHz event rate has to be shared between the different Level-0 triggers according to ATLAS physics goals and priorities. The number of events that a jet trigger can accept – i.e. how low the pT threshold can be – is thus determined by the fraction of the 1 MHz event rate allocated to it. At the same time, the majority of the events seen by the detector are minimum bias events (see Sec. 4.3.3), while interesting collisions are orders of magnitude rarer. The ability to correctly discriminate between signal and background – which, for a jet trigger, can go from correctly reconstructing the jet energy, to identifying and discarding pileup-induced jets – is essential for maximizing In the noisy environment of the HL-LHC, this task the retention of rare signal events. will be significantly more difficult, to the point that, if the hardware trigger system was kept unchanged, the current algorithms would be unable to retain the physics performance required by the experiment. The deployment of fast algorithms able to perform a more sophisticated signal to background discrimination at Level-0 is necessary to maintain ATLAS physics reach. A brief introduction to the GT system is given in Sec. 8.1. The remaining sections of this chapter describe the contributions to the GT project of this thesis. These include the development of the software simulation framework for trigger algorithms (Sec. 8.2.1), the design and validation of a new jet reconstruction and triggering strategy (Sec. 8.2 and 8.3), and studies for a pileup-jet suppression method using deep neural networks to improve multi-jet triggers (Sec. 8.4). 8.1 The Global Trigger (GT) The GT2 consists of three sub-systems: the Multiplexers, the Event Processors, and the Demultiplexers. Each sub-system consists of a farm of large FPGAs, with each FPGA corresponding to a node, a common hardware unit on which the same firmware is deployed. The serial data arriving at 40 MHz from the calorimeter detector subsystems, the Phase I FEXs (see Sec. 4.3.4), and the Muon Central Trigger Processor Interface (MUCTPI) is deserialized by Multiplexer Processor (MUX) nodes for pipelined data processing. The MUX aggregates the full event data from a specific bunch crossing (BC) on a single event processor node, called Global Event Processor (GEP). At this point the events are decoupled from the BC rate and can be processed in parallel on the 48 GEP nodes, allowing the implementation of asynchronous complex algorithms. The event data from each BC is distributed to the GEP 2The GT system is currently under development. The description presented here is mostly based on the one proposed in the Technical Design Report [10]. As this picture has been continuously evolving, certain timing and resource utilization estimates might have changed with time. 200 nodes in a round-robin fashion, with each node receiving new data every 48 BCs, increasing the latency between the arrival of two events to a GEP node from 25 ns to 1.2 µs. This process is shown schematically in Fig. 8.1. Figure 8.1: Time-multiplexing of incoming synchronous data at 40 MHz by the MUX nodes. Each MUX receives data for every bunch crossing (BC). The data is processed, organized, and dispatched to the GEP nodes. Each GEP node receives the complete event data for one BC and analyzes the data asynchronously. Results from the GEP nodes are demultiplexed by the CTPi and sent to the CTP [10]. The same set of firmware functions is executed on each GEP node to build the TOBs and produce trigger hypotheses based on object multiplicities, energy thresholds, and topological relationships, as sketched in Fig 8.2. As the data is being received, algorithms that do not require the full event data can start, fully exploiting the data transmission time. Ordering data geometrically also favors the pipelining of the steps of non-iterative algorithms on the FPGA board. For instance, if the data arrives ordered in η, a sliding window algorithm can start processing the detector plane in full slices over ϕ. Pipelined data processing and parallel execution of different algorithms, allows to drastically reduce the FPGA resource utilization and extend the Level-0 latency up to 6 µs. The output of a GEP node is called the Trigger Input (TIP), containing flag bits of which trigger requirements have been satisfied and multiplicities of reconstructed objects. A Global- to-CTP Interface (gCTPi) demultiplexes the data, re-builds the event with the correct BC number, transmits the trigger bits to the CTP, and sends the data to the readout system on request. The CTP combines trigger inputs from the GT and MUCTPI, as well as from the forward detectors and other detector calibration sub-systems, and makes the final Level-0 trigger decision. It also applies deadtime and prescales. The Level-0 accept rate is of 1 MHz. ∼ Inputs At every LHC BC, the GT receives the full granularity noise-suppressed ( ET | | > 2σ) 201 i+144i+95i+47i+96i+48i+0i+47i+95i+47i+47i+95i+95i+47i+95i+47i+47i+95i+95...i+1i+0i+47i+48...i+1i+0i+47i+48...i+1i+0i+47i+48...i+1i+0i+47i+48...i+1i+0i+47i+48...i+1i+0i+47i+48...i+1i+0i+47i+48...i+1i+0i+47i+48...i+1i+0i+47i+48i+48i+0i+0i+48i+48i+0i+1i+49i+1i+1i+49i+49...i+49i+1i+1i+49i+49i+1i+0i+48i+0i+0i+48i+48...........................i+48i+0i+0i+48i+48i+0i+1i+49i+1i+1i+49i+49i+47i+95i+47i+47i+95i+95...i+1i+0i+47...optical fiber with data from events i+0, i+1, …, i+47, … (shading indicates data source within input system) L0CaloCalorimeterL0Muon from MUCTPIMultiplexerMultiplexerMultiplexerGlobal Event Processor#0Global Event Processor#1Global Event Processor#47CTPInterfacei+97i+49i+1L0CTPi+2i+1i+0...← time Figure 8.2: Schematic view of the Global Trigger processing [10]. calorimeter data from the LAr and Tile calorimeter front-end electronics. This will be the first time that the Level-0 trigger has access to calorimeter cells. This new information will enable the implementation of topological clustering, in turn allowing for improved TOBs definitions. The GT will also receive TOBs from the L0Calo FEX processors and from the MUCTPI, which can be used as seeds for GEP algorithms. The LAr and Tile inputs are expected to arrive first in 1.4 1.7 µs. The data from L0Calo 5.3 µs. The is expected to arrive in 2 overall latency is always dictated by the muon latency. Because of the longer arrival time of the muon information, algorithms requiring inputs from the MUCTPI will be run later in the pipeline. 2.6 µs, followed last by the L0Muon inputs at 4.5 − − − Hardware The hardware is based on a common design, called the Global Common Module (GCM), to minimize the complexity of the system. A GCM with dedicated firmware is used for each of the three main components of the GT: a multiplexing module, a Global event process- ing module, and a demultiplexing CTPi module. Each GCM can support two independent FPGAs, where each FPGA can represent a GEP, MUX, or CTPi node, and a central process- ing chip for monitoring, control, and readout. The FPGA board will be the Versal Premium VP1802 developed by the company Advanced Micro Devices (AMD), providing substantial I/O and Random Access Memory (RAM) capabilities to handle the large bandwidths and buffering. Firmware The various algorithms that compute the trigger objects will be executed on the GEP hard- ware modules and will represent the majority of the resource consumption of the GT system. 202 TDAQGlobal TriggerLAr Phase-IL0CaloPhase-ILArPhase-IITilePhase-IIMuonL0Muonfrom MUCTPIMUXMUXMUXMUXL0CTPData HandlerGEPGEPGEPGEPr...CTP InterfaceFELIXGEPGlobal Event ProcessorMuonsCellsTrig. Objs.ElectronsTausJetsMuonsMETTopoclusters Topoclustering, e/γ, and τ algorithms are expected to consume less than 1% of the resources. The resource usage will be dominated by the jet finding and trigger hypothesis algorithms. Resource usage for the latter can be estimated from the current L1Topo usage to be between 36% and 68%. This leaves about 20% of the FPGA resources for jet finding. The physics performance of the algorithms is limited by latency and resource allocation, while algorithm scheduling on the board is constrained by their role in the overall dataflow, e.g. the inputs they require. A preliminary plan for algorithm scheduling on a single GEP module is shown in Fig. 8.3. The FPGA is divided into four Super Logic Regions (SLR) pipelined in latency intervals of 1.2 µs. The first SLR0 receives LAr data, so that regional algorithms, such as topological clustering, can start processing. After 1.2 µs, the processing of the current BC is moved to SLR1, while SLR0 receives LAr data for a new event. Once in SLR1, inputs from the Tile calorimeter arrive, so that the regional algorithms can ultimate their trigger objects. The topoclusters are now ready and can be used as inputs by downstream algorithms, in- cluding jet finding, which will take up the majority of the resources in SLR2. Lastly, SLR3 will receive the muon information and will run topological algorithms on the final trigger objects. This picture might evolve with time. 8.2 Trigger performance studies The trigger algorithms used to reconstruct the event and produce the trigger objects are implemented in reprogrammable firmware, which makes the GT effort primarily a firmware project. From the hardware side, the algorithms are constrained by the number of I/O ports, latency, and bandwidth requirements set by the Global Common Module. From the physics side, each algorithm is developed with the goal of providing a high signal efficiency. The development of a new candidate algorithm is thus performed with two equally important objectives: providing a high physics performance, while keeping the footprint in terms of FPGA resources within the hardware limitations. The first step in the development is gen- erally to demonstrate that the physics performance of the algorithm is sufficient to retain ATLAS physics goals. This is usually done in software, as it provides a faster turn-around and allows one to concentrate on the physics questions. Once the algorithm is mature, the next step is to perform a preliminary firmware simulation in order to provide an estimate of the resource consumption. This is often done using packages such as High-Level Synthesis (HLS), which automate hardware design by taking as input a high-level algorithmic descrip- tion in a standard language, such as C/C++, and converting it to a lower-level hardware description language (HDL) code. Often this process requires several iterations in order to simultaneously optimize the two objectives. In particular, if the resource usage significantly 203 Figure 8.3: Preliminary plan for GT algorithm dataflow on one FPGA on a GEP module. The FPGA is divided into four Super Logic Regions (SLRs) for pipelined data processing. This picture might evolve with time. Picture courtesy of Wade. exceeds the allocated lot, it is possible that substantial changes to the algorithm itself are needed, so that the software and firmware development proceed in parallel. Once the algo- rithm has been proven to be a viable option both from a physics and a firmware perspective, the firmware design is typically finalized by a hardware engineer. In the context of trigger performance studies there are two levels of reconstruction. Online reconstruction is performed at the trigger level on the live stream of data arriving from the detector. The development of the online algorithms is constrained by the latency and bandwidth limitations of the trigger environment and often results in coarser objects. After the data has been selected by the trigger and stored to disk, the offline reconstruction is performed using the standard ATLAS software. The offline algorithms, run on CPU farms, have very few limitations in terms of resources, and are therefore maximally optimized. The objects output by these two stages will be referred to as online and offline objects. It should be noted that, in the following, no calibration is applied on the offline objects, as none were 204 available at the time of these studies. 