PLACE IN RETURN BOX to remove this checkout from your record. To AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K:IProi/Aoc&Pros/ClRC/DateDuoindd UNCOVERIN G THE SINGLE TOP: OBSERVATION OF ELECTROWEAK TOP QUARK PRODUCTION By Jorge Armando Benitez A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY Physics and Astronomy 2009 ABSTRACT UNCOVERING THE SINGLE TOP: OBSERVATION OF ELECTROWEAK QUARK TOP PRODUCTION By Jorge Armando Benitez The top quark is generally produced in quark and anti—quark pairs. However, the Standard Model also predicts the production of only one top quark which is mediated by the electroweak interaction, known as “Single Top.” Single Top quark production is important because it provides a unique and direct way to measure the CKM matrix element th, and can be used to explore physics possibilities beyond the Standard Model predictions. This dissertation presents the results of the observation of Single Top using 2.3 ii)”1 of Data collected with the DO detector at the Fermilab Tevatron collider. The analysis includes the Single Top muon+ jets and electron+ jets final states and employs Boosted Decision Tress as a method to separate the signal from the background. The resulting Single Top cross section measurement is: 0(1)}? —-> tb + X, tqb + X) = 3.74 i832 pl), (1) where the errors include both statistical and systematic uncertainties. The probability to measure a cross section at this value or higher in the absence of signal is p = 1.9 x 10’6. This corresponds to a standard deviation Gaussian equivalence of 4.6. When combining this result with two other analysis methods, the resulting cross section measurement is: 0(p15 -—) tb + X, tqb + X) = 3.94 i 0.88 pl), (2) and the corresponding measurement significance is 5.0 standard deviations. This dissertation is dedicated to my family and specially to my love, Catherine. iii ACKNOWLEDGMENTS I would like to thank all those who have been a part of this process and have guided me throughout my research. In particular, I would like to thank: My advisor, Chip Brock, for his invaluable support and encouragement in the pursue of excellence in research in experimental high energy physics, and for his tremendous insights and words of wisdom that have guided me as a graduate student. Reinhard Schwienhorst for sharing his stellar understanding of physics, for our many scientific discussions, and for his unique motivation techniques. Dugan O’Neil for many useful BDT discussions and careful eye when examining results. C.-P. Yuan and Q.-H Cao for inspiring me to study Single Top physics. It was an honor to have co—authored my first published paper with these esteemed theorists. Carlos Avila for introducing me to high energy physics as an imdergraduate stu— dent and for his influence on me to pursue graduate studies. The members of my guidance connnittee for reviewing my dissertation: C.-P. Yuan, Reinhard Schwienhorst, Hendrik Schatz and S. D. Mahanti. All the DO collaborators, spokespeople, and Fermilab staff for keeping the ex- periment running, and permitting scientists to study the world arormd us. The L1 Calorimeter trigger group for their practical knowledge and formidable wOrk, specially to Dan and Philippe for sharing their engineering methods and expertise with me. The Single Top group, for carrying through this very complex endeavor. The conveners, Ann, Cecilia, and Reinhard for their unique perspectives, and for setting the bar high to make this analysis possible. Special thanks to Dag for his connnitment to EDT, and to my fellow analyzers, Monica, Andres, Zhiyi, Thomas, Aran, Yann, Supriya, Liang, Ernest, Gustavo, and Ike for their dedication, and for always burning the midnight oil. Michigan State University and the Department of Physics and Astronomy, for iv providing me with a wonderful and memorable grad school experience. To all the PA staff, afipecially Brenda and Debbie for always being helpful. All my friends who have made my grad school years unforgettable and for giving me many good (and sometimes much needed) laughs. To my friends in Colombia for all their support and to my friends in the US who have become my extended family. Special thanks to Monica, Joel, Sergio, Khang, Luis Carlos, Fernando, Monica, Dag, FIedy, Rodrigo, Diego, Roshan, Clari, Guille, Betta, Javi, Ricardin, Charly, Andres- ito, Duong, Tyler, Sensei Laurie. My family for their unconditional support and sacrifices that have allowed me to grow not only as a scientist but as a human being. A mi padres por su amor, dedicacion, e incaleulables sacrificios que me han permitido seguir adelante en la vida, y porque que pesar de estar lejos, siempre han estado comnigo. A mi madre por su entusiasmo y ternura hacia sus hijos. A mi padre por ser ejemplo de abnegacion y tenacidad. My hermanito, for being my best buddy and for always being there to share adventures and to talk, talk, and talk. To my family in Canada, mom and dad, Cris, Dan, Rob and Prime for all the love and warmth you have always given me, especially mom Ferrari for her care and genuine interest in science. A mis abuelitos por su cariiio y por ser ejemplos de vida, y a todos mis ti’os, tias, primes y primas, por tantos momentos felices compartidos. Los llevo a todos en mi corazon. My lovely wife, Cati, for being my tower of strength during the difficult times in this journey, for her incredible understanding and care, for her patience in keeping up with all the traveling and crazy hours, for her immeasurable love, for being the chief editor of this work, and for being my inspiration in life. Table of Contents List of Tables ................................. x List of Figures ................................ xv 1 Introduction ........................... 1 2 Theory ............................. 5 2.1 Standard Model .............................. 5 2.1.1 Standard Model Lagrangian ................... 9 2.1.1.1 Quantum Electrodynamics (QED) .......... 9 2.1.1.2 SU(2) synnnetry .................... 10 2.1.1.3 SU(2)L x U(1)y .................... 11 2.1.2 Cabibbo-Kobayashi-Maskawa Matrix .............. 15 2.1.3 Quantum Chromodynamics ................... 16 2.2 Top Quark ................................. 17 2.3 Single Top ................................. 20 2.3.1 Background Processes ...................... 23 2.3.2 Motivation to study Single Top ................. 23 2.3.2.1 Measurement of the CKM matrix element th . . . . 23 2.3.2.2 Top quark spin polarization .............. 25 2.3.2.3 Physics Beyond the Standard Model ......... 26 3 NLO Studies of Single Top Quark Production .......... 29 3.1 Event topology .............................. 29 3.2 NLO calculations ............................. 31 3.3 Single Top distributions at NLO ..................... 33 3.4 “Lonely Top” ............................... 34 3.4.1 “Lonely Top” at NLO ...................... 39 4 Experimental Setup ....................... 46 4.1 Accelerator complex ........................... 47 4.1.1 Cockcroft-Walton pre-accelerator ................ 48 4.1.2 LINAC .............................. 48 4.1.3 Booster Synchrotron ....................... 49 4.1.4 Main Injector ........................... 49 4.1.5 Antiproton Source and Recycler ................. 49 4.1.6 Tevatron .............................. 50 4.2 The DC Detector ............................. 51 4.2.1 Coordinate system ........................ 52 4.2.2 Luminosity Monitor ....................... 53 vi 4.2.3 Central Tracking ......................... 54 4.2.3.1 Silicon Microstrip Tracker ............... 55 4.2.3.2 Central Fiber Tracker ................. 57 4.2.3.3 2 T Solenoid ...................... 58 4.2.4 Preshower detectors ........................ 59 4.2.5 Calorimeter ............................ 60 4.2.6 Muon System ........................... 62 4.2.7 Triggering ............................. 64 5 Event Reconstruction and Object Identification ......... 68 5.1 Reconstruction .............................. 68 5.1.1 Tracks ............................... 68 5.1.2 Primary Vertices ......................... 70 5.1.3 Electrons ............................. 71 5.1.4 Muons ............................... 74 5.1.5 Jets ................................ 77 5.1.5.1 Jet Energy Scale .................... 80 5.1.6 Missing ET ............................ 81 5.1.7 b-tagging ............................. 81 6 Data and Simulation Samples .................. 84 6.1 Data Sample ................................ 84 6.2 Simulation Samples ............................ 85 6.2.1 Signal Modeling .......................... 85 6.2.2 Background Modeling ...................... 86 6.2.3 Additional Monte Carlo Treatments ............... 87 6.3 Multijets Background Modeling ..................... 89 6.3.1 Electron Channel ......................... 89 6.3.2 Muon Channel .......................... 91 6.4 Corrections ................................ 92 6.4.1 Muons ............................... 93 6.4.2 Electrons ............................. 94 6.4.3 Jets ................................ 94 6.4.4 Primary Interaction vertex .................... 99 6.4.5 Luminosity Reweighting ..................... 100 6.4.6 Beam Position Reweighting ................... 100 6.4.7 Z-pT Reweighting ......................... 100 6.4.8 Taggability ............................ 100 6.5 Trigger Efficiencies ............................ 103 7 Event Selection ......................... 106 7.1 Event Selection Cuts ........................... 106 7.1.1 Triangular Cuts .......................... 113 7.1.2 Total Transverse Energy (HT) cut ............... 114 7.2 W+jets and Multijets Background Normalization ........... 115 vii 7.2.1 Reweighting for the W+Jets Sample .............. 118 7.2.2 W+Jets Heavy-Flavor Fraction ................. 120 7.3 Number of Events After Selection .................... 125 7.4 Event Yields ................................ 127 7.5 Cross-Check Samples ........................... 134 7.6 Variables Definition ............................ 136 7.7 Data and Monte Carlo Agreement ................... 138 8 Decision Trees .......................... 158 8.1 Overview .................................. 159 8.2 Training Algorithm ........................... 162 8.2.1 Splitting a Node ......................... 163 8.2.2 Boosting .............................. 165 8.2.3 Boosted Decision Tree (BDT) Parameters ........... 167 8.2.4 Decision Tree Implementation .................. 169 8.3 BDT optimization ............................ 169 8.3.1 Variable Selection ......................... 169 8.3.2 Parameters Optimization ..................... 171 8.3.3 The AdaBoost Parameter .................... 172 8.3.4 Degradation Measures ...................... 173 8.3.5 Minimal Leaf Size ......................... 174 8.3.6 Parameters Summary ....................... 175 8.4 Discriminant Output Transformation .................. 176 8.5 Removal Of One Variable From The Training ............. 178 9 Analysis ............................. 181 9.1 Systematic Uncertainties ......................... 181 9.2 Sample Preparation ............................ 188 9.3 Measuring a Cross Section ........................ 188 9.3.1 Bayesian Approach ........................ 189 9.3.2 Systematic: Uncertainties ..................... 190 9.4 Results ................................... 192 9.4.1 Expected Results ......................... 192 9.4.2 Observed Results ......................... 196 9.5 Significance ................................ 200 9.5.1 Ensemble Tests .......................... 200 9.5.2 Significance ............................ 202 9.6 Cross Check samples ........................... 204 9.7 th measurement ............................. 205 9.8 Event Display ............................... 207 10 Results and Conclusions ..................... 209 A Decision Tree Outputs ...................... 211 B Plots of Discriminating Variables ................ 220 viii C Systematic Uncertainty Tables .................. 242 D JES, TRF, and RWT Systematic Uncertainties ......... 267 E Cross Check Samples ...................... 278 F Combination of Single Top Measurements ............ 287 G Design and Implementation of the New DO Level-1 Calorimeter Trigger ............................. 293 G1 Introduction ................................ 293 G2 Motivation for the LlCal Upgrade .................... 294 G3 Algorithms for the Run IIb LlCal .................... 296 G4 Hardware Overview ............................ 297 G5 The ADF System ............................. 302 G.5.1 Titansition System ......................... 302 G.5.2 ADF Cards ............................ 304 G.5.3 Signal Processing in the ADFs .................. 304 G.5.4 Timing and Control in the ADF System ............ 308 G.5.5 Configuring and Programming the ADF System ........ 309 G6 ADF to TAB Data Tiansfer ....................... 309 G7 The TAB/ GAB System .......................... 311 G.7.1 'Iiigger Algorithm Board ..................... 311 G.7.2 Global Algorithm Board ..................... 313 G8 Online Control .............................. 314 G9 Managing Monitoring Information .................... 316 G.10 Calibration of the LlCal ......................... 318 G101 Online Pedestal Adjustment and Noise ............. 318 G.10.2 Calorimeter Pulser ........................ 318 G103 Offline Gain Calibration ..................... 319 Bibliography .......................... 320 ix List of Tables 2.1 2.2 2.3 2.4 3.1 6.1 6.2 7.1 7.2 7.3 7.4 Elementary Particles and their properties, all particles have spin 1 / 2. Where, 6 = 1.602 x 10‘ 19 C is the magnitude of the electron charge [1]. 7 Gauge bosons properties [1]. ....................... flee parameters of Standard Model [1, 2, 3, 4, 5]. The gauge couplings 2 0i are related to g, used later in the text by a,- = $17; ......... Standard Model fermion fields and their gauge quantum numbers. T is the total weak isospin and T3 its third component, and Q the electric charge .................................... NLO corrections contributions for both 5- and t-channels for the Single Top production [6, 7] ............................ Integrated luminosities for the datasets used in this analysis. . The cross sections, branching fractions, and initial numbers of events in the Monte Carlo event samples. The symbol 8 stands for electron plus muon plus tau decays ......................... Ntunbers of data events after each selection cut is applied. ...... Numbers of MC tb channel signal events after each selection cut is applied ................................... Numbers of MC tqb channel signal events after each selection cut is applied ................................... W+jets and multijets scale factors calculated using the iterative KS- test normalization method ......................... 7 12 33 88 111 112 118 NLO/ LL K I and qu F Thmretical Factors for V+Jets Cross Sections. 120 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 9.1 Heavy-flavor scale factor corrections for the two run periods and lepton types and combinations of each, calculated using two-jet events. Number of events for the electron and 11111011 channels after selection in the p17 sample ............................... Number of events for the electron and muon channels after selection in the p20 sample. .............................. Yields after selection and before b tagging. ............... Yields after selection but before b tagging for the analysis channels and backgrounds combined. The percentages are of the total backgrormd for each component. ........................... Yields after selection for events with exactly one b—tagged jet. Yields after selection for events with exactly two b—tagged jets. . . . . Summed signal and background yields after selection with total uncer- tainties, the number of data events, and the signal:backgr01md ratio in each analysis charmel ............................ Summed signal and background yields after selection with total uncer- tainties, the number of data events, and the signalzbackground ratio for electron and muon Run 11a and Run IIb channels combined. Differences between the data and the predicted background (includ- ing SM signals) shown as a factor times the uncertainty on the sig— nal+background predictions ........................ Yields after selection in the cross-check samples, for charmels and back- grounds combined. The numbers in parentheses are the percentages of the total backgrouiid-i-signal for each source ............... Variables used with the decision trees in five categories: object kine- matics, jet reconstruction, angular correlations, event kinematics, and top quark reconstruction. For the angular variables, the subscript in— dicates the reference frame. Plots for these variables are shown in Figures 7.12 to 7.20. ........................... A summary of the relative systematic micertainties for each of the correction factors or normalizations. The uncertainty shown is the error on the correction or the efficiency, before it has been applied to the MC or data samples .......................... xi 124 126 128 129 130 131 132 133 133 135 139 186 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 0.1 A summary of the relative systematic uncertainties for each of the correction factors or normalizations. The uncertainty shown is the error on the correction or the efficiency, before it has been applied to the MC or data samples (Part II) ..................... Splitting procedure of the samples. The event number is given to a MC event during generation and is the same for all permutations of an event. ................................... Expected cross section measurements for many combinations of anal- ysis channels with all systematic uncertainties taken into account. Expected significance estimators for many combinations of analysis channels: posterior peak over half-width (top Table), Bayes Ratio Sig- nificance (middle Table), and Bayes Factor Significance (bottom Ta— ble). All systematic uncertainties are taken into account in the calcu- lations. The best values from all channels combined systematics are shown in bold type ............................. Expected cross section, peak over half-width, Bayes factor significance and Bayes ratio significance, with all systematic uncertainties taken into account, for the 24 analysis chamrels. ............... Observed cross section measurements for many combinations of anal- ysis channels with all systematic uncertainties taken into account. Observed cross section measurements for many combinations of anal- ysis channels with all systematic uncertainties taken into account. Observed posterior peak over half—width and Bayes ratio significance for many combinations of analysis channels. All systematic uncertain- ties are taken into account in the calculation. The best values from all channels combined with systematics are shown in bold type. ..... Observed cross section, peak over half-width and Bayes ratio signifi- cance, with all systematic uncertainties taken into account, for the 24 analysis channels .............................. Systematic uncertainties in percentage on the cross section factor re- quired in the measurement of th ..................... p17 electron channel uncertainties, requiring exactly one tag and two jets. .................................... xii 187 188 193 194 195 197 198 198 199 C.2 p17 electron channel uncertainties, requiring exactly two tags and two jets. .................................... 244 C3 p20 electron channel inicertainties, requiring exactly one tag and two jets. .................................... 245 C4 p20 electron channel uncertainties, requiring exactly two tags and two jets. .................................... 246 C5 p17 electron channel uncertainties, requiring exactly one tag and three jets. .................................... 247 C6 p17 electron channel uncertainties, requiring exactly two tags and three jets. .................................... 248 C7 p20 electron channel uncertainties, requiring exactly one tag and three jets. .................................... 249 C8 p20 electron channel lmcertainties, requiring exactly two tags and three jets. .................................... 250 C9 p17 electron channel uncertainties, requiring exactly one tag and four jets. .................................... 251 C.10 p17 electron channel uncertainties, requiring exactly two tags and four jets. .................................... 252 CH p20 electron charmel uncertainties, requiring exactly one tag and four jets. .................................... 253 C.12 p20 electron channel uncertainties, requiring exactly two tags and four jets. .................................... 254 C.13 p17 muon channel uncertainties, requiring exactly one tag and two jets. 255 CM p17 muon channel uncertainties, requiring exactly two tags and two jets.256 C.15 p20 muon channel uncertainties, requiring exactly one tag and two jets. 257 C.16 p20 muon channel uncertainties, requiring exactly two tags and two jets.258 C.17 p17 muon channel uncertainties, requiring exactly one tag and three jets.259 C.18 p17 muon channel uncertainties, requiring exactly two tags and three jets. .................................... 260 C.19 p20 muon cham1el uncertainties, requiring exactly one tag and three jets.261 C.20 p20 muon channel uncertainties, requiring exactly two tags and three jets. .................................... 262 C21 p17 muon channel uncertainties, requiring exactly one tag and four jets.263 C.22 p17 muon channel uncertainties, requiring exactly two tags and four jets.264 C23 p20 muon channel uncertainties, requiring exactly one tag and four jets.265 C24 p20 muon charmel uncertainties, requiring exactly two tags and four jets.266 D.1 Normalization uncertainties on the signal and combined backgrounds from the jet energy scale and the taggability plus tag-rate fimctions for each analysis channel .......................... 268 El Single Top cross section measurements .................. 290 G.1 Timing and control signals used in the LlCal system. Included are D0 global timing and control signals (SCL) used by the ADFs and the TAB / GAB system, as well as intra-system connuunication and synchronization flags described later in the text ............. 300 G2 A smmnary of the main custom electronics elements of the LlCal sys- tem. For each board, the TT region (in 17 x (b) that the board receives as input and sends on as output is given as well as the total number of each board type required in the system. ............... 301 xiv List of Figures Images in this dissertation are presented in color. 1.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Flow chart of the stages of processing for data and MC files in the Single Top analysis ............................. Summary of the particles and their interactions [8]. .......... Higgs potential. The vacuum expectation value is non-zero, sponta- neously breaking the synnnetry. This mechanism is in charge of giving the masses to the Standard Model particles [9, 10]. .......... Leading Order Feynman for the quark-antiquark annihilation process in the production of top quark pairs [11] ................. Leading Order Feynman for the gluon fusion processes in the produc- tion of top quark pairs [11]. ....................... Final states for the top quark pair production, the slide size is propor- tional to the branching ratio of each process. The final states can be divided into three classes: dileptons, leptons+jets, and alljets [11]. Leading Order Feynman diagram of the Single Top s-channel produc- tion mode [11]. .............................. Leading Order Feynman diagram of the Single Top t-channel produc- tion mode [11]. .............................. XV 13 18 19 20 22 2.8 2.9 2.10 2.11 2.12 2.13 2.14 3.1 3.2 3.3 3.4 Single Top quark production and decay. In these diagrams the W— besen decays leptonically into a muon and a neutrino [11]. The final state for the s-channel has a b—quark created along with the t-quark, a charged lepton from the W-boson decay and its respective neutrino. In the t—channel case, the main components are the spectator light quark, the lepton and the neutrino from the W decay, and the b—quark from the top quark decay. ........................... Feynman diagrams for the Single Top background processes. W+ jets (top-left), tf (top—right), and multijets (bottom) ............. Top quark decay and correlation between the charged lepton and the top quark spin on the top quark rest frame. The large arrows are the preferred direction of the polarization [12]. ............... Single Top production and a fourth generation quark b’ [12]. ..... Single Top production by means of the W’i gauge boson.[12]. . . . . F CNC couplings for the top quark decaying into a c—quark plus a gauge boson. Similar diagrams are also permitted by FCNC currents for the top quark decaying into a u-quark.[12]. ................. LO Feynman diagrams for the Single Top production by means of FCNC, g c —> t Z.[l2]. .......................... Parton level kinematical distributions for the transverse momentum PT (a,c) and pseudorapidity 17 (c,d) for final state partens in the s-channel (upper row) and t-channel (lower row) Single Top quark events. The histograms only include the final state of t, not 2. ........... Single Top LO Feynman diagrams for the s and t channels. The symbol (8) represents the separation used in the NWA method between the production and decay of the Single Top. ................ Different contributions to the Single Top NLO corrections, s-chalmel (upper row) t-channel (lower row). The black dots indicate the higher order QCD corrections, both for virtual and real emissions ....... NLO corrections effect in distributions for the Single Top s-chaimel [6]. The dotted red line represents the LO calculation, the blue line the sum of NLO contributions, and the black line the sum of L0 plus NLO. Top row: electron PT and electron 77. Second row: E and total transverse energy HT. Third row: b—jet PT and b—jet 77. Bottom row: B-jet PT and B-jet 17. Figures from Reference [7] ................. xvi 22 24 26 26 27 27 28 30 31 32 3.5 N LO effect in distributions for the Single Top t-chaimel [6]. The dotted red line represents the LO calculation, the blue line the sum of NLO contributions, and the black line the sum of L0 plus NLO. Top row: electron PT and electron 77. Second row: 3 and total transverse energy HT. Third row: b—jet PT and b—jet 77. Bottom row: light quark jet pT and light quark jet 77. Figures from Reference [6]. ........... 3.6 Double differential cross section for s—channel and t-channel. Only LO contributions are shown. The x-axis corresponds to the untagged-jet 77 and the y-axis to the lepton 77. .................... 3.7 FBAR (F), FPLUS (F+), and FMINUS (IL) asynmretry fimctions, for the s—channel (left) and t-channel (right). Only LO contributions are included in these plots ......................... 3.8 N LO corrections in the s-channel for the differential cross section (left column), F (right column). The L0 contribution is show in the first row, the smn of all NLO corrections contributions on the middle row, and the LO plus N LO corrections is Show in the last row ........ 3.9 N LO corrections in the s-channel for F+ (left column), and F _ (right column). The L0 contribution is show in the first row, the sum of all NLO corrections contributions on the middle row, and the LO plus NLO corrections is Show in the last row. ................ 3.10 NLO corrections in the t—channel for the differential cross section (left column), F (right column). The L0 contribution is show in the first row, the sum of all NLO corrections contributions on the middle row, and the LO plus NLO corrections is show in the last row ........ 3.11 NLO corrections in the t—channel for R]. (left column), and F. (right column). The LO contribution is show in the first row, the sum of all NLO corrections contributions on the middle row, and the LO plus NLO corrections is show in the last row. ................ 4.1 Aerial view of the Fermilab National Accelerator Laboratory ...... 4.2 Fermilab accelerators chain, there are 2 inter'zwtion points, CDF, and DO [13]. .................................. 4.3 LINAC alternating series of gaps and drift tubes [14]. ......... 4.4 Schematic diagram of the 13 production [14]. .............. 4.5 Schematic view of the DO detector [15]. ................ xvii 36 38 40 42 43 44 46 47 48 50 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 5.1 Coordinate system used at DC, the z-axis is along the proton direction and the y-axis upward. .......................... Schematic view of the DO Luminosity monitors [15]. ......... Integrated Luminosity delivered at D?) [16]. .............. Schematic View of the central tracking system and the preshower de- tectors [15]. ................................ 3D Schematic of the Silicon Microstrip Tracker [15] ........... Side View of a barrel for the SMT detector [15]. ............ Schematic view of Central Fiber Tracker and the clear wave guides fibers [15]. ................................. Location of the solenoid with respect to the other component of the DO detector [15]. ............................. Side view (y — z) of magnetic field for the solenoid and the toroids [15]. 3D view of the DO calerimeters, central and end caps [15]. ...... Schematic View of the transverse cut of one of the octants of the DO calorimeter. The shading pattern indicates cells for signal readout. The 77 coordinates are represented by the radial lines [15] ........ Example of an electromagnetic shower, when a photon interacts with the absorber material. X0 is the radiation length. ........... Typical calorimeter cell composed of alternating inducting and active material [15]. ............................... Schematic view of the full muon detector system [15]. ......... Muon wires [15]. ............................. Muon scintillaters [15]. .......................... Trigger overview block diagram [15]. .................. Block diagram of the L1 and L2 trigger systems [15]. ......... Illustration of the AA algorithm for track reconstruction [17] ...... xviii 57 61 62 63 64 66 66 67 70 5.2 5.3 5.4 or CI! 5.6 5.8 6.1 6.2 6.3 6.4 6.5 Illustration of the isolation parameter. EiseTot is the energy in a cone of radius 0.4. EiseCore is the energy in a cone of radius 0.2 (using EM layers). The numerator of iso subtracts EiseCore from EisoTot. Cartoon representation of the muon track segment algorithm. The Wire’s are represented by the black x’s, the MC track by the blue line, and the drift circles are red. ....................... A hollow cone in R, with the inner edge Ra and the outer edge Rb surrounding the muon. The transverse energy of the cells contained in the cone are added defining the cone Halo. ............... Illustration of the evolution of hard-scatter parton in to a jet in the calorimeter. ................................ Illustration of a jet being infrared safe, the jet clustering occurs near seeds represented by arrows of magnitude proportional to the energy. In the figure on the right, the case of two jets being merged into one due to the presence of soft radiation between them [18] ......... 72 76 79 Illustration of problems due to collinear radiation 011 jet algorithms [18]. 79 Illustration of the secondary vertex formed by the decay of a b—hadron. [17]. 82 Efake_e as a function of electron PT for Run IIa (p17) (left) and Rim IIb (p20) data (right) [19]. .......................... Electron transverse momentum distribution before (left) and after (right) multijet backgromid reshaping [19]. ................... Kinematic distributions comparing the old (red points) and new (black points) multijets background models. Upper row, pT(jet1) and E T, lower row, MT(W) and AR(jet1,jet2) [19] ................ Muon reconstruction efficiencies as a function of ”dot and d) for the data in Run IIa (left) and ratios of data and MC efficiencies (right). The muons in the hole region (bottom part of the detector) are not considered. Similar efficiencies are found for the Run IIb data. [20, 21]. Muon track match efficiencies as a function of 77CFT for the data in Run IIa (left) and ratios of data and MC efficiencies (right). Similar efficiencies are found for the Run IIb data. [20, 21]. .......... xix 90 91 92 95 96 6.6 6.7 6.8 6.9 6.10 7.1 7.2 7.3 7.4 Muon isolation efficiencies as a function of 77 for the data in Run IIa (left), ratios of data and MC efficiencies (right). Similar efficiencies are found for the Run IIb data. [20, 21] .................... 97 Electron efficiencies for preselectien and postselection corrections for Rim IIa samples.[22, 23]. ......................... 98 Primary vertex reconstruction efficiency in data as a function of z[24]. 99 The upper four plots show the fits for the derivation of the taggability. The lower four plots show the ratio of the predicted taggability rate flmction over the observed taggability. These plots are all for the elec- tron channel in the Run IIb period in the central plus primary vertex zone. Results for other channels are found in [19] ............ 102 Run IIa (p17) electron channel: Ratio of Single-Lepten—OR to Mega- OR in data-minus-multijets (top row); ratio of Single-Lepton—OR to 100% in the sum of MC backgrounds (middle row); ratio of these “effi- ciencies” in data to MC (bottom row). The ratio is calculated for the leading jet pT (left) and electron PT (right) distributions. The cor- responding plots for Run IIb, muon channel, and additional variables dependence can be found in Reference [19] ................ 105 A¢(jet1,E T) versus E T (left) and A¢(lepten,E T) versus E T (right) two-dimensional distributions for data (top), multijets (middle) and tb+tqb signal (bettern), in the electron channel in Rim IIb data. Similar distributions for the Run Ila and muon channels can be found in [19]. 113 Absolute value of the muon track curvature significance versus Ad>( u, E T). The cuts are shown as heavy black (blue) lines for Run IIa (Run IIb). 114 A4504, E T) distribution for the Run IIa before(after) the muon track curvature significance triangle cut — left(right) .............. 115 Pretagged distributions for Run IIa events with 2-jet in the electron channel for for HT(1epton, E T7 alljets) (left) and the W boson trans- verse mass before(after) the HT cuts is applied - middle(bottom). Sim- ilar distributions for other jet multiplicity channel, leptons and recon- struction version can be found in [19] .................. 116 ALPGEN W+jets reweighting factor derivation for 77(jet2). The first plot shows the disagreement between data and all backgrounds, the middle plot illustrates the numerator and denominator of Equation 7.2 and the plot to the right presents the reweighting function ....... 119 XX 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19 7.20 The Run IIa (p17) left column and Run Ila (p20) W+jets reweighting factors for 77(jet1), 77(jet2), A¢(jet1,jet2), and A77(jet1, jet2) ALPGEN. Distributions before (left) and after the reweighting (right) for the 121 muon, Run IIb channels. 77(jet1), 77(jet2), A¢(jet1,jet2) and A77(jet1,jet2). 122 Muon pseudorapidity for Run Ila before and after the reweightings are applied left and right, respectively. ................... Illustration of the composition of the datasets as a function of number of jets and number of b tags ........................ The W transverse mass distribution for the “W+jets” and “ti” cross- check samples, for all channels combined ................. Illustration of the color scheme used in plots of signals and backgrounds in the Single Top analyses ......................... Individual object kinematic variables used in the BDT analysis for all channels combined (Part I). ....................... Individual object kinematic variables used in the BDT analysis for all channels combined (Part II) ........................ Jet reconstruction variables used in the BDT analysis for all charmels combined. ................................. Angular correlation variables used in the BDT analysis for all channels combined (Part I). ............................ Angular correlation variables used in the BDT analysis for all charmels combined (Part II) ............................. Event kinematic variables used in the BDT analysis for all charmels combined (Part I). ............................ Event kinematic variables used in the BDT analysis for all charmels combined (Part II) ............................. Event kinematic variables used in the BDT analysis for all cham'iels combined (Part III). ........................... Top quark reconstruction related variables used in the BDT analysis for all charmels combined. ........................ 129 138 141 142 147 148 7.21 7.22 7.23 7.24 7.25 7.26 7.27 7.28 8.1 8.2 8.3 Top quark reconstruction related variables used in the BDT analysis for all charmels combined. ........................ The W boson transverse mass distributions in the electron charmel for 2-jet (top row), 3-jet (middle row), and 4-jet events (bottom row), for p17 (left) and p20 (right) for events before the b—tagging is applied. The W boson transverse mass distributions in the electron channel for 2—jet (top row), 3-jet (middle row), and 4—jet events (bottom row), for p17 (left) and p20 (right) for events with one b-tagged jet. ...... The W boson transverse mass distributions in the electron channel for 2-jet (top row), 3-jet (middle row), and 4—jet events (bottom row), for p17 (left) and p20 (right) for events with two b-tagged jets ....... The W boson transverse mass distributions in the electron channel for 2-jet (top row), 3—jet (middle row), and 4—jet events (bottom row), for p17 (left) and p20 (right) for events before the b—tagging is applied. The W boson transverse mass distributions in the electron channel for 2—jet (top row), 3-jet (middle row), and 4-jet events (bottom row), for p17 (left) and p20 (right) for events with one b—tagged jet. ...... The W boson transverse mass distributions in the electron charmel for 2-jet (top row), 3—jet (middle row), and 4—jet events (bottom row), for p17 (left) and p20 (right) for events with two b-tagged jets. . . . . . . The W boson transverse mass distributions in the electron and muon channels and Run IIa and Run IIb datasets combined, for 2—jet (top row), 3—jet (middle row), and 4-jet events. Single-tagged (left), and double-tagged (right) events ........................ 2D plane of a simple classification problem, and a Decision Tree solving the classification problem of signal and background. .......... Graphical representation of a DT. N odes with their associated splitting test are shown as (blue) circles and terminal nodes with their purity values are shown as (green) leaves. All nodes continue to be split until they become leaves. Note that if one event fails a cut, it does not necessarily follow that the event will fail to pass as that event can be recuperated and pass later down the tree chain [25] ........... Degradation measures comparison as a function of the purity p. The Cross Entropy has been scaled down to compare the 3 cases. . . . . . xxii 150 151 152 154 157 159 161 164 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 9.1 Relative weight, Cross Section Significance; and number of leaves as a ftmction of the number of Boosting cycles for one of the 24—charmels in the analysis ................................. Cross section Significance as a function of the nmnber of Boosting cycles for different values of the AdaBoost parameter. The uncertainty on the points is estimated to be 21:0.05. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. Note the zero suppressed vertical scale ..................... Excess significance as a function of the number “of Boosting cycles for different purity measures. The uncertainty on the points is estimated to be 21:0.05. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. .................. Excess significance as a function of the mnnber of Boosting cycles for different Minimum leaf size. The uncertainty on the points is estimated to be :l:0.05. As a reference, the zero Boosts point is added to the plot to Show the importance of Boosting. .................. CSS as a function of the number of Boosting cycles for different values of the AdaBoost parameter for the 3—jet 1-tag case. The uncertainty on the points is estimated to be 21:0.05. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. . . . . CSS as a fimction of the number of Boosting cycles for different values of the AdaBoost parameter for the 2-jet 2—tag case. The uncertainty on the points is estimated to be :l:0.05. As a reference, the zero Boosts point is added to the plot to Show the importance of Boosting. . . . . BDT discriminant output before (top left) and after (top right) the transformation, for both signal (blue) and background (red). The monotone transformation f (:12) is shown in the bottom. The plots cor- respond to one of the 24-cham1els in the analysis, similar results are obtained for other chamrels. The total number of bins is 50. ..... Relative changes in CSS after removing each variable compared to the all variables included case (first bin). The CSS for the all variable case is 5.465. The statistical uncertainty is estimated to be 1-2%. ..... Example of a 1D posterior density distribution for the Single Top cross section .................................... xxiii 168 173 174 177 178 191 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 Example of a kinematic variable showing the nominal distribution and the up—shifted and down-shifted histograms of the shape-changing sys- tematics. The plot on the right corresponds the the same distribution for only bin only. ............................. Expected posterior density distributions from Decision Tree outputs trained with s+t-charmel tb+tqb as signal for all 24 charmels combined—~ i.e., Run Ila and Run IIb, e and p, 2-4 jets and 1 or 2 are b-tagged. All systematic uncertainties are taken into account in this measurement. The theoretical cross section is 3.46 pb .................. Decision tree discriminant outputs for all 24 charmels (embined. The histograms are obtained by stacking each one of the 24 DT outputs on top of each other. The Single Top contribution in this plot is nor- malized to the measured cross section. The three plots correspond to the same distribution: linear scale (top left), log scale (top right) and a zoom in the signal region (bottom). The color key is shown in the bottom right-hand corner. ........................ Observed posterior density from s + t-channel Single Top cross section measurement using boosted Decision Trees. This is for 24 channels combined— 7.6. Run 11a and Run IIb, e+jets and p+jets, 2-4 jets and 1 or 2 are b-tagged. All systematic uncertainties are taken into account in this measurement. ........................... Measured Single Top cross sections in ensembles with various amounts of Single Top. ............................... Linear fit through the means from the Gaussian fits (Figure 9.6) of the measured cross sections in ensembles .................. Measured cross section from a large ensemble of pseudo-datasets con- taining no Single Top. The significance of a particular cross section is calculated from the number of pseudo—datasets measuring a cross sec- tion higher than the given cross section (green line). The plot above uses the Single Top Standard Model cross section and corresponds to the expected significance. The plot below the bottom uses the mea- sured cross section and therefore corresponds to the observed cross section .................................... Combined Decision rIfee outputs for the “W +jets” sample (left) and the “tf” sample (right) cross—check samples. .............. 191 192 196 197 201 202 203 9.10 9.11 9.12 Al A2 A3 A4 A5 A6 A.7 A.8 Posterior probability densities for [th|2 (left) and [th f1L|2 (right). The color bands represent different confidence bounds: 68.3 %, 95.4 ‘70 and 99.7 %. ................................ Possible candidate event display. The event contains three jets out of wich two are b—tagged, a muon, and a neutrino. Lego view of the DO detector. ............................... Possible candidate event display. The event contains three jets out of wich two are b—tagged, a muon, and a neutrino. XY view of the DO detector. ............................... Decision trees discriminant output for all 24 charmels combined. The Single Top contribution in this plot is normalized to the measured cross section. Same distribution on linear scale (above), log scale (middle) and a zoom in to the signal region (below). .............. Decision trees discriminant output for the e,,u+jets combination in RunIla+b data. The total Single Top contribution in this plots is normalized to the measured cross section. [Rowsz top =2 jets, center =3 jets, bottom =4 jets, columns: left =1 b-tag, right =2 b—tags.] Decision trees discriminant output for event with exactly two jets in the final state. One b—jet (left) two b-jet (right) ............. Decision trees discriminant output for event with exactly two jets in the final state. One b-jet (left) two b-jet (right) ............. Decision trees discriminant output for event with exactly two jets in the final state. One b—jet (left) two b—jet (right) ............. Decision trees discriminant output for event with exactly two jets in the final state. One b-jet (left) two b-jet (right). Signal region only, ODT > 0.8. ................................ Decision trees discriminant output for event with exactly two jets in the final state. One b-jet (left) two b-jet (right). Signal region only, ODT > 0.8. ................................ Decision trees discriminant output for event with exactly two jets in the final state. One b-jet (left) two b—jet (right). Signal region only, ODT > 0.8. ................................ XXV 207 213 214 215 216 217 218 219 B.1 B2 B3 B4 B6 B7 B8 B9 The transverse momentum of the lepton for channels with exactly two jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2—btag. . The transverse momentum of the lepton for channels with exactly three jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. The transverse momentum of the lepton for chamiels with exactly four jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2—btag. . The missing transverse energy for channels with exactly two jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag ........ The missing transverse energy for chalmels with exactly three jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag ........ The missing transverse energy for channels with exactly four jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag ........ The transverse energy of the leading jet for channels with exactly two jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2—btag. . The transverse energy of the leading jet for channels with exactly three jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. The transverse energy of the leading jet for chamiels with exactly four jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2—btag. . BID The transverse energy of the second leading jet for chamrels with ex- actly two jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2—btag .................................... 