8.2.1 The GT software simulation framework Part of this thesis work included the development of the software simulation framework for the GT. The package was written in C++ and Python as part of the ATLAS offline software Athena [105]. A sketch of the functionalities of the framework is shown in Fig. 8.4. The Figure 8.4: Sketch of the software simulation framework for the Global Trigger. framework was designed to provide an efficient way to develop and study new candidate algorithms for the GT, as well as to provide Level-0 objects as input to physics performance studies for the HL-LHC. The first point was particularly important at the time of this work, as all GT algorithms were under development. The framework was therefore developed with a modular structure, where algorithms could be easily integrated for testing, while shielding the developer from direct interaction with the Athena software. In the diagram, the label “custom” represents a possible plug-in for developers to interface their C++ code with the Athena workflow. In addition, the ATLAS offline versions of the algorithms are always provided for a solid baseline comparison. As most algorithms require topocluster or jet information, the focus was put on the reconstruction chain from calorimeter inputs to jets, which includes topological clustering, constituent-level pileup suppression, and jet reconstruction. This covers the main algorithms in the first three SLRs. Other algorithms, such as e/γ, hadronic event reconstruction, muons and topological algorithms are expected to be added in the future. The MC samples read by the framework and used in the following studies were produced 205 GepOutputReader•ROOT Histograms •TTreePrivate codeathena/TrigL0GepPerfPackageTopological clustering•Offline 420 •Offline 422 •CustomPileup suppression•Offline Soft-Killer (SK) •Offline Voronoi + SK •CustomJet reconstruction•Offline anti-kT •Custom•Cells Simulation <>=200μ ⟩ µ ⟨ with the standard ATLAS MC production path, but with HL-LHC settings. The samples were simulated at a center-of-mass energy of √s = 14 TeV, including the simulation of the new detector components, and with the number of simultaneous pp interactions per = 200. This represents the extreme pileup scenario that the bunch crossing set to trigger is expected to handle. Di-jet events were generated using Pythia8 [192], with the NNPDF23LO set and A14 ATLAS parameter tuning. These samples were produced in slices of pT in order to provide sufficient statistics across a wide kinematic range. The first slice, simulated for truth jet pT in the range [0, 20] GeV, was used as representative of a minimum bias sample, while the remaining slices were taken as representative of QCD multi-jet events. t¯t events was used. The For single-jet trigger studies, a simulation of fully-hadronic Z′ → sample was generated using POWHEG [198] interfaced with Pythia with the NNPDF23LO set and the A14 tune for the parton shower. For multi-jet trigger studies, di-Higgs events, with each Higgs boson decaying to a pair of b-quarks, were used. The samples were produced for gluon-gluon fusion (ggF) Higgs boson production and assuming the SM trilinear coupling. The matrix element was calculated using POWHEG at NLO, including finite top mass loop calculations. The showering was performed using Pythia8. The primary input objects to the framework are calorimeter cells output by the digitiza- tion step of the ATLAS MC simulation path. The cells are fed as input to the topological clustering algorithm. The standard ATLAS offline topoclustering algorithm (see Sec. 4.4.4) provides topoclusters at the EM scale built with the 4-2-0 setting (Calo420). The same al- gorithm is also run with the 4-2-2 setting (Calo422), which does not include the outer layer > 0, resulting in smaller topoclusters. A collection with 4-2-0 topoclus- of cells with ters LCW calibrated (CaloCal) is also provided for offline large-R jet reconstruction. As a form of noise suppression, as well as to reduce the bandwidth and the processing time of downstream algorithms, the GT will only receive cells with E > 2σ. Therefore, the Calo422 offline collection represents the “best case scenario” for topoclustering at Level-0. As the online topoclustering algorithm for the GT is still under development, the Calo422 collection was used as representative of the GT topoclusters in the studies presented here. |S| Next, the topoclusters can be pileup suppressed using the recently developed constituent- level methods described in Sec. 5.5. Both the Soft-Killer (SK) and the Voronoi (Vor) offline algorithms are provided, including the option of combining them by running SK on the Voronoi-subtracted topoclusters (VorSK). The modified topocluster collection can then be fed to downstream algorithms, such as jet reconstruction. In ATLAS internal studies, it was shown that running the Voronoi algorithm alone was not as effective. For this reason, in the following studies only the SK and VorSK options are discussed. No online version of these algorithms was available at the time of these studies. 206 Lastly, the resulting topocluster collection is fed to the jet reconstruction algorithm. The offline anti-kt algorithm (see Sec. 5.2) can be run with the choice of R = 0.4 or R = 1.0. The jet collection produced by running the offline anti-kt algorithm on the offline Calo422 collection represents the “best case scenario” for small-R jet reconstruction in the GT. The development of a new jet reconstruction strategy for the GT was a major part of this work and will be discussed in detail in the next sections. 8.2.2 Developing a jet trigger As mentioned in the introduction, a one-jet trigger targets signatures with one energetic small-R jet by applying a pT threshold on the leading small-R jet in the event. Similarly, multi-jet triggers require the presence of three or four jets above a pT threshold, where the higher jet multiplicity requirement typically allows to lower the pT threshold. In the following, the cut on the online jet pT is referred to as pcut T . The performance of a jet trigger is studied with MC simulations in terms of the offline signal efficiency. As shown in Fig. 8.5, the efficiency is analyzed as a function of the offline- Figure 8.5: Example of trigger efficiency curve (see text for explanation). In the case of jets, if the version of the variable used to apply the online selection cut. trigger selects on the nth leading online jet pT , the efficiency is displayed as a function of the nth leading offline jet pT . This visualization is important, as the offline analysis will only 207 050100050001000015000EventsAllPass trigger255075100125Offline Jet pT0.00.51.0RatioOffline pT threshold at =98% accept events with the nth leading offline jet pT above the 98% efficiency point (the dashed line in Fig. 8.5). This ensures that the trigger selection does not bias the MC simulation in unpredictable ways. In the following, we will refer to the offline pT value at the point where the turn-on curve reaches 98% efficiency as pthresh , the T broader the pT range covered by the analysis. Hence, improving the trigger performance means reducing the pthresh T by means of reducing the rates of high energy background jets. However, it also depends on the online reconstruction performance with respect to offline reconstruction, as explained more in detail in the following. . Intuitively, this can be obtained by lowering the online pcut . In practice, the lower the pthresh T T Recall that offline reconstruction represents the best one can do when virtually no latency or resources limitations are present. Then, one could say that the ideal online algorithm is the one that reconstructs the same objects as the offline one. Consider first the ideal scenario of perfect online reconstruction, with a one-to-one correspondence between online and offline T = pthresh objects. In this case, the efficiency curve would look like a step function at pcut , T with zero efficiency for offline pT values below the online pT cut and 100% efficiency for values above. Mistakes in online reconstruction result in a deviation from this scenario. One can identify two ways in which online jet reconstruction can go wrong: one can reconstruct the correct jet, but with an incorrect energy; or one can reconstruct the incorrect jet. The first case occurs when the online and offline jets represent the same energy deposi- tion in the detector (they have the same (η, ϕ) coordinates), but have different reconstructed transverse momenta. This can happen because offline and online reconstruction use dif- ferent inputs and possibly different algorithms. For instance, while offline small-R jets are produced using the Calo420 topocluster collection, online jets in the GT are produced us- ing Calo422 topoclusters, which are by construction lower in energy, as they are built from fewer cells. Therefore, one can expect online jets to have lower transverse momenta than offline jets. Similarly, a cone algorithm without any overlap removal strategy will, on aver- age, produce more energetic jets than an algorithm that takes care of removing any energy double-counting, such as anti-kt. If the transverse momentum of every online jet differs from the corresponding offline jet by the same factor, this is just a matter of normalization that does not affect the value of pthresh (i.e. the same set of events would pass the trigger). However, issues arise when the T factor is not constant, but dependent on the phase space. As an example, consider the case of two nearby jets. A cone algorithm might find the two true jets and draw cones around them, but the cones might overlap. In this case, energy is being double-counted and the two jets might see their energy increase. Because nearby jets are characteristic of more boosted scenarios, the cone algorithm would produce an artificial increase in the number of high 208 energy jets, which would be more pronounced for more boosted signatures. The preferential increase in the rate of high energy jets can determine a higher online pcut and cause different events to pass the trigger. An event with well isolated jets, whose online pT was just above the threshold and did not get augmented, will now fail to pass the higher trigger threshold, resulting in a loss of offline efficiency and hence a higher pthresh value. Similarly, a non-zero T efficiency below the pthresh value could also occur, as online jets that should have not passed the trigger can now have their energy increased sufficiently to pass the selection. T T The second case occurs when the reconstructed online and offline nth leading jets corre- spond to different objects. This can often happen for a seeded algorithm, where a choice has to be made on how close the seeds can be. Assuming no constraint on how close two seeds can be, it is possible that the same offline jet is reconstructed twice. Consider an event with two high energy offline jets. Online reconstruction should produce two high energy online jets and soft 3rd and 4th leading jets. However, if two seeds are found around the leading jet, two online jets will be reconstructed with the energy of the leading jet. The result will be three high energy online jets in the event. This means that the event will most likely pass the three-jet trigger, as the online pT cut meant for the 3rd leading jet is really being applied to the leading jet. This will result in a non-zero efficiency at a pT value below pthresh . T Consider instead the case where seeds are required to be at a minimum distance of dR = 0.5 from each other. Consider then a signal topology where two pairs of nearby jets b¯bb¯b) and where, for certain percentage of events, at least one pair are created (e.g. hh is closer than dR = 0.5. While offline jet reconstruction will always find four jets, for this subset of events the online cone algorithm will not be able to reconstruct the 4th jet, resulting in an inefficient four-jet trigger. For signal samples characterized by this topology, this can produce an offline plateau inefficiency. → Summed over all events, these contributions change the step-function into a turn-on curve, as the one shown in Fig. 8.5. In practice, mismatches between online and offline objects do not affect the performance of the trigger, as long as the event passes the selection anyway. This is why no jet truth-matching is performed when looking at the signal efficiency curves. However, as the examples described above demonstrate, these errors can have undesirable consequences, as they can result in a higher pthresh to be adopted by the analysis. Any efficiency below pthresh is also undesirable, as it represents an inefficiency from the point of view of the TDAQ system, which utilizes time and resources to process events that are not usable by most analyses. T T The development and optimization of a trigger algorithm has therefore two goals: 1. Reduce the rate of high energy background jets, while keeping the signal efficiency 209 high, i.e. reduce pthresh T as much as possible. 2. Improve the jet energy resolution of the online vs. offline jet reconstruction, i.e. make the turn on as steep as possible. Both can be studied by comparing trigger efficiency curves produced by different algorithms. The first point can be studied by comparing trigger efficiency curves at a fixed trigger rate: a maximum trigger rate is assumed, the online pT cut is found that allows to remain below the given rate threshold, and the offline trigger efficiency is built. The second point can be studied by adjusting the online pT threshold of each algorithm so that the offline pT thresholds are aligned. This decouples the problem from the choice of online pT cut, and allows to study only the jet energy resolution, where the algorithm with the best resolution is the one with the fastest slope of increase. Since the resolution can be pT dependent, different choices of offline pT threshold allow one to test the resolution in different phase spaces. Clearly, the performance of a trigger algorithm closely relies on the jet reconstruction strategy, with the development and optimization of the two aspects being closely inter- twined. In the following, a new strategy for jet reconstruction and triggering for the GT is presented, where the two components are treated as one individual task with the shared goal of improving the trigger efficiency curve. 8.3 A cone jet reconstruction algorithm The offline anti-kt algorithm (see Sec. 5.2.3) is the optimal choice for jet reconstruction. Nevertheless, it is also a computationally intensive algorithm, necessitating the calculation of dR distances and execution of 1/p2 T divisions for each iteration. Additionally, anti-kt is a highly iterative algorithm, with a non-deterministic number of operations. This makes it non-scalable on parallelizable firmware, thereby losing one of the main advantages of fast FPGA hardware. Consequently, its deployment on the Global Event Processor would require a substantial allocation of resources, making it an impractical, if not prohibitively expensive, choice. The work presented here aimed to find an alternative to anti-kt that would allow to retain the necessary physics performance, while requiring fewer resources. The main advantages of anti-kt are IRC safety and its ability to correctly identify the boundary between nearby jets. At the Level-0 trigger, IRC safety is not a requirement, as the goal of the trigger is to accept the right events, not to reconstruct physics-analysis-ready objects. If the event passes the Level-0 trigger selection, the objects are reconstructed again with the offline algorithms first at the Event Filter level, and then offline for use in analyses. 210 The ability to identify nearby jets is instead highly desirable, if not necessary in order to retain high signal efficiencies for multi-jet triggers. The jet reconstruction strategy proposed in this work is based on the other class of algorithms: cone algorithms (see Sec. 5.2.2). While the choice of seeding strategy is not straightforward, seeding provides a fixed handle on the number of computations. It also makes jet building highly parallelizable, as each seeded jet can be built independently. The studies presented here focus on small-R jet reconstruction, where the radius parameter is fixed to the standard R = 0.4. Different possible extensions of this work to large-R jet reconstruction are envisioned, including using the leading small-R cone jets as seeds for another iteration of the cone algorithm with a larger radius parameter, or as input to a reclustering algorithm. However, this goes beyond the scope of this work. In the performance studies shown in this section the reference offline jet collection is produced by running offline anti-kt on Calo4203 topoclusters at the EM scale. This will be referred to as AntiKt420. The inputs to jet reconstruction in the GT will be the Calo422 topoclusters. It follows that the upper bound on jet reconstruction performance at the GT level is set by the anti-kt algorithm run on Calo422 topoclusters. The development of the cone algorithm is therefore benchmarked against this jet collection, which will be referred to as AntiKt422. All selected jets in these studies are required to be in the central region of the detector < 2.5 and to have pT > 10 GeV. The performance of the algorithm was benchmarked against target signal simulations. t¯t sample was used as the representative signal for one-jet trigger studies. It also The Z′ → provided an event topology useful to study the effect of nearby jets for multi-jet triggers. b¯bb¯b sample was used as representative for signals relying on three- and four-jet The hh triggers. In particular, the event topology is characterized by well separated low energy jets, making this type of signature particularly sensitive to the online pT threshold. → η | | The studies were performed for the most part assuming a fixed rate threshold. In these studies this will be assumed to be 60 kHz for a one-jet trigger and 50 kHz for three- and four-jet triggers, as it was assumed in the Phase II Upgrade Technical Design Report for the TDAQ system [10]. Some studies are performed at fixed offline threshold, in order to compare the energy resolution of different jet collections. In In Sec. 8.3.1 the development process of the new cone jet algorithm is discussed. Sec. 8.3.2 the performance of the optimized version of the algorithm is benchmarked against the online AntiKt422 jet collection. The efficacy of offline pileup suppression schemes will also be evaluated. Lastly, Sec. 8.3.4 discusses the results of a preliminary firmware simulation, 3See Sec. 8.2.1 for an overview of the object collections available in the framework. 211 providing insights into the practical implementation of the algorithm. 8.3.1 Development Recall that a jet definition is defined by the jet algorithm, the jet inputs, and the recombi- nation strategy (see Sec. 5.2). These choices are discussed in the following. Inputs As mentioned earlier, the inputs to jet reconstruction in the GT will be 4-2-2 topoclusters, which, for the purpose of these studies, will be the Calo422 collection. Pileup suppression is expected to be applied on the topoclusters before these are provided to the jet recon- struction process. However, the jet algorithm development was performed without pileup suppression applied, as no online pileup suppression algorithm was available. This approach also simplified the optimization process by reducing the number of factors involved. In the absence of any ET cut on the topoclusters, the number of topoclusters recon- structed per event is several hundreds, as shown in Fig. 8.6. Processing such a large number of inputs for each event is unfeasible, making thresholding the input topoclusters necessary. Additionally, the maximum number of inputs that can be processed must be predetermined in firmware, and the lower this limit, the smaller the algorithm’s footprint on the FPGA. However, as this choice depends on the resources available in the firmware, the study of this trade-off was left for future work and only the ET thresholding was studied here. The ET cuts at 1, 2, and 3 GeV were considered, motivated by the range of the constituent-level pT cut produced by the Soft-Killer algorithm reported in Ref. [154]. The effect of the different cuts on the jet energy resolution was studied in different energy regimes using the AntiKt422 online jet collection. Fig. 8.7 and Fig. 8.8 show the trigger efficiencies for the di-Higgs signal with the offline pT threshold fixed at 50 GeV and 100 GeV, respectively. The energy reso- lution worsens with increasing topocluster ET cut, and the effect is greater for regions of phase space with higher pT jets. It follows that the choice of the ET threshold is a trade-off between reducing the number of inputs and keeping the energy resolution high. Note that the performance of the AntiKt422 jets with no ET cut on the topoclusters, where the only difference between offline and online reconstruction is the topocluster collection, shows the effect on the jet energy resolution from using the Calo422 instead of the Calo420 topocluster collection. The conclusion from these studies was to exclude the 3 GeV cut as a viable option. The final choice between 1 GeV and a 2 GeV cuts will likely be determined by the available resources on the firmware. 212 (a) (b) (c) Figure 8.6: Number of topoclusters per event passing different values of ET thresholding for minimum bias (left), Z′ (center) and di-Higgs (right) samples. Plots made by Garrit. (a) (b) (c) Figure 8.7: One (left), three (center), and four (right) jet trigger efficiency curves built with the AntiKt422 online jet collection and a fixed offline pT threshold of 50 GeV using di-Higgs events. The jets are reconstructed using input topoclusters with different ET thresholding applied: 1, 2, and 3 GeV thresholds and no threshold. Recombination scheme − The most commonly used recombination strategy is the E scheme, where the jet four- vector is given by the sum of the four-vector components of its constituents. In the first stages of development, this was the recombination scheme used, again as a way to keep the interacting factors in the optimization process low. Once the algorithm development was mature and a first firmware simulation was performed, the E scheme computations involving trigonometric functions were observed to increase the FPGA resource utilization beyond acceptable limits. A new scheme was therefore designed, which will be referred to as the “Approximate-ET scheme”. In this scheme, the transverse energy of the jet is given by the scalar sum of the transverse energy of its constituents, the (η, ϕ) coordinates are given − 213 20406080 [GeV]T1st offline leading jet p00.511.5EfficiencyHL-LHC Simulation>=200m, =200m, =200m, =200m, =200m, =200m, =200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|60 kHzNo overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR020406080 [GeV]T3rd Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzNo overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR02040 [GeV]T4th Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzNo overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|No overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|No overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|No overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR (a) (b) (c) Figure 8.13: One-jet and multi-jet trigger efficiencies for di-Higgs signal using cone jets with different overlap removal strategies. 8.3.2 Physics performance This section presents the performance of the optimized cone algorithm. The final cone jet collection, referred to as ConeTopo, is reconstructed with the following settings: • Inputs: Topoclusters with ET > 2 GeV. • Seeds: Topoclusters with ET > 5 GeV. • Recombination scheme: Approximate-ET . • Overlap removal: EOR. The performance is benchmarked against the online jet collection Antikt422, which represents the upper limit on performance when using 4-2-2 topoclusters as inputs. The same ET threshold is applied to select the input list of topoclusters for both algorithms. Similar results are observed for ET > 1 GeV and ET > 3 GeV topocluster thresholds. Trigger efficiencies → Fig. 8.14 shows the trigger rates for the minimum bias sample. The rates are identical for t¯t ConeTopo and Antikt422 jets. Fig. 8.15 and 8.16 show the trigger efficiencies for Z′ → b¯bb¯b signals, respectively. Again, the performance is almost identical. The only and hh t¯t sample. observable difference is a slight over-efficiency for multi-jet triggers with the Z′ → This over-efficiency is not due to nearby jets, as it does not go away after requiring offline jets to be at a distance dR > 0.8. It could be due to cone jets over-estimating the jet area of lower energy jets. 219 50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|No overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|No overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|No overlap removalSeed removal dR=0.4EORSeed removal dR=0.4 & EOR (a) (b) (c) Figure 8.14: One-jet and multi-jet trigger rates comparing ConeTopo and AntiKt422 online jet collections. (a) (b) (c) Figure 8.15: One-jet and multi-jet trigger efficiencies for Z′ → and AntiKt422 online jet collection. t¯t signal comparing ConeTopo (a) (b) (c) Figure 8.16: One-jet and multi-jet trigger efficiencies for di-Higgs signal comparing ConeTopo and AntiKt422 online jet collection. 220 050100150 [GeV]T1st Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|60 kHzTAnti-kConeTopo+EOR020406080 [GeV]T3rd Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzTAnti-kConeTopo+EOR0204060 [GeV]T4th Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzTAnti-kConeTopo+EOR50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopo+EOR50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopo+EOR50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopo+EOR50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopo+EOR50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopo+EOR50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopo+EOR Di-Higgs mHH signal efficiency After examining the trigger performance, the impact of the trigger selection on a metric more closely related to the offline analysis was assessed. In particular, it was important to check that the cone algorithm was not introducing unexpected bias, for instance, through the energy overlap removal strategy. This was studied in the context of the di-Higgs analysis. An important metric for the di-Higgs analysis is the reconstructed invariant mass of the di- Higgs (mhh) system, as only the low mhh region is sensitive to the value of kλ (see Sec. 8.4). A full set of calibrations and b-tagging was not available for the HL-LHC MC samples used in this study. For this reason, the study was performed using truth information and the final hh state was reconstructed by finding the four reconstructed small-R jets truth matched to the four truth b-quarks using the procedure described in Sec. 5.3.2 with dR = 0.35. Only < 2.5 and four truth matched reconstructed jets events with all four b-quarks within are retained. The signal efficiency as a function of mhh is studied for events that pass a three- and a four-jet trigger, comparing the performance when using online ConeTopo and AntiKt422 jets. As shown in Fig. 8.17, no difference in performance is observed. η | | 221 (a) (b) (c) (d) (e) (f) Figure 8.17: Efficiency as a function of reconstructed mhh after passing the three-jet (top row) and four-jet (bottom row) trigger comparing the performance of ConeTopo and AntiKt422 online jet collections. 