8.11 The transverse energy of the second leading jet for channels with ex- actly three jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag .................................... xxvi 221 222 223 224 226 227 228 229 230 231 B.12 The transverse energy of the second leading jet for charmels with ex- actly four jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag .................................... B.13 The scalar transverse energy sumfor channels with exactly two jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag ........ RM The scalar transverse energy sum for channels with exactly three jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. B.15 The scalar transverse energy sum for charmels with exactly four jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag ........ B.16 The top quark mass for chamiels with exactly two jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. ............... 8.17 The top quark mass for charmels with exactly three jets in the final state. Run IIa (left) and Rim IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. .......... B.18 The top quark mass for channels with exactly four jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2—btag. .......... B.19 The pseudorapidity of the light quark jet times lepton charge for chan- nels with exactly two jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1—btag and 2-btag. . . .......................... B.20 The pseudorapidity of the light quark jet times lepton charge for chan- nels with exactly three jets in the final state. Run IIa (left) and Rim IIb (right). Electron (top four) muon (bottom four). Alternating rows 1- btag and 2-btag. ............................. B.21 The pseudorapidity of the light quark jet times lepton charge for chan- nels with exactly four jets in the final state. Rim Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1- btag and 2—btag. ............................. xxvii 232 233 234 235 236 237 238 D1 D2 D.3 D4 D5 D6 D7 D8 D9 Systematic shift when varying the JES signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag .................... Systematic shift when varying the J ES signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top fom') muon (bottom four). Alternating rows 1-btag and 2-btag .................... Systematic shift when varying the J ES signal distributions by i10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag .................... Systematic shift when varying the TRF signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and R1111 IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag .................... Systematic shift when varying the TRF signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2—btag .................... Systematic shift when varying the TRF signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag .................... Systematic shift when varying the RWT background distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. ............... Systematic shift when varying the RWT background distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. ............... Systematic shift when varying the RWT background distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. ............... xxviii 269 270 271 272 273 274 276 277 El E2 E3 E4 E.6 E7 E8 El F2 F3 F4 G.1 Cross-check plots for several variables in the W+ jets cross-check sample.279 Cross-check plots for several variables in the W+ jets cross-check sample.280 More cross-check plots for variables in the W + jets cross-check sample. Cross-check plots for several variables in the tf cross-check sample. . . Cross—check plots for several variables in the tf cross-check sample. . . More cross-check plots for variables in the 155 cross-check sample. . . . Decision tree outputs for the cross-check sample “W+ jets” on a linear scale. Upper row: electron charmel; second row: muon charmel. Left column: Run Ila; right collmm: Run IIb. The last two rows are the same plots that are in first and second row but in log scale ...... Decision tree outputs for the cross-check sample “tf” on a linear scale. Upper row: electron charmel; second row: muon channel. Left colunm: Run Ila; right column: Run 11b. The last two rows are the same plots that are in first and second row but in log scale ............ Correlations among the three Single Top analyses pseudo-datasets: (BNN vs BDT), (ME vs. BDT), and (ME vs. BNN). ......... Discriminant output for the three analyses methods. The bottom row corresponds to the combined BNN output discriminant, and a zoom into the signal region (BNN discriminant > 0.8) ............. Posterior probability densities (left colunm) and significance measure— ments (right colunm) for the BDT, BN N , ME, and the combination of the three analyses methods. ....................... Posterior probability densities for [th|2 (left) and [thfll‘l2 (right). The color bands represent different confidence bounds: 68.3 %, 95.4 % and 99.7 %. ................................ The stages of algoritlnn flow for the sliding windows algorithm. In this example, which corresponds to the Run IIb Jet algoritlnn, a 2x2 T T TTCL is used, indexed by the position of its smallest 77, ab TT. Baseline subtracted TT energies are indicated by numbers, and local maxima are required to be separated by at least 1 TT. Jet objects are defined as the ET sum of the 4x4 TTs centered on the TTCL. Light. gray regions in the diagrams indicate areas for which the object in question cannot be constructed because of boimdary effects. .......... xxix 281 282 283 284 286 288 289 291 292 G2 G3 G4 G5 G6 G7 G8 G9 A block diagram of the main hardware elements of the Run IIb LlCal system and their interconnections ..................... 298 Logic diagrams for a Bit-serial adder (a) and a bit-serial comparator (b).302 ADF card block diagram. ........................ 305 Block diagram of signal processing for a single TT in the ADF. . . . . 306 ADF to TAB data transmission, reception and the dual-port-memory transition from 8-bit to 12-bit data .................... 310 Block diagram of the TAB ......................... 312 Block diagram of the GAB. ....................... 314 Communications in the LlCal system. ................. 315 G.10 Precision versus TT ET for one EM (a) and one HD (b) trigger tower. The linear relationship with slope=1 indicates the good calibration of the tower. The excursion away from an absolute correlation is an indication of the inherent noise of the system. ............. 319 XXX Chapter 1 Introduction The Standard Model of elementary particles has been successful at describing the building blocks of nature and their interactions. The top quark is the currently heaviest component of the Standard Model. With a mass close to that of a gold atom, the top quark was theoretically predicted in 1973 [26], but it was not until 1995 that it was discovered at the Tevatron collider at Fermilab. Fermilab is the only place in the world where top quark physics studies can be made, and where the production of top quarks, by means of the electroweak interaction, was recently armounced [27, 28]. Electreweak top quark production is also known as “Single Top” because only one top quark is produced in the final state. Single Top serves as an important validation tool for the Standard Model as well as a window to new physics. In addition, Single Top is one of the backgrounds for many reactions including the missing particle of the Standard Model, the Higgs boson. There are various computational challenges related to Single Top searches, including advanced techniques to separate small sig- nals from difficult-to-discriminate backgrounds. This will be a common task during future analyses in the experiments at the Large Hadron Collider (LHC). To properly “observe” the interactions that take place at Fermilab, a complex detection system is required. Fermilab has two main detector systems, CDF and DC’). The analysis presented in this dissertation accounts for the seach for Single Top with the latter. In the past five years at DC, Single Top has been the subject of many doctoral dissertations [29, 30, 31, 32, 33, 34, 35, 36] and more recently [37, 38, 39]. This disser- tation continues from this previous work and presents the results of the research I con- ducted, together with DC collaborators at Fermilab, that led to the ground-breaking discovery of Single Top production. For Single Top, the signal-over—background ratio is of the order of 10-3, thereby requiring that all the possible information from known well-modelled variables be obtained. I11 this study, I use the multivariate technique known as Boosted Decision 'Ifees (BDT) to analyze Single Top signal. A decision tree (DT) is an algorithm that can be used to classify events as signal or background, and is built by recursively splitting a sample into two disjointed subsets. Each split is based on a selection cut that maximizes the signal-to-backgrmmd ratio of the re- sulting subsets. The separation generated by the DT is then enlarged by a technique called Boosting, for which a series of trees is generated that increasingly gives more importance to events that are difficult to classify. The Single Top signal and its backgrounds are modeled using Monte Carlo tech— niques. This modeling is based on the current particle physics theory, which also includes a complete simulation of the particles interaction with the detector. All of the BDT training is performed using the Monte Carlo samples, while the collected data in the detector is only used in the final measurements. This dissertation is organized as follows: Chapter 2 gives the theoretical grounds for Single Top quark production; Chapter 3 presents some of the work I completed, together with the theory group at Michigan State University, where the influence of N LO correction to the Single Top kinematical distributions and cross section are explored; Chapter 4 introduces the experimental facilities at Fermilab and the DO de- tector; Chapter 5 presents a discussion on particle identification using the available experimental tools; Chapter 6 contains a description of the data and the Monte Carlo samples used in the Single Top analysis together with the corrections applied to them; Chapter 7 describes the selection cuts applied to the Single Top samples and illus- trates the agreement between the simulations and the data; Chapter 8 provides an explanation on Decision Tress, Boosting, and BDT optimization studies; Chapter 9 presents the uncertainties taken into consideration in the analysis, the measurements of the Single Top cross section, the th matrix element, as well as the significance of the cross section measurement and Chapter 10 summarizes the results of the analysis and provides a future outlook for Single Top. Both the Data and the Monte Carlo go through a very intricate processing proce- dure before they are used in any multivariate technique (such procedure is outlined in the flow chart in Figure 1.1). The flow chart allows us to visualize where in the processing of the samples all the corrections have relevance, the selection cuts are ap— plied, and what samples are modified by some procedures and not by others. There are four main stages in the processing of the data and Monte Carlo. stage 1 is the processing of the samples into the Common Analysis Framework (CAF) format; stage 2 contains the general selection of the DO V+jets group; stage 3 is the DO Top group selection criteria; and the stage 4 consists of the corrections, reweightings, selections, and scale factors directly related to the DO Single Top group. Single Top analysis Data and Monte Carlo processing chain ' ' tb and tqb EMincIusive & MUincIusive TMB data files ttbar l+jets, ll :. Z+jets diboson Alpgen MC % Alpgen/Pythia MC ., Stage 1 ttbar l+jets, II 2. CCAF..tree. ncaf_ mc_ uti/ (V+Jets Group) ) Remove extra h-eavy -:t|avor b & c jets I Stage Data CAF trees un vjets_ cafe (V+Jets Group): R data quality cuts, jet energy scal MEl' corrections ultraloose lepton lD ‘ QCD data . CAF trees I Run vjets_cafe (V+Jets Group): data quality cuts, duplicate event removal, particle ID, lepton lD correction factors, lumi reweighting, PV 2 reweighting, jet energy scale. jet shifting and smearing, MET corrections i l I I Run top cafe (Singletop subgrou): Run top_cafe (SIngletop apply event selection cuts( (including H cuts) subgrup): event selection cuts, "@9803 niggers QippIy K’ = (N)NLO/LL factors and K @| Run top_ cafe (Singletop sub- Normalize to theory cross sections Stage group): reshape “electronpr and integrated luminosity l l l tight lepton lD Si nal data C F trees 3 remove jet nlear muon Split pretagged samples by Njets (1 ,2,3 ,4) l l T l Si nal data QCD data W+'ets 2 Z+jets, dibosons ttbari+jets ; an tqe C Ftrees , CAF trees MC CAF trees MC CAF tree CCAE . 1 ~ ‘21:. ' D ,, +Ies , Z+jelS.d|bOSOllSi ttbarl+jets,l; "a toSIQCaaisdtaibaes ,togl/argatlges ovars tree topovars "995 t999varsiree ,. Wars tree Run top_cafe (Singletop subgroup): Stage Iterative-KS normalization using average of three variables 4 . C Reweight instantaneous luminosity distribution D ReweIght muon eta, jet1 eta, jet2 eta, Aphi(jet1,jet2), Aeta(jet1,jet2), jet3 eta, jet4 eta ly ta ability and tag-rate iunctions D Appl leading b—tag ed jet pT cut Sp Itsamp es by tags (0.1.2) I Qprly SHFheavy flavor correction) C Split samples into training, testing, and yield sets 3 Signal data ; QCD data 3 Z+jets dibosons ttbarl+jets ll tbaridtqb ,; finaltopovars final topovars nal tovar‘ finajtopovars finaltopovars2. iinaltopovar, Figure 1.1: Flow chart. of the stages of processing for data and MC files in the Single Appl b-ta ing Top analysis. Chapter 2 Theory The particles we know today, and their interactions, have been successfully described by the Standard Model of Elementary Particles [40, 10, 41, 42]. For many years, scien- tists have conducted experiments to understand, confirm or contradict the Standard Model’s predictions. In 1995, the heaviest particle in the Standard Model was discovered at the Teva- tron collider at Fermilab. This particle has a mass of approximately 173.1i1.3 GeV/c2 [43] and is now known as the “top quark” [44, 45]. C.P- Yuan et a1 [46] and S. Willenbrock [47] predicted a particular production mode of the top quark by means of the electroweak interaction. This production mode has been recently observed at the Tevatron [27, 28] and is also known as Single Top quark production; the name derives from the fact that the top quark is produced singly rather than in pairs (quark-antiquark). The production of the Single Top quark is the topic of this dissertation. 