222 2004006008001000 [GeV]HHTruth m05101520310·CountsHL-LHC Simulation>=200m, =200m, =200m, =200m, =200m, =200m, 1 GeV. 224 050100150 [GeV]T1st Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 1 GeVT42 EM Topoclusters EInput-level pileup suppression60 kHzNoneSKVorSK020406080 [GeV]T3rd Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 1 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzConeTopo+EOR ConeTopo+EOR SKConeTopo+EOR VorSK0204060 [GeV]T4th Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 1 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzConeTopo+EOR ConeTopo+EOR SKConeTopo+EOR VorSK50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 1 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 1 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 1 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK (a) (b) (c) (d) (e) (f) Figure 8.19: Trigger rates (top) and efficiencies (bottom) using different constituent-level pileup suppression methods, as well as no pileup suppression. The turn-on curves are built with online pT cuts at fixed-rate threshold. The efficiencies are shown for the di-Higgs signal sample and the ConeTopo online jet collection built from input topoclusters with ET > 2 GeV. 225 050100150 [GeV]T1st Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters EInput-level pileup suppression60 kHzNoneSKVorSK020406080 [GeV]T3rd Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzConeTopo+EOR ConeTopo+EOR SKConeTopo+EOR VorSK02040 [GeV]T4th Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 2 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzConeTopo+EOR ConeTopo+EOR SKConeTopo+EOR VorSK50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK (a) (b) (c) (d) (e) (f) Figure 8.20: Trigger rates (top) and efficiencies (bottom) using different constituent-level pileup suppression methods, as well as no pileup suppression. The turn-on curves are built with online pT cuts at fixed-rate threshold. The efficiencies are shown for the di-Higgs signal sample and the ConeTopo online jet collection built from input topoclusters with ET > 3 GeV. 226 050100150 [GeV]T1st Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 3 GeVT42 EM Topoclusters EInput-level pileup suppression60 kHzNoneSKVorSK0204060 [GeV]T3rd Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 3 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzConeTopo+EOR ConeTopo+EOR SKConeTopo+EOR VorSK02040 [GeV]T4th Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 3 GeVT42 EM Topoclusters E| < 2.5jeth|50 kHzConeTopo+EOR ConeTopo+EOR SKConeTopo+EOR VorSK50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 3 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 3 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 3 GeVT42 EM Topoclusters EInput-level pileup suppressionNoneSKVorSK 8.3.4 Preliminary firmware simulation A preliminary firmware simulation of the cone jet algorithm was performed in order to get an estimate of FPGA resource utilization. As seen in the previous sections, this simulation informed the development process. The simulation was performed using the Vitis High-Level Synthesis (HLS) software suite provided by the company Advanced Micro Devices (AMD), the same company manufacturing the FPGA boards that will be used in the GT. The package provides a software developer friendly interface to synthesize hardware code starting from a software algorithm written in C/C++. For the purpose of this study, HLS was used to have a fast turn-around for an estimate of the utilization of resources. However, this workflow would similarly speed up future optimization work in terms of throughput, power, and latency. The workflow to go from the software version of the algorithm, to the register-transfer level (RTL) abstraction used in hardware description languages, is the following: 1. Software algorithm. Develop the algorithm in software. If not already the case, provide a version written in C. In practice, the main requirement is to avoid dynamic memory allocation. As the set of resources is fixed on the FPGA, dynamic creation and freeing of memory cannot be implemented. 2. Testbench. Provide a set of input samples for testing. For each sample, provide the expected output for validating the results. Write a testbench that reads the input test files, runs the software algorithm, and compares the output with the expected result. This will be used to check that the C function is functionally correct prior to synthesis. It is also used to verify the RTL output. 3. C-simulation. The testbench is used to compile and execute the C simulation and validate that the C design of the algorithm produces the expected output. 4. Synthesis: Synthesize the C algorithm in an RTL implementation. Vitis HLS will effectively compile the C code into hardware description language. Both VHDL and Verilog are provided. 5. C-RTL Cosimulation.: Use the C testbench to validate the RTL design and to confirm that the hardware implementation produces the same output as the C-level code. 6. Analysis. Fine-tune the hardware design with code directives. Produce different RTL versions and analyze the designs by looking at the reports of the resource utilization, latency, and throughput. 227 7. IP-Block. Export RTL design as an IP block that can be integrated into the hardware. In the studies presented here, steps 1–5 were performed. The software algorithm to be analyzed was the cone jet algorithm described in the previous section, with a few differences. The energy overlap removal step was not included in the simulation. It was also assumed that the input list of topoclusters would be provided already sorted by ET . This is a reasonable assumption, as several downstream algorithms using topoclusters as inputs might require some type of sorting, motivating centralizing this step in the first SLRs. The C version of the algorithm was provided assuming the non-optimized values of N MAX SEED = 10 and N MAX CONSTITUENT = 40. To perform the simulation, the user has to input the clock period, the clock uncertainty, and the FPGA target. The target clock period was set to the GT rate of 240 MHz, or 4.17 ns. The uncertainty was left as the default one, taken to be 12.5% of the clock period. The target device was left as the default target device, a Virtex UltraScale+ FPGA, as Vitis did not offer the target device for the GT. The clock latency is the latency of a clock cycle. Therefore, the latency of the algorithm is defined as the number of cycles it takes to produce the output multiplied by the clock latency. When synthesizing the hardware implementation, HLS determines which operations occur during each clock cycle according to the target clock frequency and the time it takes for the operation to complete on the target device. This is referred to as scheduling. The next step is binding, where the software organizes the scheduled operations onto the chip, determining which hardware resources will implement them. Once the sequence of operations is finalized, it is extracted as an RTL design, which is analyzed to obtain the performance and resource estimates. The resource utilization is examined in terms of the following resources: the num- ber of digital signal processors (DSPs), specialized units for multiplication and arithmetic; the number of look-up tables (LUTs), units for logic and storage functionalities; and the number Flip-Flops (FFs), binary shift registers used to register data in time with the clock. The result of the synthesis of the cone algorithm was the following. The estimate of the fastest achievable clock frequency was 3.027 ns, while the latency of the algorithm was 378 cycles. This gives a latency of 1.144µs, which is within the GT requirements. The resources used to implement the design are shown in Tab. 8.1, both in terms of absolute numbers and of fraction of resources of a single SLR on a VP1802, the target device for the GT. The estimates are close to the expected FPGA budget for jet reconstruction, currently set at 20% of one SLR. Note that the simulation was performed using floating point data-types, but a more accurate and conservative estimate should be obtained with fixed-point precision. The simulation served to understand roadblocks in the algorithm design. For instance, earlier results prompted the investigation of a different recombination scheme to reduce the 228 Absolute numbers % VP1802 single SLR resources DSP 681 19 FF 131719 7.8 LUT 81755 9.7 Table 8.1: FPGA resources utilization of the cone jet algorithm from a preliminary firmware simulation. FPGA footprint. Ultimately, the purpose of this study was to confirm that the algorithm could be a viable option for the GT. The optimization of the firmware was deferred, as this required a final version of the cone jet algorithm, which will only be possible once a more mature picture of the other algorithms on the Global Event Processor will be available. Nonetheless, these preliminary results were indeed promising. 8.4 Pileup-jet rejection with neural networks The cone jet reconstruction algorithm described in the previous section was shown to have equivalent performance to the offline anti-kt algorithm run on online topological clusters (AntiKt422). This was already a significant result, as the AntiKt422 collection represents the upper bound on jet reconstruction performance in the GT. Nevertheless, the question remained of whether this performance sufficed to meet the physics objectives of the experi- ment. If not, it would become crucial to find new avenues to further improve the algorithm’s effectiveness. One of the main difficulties foreseen at the HL-LHC is the extreme pileup environment, with up to 200 secondary interactions per bunch crossing. As described in Sec. 5.5, pileup can significantly impact object reconstruction. In the case of jets, pileup introduces a positive bias in the reconstructed transverse momentum and causes an overall resolution degradation of the reconstructed kinematic quantities. While these effects were discussed in the context of offline reconstruction, they similarly affect the online reconstructed jets, with additional consequences. On one side, the positive bias has the effect of artificially increasing the rate of high energy background jets, which, as discussed in the previous section, pushes the accep- tance thresholds to higher pT values. On the other, the smearing due to pileup fluctuations worsens the online jet pT resolution, making the turn-on curve less steep. In addition, pileup represents a source of noise in the event reconstruction and identification process, further complicating the trigger selection task and requiring more sophisticated trigger algorithms to retain the same signal-to-background discrimination power. Clearly, pileup mitigation is an important factor in hadronic triggers performance and it is particularly relevant for signals sensitive to the trigger pT thresholds, such as hh b¯bb¯b. → 229 Measurement of di-Higgs production is one of the most pressing experimental goals of the collaboration, being a direct probe of the Higgs boson self-coupling λ, which is still unmeasured (see Sec. 3.1). This is a challenging measurement, as the production cross section of a Higgs boson pair is very low, with two Higgs bosons being produced every one in a trillion events. Sensitivity to λ4 is complicated further by a destructive interference between the two contributing diagrams, shown in Fig. 8.21. Only the low mhh mass region remains sensitive to possible deviations from the SM Higgs self-coupling, an experimentally difficult phase space dominated by pileup. Due to these difficulties, the latest results from ATLAS and CMS using the full Run 2 dataset have only been able to set limits [7, 8]. However, the HL-LHC is expected to reach the ultimate sensitivity, with the current projected signal significance with (without) systematic uncertainties at 4.0 σ (4.5 σ) [9]. Advances in trigger, reconstruction, and analysis strategies in the incoming years could push these predictions to the level of a 5σ discovery. This unprecedented opportunity makes di-Higgs production one of the flagship signatures of the HL-LHC upgrade. → The decay channel hh b¯bb¯b (hh4b) has one of the largest sensitivities thanks to the largest decay branching ratio of the Higgs boson into b-quarks. In the low mass non-resonant region, the hh4b final state is characterized by four low energy jets, a region of phase space dominated by multi-jet background and pileup. Measurement of non-resonant hh4b critically relies on multi-jet trigger thresholds and is one of the key challenges and drivers of the HL- LHC trigger upgrade, starting from the GT. In this section, a new method for mitigating b¯bb¯b signal the impact of pileup on the Level-0 multi-jet trigger performance targeting hh is investigated. → Figure 8.21: Leading order diagrams contributing to gluon-gluon fusion di-Higgs production cross section. Only the left diagram depends on the Higgs self-coupling λ. 8.4.1 Pileup jet identification Pileup collisions are uncorrelated from the hard scatter and produce an approximately uni- form distribution of low transverse momentum particles in the detector volume. When run- 4Results for measurements of the Higgs boson couplings are typically presented in terms of coupling mod- /λSM . 3 ifiers. For instance, the coupling modifier of the Higgs trilinear self-coupling is given by κλ = λ Obs 3 230 ggHHκλHgHgHκtκt ning a jet reconstruction algorithm, these low energy deposits can end up being recombined into a jet. As the pileup levels increase, the number of these soft pileup particles increases as well and the overlap of these low energy depositions can lead to the reconstruction of high energy topoclusters and jets. In the following, a jet whose transverse momentum is mostly due to pileup particles will be referred to as pileup jet, while a jet originating from a hard quark or gluon produced in the hard scatter is referred to as signal jet. It is precisely these high energy pileup jets that are problematic for the trigger, as they fictitiously increase the rates of high energy jets, pushing the pT thresholds up. This is particularly relevant for multi-jet triggers. To improve the trigger performance, one would like to identify and reject high energy pileup jets before the trigger selection is applied. This is expected to reduce the background rates, which in turn allows to reduce the pT thresholds. In this study, the use of deep learning to identify and reject pileup jets in the GT is investigated5. The likelihood of a jet to be a pileup jet is determined by the amount of pileup con- tamination that contributes to the jet energy. Different pieces of information are typically used to identify pileup particles offline, but not all of them will be available in the GT. Tracking information is an effective tool, as it allows to determine the number of associated tracks originating from pileup vertices. However, this information will not be accessible in the ATLAS Level-0 trigger. Another good metric to identify pileup particles is that they are soft. Because pileup contributes uniformly to the event kinematics and the level of pileup fluctuates between events, how soft a particle has to be for it to be identified as pileup is event-dependent. A metric of the pileup activity in the event is necessary to make the most well-informed decision on this cutoff. This is, in fact, the strategy adopted by offline pileup suppression algorithms, such as Soft-Killer. Whether a metric of the pileup event density or Soft-Killer itself will be available in the GT is still under study. One last piece of information remains, which is the local energy and multiplicity distribution of the jet’s constituents. In fact, this information will be accessible for the first time in the Level-0 trigger thanks to the ability to reconstruct topoclusters from the full granularity calorimeter information. How this information can be useful is discussed next. Pileup particles are uniformly distributed in the detector and, when clustered into a jet, they cause a uniform smearing of the jet image. This results in distinctly different energy profiles between signal and pileup jets, as shown in Fig. 8.22. These plots were produced in the following way. The jets6 were built with all the topoclusters above a given ET threshold, 5Pileup contamination of signal jets can also occur, causing a loss of energy resolution. Therefore, another avenue to improve the trigger performance would be to improve the jet energy resolution and make the turn- on curve steeper, which, for instance, could be implemented as a regression task of the true online jet energy. While this is an option worth investigating, this work focused only on the jet-rejection strategy. 6These studies were performed using jets produced with an earlier version of the cone algorithm. The jets 231 without pileup suppression. After the jets were formed, each jet’s constituents were compared with the Soft-Killer pileup suppressed topocluster collection to determine whether a given topocluster would have been pileup suppressed or not. The jet energy profile was then plotted by separating the contribution from the constituents that would have been pileup suppressed and the ones that would have not. This is shown for both signal (QCD)7 and pileup jets. The content of each bin is given by the sum of the ET of the jet constituents at the given dR distance from the jet center. The histograms are shown in bins of reconstructed jet pT : [15, 35], [35, 50], and [50, 70] GeV. Radiation that is deemed “pileup-like” by Soft-Killer is uniform and low in energy, producing a linearly increasing energy profile. This feature is identical for signal and pileup jets, subject to the same uniform pileup contamination. After pileup-suppressed topoclusters are removed, the energy profile of signal jets peaks close to the center of the jet and falls off rapidly at large radii, while the profile of pileup jets in the lowest pT bin remains uniform. As the jet pT increases, the jet energy profile of pileup jets becomes increasingly more signal-like even after pileup suppression, losing most of the discrimination power for jets with pT above 50 GeV. Nevertheless, as the region of interest for multi-jet trigger rates falls below this threshold, local information on the jet’s constituents is a promising discriminant. The goal of this study was therefore to determine whether the local distribution of a jet’s constituents could be sufficient to identify pileup jets. Clearly, this approach does not address the fact that the difference in energy profile is still dependent on the pileup event- density. In order to address this, the use of additional information from the output of offline particle-level pileup suppression algorithms was also investigated, representing the upper bound on the performance of this pileup jet rejection technique in the GT. were built with input topoclusters with ET > 1 GeV and with a seed removal strategy that used dR = 0.3. This is the cause of the upward shift in some histograms at dR = 0.3, where jets overlap starts being allowed. 7The signal jets in this study are jets reconstructed in di-jet events and truth matched to a truth quark. 232 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 8.22: Jet energy profile of cone jets built with seed removal using dR = 0.3. Com- paring all constituents (left), only constituents that would have not been pileup suppressed (center), and constituents that would have been pileup suppressed (right). The jets are sep- arated into pT bins (from top to bottom): [15, 35], [35, 50], and [50, 70] GeV. 233 00.10.20.30.4dR(cluster, seed)00.050.10.15constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [15, 35] GeVjetT| < 2.5, pjeth|All clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.15constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [15, 35] GeVjetT| < 2.5, pjeth|Not SK pileup suppressed clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.15constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [15, 35] GeVjetT| < 2.5, pjeth|SK pileup suppressed clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.15constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [35, 50] GeVjetT| < 2.5, pjeth|All clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.150.2constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [35, 50] GeVjetT| < 2.5, pjeth|Not SK pileup suppressed clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.15constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [35, 50] GeVjetT| < 2.5, pjeth|SK pileup suppressed clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.150.2constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [50, 70] GeVjetT| < 2.5, pjeth|All clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.150.2constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [50, 70] GeVjetT| < 2.5, pjeth|Not SK pileup suppressed clustersQCD jetPileup jet00.10.20.30.4dR(cluster, seed)00.050.10.15constTNormalized Energy Profile EHL-LHC Simulation>=200m<> 1 GeVconstTConeTopoJets, E = [50, 70] GeVjetT| < 2.5, pjeth|SK pileup suppressed clustersQCD jetPileup jet 8.4.2 Neural network development A deep neural network (DNN) was developed as a jet-by-jet classifier to output the proba- bility p of a jet to be signal (p = 1) or pileup (p = 0). Two different DNNs were trained using different input variables. Training samples The training samples were formed starting from the multi-jet samples described in Sec. 8.2.1. The subset of pileup jets was selected from the minimum bias sample, which is generated with truth di-jet transverse momenta in the range [0, 20] GeV, while requiring the jets not to be truth-matched. The subset of signal jets was obtained from the combination of several pT slices of multi-jet samples, with truth di-jet transverse momenta up to 800 GeV. The jets were further required to be truth-matched to one of the two truth quarks. For this reason, in the following “signal jet” and “QCD jet” is used interchangeably. This choice of signal jets avoided the issue of training the networks on the same set of hh4b events of interest. The jet collection used for the training jets were ConeTopo jets built with topoclusters with ET > 1 GeV and the seed removal strategy with dR = 0.4 applied. Energy overlap removal was not applied in order to preserve the circular shape of the jets and avoid confusing the network during training. For the same reason, only jets whose leading ET constituent corresponded to the seed were accepted, to avoid the rare case of a higher energy seed removed by the seed removal strategy having entered a jet built from a lower energy seed. The selected signal and background samples are characterized by distinctly different pT distributions, with signal jets covering a wide pT range, and background jets peaking at small values. To prevent the network from classifying merely based on jet pT , different measures were implemented. First, the training was performed only in the region around the region of interest, targeting jets with pT between 25 and 50 GeV. Jets below this threshold were excluded as they would have negligible impact on the rates determining the online trigger pT cut. For jets above this threshold, the discrimination power in the local distribution of the jet constituents was observed to degrade, as shown in Fig. 8.22h. In addition, the samples were reweighted to have a uniform pT distribution and balanced class normalization. The dataset was split into training, testing, and validation subsets. After requiring the [25, 50] GeV, the number of training samples was reduced to approximately jets to have pT ∈ 500, 000. Input variables A set of input variables was optimized to describe the N constituents with highest ET . Three types of information were identified to describe each topocluster in the jet: the spatial 234 location in the jet’s reference frame, the transverse energy, and some metric of the likelihood of the topocluster of being a pileup-particle. Different input variables were considered for each case. In the following, the selection process is described, while the distributions are provided later with the network performance. The number of leading topoclusters to provide to the network was fixed at N = 10. This was motivated by the fact that the jet constituent multiplicity distributions peak below 10 (see Fig. 9.10) and the discrimination power of the input variables between signal and background for the nth leading topocluster decreases for increasing n, as will be shown in Fig. 8.25 and 8.24. The inclusion of an input variable providing the number of jet constituents was tested to compensate for this approximation, but was observed to not bring any improvement. The expectation is that an even smaller value of N might be used, but this choice was not optimized. The location of a given constituent was provided both in terms of ∆η and ∆ϕ distances between the