2.1 Standard Model The Standard Model is a non-abelian gauge theory that characterizes the building blocks of nature and their interaction. The Standard Model is built from the sytmne- try group SU(3) x SU(2) x U(1), from which the electroweak and strong forces can be derived; the gravitational force is not part of the model. The components of the Standard Model can be grouped into “particles of matter” and “mediators”: 24 particles of matter, and four mediators. The particles of matter can be classified into 6 leptons and 6 quarks together with their respective antimatter partners. All of the matter particles have spin 1/2 while the mediators have spin 1. Figure 2.1 shows a cartoon representation of all particles and their mediators. Leptons Quarks e, ,u, T u, c, t V... 11., v, d, s, b Higgs Boson Figure 2.1: Summary of the particles and their interactions [8]. All the Standard Model particles are summarized in Table 2.1. The quarks and the leptons can be grouped into three. generations. The first generation contains the lightest components. In addition, quarks form baryons (3-quark composites, i.e. protons and neutrons) and mesons (quark-antiquark composites). The Stande Model explains the interaction of particles by means of the medi- ators which are exchanged when the interaction occurs. The electromagnetic inter- Quark Lepton Generation Flavor Charge Mass [ MeV/c2] Flavor Charge Mass [ MeV/c2] I Up (u) +2/3e 1.5 to 3.0 Electron (e) —e 0.511 Down (d) —1/3e 3.0 to 7.0 Neutrino (V8) 0 < 2.0 x 10‘6 II Charm (c) +2/3e 1.25 x 103 Muon (II) —e 0.511 Strange (3) —1/36 80-130 neutrino (up) 0 < 1.7 x 10‘4 III Top (t) +2/3e 171.4 x 103 Tau (1') —e 1777 Bottom (b) —1/38 4.7 x 103 Neutrino (VT) 0 < 15.5 Table 2.1: Elementary Particles and their properties, all particles have spin 1 / 2. Where, 6 = 1.602 x 10‘19 C is the magnitude of the electron charge [1]. action mediator is the photon, the weak interaction mediators are the W+, W‘ and Z gauge bosons, and the gluons mediate the strong interactions. See Table 2.2 for a summary of the gauge bosons properties. Force Mediator boson Charge Mass [GeV/cz] Strong Gluon (g) 0 0 Weak Wi i 6 80.398 :l: 0.025 Weak Z () 91.1876 :i: 0.0021 ElectroMagnetic Photon (7) 0 0 Table 2.2: Gauge bosons properties [1] There are a total of 19 free parameters in the SM, most of which have been established experimentally, Table 2.3. Parameter Value Electron mass (me) Muon mass (mp) Tau mass (m) Up quark mass (mu) Down quark mass (7nd) Strange quark mass (m3) Charm quark mass (mo) Bottom quark mass (mb) Top quark mass (mt) CKM element Vus CKM element Vcb CKM element Vub CKM CP-Violating Phase (6) U(1) gauge coupling a-1(MZ) SU(2) gauge coupling a’_1(MZ) SU(3) gauge coupling a§1(MZ) QCD Vacuum Angle (QQCD) Higgs quadratic coupling (,0) Higgs self-coupling strength (A) 0.510998910 i 0000000013 MeV/c2 105658367 i 0.000004 MeV/c2 1776.84 i 0.17 MeV/c2 1.5 to 3.3 MeV/c2 3.5 to 6.0 MeV/c2 1051'? MeV/c2 1271:8391 GeV/c2 4207:811); GeV/c2 173.1 1 1.3 (1er2 0.2257 :l: 0.0010 +0.0010 0.041540011 0.00359 i 0.00016 57° :L- 8.70 98.70 :i: 0.21 30.10 :i: 0.23 9.25 :i: 0.43 0 Unknown Unknown Table 2.3: Free parameters of Standard Model [1, 2, 3, 4, 5]. The gauge couplings a; 2 are related to 9; used later in the text by a; = g]? 2.1.1 Standard Model Lagrangian 2.1.1.1 Quantum Electrodynamics (QED) The Lagrangian .C for a massless electroinagiretic field A), interacting with a spin—1/2 field 7,0 of mass m is given by: L = —%FIUVF”V + rifle/“Du —-m)1/J, (2.1) where F “V is the electromagnetic field tensor, FMV = BLIAV — 81/14)), (2.2) and D” is the covariant derivative, DH = 8], + z’eAuQ; (2.3) where Q is the charge operator and e is the electron charge. This Lagrangian is invariant under local gauge transformations: 1/J($) —> U(x)¢’(:c), A], —> A#(:r) + Buds), (2.4) with U (:c) = exp(—ieQa(:v)), Which for infinitesimal a(:I:): M1?) -7 (1 - ieQa(r))- (2.5) . . . . . . I, . The invarlance implies the conservatlon of the electric current Jém and electric charge q[10]: , M __ 0 3 .- aMJem q — Jemd x (21’) 9 2.1.1.2 SU(2) symmetry The Lagrangian of an internal symmetry group SU(2), such as the isospin, for spin-1 / 2 fields 212 is given by [10]: L = 15(i’iflap - m)w9 (2-7) where d) transforms as a doublet in the isospin space, and it is required to be invariant under infinitesimal local gauge transformations: 1W?) —* [1 - i9 aim) Tin/2(a), (2-8) where a(.1:) is a vector in isospin space, and T 1 is the isospin operator, with the SU( 2) generators as components. The w-field part of the Lagrangian can be made invariant by introducing the (tovariallt derivative DH : given a. gauge field WW2, which transforms as: W#(a:) —> Wu(a:) + 8#a(a:) + ga(a:) x W,I(x). (2.10) The W~field part of the Lagrangian can be written as: 1 with N WW = auWu - auwy - 9W). x Wu. (2.12) 2. § 2 . I . 1% 1 21 / 21',- where T,- are the Pauli matrices. ’ s :3 10 ‘ For each independent generator Ti there is a corresponding gauge field will with the Lagrangian defined as: 1 1:: ——W,- 4 Wf" + 507%,, — mm (2.13) Iw which by requiring invariance under infinitesimal gauge transformations result in the conservation of the current: J“ = W‘Tw + WW X WI, (2.14) is conserved. Although the SU(2) gauge model is a candidate model to explain the weak interaction, it does not explain the gauge boson masses nor the left-handed nature of charged currents. Further, the SU(2) model does not unify the weak and Electromagnetic forces. However, it would serve as a building block for the SU(2) L x U(1)}; model explained below. 2.1.1.3 SU(2)L x U(1)Y The electromagnetic and weak interactions are unified in the gauge group SU(2) L X W”)? - The generators for this group are the weak hypercharge Y and the weak i308mm T, related to the electric charge Q by Q : T3 + Y/2. The electromagnetic force is characterized by a one-dimensional unitary transformation and the weak force is Clescribed by SU(2). The weak force transforms particles according to their helicity, such that left-handed components transform as doublets, and right-handed (fompOI . . lents as weak isosmglets. See Table 2.4. The _ f f"E}:l‘3triion mass term mww is not invariant. tuider SU(2)L, for this reason the (‘MjOlhg - 111 this model are consider massless. Therefore the SU(2) L x U(1)y La— grangj a1 1 g 1 8 given by: 11 Field U(3) SU(2) U(1) T T3 Q c L Y 2- UL CL tL . +1/2 +2/3 QL (dL) (3L) (bL) 3 2 1/6 1/2 ’1/2 ‘1/3 u}? UR CR tR 3 1 2/3 0 0 +2/3 dz}; dB 3}; b3 3 1 -1/3 0 0 —1/3 2‘ VeL VpL VTL - +1/2 0 L.L (6L) (#L) (TL) 1 2 1/2 1/2 ‘1/2 ‘1 6;? 6R “R TR 1 1 -l 0 0 -1 1,12}; 1263 WR MR 0 0 0 0 0 0 Table 2 .4: Standard Model fermion fields and their gauge quantum numbers. T is the total weak isospin and T3 its third component, and Q the electric charge. 1 1 - LEW = — 4W’“’ . WW — ZBWBW + wi’yflDpd) (2.15) With a separate term for right and left handed fields. The fields 1/1 involved in the La- grangi all are shown in Table 2.4. The massless gauge fields are model as an isotriplet W” for SU(2) L and a singlet B,“ for U(l)y. With the field tensor WW defined as in Equation 2.12, By]; 2 8,18,, — 61/8)“ and the covariant derivative as 1 23px Du = a” + ig’Wfl - T + ig (2.16) The Lagrangian is invariant under infinitesimal local gauge transformations for each S U ( 2) L and U(1)Y independently. One must note, however, this electroweak model (10% not include the masses of the W35 and Z bosons nor the masses of [emu-0118 - The mass problem is solved by the spontaneous symmetry breaking mech- anism blow as the Higgs mechanism, which consists of the introduction of an SU(2) d Ollblet of scalar fields (I): (2.17) 12 which results in two additional Lagrangian terms: £11,993 and LYukawa' The Higgs Lagrangian incorporates the kinetic energy of the Higgs field, its gauge interactions, and the Higgs potential: ['Hz'ggs = (D#¢)TDM¢ — V(‘I’) (2.18) we = —u%% + was)? (2.19) where It is a parameter of the Standard Model, the sign of the term is chosen such that the vacuum expectation value is non-zero, < T >0: 212/2 with v = n/x/X. Which results in the generation of the gauge bosons masses. The Higgs potential is shown in Figure 2.2. - ...‘ :.:—_3. =- - .‘.. V(<15 ) :3- m t‘afi'o'.‘ u‘o’: figure 2 - 2: Higgs potential. The vacuum expectation value is non-zero, spontaneously edkulg the symmetry. This mechanism is in charge of giving the masses to the S . tandard Model particles [9, 10]- Wi thloll‘t losing generality, one can choose the vaculun state to be: < <1) >0: (2.20) 0 v/xfl2) and Pa 1 111 00, the strength of the interaction decreases with the energy of the process- At very high energies (short distances), quarks and gluons interact weakly, whereas at large distances, the interaction increases in strength. The coupling parameter energy dependence has some implications when a quark receives a large amount of energy as a result of a high energy collision. As the quark moves away from the quarks to which it is color—bounded, the color field grows mitil it is energetically favorable to produce a quark-antiquark pair. This process is repeated many times producing a cascade of hadrons that are later reconstructed as jets in the detector - 2'2 'I‘op Quark The t0p quark is a spin-1/2 fermion with electric charge +2/3. The D0 and CDF 0Xperim(}llts have measured the top quark mass to be mt = 173.1 i 0.6(stat) :1: “(89835) GeV/c2 [43]. H‘oln its discovery in 1995, until the recent Single Top quark production discovery, 8.” Stud - 1651 and measurements of the top quark have taken place at the Fermilab TeVatr 01) tfb Collider. At the Tevatron, the top quark is produced dominantly in pairs y 1119. . ““1113 of the strong interaction. Top quarks may be produced through two different 1Strong interaction processes: the quark-antiquark annihilation (Figure 2.3) 17 and the gluon fusion processes (Figure 2.4). At 1.96 TeV, the tt— production cross section is of approximately 7 pb, mainly from contributions from the quark-antiquark annhilation process: qq -—+ tt- [49, 50, 51]. r ‘v‘ . Maj: V ’. :r.“‘ 4'1“"; _ .. p' 0 on ‘5‘“ #3152" 2:, _, ' If?! antiproton Figure 2.3: Leading Order Feynman for the quark-antiquark annihilation process in the production of top quark pairs [11]. The Standard Model predicts the top quark to decay in one of the down-type quarks (u, s or b). The branching fractions are proportional to the diagonal elements of the CKM matrix [52], Section 2.1.2: . B(t ~+ W + d) m 0.006%, 0 B(t ~+ W + s) an: 0.17%, 0 13(t H w + b) m 99.8%; ther efore, the top quark decay is expected to be dominated by t —-> W b. Then, the b 08011 produced by the top quark decays with the following branching ratios: 0 BR(W+ —* e+ue)=1/9, BR(W+ —+ ya”) = 1/9, . BR(W+ —+ #117): 1/9, 18 1"; g l t- g Q .m l‘ g ‘ 5 it W [T 9 m t g ;_,,,..____ f Figure 2.4: Leading Order Feynman for the gluon fusion processes in the production 0f top qllark pairs [11]. ° BR-(W+ —> ud) = 3/9, and ' BR(W+ —+ c3) = 3/9. In tll .\ _ . . . . . L tt Case, the possible final products are summarized in the pie chart shown 111 Figure 2 _ 5 _ At ll(‘J'Ct—to-leading-order (NLO), the Standard l\rlodel prediction of the top quark decay Width iS l1]: 2 1fit =§:£F_m% 1_&%V_ 1+2% 1_% fi_§ (235) 87r\/§ m? m? 37T 3 2 , ' “’htfil") r V mt is the quark top mass. The correspomling lifetime is roughly 1 x Ill—2%, 19 Top Pair Branching Fractions "alljets" 46% r+jets 15% 1% m3» 2°43 w 2%,, ° \l “a; \ I . e+jets 15% _ "dileptons" "leptonflets" Figure 2- 5: Final states for the top quark pair production, the slide size is proportional to the branching ratio of each process. The final states can be divided into three classes: dileptons, leptoris+jets, and alljets [11]. WhiCh is approximately 20 times smaller than the timescale of strong interactions. As a consequence, the top quark decays before it has a chance to hadronize, resulting in a “Highe— opportunity to study a bare quark. 2'3 Single Top Th . . e t0p quark can also be produced by means of the electroweak interactlon, which in c . ontrmt with the strong interaction production, results in one single top quark rath er than a pair. At the Tevatron collider, to Leading Order (LO) there are two donn- 118.111; Single Top channels: STQhaimel: produced by a virtual, time-like W boson from 8. qt? armihilation, which then decays into a top and bottom quarks, as shown in Figure 2.6. At 20 NLO, the predicted s—channel cross section is 1.12 :l: 0.05 pb [53]. The 3- channel is sometimes referred as “tb” production, where tb includes both t5 and {b states. W1- Figure 2.6: Leading Order Feynman diagram of the Single Top s-channel production mode [1 1]. 0 t—channel: produced by a vitual, space-like W' boson from light and bottom quark and resulting in a forward scattered light quark and a top quark, as Shown in Figure 2.7. At NLO, the predicted t-channel cross section is 2.34 i 0. 13 pb [53]. The t-charmel is sometimes referred as “tqb” production, where tqb includes both tqh and fqb states. There is an additional production mode in which the Single Top created in association With an Oll-Shell W boson. However, this channel has too small of a cross section at the Tevat r01; energies to be observed. AS mentioned in Section 2.2 above, the top quark decays in W —boson plus a b- quark, 111 cases where the W decays hadronically, the Single Top signal will be very difficult to separate from the overwhelming QCD background. For this reason the StUdieS presented in this dissertation are limited to the electron and muon leptonic final States , . ‘ ‘ - . - . .. . of Single Top. The Feynman diagrams for the Single Top muon final states are sh( )WTI in Figure 2.8 for both the s and t channels. 21 Figure 2.7: Leading Order Feynman diagram of the Single Top t—channel production mode [1 1] . proton O. a 0' + y W W+ v t b g . b c ‘ ‘ 5 antiproton 3:21;: 2-8: Single Top quark production and decay. In these diagrams the W-boson has a. b‘eptonically into a muon and a neutrino [11]. The final state for the s—channel decay ‘ QUark created along with the t-quark, a charged lepton from the W-boson the SD and its respective neutrino. In the t-chaimcl case, the main components are ectator light quark, the lepton and the neutrino from the W decay, and the “ma rk from the top quark decay. 22 2.3.1 Background Processes The Single Top background processes have the same final state as the Single T0p signal. These backgrounds are characterized to be enormous compared to the signal. In this analysis, the main backgrounds considered are: 0 EV bosons produced with multiple jets (some of which could be fragmented bl; quark pairs and therefore lead to legitimate heavy flavor tags), referred as W+ jets, o radiatively produced jets which either produce b5 quark pairs or lead to fake vertex tags (called “QCD” backgrounds), and O the production of conventional tt_ quark pairs. The Leading Order Feynman diagrams for these processes are presented in F ig- ure 2-9- 2.3- 2 Motivation to study Single TOP 2.3-2 - 1 Measurement of the CKM matrix element th Single Top offers a unique and direct way to measure the element [th| of the CKM matrix, Section 2.1.2. The measurement presented in this analysis does not assume the lulitarity of the CKM matrix nor the number of quark families. There are three inain a-Ssumptions on the direct measurement of th. First, the Single Top production is assulned to include only the electroweak interaction, thereby not considering scenar— ios beyond the Standard Model. Second, it is assumed that [thl2 >> [thI2 + [Vtsl2- Thig ‘ ‘ l ‘ ‘ I C S QXperimentally supported by the measurements [54, 55] of the ratio: 3(t —* W 61) IVMI2 + We!2 + Ithl2 23 ‘Q Q! 010‘ q 7-,” W Elguxxe 2.9: Feynman diagrams for the Single Top background processes. W+jets 01" left), tt_ (top-right), and multijets (bottom). T ' . . hlrcl, although it is further assumed that the Wtb vertex 1s CP-conservmg and of th - P V x A type, it is allowed to have anomalous strength. The most general Wtb v, , - ertex 1n the Standard Model is given by: I 9 L 1‘5th = — «2th U(PT) [7W1 PL] u(pT). (2.37) ' ff” is the left-handed Vth coupling, and PL is the left-handed projection Opera l t()ra PL 2 (1 — 75) / 2. The Single Top cross section is directly proportional to he 8( 7111 fine of the effective Vth coupling, from where a measurement of th can be inffnr ‘ 1‘(> ('1 ~ References [56, 48, 57] present the results of the th measurement and a 24 more in depth discussion. Section 9.7 contains the results of the th measurement With 2.3 fb’l of D6 data. 2.3.2.2 Top quark spin polarization The Single Top quarks are produced by means of the left-handed electroweak inter- acti011 , resulting in highly polarized top quarks [58, 59, 60]. Since the the top quark decays before it has a chance to hadronize, the top quark spin polarization can be studied in the top quark rest frame through its decay products: t ——> W+b —> 1 Hz b, [12, 61 , 7, 6]. Wllen the W is polarized longitudinally: the b—quark moves in the direction oppo- site to the top quark spin and the W prefers to move in the direction of the top quark Spin. The W decay products prefer to align along the W polarization, and since the W iS boosted in the direction of the spin polarization, the charged lepton prefers to move along the top quark spin axis, as illustrated in Figure 2.10. For the case of left-handed W, the b quark moves in the direction of the top quark spin, and the W in the opposite direction. The right-handed lepton then prefers to move against the W direction, which corresponds to the same direction as the top quark polarization, also shown in Figure 2.10. The angular decay distribution for the charged lepton follows the angular distri- butioll [1 2], 1 OT 1 ‘ _ I‘dcosfl _ 2(1 + 0) (238) Wher » . Q 6 18 the angle between the direction of the charged lepton and the top quark Polar ‘ » léation. These angular correlations play an important role when separating the Single- ' T01) signal from the overwhehning background. Figure 2.10: Top quark decay and correlation between the charged lepton and the top quark spin on the top quark rest frame. The large arrows are the preferred direction of the polarization [12]. 