constituent and the jet, as well as simply in terms of the ∆R. The additional information from the coordinates was found to not bring any improvement, so only the ∆R(constituent, jet) values were provided. Note that, by construction, the coordinates of the jet are identical to the coordinates of the seed and of the leading topocluster. The raw energy of the constituents is highly correlated to the jet pT and providing this information to the network resulted in the classification being based almost exclusively on the jet pT . In order to remove this dependence, but still provide a metric representative of the jet’s energy profile, the transverse energy of the constituents was normalized to the transverse energy of the leading constituent. Equivalent results were obtained by normalizing to the jet pT , with no improvement observed by providing both. The likelihood of a topocluster being pileup suppressed depends on the topocluster ET in relation to the event-wide pileup density. However, it is unclear whether such a metric will be available, so two strategies were employed. The first model was trained without any information related to pileup suppression. This will be referred to as DNN-A. The second model was trained including for each jet constituent a boolean flag of whether the topocluster was suppressed by the SK algorithm, in practice providing the same information as what shown in Fig. 8.22. This will be referred to as DNN-B. The training was performed using cone jets built with non-pileup suppressed topoclusters. The performance of DNN-B is expected to be an upper bound on what can be obtained form this technique. If DNN-A is sufficient to improve the trigger performance, the conclusion is that SK is not needed in the GT. If, instead, DNN-A is not sufficient, then DNN-B allows to test whether including information from the SK algorithm can further improve the trigger performance more than running jet reconstruction on pileup suppressed topoclusters. 235 8.4.3 Training and performance evaluation The DNNs were trained using Keras with TensorFlow [197] backend. The model hyper- parameters were optimized using a grid-search. The same architecture was used for both networks, as no significant variations were observed by varying the hyperparameters. The final model was a deep fully-connected NN with two hidden layers with 50 nodes each and ReLU activation functions. The model had one output node with sigmoid activation function representing the probability of a jet to be signal. The NN was trained optimizing the binary cross-entropy loss with the Adam optimizer, using a learning rate of 1.e-4, 80 epochs, and a batch size of 500. T /Elead cl T The input variables were defined to describe each of the 10 leading topoclusters in the jet. The final set of input variables were chosen to be the distance ∆R(cl, lead cl) and the energy ratio Ecl between each topocluster and the leading topocluster in the Information on the leading topocluster was removed, as by construction the leading jet. topocluster has ∆R = 0 and Ecl = 1. In addition, a boolean pileup-suppression flag was included only for the training of DNN-B. This gives 18 input variables for DNN-A and 27 input variables for DNN-B. The training dataset was reweighted to have flat jet pT and class distributions, and only jets with pT in the range [25, 50] GeV were used for training. Note that no reweighting was applied to the validation and testing datasets. T /Elead cl T The final metrics computed on the validation dataset for DNN-A and DNN-B are shown in Tab. 8.2. The accuracy is the percentage of correct predictions, or the sum of the true positive and true negative rates. The recall represents the rate of true positives: the percentage of signal samples correctly identified as signal. The precision is inversely proportional to the rate of false positives: the higher the precision, the larger the percentage of samples identified as signal that are true signals. The area under the ROC curve (AUC ), or the true positive rate as a function of the true negative rate, represents the trade-off between signal efficiency and background rejection. The higher the area, the smaller the trade-off. The precision- recall curve (PRC ) represents the trade-off between accurate positive results and relevant positive results. A high area under the PRC curve indicates low false positive and low false negative rates. The precision is equivalent between the two models, while DNN-A has a lower accuracy and recall, resulting in lower AUC and PRC. In particular, DNN-A has a harder time at accurately classifying signal jets, with a higher rate of false negatives (true signal predicted as background). An unbiased evaluation of the model performance was obtained on the unseen testing dataset. Fig. 8.23 shows the comparison between DNN-A and DNN-B performance in terms In particular, for the latter, of raw output scores, confusion matrices, and ROC curves. 236 DNN-A DNN-B Accuracy Precision Recall AUC PRC 0.73 0.80 0.77 0.76 0.82 0.76 0.81 0.82 0.80 0.85 Table 8.2: Training metrics computed on validation dataset for DNN-A and DNN-B. See text for explanation. specific working points (WPs) at fixed signal efficiency are provided for comparison and for later use. As expected from the training results, DNN-A has a slightly lower performance. From the confusion matrices, which are built using the default classification score at 0.5, one can see that DNN-A has a higher rate of signal jets identified as background (23% instead of 18%). While this difference is not dramatic, one has to look at WPs relevant for the scope of the trigger, where only a minimum signal loss can be tolerated. For signal efficiencies above 85%, DNN-A shows a significantly larger background efficiency than DNN-B. As shown later, this difference will have a significant impact in trigger performance. In Fig. 8.24 and 8.25, the input variables are shown for selected nth leading topoclusters. In order to visualize what the network is learning, the distributions are shown separately for samples tagged according to the true and predicted label. Note that the predicted label is set by using a cut score of 0.5. The results are shown for DNN-B and similar results were obtained for DNN-A. The agreement between the true and predicted distributions indicates that the network is learning the true PDFs. Deviations appear mostly in the distribution of the dR between the higher energy topoclusters and the leading one, as the network learns that signal jets are more collimated and with the leading constituents carrying most of the jet transverse energy, while background jets are more diffuse and with a move even energy sharing among the constituents. Fig. 8.26 shows similar distributions for out-of-training variables. From Figs. 8.26a and 8.26b, one can see that the network learns that signal jets have, on average, fewer constituents and fewer pileup suppressed constituents. Figs. 8.26c and 8.26d show that the network is not biased by the ET of the leading topocluster as a result of reweighting the training dataset to have a flat jet pT distribution, and that it correctly learns the correlation between the ET of the leading topocluster and the pT of the jet. Lastly, Fig. 8.27 compares the true and predicted distributions in terms of the jet pT for DNN-A and DNN-B. While the pT reweighting mostly succeeds in removing the bias from the jet pT , some pT dependence remains. From these plots it is clear that the source of false negatives (true signal classified as background) identified in the previous discussion comes from low transverse momentum signal jets. The misclassification is more pronounced 237 (a) (b) (c) (d) (e) (f) Figure 8.23: Comparison of testing performance in terms of output score (left), confusion matrix (center), and ROC curve (right) between DNN-A (top) and DNN-B (bottom). for DNN-A, as expected. These low energy signal jets are the ones with a less collimated energy profile and without a handle on the pileup event density through the Soft-Killer flag, a greater number of these jets is wrongly identified as pileup. 8.4.4 Trigger performance The two DNNs were deployed in the Global Trigger simulation framework to study their effect at on the trigger performance. The same ConeTopo jet collection used for training was used here, with the addition of energy overlap removal. However, similar results were observed for the cone jet collection without EOR, as well as for AntiKt422 jets. In the following, a jet is said to be “in-training” if its transverse momentum is in the training range [25, 50] GeV. For each model, the procedure was as follows. Every reconstructed jet that would normally enter the trigger workflow is passed through 238 0.00.20.40.60.8DNNScore0123456A.U.normalizedtounityTrueclassPileupQCDPileupQCDPredictedLabelPileupQCDTrueLabel0.640.360.230.77Testingsample–DNN-A0.00.20.40.60.81.00.00.20.40.60.81.0QCDsignalefficiency100101Pileprejection(1/(cid:15)bkg)(cid:15)bkg=84.0%,(cid:15)sig=98.0%,score=0.17(cid:15)bkg=70.4%,(cid:15)sig=95.0%,score=0.26(cid:15)bkg=55.9%,(cid:15)sig=90.0%,score=0.35(cid:15)bkg=46.2%,(cid:15)sig=85.0%,score=0.42(cid:15)bkg=39.0%,(cid:15)sig=80.0%,score=0.48TestingSample–DNN-A0.00.20.40.60.8DNNScore0123456A.U.normalizedtounityTrueclassPileupQCDPileupQCDPredictedLabelPileupQCDTrueLabel0.660.340.180.82Testingsample–DNN-B0.00.20.40.60.81.00.00.20.40.60.81.0QCDsignalefficiency100101Pileprejection(1/(cid:15)bkg)(cid:15)bkg=71.8%,(cid:15)sig=98.0%,score=0.17(cid:15)bkg=57.4%,(cid:15)sig=95.0%,score=0.29(cid:15)bkg=45.5%,(cid:15)sig=90.0%,score=0.4(cid:15)bkg=37.9%,(cid:15)sig=85.0%,score=0.47(cid:15)bkg=32.3%,(cid:15)sig=80.0%,score=0.52TestingSample–DNN-B (a) (b) (c) (d) (e) (f) (g) (h) Figure 8.24: Transverse energy of the nth leading constituent normalized to transverse en- ergy of the leading constituent. The distributions are separated according to the true and predicted label. each of the two DNNs. The scores for the four leading jets with in-training pT are shown in Fig. 8.28 for the minimum bias, hh4b, and di-jet samples. Note that the DNNs correctly identify jets from the di-Higgs sample as signal-like. More confusion is present for the di-jet 800] GeV truth pT slice is used in these studies), where the third sample (only the [400 and fourth jets are typically soft. Note that the two leading jets in the di-jet sample have very few statistics, as they populate higher pT bins. − Next, a cut on the score at a fixed signal efficiency WP (according to Figs. 8.23c and 8.23f) is applied to all jets that enter the study. Each WP produces a new jet collection of “DNN pileup suppressed” jets, where only jets that have a score above the given cut are retained. The “baseline” jet collection without any DNN selection is also shown for comparison. The pT spectra of the fourth leading jet after the DNN selection at different WPs are shown in Fig. 8.29 and 8.30 for DNN-A and DNN-B, respectively. Notably, these plots show that to retain a high enough signal efficiency for low pT jets, the background rejection of DNN-A is significantly reduced, while for DNN-B more than 50% of background jets are rejected across the full pT range. This has direct consequences on the rates. The trigger rates are built with the minimum bias sample for the different jet collections. 239 0.00.20.40.60.81.0ECl2T/ECl1T0.00.51.01.52.0A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.20.40.60.81.0ECl3T/ECl1T0.00.51.01.52.02.53.0A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.20.40.60.81.0ECl4T/ECl1T012345A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.20.40.60.8ECl5T/ECl1T01234567A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.20.40.60.8ECl6T/ECl1T02468A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.20.40.6ECl8T/ECl1T024681012A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.40.50.6ECl9T/ECl1T024681012A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.40.50.6ECl10T/ECl1T02468101214A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD (a) (b) (c) (d) (e) (f) (g) (h) Figure 8.25: Distance ∆R between the nth leading constituent and jet. The distributions are separated according to the true and predicted label. (a) (b) (c) (d) Figure 8.26: Selected out-of-training variables. The distributions are separated according to the true and predicted label. These are shown in Fig. 8.31 for both models. Note that two strategies are compared in these plots. One strategy applies the DNN cut on all jets, while the other only on in-training jets. As these plots show, applying the DNN cut on all jets has a negligible impact on the rates, mostly because very few minimum bias events have fourth-leading jets with pT above It was therefore decided to only apply the DNN cut on jets with pT < 50 GeV 50 GeV. in order to retain the maximum signal efficiency. As expected, the lower the WP signal 240 0.00.10.20.30.4dRCl1,Cl2024681012A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.4dRCl1,Cl3012345678A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.4dRCl1,Cl401234567A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.4dRCl1,Cl501234567A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.4dRCl1,Cl601234567A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.4dRCl1,Cl8012345678A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.4dRCl1,Cl901234567A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.00.10.20.30.4dRCl1,Cl10012345678A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD05101520Nconstituents0.00.20.40.60.81.01.21.4A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD05101520NPUsuppressedconstituents0.000.250.500.751.001.251.501.75A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD1020304050ECl1T0.000.050.100.150.20A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD0.20.40.60.81.0ECl1T/pjetT01234567A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD (a) (b) Figure 8.27: Out-of-training jet pT distribution tagged according to true and predicted label for DNN-A (left) and DNN-B (right). efficiency, the more background jets are rejected, and hence the larger the decrease in high energy pileup jets. Because DNN-B reaches a higher background rejection at fixed signal efficiency, it can obtain lower online pT cuts. Lastly, the effect on the trigger efficiencies was studied. Fig. 8.32 shows the trigger ef- ficiencies comparing different WPs for both models. Increasing the background rejection with tighter WPs is observed to worsen the resolution while not improving the 100% ef- ficiency threshold, so the 95% WP was selected for both models as the best performing option. Fig. 8.33 shows the final comparison of the best WPs for DNN-A and DNN-B. For comparison, the plot includes also the trigger efficiencies obtained by running the same cone jet reconstruction algorithm without DNN cut on pileup suppressed topoclusters using both Soft-Killer alone and Voronoi+Soft-Killer. The lower background rejection of DNN-A, which keeps the rates and the online pT cut higher, results in only a minor improvement with re- spect to the baseline scenario. On the other hand, DNN-B has a visible impact on the offline pT threshold. However, when compared to applying Soft-Killer on the input topocluster collection, it results in a similar performance. 241 253035404550JetpT[GeV]0.000.050.100.150.20A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD253035404550JetpT[GeV]0.000.050.100.150.20A.U.normalizedtounityTruePileupTrueQCDPredPileupPredQCD (a) (b) (c) (d) (e) (f) Figure 8.28: Output DNN-A (top) and DNN-B (bottom) scores for the four leading jets in minimum bias (left), di-Higgs (center), and di-jet (right) events, when the jet has an in-training pT . (a) (b) (c) Figure 8.29: Fourth-leading jet pT distribution after applying DNN-A selection at different WPs in minimum bias (left), di-Higgs (center), and di-jet (right) events. 242 00.20.40.60.8DNN-A Score020403-10·Normalized to unityHL-LHC Simulation>=200m=200m=200m< = [400,800] GeVtruthTDi-jet, pConeTopo+EOR Jets = [25, 50] GeVTpJet 1Jet 2Jet 3Jet 400.20.40.60.8DNN-B Score00.050.1Normalized to unityHL-LHC Simulation>=200m=200m=200m< = [400,800] GeVtruthTDi-jet, pConeTopo+EOR Jets = [25, 50] GeVTpJet 1Jet 2Jet 3Jet 4110210310410510610A.U.HL-LHC Simulation>=200m=200m=200m< = [400,800] GeVtruthTDi-jet, pConeTopo+EOR JetsDNN-ABaseline98 % WP95 % WP90 % WP85 % WP80 % WP2030405060 Jet 4 [GeV]Tp00.51Ratio (a) (b) (c) Figure 8.30: Fourth-leading jet pT distribution after applying DNN-B selection at different WPs in minimum bias (left), di-Higgs (center), and di-jet (right) events. (a) (b) Figure 8.31: Four-jet trigger rates produced with minimum bias sample after applying the DNN selection at 80% and 95% WPs, as well as when using the baseline jet collection. For each WP, the rates are compared when applying the cut to all jets or only to in-training jets with pT ∈ [20, 50] GeV. The results are shown for DNN-A (left) and DNN-B (right). 243 110210310410510610A.U.HL-LHC Simulation>=200m=200m=200m< = [400,800] GeVtruthTDi-jet, pConeTopo+EOR JetsDNN-BBaseline98 % WP95 % WP90 % WP85 % WP80 % WP2030405060 Jet 4 [GeV]Tp00.51Ratio0204060 [GeV]T4th Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 1 GeVTCalo422 Topoclusters EDNN-A50 kHzBaseline95 % WP All events95 % WP In-training80 % WP All events80 % WP In-training0204060 [GeV]T4th Leading jet p110210310410510610Trigger rate [kHz]HL-LHC Simulation>=200m 1 GeVTCalo422 Topoclusters EDNN-B50 kHzBaseline95 % WP All events95 % WP In-training80 % WP All events80 % WP In-training (a) (b) Figure 8.32: Four-jet trigger efficiencies for hh4b signal sample after applying the DNN selection at different WPs to jets with pT < 50 GeV, as well as when using the baseline jet collection. The results are shown for DNN-A (left) and DNN-B (right). Figure 8.33: Four-jet trigger efficiencies for hh4b signal sample after applying the DNN-A and DNN-B selections at 95% WP, as well as the baseline jet collection and the jet collections produced with the same ConeTopo+EOR algorithm run on SK or VorSK pileup suppressed topocluster collections. 244 20406080100 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 1 GeVTCalo422 Topoclusters EDNN-A WPs In-trainingBaseline95 % WP90 % WP80 % WP20406080100 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 1 GeVTCalo422 Topoclusters EDNN-B WPs In-trainingBaseline95 % WP90 % WP80 % WP20406080100 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 1 GeVTCalo422 Topoclusters EBaselineDNN-A DNN 95 % WP In-trainingDNN-B DNN 95 % WP In-trainingSKVorSK Chapter 9 Conclusion and outlook Search for new heavy resonances The search for heavy resonances has been the focus of intense efforts by the ATLAS Col- laboration in looking for physics beyond the Standard Model (SM). Several well-motivated models predict that new heavy particles should appear at the TeV scale and decay into highly Lorentz-boosted SM bosons. These models are often interpreted in the context of two general frameworks, the Heavy Vector Triplet model, which predicts an additional SU(2) triplet, and the Two-Higgs-Doublet-Model, which predicts the simplest extension of the SM scalar sector, by including an additional scalar SU(2) doublet. Since the largest branching ratios of W, Z, and Higgs boson decays are into a pair of quarks, boosted jet tagging plays an essential role in this type of searches. The work performed in this thesis contributed to the search for such new heavy resonances by looking for decays of the new particles into two SM bosons (VV or VH) in semi-leptonic final states. To increase the physics reach of this type of search, a new analysis strategy based on deep-learning algorithms was implemented, with several potential extensions envisioned for the future. The main contribution of this work was the development of a new deep neural network for the identification of the hadronic decay as coming from a Higgs boson, a W boson, a Z boson, a top quark, or light quarks and gluons. The development of the Multi-Class Tagger (MCT) focused first on large-R jet classification for general boosted decays and was then extended to the resolved jet topology in the context of the analysis. The development included the training of the DNNs, as well as the deployment within the analysis. The latter included the design of a new orthogonalization strategy of the final regions of the analysis, to compare with previous strategies in other VV and VH combination efforts. The conclusion was that the new MCT strategy does not cause any loss in sensitivity, while it allows to recover up to 20% loss in sensitivity at high resonance mass with respect to the previous efforts. Lastly, the modeling of the MCT scores was studied in the pre-selection and control regions of the analysis. After accounting for normalization differences between background and data by deriving normalization scale factors, the MCT was shown to be 245 well-modeled and to not need calibrations. Although not discussed in this thesis, the way the MCT was envisioned allows for a straightforward extension to aid in the definition of top- and QCD-enriched control regions. Output scores of the MCT would also be candidate high-level inputs to a possible event-level classifier. These are ideas that can be explored in the future, both in the VV/VH semi-leptonic search, and in other similar searches for heavy resonances. Upgrade of the HL-LHC Level-0 Trigger × 2s− 1034cm− The LHC will soon undergo a major upgrade that will raise the center-of-mass energy to √s = 1. The resulting High- 14 TeV and bring the instantaneous luminosity up to 5 Luminosity LHC (HL-LHC) will bring a tenfold increase in the data collected by ATLAS, which will extend the physics reach of the experiment largely beyond the original design. At the same time, the increase in luminosity will inevitably generate higher levels of pileup and radiation, requiring substantial upgrades of the ATLAS detector and TDAQ system to face the harsher conditions. A significant part of this thesis work has involved contributions to the Phase II upgrade of the hardware-based trigger system in preparation for the HL-LHC. This included the development and maintenance of a software simulation framework for the study of new firmware algorithms, as well as the development of a new jet reconstruction and triggering strategy. A cone algorithm was developed for jet reconstruction in the Global Trigger. While a coarser option than anti-kt, the standard for offline jet reconstruction, the cone algorithm has been shown to provide equivalent performance. This includes performance metrics such as trigger rates, trigger efficiencies, and signal efficiencies for the specific offline analysis tar- geting di-Higgs production. Several parameters had to be optimized and their effect and correlations had to be understood to arrive to this result. Different viable options have been identified, with their respective advantages and drawbacks. The finalized set of parameters will be determined by the trade-off between physics performance and hardware resource con- sumption. Both of these factors are deeply interconnected to the requirements of the other algorithms that will run on the hardware, most of which are still under development. Nev- ertheless, this research demonstrated what choices and trade-offs will need to be addressed before arriving to the final version, and conclusively established the cone jet algorithm as a viable option for the Global Trigger, with promising avenues for extension to τ -lepton and large-R jet reconstruction. Due to the nature of hadron-hadron collisions, pileup is an ever-present issue at the LHC, affecting the reconstruction of physical observables and stressing the detector and TDAQ systems. This is particularly true for a multi-jet trigger, which looks for jets in kinematic 246 b¯bb¯b. As regions dominated by pileup, and on which important signatures rely, such as HH the LHC moves towards the high-luminosity era, pileup mitigation will become increasingly challenging, but also necessary to retain the physics reach of the experiment. → This work introduced a novel deep-learning approach for pileup mitigation, with the goal of reducing the rates of high energy background jets in the Level-0 trigger. To accomplish this, two neural networks were trained for the identification and removal of pileup jets us- ing only information about the constituent topological clusters, making full use of the full granularity calorimeter information that will become accessible for the first time at the first stage of the trigger. The first model (DNN-A) utilizes only energy and spatial information of the topological clusters, while the second model (DNN-B) was additionally provided with boolean flags representing the outcome of the Soft-Killer pileup suppression algorithm for each constituent. Both neural networks were found to reduce the rate of background pileup jets. However, including the results of the offline pileup suppression in the input data proved necessary to achieve substantial improvements in the trigger efficiencies. These results suggested that an event-level characterization of the pileup density is needed in the input data to observe a substantial reduction in the trigger thresholds. Nevertheless, this study demonstrated that significant discrimination power between signal and pileup jets is available in the energy profile of the jet constituents, making this an interesting area for future developments. Outlook High energy physics is approaching an exciting phase, as the HL-LHC will open up new search channels, previously inaccessible cross-sections, and more precise measurements of SM observables. New revolutionary discoveries might be around the corner and it is critical that we have all the tools at our disposal ready to get the most out of the data. The unprecedented challenges of data-intensive physics research have made it increasingly clear that standard approaches used to extract meaningful physics have to be rethought. The multi-class jet tagger and the neural network for pileup-jet rejection discussed in this work are allustrative of the broader array of applications where deep learning can significantly enhance our ability to analyze complex data and further our understanding of the universe. 