2.3-2-3 Physics Beyond the Standard Model 801110 of the possible extensions of the Standard Model include: existence of more thall three quark families, additional gauge bosons, extra scalar bosons, and modi- fied top quark interactions. Each extension affects the structure of the Single Top quark production, the final state kinematics, and thus the Single Top quark cross SCOtiOll [12], III the event of a fourth quark generation, the direct production of such quarks can be Observed through Single Top production qci’ —» W* —+ tl—J’, where b’ is the b-like quark Of the fourth generation and W* is the mediator gauge boson. This process IS 11lllStl‘axed in Figure 2.11. The associated production cross section will depend 011 the Inagnitude of the W* t b’ coupling and the mass of the b’ . q a" . 5’ E igure 2.11: Single Top production and a fourth generation quark b’ [12]. 1V1 . (‘5 Gels like the topflavor [62] predict the existence of additional weak bosons 6‘“ 1(1 Z’. In this model Single Top is produced by the exchange of a W’_ boson 26 having the same finals states as the Standard Model Single Top production, as shown in Figure 2.12. The W’i can be study by searching for resonances in the invariant mass distribution of the W'i t b system at the MW’i' q I b Figure 2.12: Single Top production by means of the W ’ i gauge boson.[12]. The Single Top production can also be affected by flavor-changing neutral currents (FCN C) , which are forbidden in the Standard Model. These currents allow the top quark to have anomalous couplings such as those in Figure 2.13, where the top quark decays illto a gauge boson and a c-quark. The resulting FCN C Single Top production (li' ° dgraxns are shown in 2.14. C C C t t t m2 Z Y 03 g (a) (b) (C) 13030“ ' 2 - 13: FCNC couplings for the top quark decaying into a c—quark plus a gauge (lrx:ay{1 Similar diagrams are also permitted by FCNC currents for the top quark 15% into a u-quark.[12]. 8111 ., tlu S llll‘lmizing, the Single Top quark production can be used as tool to test Beyond ' f . D \lldard Model theories. These theories Will permit the understanding of new 27 6 (6 2 g g(66 t Figure 2. 14: L0 Feynman diagrams for the Single Top production by means of FCNC, 9 c ——> t Z .[12]. DhYSiCS phenomena, and also help in the search of new particles such as the Higgs l)()S()Il - 28 Chapter 3 N LO Studies of Single Top Quark Production The Single Top quark production is predicted by the well-confirmed Standard Model. Whicll can be considered not only as a tool to test the Standard Model, but also as a Window to physics beyond it. Consequently, accurate calculations are required which include higher order QCD corrections to make the Single Top distinguishable from other processes. Such calculations, should not only include effects on the production cross Section, but should also include the event topology of both the production and decay of the top quark. Therefore, the theoretical calculation can be directly compa-I‘ed to the experimental findings in the Tevatron collider at Fermilab. TmS Chapter presents the NLO corrections effects on the Single Top quark produc— tion, a11(1 the work I conducted, together with the Michigan State University theory group - 3. 1 Event topology The 8 ~ A o o u . ‘ ‘ ‘ llgle Top 3 and t channels have common elements in their event signatures as well .3 § I O I '7 — ("lifferential features. They both have at least one b—jet, missing transverse 29 ~ -—- _ "' 100 — g 10 (a) b from top a (b) l_) from top D H b from top 0 b from top 8 lepton 80 :..; 1 -~~ lepton neutrino 60 40 -§: 3 . --. x r. 20 Q) 50 100 150 I p, [GeV] E —b from top .3 o 1 o u E ght quark 8 ’ ‘ 5 from gluon ....... I to 6 ep 11 4 =" ‘ . 2 0 150 I Figure 3- 1: Parton level kinematical distributions for the transverse momentum PT (a,c) and pseudorapidity n (c,d) for final state partens in the s—channel (upper row) and t‘channel (lower row) Single Top quark events. The histograms only include the final St ate of t, not i. finer-Q, and a lepton, but their kinematical distributions have different shapes. More s , ' Peclficiilly at the parton level: . S‘Channel: there are two b quark jets, one from the top quark decay and one pro duced with the top quark itself. As well, there are one high-pT lepton and a. Ileutrino. In the detector, the neutrino is represented by missing transverse (allergy (MET) coming from the W boson decay. Illustrated in Figure 2.8. O t\ . (thannel: there is one b quark jet from the top quark decay, one light quark J Qt recoiling against the top quark, one high—pT lepton, and a neutrino coming f 1‘91): the W boson decay. In addition, there is a target fragment b quark that ("lids to be relatively soft at high rapidity, and collinear to the nntial gluon. 30 This results in a b—jet that is difficult to observe in the detector. Illustrated in Figure 2.8. Figure 3.1 shows some of the parton level distributions for the Single Top final prod- ucts. Although experimentally is it not possible to determine whether a b jet comes frorn the top quark or not, the jet distributions are shown separately for each b jet for illustrative purposes. The b quark coming from the top quark decay tends to be central and to have a hard PT spectrum. The lepton from the W decay prefers to move in the direction of the top quark polarization (see Section 2.3.2.2) which results in a. softer lepton spectrum compared to the neutrino. Also, note the asymmetry on the light quark 17 distribution for the t channel, which comes from the nature of the p15 collider. 3. 2 N LO calculations b W l' u t W 1/ (j (3 Fi c 8, grime <3- 2: Single Top LO Feymnan diagrams for the s and t charmels. The symbol ep may I“asents the separation used in the NWA method between the production and ()f the Single Top. A (:thplete N LO calculation should include the contributions from top quark produ - .. C‘ t 1(3n and decay including the angular correlations of the final state particles to Study t h the top quark polarization. References [61, 7, 6] present such corrections, at e 0 I‘(i W'd er of (1(8), using the one scale, space-slicing method together with the Narrow l t. Approximation (NWA). 31 The NWA is used to separate the study of Single Top into two stages: production, and decay, as depicted in Figure 3.2. The two parts can then be related using the po- larization information of the top quark. In the NLO corrections, there are mainly two kind of divergences: ultraviolet (UV) and infrared (IR). The ultraviolet divergences are removed by renormalizating the wave functions. The IR divergences are handled by considering virtual and real corrections. The Phase Space Slicing (PSS) method uses the cut off scale parameter 3min to separate the phase space into two regions: the resolved and the unresolved region. The amplitude in the resolved region has no divergence and can be integrated using Monte Carlo methods. The amplitude in the unresolved region contains all the soft and colinear divergences and can be integrated analytically [61]. b 1+ [4 u t u t u t l/ l/ I/ ‘1 1 NIT b (1 FINAL b J. SDEC b b b b b b' b t ll ll ll- d I/ u . LIGHT U II 15.1w u TDEC F ' u r ,, If) (3 ~3 -3: Different contributions to the Single Top N LO corrections, s-chalmel per row) t-channel (lower row). The black dots indicate the higher order QCD Con-QC. - , . . ’thns, both for Virtual and real ermssrons. T1 (3 process involved in the NL() calculation can be separated mto categories, as showl - 1 1 11 Figure 3.3. For the s-channel: - I 1\TIT: corrections to the initial state of the single top production. I N AL: corrections to the final state of the single top production. ‘ S DEC: corrections to the decay of the top quark. 32 For the t-channel: o LIGHT: corrections in which the gluon is comiected to the light quark. o HEAVY: correction in which the gluon is connected to the heavy quark. o TDEC: corrections to the top quark decay process. The contributions to the total cross sections are presented in Table 3.1, the NLO corrections effect on particular distributions is shown in Section 3.3 below. s-channel t-channel Cross NLO Cross NLO Section Fraction Section Fraction (fb) (%) (ib) (‘%>) L0 31.2 65.0 L0 99.2 94.6 INIT 10.7 22.3 LIGHT 5.56 5.31 FINAL 5.5 11.5 HEAVY 1.03 0.98 SDEC 0.57 1.19 TDEC -0.81 -0.77 C(as) sum 16.8 35.0 0(a3) sum 5.54 5.28 NLO 47.9 100 NLO 104.8 100 Tab . . . . T 18 3 - 1: NLO corrections contrllgmtlons for both 3- and t-charmels for the Single op pr0(iuction [5, 7]- 3°3 Single Top distributions at NLO thfx ’11 ‘ . . . . . . 5‘3 lidymg Single Top experm'lentally, 1t 1s 110(1‘88211')’ to apply selection cuts to t 11 Q . Collected samples to remove lmwanted backgrounds. Although no detector 81111111 t l t‘1()ns are included in 131118 study, there are some selection criteria applied to m ' go ‘1 1(‘—rated samples that allow comparison of the NLO corrmtions results with the 33 experimental counterparts. In particular, it is required that the events contain one lepton, MET, two to four jets, and the following cuts: 0 Lepton: PT > 15 GeV, | n |< 2.5. o MET: > 15 GeV. 0 All jets: PT > 15 GeV, I 17 |< 3.0. O jet conesize: AR 2 0.5. Plots in F iguras 3.4 and 3.5 show NLO effect on selected Single Top distributions. The Size of the NLO effect is larger in the s-channel compared to the t-chalmel. However, in general, the NLO effect has a very similar shape as LO for both channels. h4ore specifically, the NLO QCD corrections: 0 for the lepton and ET (first row of Figures 3.4 and 3.5), have very similar Shapes to the LO distributions. This is explained by the fact that they are not quwk distributions. for the b—jets, shift and widen the PT distributions. The peak value moves to - lovver values. The b-jet 7] distribution for the s-channel becomes more central, Wllile the shape for the b-jet 77 remains almost michanged. The HT distributions are broadened as a consequence of the NLO corrections. . for the t-channel spectator (light) jet, move the pseudorapidity distribution Slightly forward, due to the additional gluon radiation. 3. 4 “Lonely Top” The ‘I‘Q: _ 11 five been many studies regarding the separation of the Single Top signal from its 0V? : Whelmin background. 0110 Of these. Stlldlflh‘, \Vthh IS I'(‘.f(‘,IT(".(l 8b “LOIICIy g 34 y 16: E _14;- G a 12:— H : .3; o 10.— ‘6‘ '- s.» 4:— 2:— e: , o [fblGeV] IX "2:1:- . 00 150 200 250 00 516“ 1 JetbPTIGeVI 100 150" ‘“ so {pl-gut“ - Jet; pT [GeV] The ' 3-4: NLO corrections effect in distributions for the Single Top s—channel [6]. contr i fitted red line represents the LO calculation, the blue line the sum of NLO elec tr )lltions, and the black line the sum of L0 plus NLO. Top row: electron PT and b'let Q11 7). Second row: E and total transverse. energy HT- Third row: b—jet PT and ‘ Bottom row: b—jet PT and b-jet 77. Figures from Reference [7] 50 ‘ — NLO LO 0 so ”100 150 200 Jetb p-r [GeV] 1. - NLO % . m g 0.3 -~ 0(as)suln 330.6 so" 100 fifflw F“ Jetspectator PTlGeV] reg???) 3.5: NLO effect in distributions for the Single Top t—channel [6] The dotted 1111c represents the LO calculation, the blue line the sum of NLO contrilmtions, and the black line the sum of L() plus NL(). Top row: electron PT and electron I]. Biol“! row: E and total transverse energy HT- Third row: b-jet PT and b-jet 7]. tom row: light quark jet. pT and light quark jet ‘7). Figures from Reference [6]. 36 Top” [63, 64], is based on the usage of correlation functions between pseudorapidity distributions of the final lepton and the untagged jet. The “Lonely Top” calculations were performed at LO. However, as shown in the previous section, the NLO correc- tions affect the kinematics in Single Top quark production. With that consideration, this Section explores the N LO effects on the “Lonely Top” correlation functions. In order to have a similar sample to the one used in Reference [63], the following additional selection criteria are required: a Lepton: I’T > 15 GeV, ] 7) |< 2.0. o MET: > 15 GeV. 0 All jets: PT > 30 GeV, [ 77 |< 2.5. 0 Leading jet (Jet in the event. with the highest. pT): pT > 40 GeV, I n |< 2.0. 0 HT (total event transverse energy): < 300 GeV. 0 Reconstructed top mass: 155 GeV < mT < 200 GeV. 0 jet conesize: AR = 0.5. The b—tagging effect on the sample is included by using a probability distribution, Which determines whether each jet would be b—tagged or misstagged [63]. For a b—jet, the probability to be b-tagged is given by ptagged,bjet(pT) : 0.5 tanh(pT/36GeV), While for any other jet, the misstaggcd probability is given by pmisstagged,jet(pT) = 0.01 tanh(pT/8()GeV). 37 Difl‘ cross section - s-channel leI' cross sectlon - t-channel Eta Lepton Eta Lepton 55 U" I p 01 o 2 -3 -2 -1 o 2 3 Eta Untagged ng1hest Pt Jet Eta Untagged Highest Pt Jet Figure 3.6: Double differential cross section for s-chaimel and t—chaimel. Only LO contributions are shown. The x—axis corresponds to the untagged-jet I) and the y-axis to the lepton 7]. The asymmetry functions presented in Reference [63] are based on the CP invari— ance of initial p15 state of the at the Tevatron collider. The Single Top differential cross sections shown in Figure 3.6 exhibits some asymmetrical behavior in both 3- and t-channels. This motivates writing the differential cross section as the sum of three orthogonal fimctions: 20 dnj d7?) —_—(nj;nl): FUIJ’JII) +F+(nj 7”) +F—(nj m) where, each one of asymmetry flmctions (F) is defined as: — d___2 a +d—_2.—0 +_d_20 +d_20 _d_2a d_2a . _d_2a d2a . F+ - l’! -—>A —_P\——A_— — .7 A 1 2 A, , d2a F— (7733771): fl] ‘1” (n > ( ‘ 2 - )1 2 d7)] d-I)l [73’7” dfijdfn 77]» 771 where by construction, the Fand F _ functions have even parity while the F+ has odd parity. If the four quadrants of the (173,171) plane are label as A, B, C and D, 38 where B corresponds to first quadrant, A to the second, C to the third, and D to the fourth, AB CD. Thus the definition of these variables, implies that the information on: FM) = F(B) = RC) = 7(0), F+(A)=F+(D) , F+(B) =F+(C) , FHA) =—F+(B), and F—(A)#F—(B) , F—(A)=F—(D) , F—(B)=F—(C) The above indicates that all the information in F and F+ is contained in one quadrant, and in two quadrants for F_. These asymmetry functions are shown in in Figure 3.7, including only the LO contributions. Based on the description of these functions, it is expected that the N LO corrections contributions would result in changes on the function shapes. Such changes are related to those encountered in the Single Top kinematical distributions. These N LO effects are shown in Figures 3.8 to 3.11, and reviewed in the next Section below. 3.4.1 “Lonely Top” at NLO The asymmetry functions at NLO for the Single Top 3- and t-channels are presented in Figures 3.8 to 3.11. The NLO contributions are shown in the middle colunm and the final distribution, including L0 and N LO corrections, is shown in the third column. The unique features of these functions can be used to separate the Single Top signal 39 Eta Lepton s5 on Eta Lepton O -'l I - . M 01 d FBAR - t-channel FBAR - s-channei —A .0! d b1 M Eta Lepton P . 