247 BIBLIOGRAPHY [1] S. Weinberg, “Gauge hierarchies,” Phys. Lett. B 82, 387 (1979). [2] G. F. 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Duhr, and B. Fuks, “FeynRules 2.0 – A complete toolbox for tree-level phenomenology,” Comput. Phys. Commun. 185, 2250 (2014). [195] ATLAS Collaboration, Tagging and suppression of pileup jets with the ATLAS detec- tor , Tech. Rep. (CERN, 2014). [196] ATLAS Collaboration, Measurement of the tau lepton reconstruction and identification performance in the ATLAS experiment using pp collisions at √s = 13 TeV, Tech. Rep. (CERN, 2017). [197] Mart´ın Abadi et al., “TensorFlow: Large-scale machine learning on heterogeneous systems,” (2016). [198] S. Frixione, P. Nason, and C. Oleari, “Matching NLO QCD computations with parton shower simulations: the POWHEG method,” J. High Energ. Phys. 11, 070 (2007). 260 MCT Modeling in 0- and 1-lepton pre-selection regions APPENDIX A. Analysis This appendix is the continuation of the studies presented in Sec. 7.11. (a) (b) (c) (d) (e) (f) Figure 9.1: Data and MC comparison in the inclusive merged pre-selection region in the 0-lepton channel. Distributions of the large-R jet mass and the raw merged MCT scores p(h) and p(V ) are shown before (top) and after (bottom) applying the normalization SFs. 261 010000200003000040000EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-1010310510710EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC010000200003000040000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 9.2: Data and MC comparison in the merged pre-selection regions separated by the number of b-tagged jets in the 0-lepton channel. Distributions of the large-R jet mass and the raw merged MCT scores p(h) and p(V ) are shown after applying the normalization SFs in the 0 b-tag (top), 1 b-tag (middle), and 2 b-tag (bottom) regions. 262 0100002000030000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L0 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L0 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L0 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC0100020003000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L1 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L1 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L1 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC0200400Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L2 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410510Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L2 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 0L2 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) Figure 9.3: Data and MC comparison in the inclusive resolved pre-selection region in the 0-lepton channel. Distributions of the di-jet mass and the raw resolved MCT scores p(h) and p(V ) are shown before (top) and after (bottom) applying the normalization SFs. 263 0200004000060000EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC0200004000060000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC (g) (h) (i) (j) (k) (l) (m) (n) (o) Figure 9.3: Data and MC comparison in the resolved pre-selection regions separated by the number of b-tagged jets in the 0-lepton channel. Distributions of the di-jet mass and the raw resolved MCT scores p(h) and p(V ) are shown after applying the normalization SFs in the 0 b-tag (top), 1 b-tag (middle), and 2 b-tag (bottom) regions. 264 02000040000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L0 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L0 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L0 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC0500010000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L1 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L1 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L1 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC01000200030004000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L2 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L2 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 0L2 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) Figure 9.4: Data and MC comparison in the inclusive merged pre-selection region in the 1-lepton channel. Distributions of the large-R jet mass and the raw merged MCT scores p(h) and p(V ) are shown before (top) and after (bottom) applying the normalization SFs. 265 010000200003000040000EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710810EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-1010310510710EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC010000200003000040000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 9.5: Data and MC comparison in the merged pre-selection regions separated by the number of b-tagged jets in the 1-lepton channel. Distributions of the large-R jet mass and the raw merged MCT scores p(h) and p(V ) are shown after applying the normalization SFs in the 0 b-tag (top), 1 b-tag (middle), and 2 b-tag (bottom) regions. 266 0100002000030000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L0 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L0 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L0 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC0200040006000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L1 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410510610Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L1 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L1 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC0200400600Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L2 b-tag50100150Large-R jet m [GeV]0.60.811.21.4Data/MC1-10110210310410510Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L2 b-tag00.20.40.60.81MergMCT p(h)0.60.811.21.4Data/MC1-10110210310410510Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Merged QCD+MCT Pre-selection 1L2 b-tag00.20.40.60.81MergMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) Figure 9.6: Data and MC comparison in the inclusive resolved pre-selection region in the 0-lepton channel. Distributions of the di-jet mass and the raw resolved MCT scores p(h) and p(V ) are shown before (top) and after (bottom) applying the normalization SFs. 267 050100150200310·EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810EventsDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC050100150200310·Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 9.7: Data and MC comparison in the resolved pre-selection regions separated by the number of b-tagged jets in the 1-lepton channel. Distributions of the di-jet mass and the raw resolved MCT scores p(h) and p(V ) are shown after applying the normalization SFs in the 0 b-tag (top), 1 b-tag (middle), and 2 b-tag (bottom) regions. 268 050100150310·Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L0 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L0 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L0 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC02000040000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L1 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L1 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710810Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L1 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC01000020000Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L2 b-tag50100150 [GeV]qqm0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L2 b-tag00.20.40.60.81ResMCT p(h)0.60.811.21.4Data/MC1-1010310510710Events * NormSFDatattbarstopDibosonttVttHSMVHWlWblWclWbbWbcWccWWcWbZlZblZclZbbZbcZccZZcZb-1 TeV, 36.1 fb13Resolved QCD+MCT Pre-selection 1L2 b-tag00.20.40.60.81ResMCT p(V)0.60.811.21.4Data/MC Cone jets performance with jFEX seeding APPENDIX B. Trigger This study checked the use of jFEX trigger objects (TOBs) as seeds for the cone jet algorithm discussed in Sec. 8.3 (see Sec. 4.3.4 for an overview of the jFEX algorithm). The resulting jets have the same location as the corresponding jFEX jets, but different energy: while the jFEX jet is built with towers, the cone jet is built with the higher energy resolution of the topoclusters. As with the standard ConeTopo jets, the input topoclusters are thresholded according to the specified ET cut and energy-overlap removal is applied. The resulting jet collection is referred to as ConeJFEX. Note that the jFEX algorithm is characterized by a minimum distance requirement between the towers seeding the jFEX objects, which enforces a minimum distance requirement on the seeds of the cone algorithm. The performance of the ConeJFEX collection was compared to the ConeTopo and AntiKt422 jets. Fig. 9.8 shows one- and multi-jet trigger efficiencies for di-Higgs and Z′ signals. The trigger efficiencies were built using a common arbitrary online pT cut of 30 GeV, which al- lowed to overlay the turn-on curves for better comparison. While equivalent performance was observed for the di-Higgs signal, the Z′ sample showed a plateau inefficiency for the ConeJFEX online jet collection. The cause of this behavior was identified by separating the events according to how isolated the nthoffline leading jet is. Fig. 9.9 shows the ConeJFEX trigger efficiencies separated in bins of dR of isolation of the offline jets. For instance, an event enters the 0.4 < dR < 0.6 bin if the closest dR distance between any pair of the four leading jets is a value between 0.4 and 0.6. Clearly, the plateau inefficiency was mostly orig- inating from the first bin, which had jets closer than dR = 0.6, indicating that the ConeJFEX algorithm was failing to reconstruct nearby jets. No plateau inefficiency was observed for ConeTopo jets thanks to the absence of any restriction on the minimum distance between the seeding topoclusters. Constituent multiplicity in cone jets Fig. 9.10 compares the number of constituents in AntiKt422 jets and in the final version of the ConeTopo jets, with the energy overlap removal strategy applied. The results are shown for ET > 1 GeV topocluster thresholding, but similar results were observed for other thresholding options. A requirement on the jet pT to be larger than 20 GeV was imposed to select typical jets that would pass the trigger. One can note that AntiKt422 jets tend to have a slightly larger number of constituents. As this is more accentuated for softer jets, it is likely the result of AntiKt422 finding a balanced boundary between two equally energetic 269 (a) (b) (c) (d) (e) (f) Figure 9.8: Comparison of one-, three-, and four-jet trigger efficiencies when the online jets are reconstructed as AntiKt422, ConeTopo, or ConeJFEX jets. The results are shown for t¯t (bottom) signals and 2 GeV input topoclusters ET thresholding. di-Higgs (top) and Z′ → jets, as opposed to the overlap removal step of the cone algorithm which always adopts a winner-take-all strategy, removing a greater number of constituents from the lower energy jet. 270 50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopoConeJFEX50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopoConeJFEX50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopoConeJFEX50100150200250 [GeV]T1st offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopoConeJFEX50100150 [GeV]T3rd offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopoConeJFEX50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyHL-LHC Simulation>=200m, 2 GeVT42 EM Topoclusters E| < 2.5jeth|TAnti-kConeTopoConeJFEX (a) (b) (c) Figure 9.9: Comparison of one-, three-, and four-jet trigger efficiencies in different offline jet isolation bins when the online jets are reconstructed as AntiKt422, ConeTopo, or ConeJFEX t¯t signal and 2 GeV input topoclusters ET thresholding. jets. The results are shown for Z′ → 271 50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyATLASSimulation Internal>=200mHL-LHC 2 GeVT42 EM Topoclusters E| < 2.5jeth| jets overlap 0.4 < dR < 0.6TOff-line anti-kTAnti-kConeTopoConeJFEX50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyATLASSimulation Internal>=200mHL-LHC 2 GeVT42 EM Topoclusters E| < 2.5jeth| jets overlap 0.6 < dR < 0.8TOff-line anti-kTAnti-kConeTopoConeJFEX50100150 [GeV]T4th offline leading jet p00.511.52EfficiencyATLASSimulation Internal>=200mHL-LHC 2 GeVT42 EM Topoclusters E| < 2.5jeth| jets overlap dR > 0.8TOff-line anti-kTAnti-kConeTopoConeJFEX (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 9.10: Number of constituents in the 1st, 3rd, and 4th leading jet. Comparing AntiKt422 and ConeTopo+EOR jets with ET > 1 GeV topocluster thresholding and a min- t¯t (center), and di-Higgs (right) imum jet pt of 20 GeV, for minimum bias (left), Z′ → samples. Plots made by Garrit. 272