01 .5 UI N O O I O 01 L ..,. -3 -2 -1 0 1 2 3 Eta Untagged Highest Pt Jet -3 -2 -1 0 1 2 3 Eta Untagged Highest Pt Jet FPLUS - t-channel FPLUS - s-channel d d Eta Lepton ill .A in N ill—sink) O O O O I .° 01 b 01 -1 -1 -1.5 -1.5 '2-3-2-10123 '2-3-2-10 123 Eta Untagged Highest Pt Jet Eta Untagged Highest Pt Jet FMINUS - s-channel x1 0'3 FMINUS - t-channel c 2 c 2 *3 1.5 0-2 g 1.5 3 1 3 1 a 0.1 (B m 0.5 ‘ui 0.5 A b 01.5010 I o —l '2-3-2-10 1 2 3 Eta Untagged Highest Pt Jet -2 -3 -2 -1 o 1 2 3 Eta Untagged Highest Pt Jet Figure 3.7: F BAR (F), FPLUS (F+), and FMINUS (F_) asymmetry functions, for the s-channel (left) and t—channel (right). Only LO contributions are included in these plots. 40 from the background, and to differentiate the s—channel from the t-channel. The difference between the two channels arises from the angular distribution asylmnetry on the spectator jet on the t-channel, as shown in Section 3.1. This asymmetry also causes the two distinct peaks on the F function of the t—channel, which for the s-channel corresponds to a central distribution. One observes that the NLO corrections indeed add information to the functions that was not available at the LO. Although, these contributions are not so dissimilar to dramatically modify the asymmetry functions, it is safe to consider that the new features that appear as a result of the N LO corrections would contribute to the dif- ferentiation of the Single Top signal. This is also despite the fact that no background was included in the study. The Single Top analysis presented in this dissertation does not include the asym- metry function as part of the Decision Tree variables list; however, they should be consider for future multivariate analyses. 41 Diff cross section - s-channei FBAR - s-channei C c 2 g . 0.0014 a 15 3 .0012 3 1 5 -001 a 0.5 .0008 S _ 0.0006 _o.5 0.0004 0.0002 0 -2-10123 -3-2-10123 Eta Untagged Highest Pt Jet Eta Untagged Highea Pt Jet c 2 Dirt cross section - s-channel 2 FBAR - s-channel C ‘2, 1.5 g 1.5 3 1 3 1 5 0.5 {E 0.5 E 0 ,‘i 43.5 -o.5 C” 1 d - ‘6 .'. thin -3-2-10123 -3-2-1 3 Eta Untagged Highest Pt Jet Eta Untagged Highem Pt Jet Difl cross section - s-channel FBAR - s-channel 2 C C '3 131.5 3 3 1 lg 30.5 .6 Leno -2 2 3 -3 -2 -1 o 3 Eta Untagged Highea Pt Jet Eta Untagged Highest Pt Jet -2-101 Figure 3.8: NLO corrections in the s—chamiel for the differential cross section (left column), F (right column). The L0 contribution is show in the first row, the sum of all NLO corrections contributions on the middle row, and the LO plus NLO corrections is show in the last row. 42 FMINUS - s-channel x1o'3 FPLUS - s-channel c 2 21.5 -2 3 1 a .1 iii 0.5 o -o.5 _1 -o.1 -1-5 -o.2 -2-1o123 '2-3-2-10123 Eta Untagged Highest Pt Jet Eta Untagged Highest Pt Jet FPLUS - s-channei FMINUS - s-channel x1o'3 C 2 c 2 *3 1.5 ‘3 1.5 0-2 3 1 3 1 at a 0.1 m 0.5 a: 0.5 3 ° 0 ,‘i 41.5 -o.5 -01 g0 -1 -1 ' ‘o’ -1.5 -1.5 .03 '2 -3 -2 -1 2 3 '2 -3 -2 -1 1 2 3 Eta Untagged Highem Pt Jet Eta Untagged Highest Pt Jet FPLUS - s-channel 2 FMINUS - s-channel x10-3 C C 23 311.5 -2 3 3 1 01 5 5 0.5 ' o O a -o.5 Z -0.1 -1 -1-5 -o.2 -2 -1 o 1 2 3 '2 - -2 -1 1 2 3 Eta Untagged Highest Pt Jet Eta Untagged Highest Pt Jet Figure 3.9: NLO corrections in the s-channel for F+ (left colunm), anti F_ (right column). The L0 contribution is show in the first row, the sum of all NLO corrections contributions on the middle row, and the LO plus NLO corrections is show in the last row. Dlfl cross section - t-channei FBAR - t-channel 2 2 5 .0025 S 31.5 31.5 3 1 0.002 3 1 50.5 °-°°‘5 50.5 o 0.001 0 0 0.0005 g -o.5 -o.5 0 -0.0005 I Id _'. thin I —A 1901:. -3-2-10123 -3 -2 -1 0 1 2 3 Eta Untagged Highest Pt Jet Eta Untagged Highest Pt Jet Dlit cross section - t-channel FBAR - t-channel : 2 c . O .315 00025 a 3 1 .002 3 a 3 0.5 -°°‘5 m g o 0.001 ,‘1 -0.5 0-0005 -o.5 g3 -1 0 -1 ‘5 -15 -o.0005 -1.5 -2 it: -3-2-1 -3-2-10123 Eta untagged Highest Pt Jet Eta Untagged Highest Pt Jet Diff cross section - t-channel FBAR - t-channel Eta Lepton Q .5 Eta Lepton P .-‘ 01 .s at M NLO 9,6 Old I M -3-2-10123 -3-2-10123 Eh Untagged Highest Pt Jet Eta Untagged Highest Pt Jet Figure 3.10: NLO corrections in the t—channei for the differential cross section (left column), F (right colunm). The L0 contribution is show in the first row, the sum of all NLO corrections contributions 011 the middle row, and the LO plus NLO corrections is show in the last row. 44 FPLUS - t-channei 1 (II—hill” o uh i: .9. a. 3 3 I.“ LO .-'t,s'-= 9 ("AGO I M -3 -2 -1 0 1 2 3 Eta Untagged Highest Pt Jet FPLUS - t-channel x10-3 S 2 § 1-5 0.4 .1 1 a u, .11 0.5 0'2 g 0 1;, '°'5 -o.2 C, -1 ‘6 -1.5 '0-4 '2-3-2-1012 3 Eta Untagged Highest Pt Jet 2 FPLUS-t-channel x10'3 C £15 0 —I 1 fi m 0.5 O 0 1.3 -0.5 2'. _'t I - . M U! .s -3 -2 -1 o 1 2 3 Eta Untagged Highest Pt Jet FMINUS - t-channel —l Eta Lepton b .o . 0" 0 0'1 —A 01 M _'s . . . . N 01 .a -3 -2 -1 0 1 2 3 Eta Untagged Highest Pt Jet FMINUS - t-channel d 0|th Eta Lepton P 55 01° _'. thin; -3 -2 -1 0 1 2 3 Eta Untagged Highest Pt Jet FMINUS - t-channei —l Eta Lepton s5 .o . 01 O 01 .s at M 1. '01:. '2-3-2-1012 3 Eta Untagged Highest Pt Jet Figure 3.11: NLO corrections in the t-channel for F + (left colunm), and F_. (right column). The L0 contribution is show in the first row, the sum of all N LO corrections contributions on the middle row, and the LO plus NLO corrections is show in the last row. 45 Chapter 4 Experimental Setup Figure 4.1: Aerial view of the Fermilab National Accelerator Laboratory. The Fermi National Accelerator Laboratory (Fermilab) [65, 13] is located near Chicago, Illinois in the USA. Currently, Fermilab is the only facility in the world where the high energy collisions of protons and anti-protons are possible at a center— of-mass energy of s 2 v1.96 TeV [13. 66]. It all begins from a bottle of hydrogen 46 and culminates with the collision of protons and anti-protons traveling very close to the speed of light. To properly study the interactions that take place at Fermilab, a complex detection system is required which would allow one to “observe” the details of these energetic collisions, and study interesting physics processes such as the Single Top. The two main detectors at Fermilab are known as DC and CDF. This chapter presents a description of the accelerator complex and the D0) detector at Fermilab. 4. 1 Accelerator complex Fermilab’s Acceleration Chain ,2; - Main In actor R I \- Tevatron . i§ .(ecyc er \ , Km *‘f‘ _ __ \ \ ) Target Hall r , Dfl st / . ,. ‘ \K \ //Debuncher g y p \_ / Accumulator \ CDF j 3 .\\ ‘/ B t g Y“ j - c/, oos er / ' \\LINAC Proton / 7/7 , / . / Cockcroft-Walton Neutrino]. .1 4' " . " ' Antiproton Proton 7}? ~ /74// Meson Erection m Figure 4.2: Fermilab accelerators chain, there are 2 interaction points, CDF, and D?) [13]. The Fermilab accelerator complex is composed of seven chained machines that have, as their ultimate purpose, the generation of protons and anti-protons at Ebeam = \/ 980 GeV each [16]. These machines are known as: a Cockcroft-Walton preaccelerator, linear accelerator (LINAC), booster synchrotron, main injector, antiproton source, antiproton recycler, and the Tevatron [14]. In the following sections a description of 47 each segment of the acceleration chain is presented. Figure 4.2 is an schematic view of the full chain. 4. 1 . 1 Cockcroft-Walton pre—accelerator The acceleration process starts by using hydrogen H2 and turning it into H _ ions. The charged hydrogen is accelerated by an electric field produced by a potential difference of 750 kV. Such high voltage is achieved by charging in parallel capacitors fromian AC source, and by using diodes to discharge them in series. The H - ions are accelerated to 750 keV. 4.1.2 LINAC The energy of the H "' ions coming from the Cockcroft-Walton accelerator is increased further by using a linear accelerator, which augments the ions’ energy from 750 keV to 400 MeV [14]. The LINAC uses a series of RF cavities to accelerate the particles by alternating the electric field in the cavity and giving a small boost to the ions when they pass the gaps between cavities. Since the acceleration of the ion occurs only at specific conditions of location (gap) and electric field, the ions are confined in bunches. Before the ions continue to the next acceleration step they pass through a carbon foil to remove the electrons. A schematic view of the LINAC is shown in 5.2:. «i l Beam direction TANK (under vacuum) Figure 4.3: LINAC alternating series of gaps and drift tubes [14]. 48 4.1.3 Booster Synchrotron The booster is the first synchrotron of the accelerator chain with a diameter of ap- proximately 150 In. It uses RF cavities for the acceleration of the particles. The charged particles travel in a circular path due to magnetic fields and receive an accel- eration due to electric fields during each revolution. The particles’ energy after the Booster is 8 GeV. 4.1.4 Main Injector The Main Injector is a synchrotron that serves several purposes. The most relevant task of the Main Injector is to accelerate both protons and antiprotons to energies of 150 GeV which is the initial energy of the particles in the Tevatron. In addition, the Main Injector also accelerates the protons coming from the Booster to 120 GeV and sends them to the antiproton production chain. 4.1.5 Antiproton Source and Recycler The antiprotons are selected from the particles produced from the collision of 120 GeV protons coming from the Main Injectors into a fixed, nickel target. A lithium lens is used to focus the secondary particles produced after the collision, from which only the 8 GeV antiprotons are selected by a dipole magnet. A cartoon schematic of this procedure is presented in Figure 4.4. Once the antiprotons are produced they are sent to the Debuncher, which is a triangular shaped synchrotron that reduces the spread 011 the antiprotons’ momenta. After the Debuncher, the protons are stored in the Accmnulator until they are ready to go back to the Main Injector for further acceleration or into the Recycler for later usage. The antiproton production efficiency is very low taking about 12 hours to produce 49 enough antiprotons to start the p13 collisions. Due to this fact, there is an additional component in the Fermilab complex, the Recycler whose main purpose is to temporar- ily store remaining antiprotons from Tevatron or those coming from the Accumulator. Secondary Particles Collection Target Lens — ———> —-—> Primary Protons Figure 4.4: Schematic diagram of the 15 production [14]. 4.1.6 Tevatron The Tevatron [67] is the final stage in the acceleration chain (The circumference of the Tevatron is about 6.3 km). It uses RF cavities to bring the energy of the protons and the antiprotons to 980 GeV, which is equivalent to a center-of-mass energy of 1.96 TeV. While sharing the same beam pipe, the protons rotate clockwise while the antiprotons travel in the opposite direction. The Main Injector sends 36 bunches of protons and 36 bimches of antiprotons to the Tevatron. These sets of bunches constitute a “store”. The spacing between bunches is 396 us with a gap of 2.64 as every 12 bunches. The beams are magnetically squeezed and forced to interact with each other at two points, D?) and CDF. 4.2 The D0 Detector Muon Central Muon MUD" Tracldng 0310" rneetr Trigger VSystern 1 Detectors ’III VIII—IIIIIII \\ L‘“‘\\\‘ \\ \\\\\\\\\\\\\\\\ ’I’ III/I’IIIIII \\\\\\\\\\\\\\\‘ 1.. . \\\\\\\\\\\ V 0 meters 5 Figure 4.5: Schematic view of the D0 detector [15]. The DG detector was designed to study collisions of protons and anti-protons at a center of mass energy of 1.96 TeV [15] [68] , and optimized to study high mass states and large pT phenomena. The D0 detector consists of four major subsystems: central tracking, calorimeter, muon spectrometer, and trigger systems, as shown Figure 4.5. The central tracker allows precise measurement of particles near the collision point; it is composed of a silicon micro-strip tracker (SMT), a central fiber tracker (CFT), and a. 2 T solenoid. Between the solenoid and the calorimeter there are preshower detectors used for the electron identification. The calorimeter is divided into three sections: one in the central region and two end caps. The purpose of the calorimeter is to identify and measure energy depositions of electromagnetic and hadronic particles. 51 The outer-most layer of D0 is used to detect muons. DQ) also incorporates a trigger system that receives the signals from all the sub-detectors and selects events that are considered to be interesting enough to be analyzed. 4.2.1 Coordinate system Y fit P 3 ¢ / ’ X_ \ Tevatron a ———> p Figure 4.6: Coordinate system used at D0, the z-axis is along the proton direction and the y-axis upward. DQ uses a right-handed coordinate system with the z-axis along the proton di- rection, and the y-axis pointing upward. The angles (1) and 6 are the azimuthal and polar angles, as shown in Figure 4.6. The polar angle is commonly described by the pseudo-rapidity 77, defined as: nattgfl (4.1) in the limit of m << E, the pseudo—rapidity approximates the true rapidity y, defined as: l E+pz =——1 4.2 y 20g[E_pz] ( ) which is an invariant quantity under Lorentz boosts along the z—axis. This quantity is zero for particles with 0 = 90°, and high values for 0 ——> 0°. 4.2.2 Luminosity Monitor proton direction _______.._______.____________.> LM Forward .. Ixx”, calorimeter f SllJCOll track I \, , , , , , Tl = 4.4 j j- ----------- be-am pipe It North \\ South I 1]! -l40 cm 140 cm Figure 4.7: Schematic View of the D0 Luminosity monitors [15]. Luminosity is a quantity that represents the number of particles per unit of area per unit time, and is related to the rate of a given process as follows: N Rate = ddf = a x C (4.3) where a is the total cross section. D0 uses the Luminosity Monitor (LM) described in detail the in [69] to collect information about inelastic pp“ collisions for each bunch crossing. The LM consists of two arrays of 24 plastic scintillator wedges located at z 2 i140 cm, and covering the pseudo-rapidity region of 2.5 < lnl < 4.4, see Figure 4.7. In addition to determining the Luminosity, the LM also measures the beam halo rates and the z—coordinate of the interaction vertex. The instantaneous Luminosity is measured as: L = ——fNLM (4.4) ULM where f is the beam crossing frequency 2.53 MHz, N L M is the average number of p15 inelastic collisions, and a L M is the effective cross section. The integrated luminosity I delivered at D0 is presented in Figure 4.8. The z-vertex can be measured using the time of flight from North and South detectors: thz = 5(TS — TN). The approximate resolution of z is about 6 cm. vtx Fermilab Tevatron Run II Integrated Luminosity * ‘ ‘ Delivered 6 j .1 /-l 6.11 m" : E , *1 _’Recorded 5 ., / 5.37 fb‘1 3 f 2.3 fb" - Observation Analysis Integrated Luminosity [fb"] .5 0.9 fb‘1 1 Evidence ‘ Analysis ' , 0 M 2002 72003 2004 2005 2006 2007 2008 2009 Figure 4.8: Integrated Luminosity delivered at DC [16]. 4.2.3 Central Tracking There are two central tracking detectors: the Silicon Microstrip Tracker (SMT) and the Central Fiber Tracker (CFT), which are contained in a 2 T magnetic field. The purpose of the SMT is to measure the momenta of charged particles and the location of the primary vertex. The resolution of the central tracking system is 35 nm. Figure 4.9 1 The integrated luminosity L, is defined as the instantanmus luminosity £ inte- grated over time, f£dt lntercryostat Detector Central Fiber Tracker Solenoidal Central Preshower Detector Figure 4.9: Schematic view of the central tracking system and the preshower detec— tors [15]. shows the location of the system within the DI?) detector. 4.2.3.1 Silicon Microstrip Tracker 7 ,; 1“": ‘J A . '1; \‘l .. t- I ‘ , ,s 5 . - "A If,“ ‘ < 6 Barrel 4 H-DiS_kS sections/ modules (fowvard. high-n) Figure 4.10: 3D Schematic of the Silicon Microstrip Tracker [15]. The SMT is located near the collision point at DC and provides information about the vertex and tracks of the interactions. It contains an array of silicon barrels and disks positioned to maximize the 17 coverage. The barrel detectors measure the r and 45 coordinates, and the disks 7", z and q). The barrels and the disk are made of doped silicon with a reverse bias voltage applied. When charged particles pass through the silicon, electron—hole pairs are created, and an electric current can then be measured. Each barrel has 4 layers. Layers 1 and 2 have 12 ladders each; and layers 3 and 4 have 24, see Figure 4.11. There are 6 barrels for a total of 432 ladders. The centers of the barrels are located at [2| : 6.2, 19.0 and 31.8 cm. There are two types of known as disks “F—disks” and “H-(lisks”. ()ne F—disk has 12 double—sided wedges, and an H—disk has 24 full wedges. The F-disks are. located at lzl = 12.5, 25.3, 38.2, 43.1, 48.1 and 53.1 cm, the H—disks |z| : 100.4 and 121 cm. The SMT has total of 932 readout modules, for a total of 792,576 chaimels. Figure 4.10 is a 3D view of the full SMT detector. ladder (layer 4) beryllium bulkhead ' cooling pipe carbon fiber support Figure 4.11: Side view of a barrel for the SMT detector [15]. 4.2.3.2 Central Fiber Tracker Strain relief ring for CFI', CPS waveguides 256-channel fiber CFT or CPS /' Central calorimeter I waveguide bundle cryostat wall Clearance for FPS waveguides (not shown) "u 0, I florist}; i l/ r “\\.\\\ tI/i‘lt Ulilllh , 7 “ha"; L‘ ‘ Solenoid . , "7 ' ‘1 . ‘ . i.‘ ,i‘ _/A servrces ' I Calorimeter support J" """"" structure Vertical waveguide chutes toD¢ readout platform (VLPC cryostats) Figure 4.12: Schematic view of Central Fiber Tracker and the clear wave guides fibers [15]. The CFT surromids the SMT and consists of scintillating fibers positioned in 8 concentric cylinders covering the region r = 20 cm to r = 52 cm, and |n| < 1.7. Each cylinder has two doublet layers, one layer parallel to the z—axis, and the second layer aligned at a stereo angle (23 = :l:3°. When charged particles travel through the fibers, the atoms of the scintillating fiber get excited and emit light with a wavelength of 340 nm. The fibers have a dye which absorbs the 340 mn light which is then emitted at 530 um. The light is extracted from the fiber using a waveguide and finally, it is collected by a visible light photon counter (VLPC). The position of a particle is determined by the crossing of the fibers. The CFT resolution is approximately 100 mm. Figure 4.12 shows the south face of the CFT and the waveguides. 4.2.3.3 2 T Solenoid Toroids Calorimeters CC /EC 5 Power i. /’ Leads i , Control ..\ . ’ Dewar ! / I, .’ Platform N Central \ I K Beam I , V P 2T Solenoid acuum ”mp Chimney Cryobridge Figure 4.13: Location of the solenoid with respect to the other component of the DC detector [15]. The 2 T superconducting solenoid, containing both the CFT and the SMT, was designed to optimize the momentum resolution. The size of the magnet is 2.73 m in length by 1.42 cm in diameter. Figure 4.13 shows the location of the solenoid with respect to the other parts of DC. The magnet has two layers of superconducting conductors made of CuszTi. The cooling system uses liquid helium to maintain its superconducting state. The operat— ing current of the solenoid is 4749 A. In Figure 4.14 the magnetic field for both the solenoid and the toroid is shown. Toroid G A (II V (cm) 400 .260 6 200 400 z (cm) Figure 4.14: Side view (y — z) of magnetic field for the solenoid and the toroids [15]. 4.2.4 Preshower detectors The preshower detector assists in the reconstruction of electrons, photon identification and background rejection. It is composed of three parts: the Central Preshower 59 (CPS) covering the region lnl < 1.3 and located between the solenoid and the Central Calorimeter at r = 72 cm, and two Forward Preshower (FPS) covering the region 1.5 < I17| < 2.5 located next to the faces of the end calorimeters. The preshower detectors can be seen in Figure 4.9. The CPS has three layers of scintillating fibers, one parallel to the z—axis and the other two at an stereo angle of d) = +23.8° and 43 = —24.0°, respectively. There are a total of 1280 strips in the CPS. The FPS has four double layers of triangular-shaped scintillating strips; the first two layers are at an angle of 225° relative to each other, a radiator 11 cm thick follows and finally two more scintillating layers. Charged particles appear in the first two layers or minimum ionizing particle (MIP) layers. The radiator causes both electrons and muons to start showering, and the final two layers are used to detect the showering of electrons and photons, and separate them from hadrons. 4.2.5 Calorimeter The calorimeter is composed of one central calorimeter (CC) and two end caps (EC) — north and south. It provides energy measurements for photons, electrons and jets. The three parts of the calorimeter are illustrated in Figures 4.15 and 4.16. The calorimeter intercepts most of the particles energy, causing them to interact within the detector volume producing “showers” of increasingly lower-energy particles. A cartoon diagram of the showering process is shown in Figure 4.17. The CC covers In] § 1.0, and the two end calorimeters extend the coverage to 77 z 4.0. Each calorimeter is built similarly with an electromagnetic region, a fine hadronic section and a coarse hadronic section. The EM section uses plates of depleted uranium as absorbing material and liquid argon as the active medium. The fine hadronic section uses uranium-niobium plates as absorbing material, and the coarse hadronic section uses copper and stainless steel plates. Both of the hadronic sections use liquid 60 END CALORIMETER Outer Hadronlc (Coarse) Middle Hadronlc (Fine 8. Coarse) 99 .4 .45, E \ i/ set \~§ \ six 9“- \ . t\\i \ ,\ § \ E/ C / CENTRAL CALORIMETER Electromagnetic Fine Hadronlc Coarse Hadronic 2, \j 7) ya 47 I) // Inner Hadronlc (Fine & Coarse) Electromagnetic Figure 4.15: 3D view of the DC calorimeters, central and end caps {15]. 11:00 0.2 0.4 0.6 0.8 1.0 Figure 4.16: Schematic View of the transverse cut of one of the octants of the DC calorimeter. The shading pattern indicates cells for signal readout. The n coor- dinates are represented by the radial lines [15]. 61 argon as the active medium. A typical calorimeter cell is shown in Figure 4.18, where an electric field is estab- lished by grounding the metal absorber plates and connecting the resistive surfaces to a 2 kV high voltage. Particles deposit some energy into the. inducting material and ion- ize the liquid argon as they shower through the cell producing a current proportional to the particle’s energy. The calorimeter cells are positioned in a “pseudo-projective” set of readout towers, see Figure 4.16, with the center of each cell aligned for each tower. The tower size is generally A77 : 0.1, Ad) : 0.1. ABSORBER Figure 4.17: Example. of an elmztromagnetic shower, when a photon interacts with the absorber material. X0 is the radiation length. 4.2.6 Muon System Muons do not deposit much energy in the tracker or the calorimeter, therefore a spe— cial sub-detector is needed to confirm the muon’s detection. The DC muon measuring system consists of toroidal magnets, proportional drift tubes (PDT), central scintil- lation cormters, and mini drift tubes (MDT). The central system covers the region of 7) § 1.0, and the forward system extends the coverage 11p to n z 2.0. The muon detec- tor has three layers: A, B and C, with layer A located closer to the interaction point, 62 Resistive N ‘-—-—- \ ______________ I |‘—1 Unit Cell —>| Figure 4.18: Typical calorimeter cell composed of alternating inducting and active material [15]. and within the iron toroid magnet between layers A and B. The full system location with respect to other sub-detectors in D0 can be appreciated in Figure 4.5. Exploded views of the wire chambers and the scintillation counters are shown in Figure 4.20 and 4.21. The drift chambers are used to measure the muon position and momentum. Each chamber consist of two walls held at a negative voltage, and a central wire with a positive voltage. Both walls and the central wire are surrounded by an inert gas that is ionized when the muons travel through the chamber. The scintillators provide precise timing measurements which are used by the triggering system. When the muons pass through the scintillator counters, light is produced, which is then collected by a photomultiplier. The photomultiplier sends the signal to the read out system. The outer most scintillator counters are used to reject cosmic rays muons signals, by associating a muon in a PDT with the appropriate bunch crossing. The toroid improves the measuring capabilities of the muon momentum by bending the muons as they enter the 1.8 T magnetic field. 63 Mini-Drift Tubes (MDT) Proportional Drift Tube (PDT) A layer MDTs Muon 8 layer MDTs WWC layer PDTs C layer MDTs ‘ B layer PDTs A layer PDTs Shie|ding 5.0.0.0...0.0.0.0.0.0.‘ A-g .' ; If: """ Scint. Counters C Pixels Wm B P' els Ix B Scint. A Pixe's c Scint. Figure 4.19: Schematic view of the full muon detector system [15]. 4.2.7 Triggering The trigger system uses the information provided by each of the sub-detectors to select interesting physics events to be stored to tape. There are three levels of triggering, each one reducing the number of events, but with an increasing complexity in the processing. The first level (Level 1 —- L1) handles all the processing by a collection of hardware elements and reduces the event rate from 1.7 MHz to 2 KHz. The second level ( Level 2 — L2) incorporates more sophisticated hardware computing engines and delivers a trigger decision based not only on individual detector elements, but also correlations among them; the acceptance rate for L2 is 1 kHz. Finally, events passing L1 and L2 are sent to a processing farm of microprocessors, Level 3 — L3. At. 64 Proportional Drift \. -z Nonh \ +x East Figure 4.20: Muon wires [15]. L3, complex algorithms reduce the acceptance rate to about 50 Hz, which is the rate the events are stored for offline reconstruction. The overall operation of the trigger is controlled by the COOR package, whidi interacts with the trigger framework (TFW) and the data acquisition system (DAQ). A block diagram of the D0) trigger system is shown in Figure 4.22. Due to the fact that all Level 1 decisions should be made quickly, the tools available are limited compared to the other triggering levels where more complex operations are done. At L1, only the calorimeter trigger tower information, the muon detector signals and the transverse momentum of charged particles tracks in the CFT are available. At Level 2, the correlations among different sub-detectors use global physics objects such jets and electrons to based the decision made at this stage (L2Global). Figure 4.23 shows a. flow diagram for both L1 and L2 triggering. The final portion of the triggering system is the L3 computer farm, which consists a“ SQXG.‘ _ g:\\“\\\\\\\ . \ I \\\\\\ e“ ...\\‘ l Trigger Scintillation Counters e ' +y 5 -z North Slim 5;; Figure 4.21: Muon scintillators [15]. Detector Data 1.7MHz L1 Buffers 2kHzIIIUfle'1kHz Level 3 50H: “an“, I I Host , L1 7 :A°°°F" v * Level 1 I Level 2 Tape Trigger : Trigger Storage Trigger Framework Figure 4.22: Trigger overview block diagram [15]. 66 of approximately 100 nodes. The Level 3 trigger collects the information from all the sub-detectors for events that passed the Level 1 and Level 2 requirements. The selection done at this level is complex where some partial reconstruction of events occurs and more elaborate cuts can be applied. The reconstruction algorithms are similar to those encountered in the offline processing. Detector Leve|1 Level2 CAL + L1CAL :* LZCAL a CPS I, l FPS —> L1 CTT l h CFT y L2+CTT SMT v LZSTT MUO *‘* L1 MUO Fl L2MUO —— FPD Ll FPD .1 _) V - Trigger I: Global Luml +“Framework * L2 Figure 4.23: Block diagram of the L1 and L2 trigger systems [15]. > L2PS e ll YY 67 Chapter 5 Event Reconstruction and Object Identification To fully represent the interactions that occur at the D?) detector one must refer to the results of reconstruction algorithm known as dOreco [70], rather than the subdetec- tors. These algorithms process the raw data and produce final physics objects such as electrons, muons or jets. The aim of this chapter is to describe these reconstruction algorithms and the requirements used to define physics objects. 5.1 Reconstruction 5.1.1 Tracks W'hen charged particles travel through the Central Tracking System (see Figure 4.5) energy is deposited in the silicon strips of the SMT and in the fibers of the CFT. These energy deposits are known as “hits.” The tracking system uses the information from sequences of hits to defined tracks to determine the trajectories of the particles immersed in the 2 T magnetic field present in the solenoid. D9) uses two algorithms to find tracks: Histograming Track Finding (HF T), and the Alternative Algorithm (AA). Both are combined using a Kalman filter by a Global (58 'I‘rack Reconstruction (GTR) algorithm, defining the final set of tracks in the event. Histogramming Track Finding (HTF) The HTF [71] algorithm uses a Hough Transformation to map points from the (x, y) space into the (p, c5) space. This algorithm uses the principle that if a hit occurs in the point (11:, y) then there must be a track coming from the origin with curvature p and direction 4). When all the hits are mapped to the p and <15 plane, they will populate a peak rather than being uniformly distributed in the plane which is the case for random hits. A histogram is populated with the information of the (p, (1)) plane and passed by a Kalman filter for further cleaning and fitting tracks. The passing tracks go through a second, similar histogramming procedure that uses the hits locations (1‘, z) to form lines in the (20, C) plane, with :50 defined as the starting position of the track along the z-axis and C = dz/dr, the track inclination. The tracks are then formed by passing the histograms through another Kalman filter and finally by extrapolating the points to tracks. Alternate Algorithm (AA) The AA [17] constructs tracks by progressively adding layers from both the SMT and the CFT to the track definition starting from hits in the SMT detector. The first step in the reconstruction consists of pattern recognition of possible trackswith hits in at least three layers of the SMT detectors. The first hit must come from one of the F-Disks of the SMT detector, the next hit must be within Agb < 0.18 with respect to the first point, and the last hit is chosen where the track hypothesis has a circle radius of at least 30 cm (corresponding to having a track with at least 180 GeV) and an axial impact parameter of less than 2.5 cm with respect to the beam spot. The reconstruction algorithm is illustrated in Figure 5.1. The hypothesis track is then extrapolated to subsequent layers and hits are added (59 Figure 5.1: Illustration of the AA algoritlnn for track reconstruction [17]. to the hypothesis if the x2 < 16; if there multiple hits in a layer, a new hypothesis is then created. The fitting continues until there are three consecutively missed layers or the end of the detector is reached. The quality of a hypothesis is measured by the number of missed layers, nlnnber of hits, the X2 associated to it, and some other goodness measurements. The pool of available hypothesis is then ranked. Similarly, tracks can be reconstructed with the CFT-only information, but the quality of these tracks is not as good as those defined using the SMT. 5. 1 .2 Primary Vertices The primary vertices (PV) correspond to the location of the hard scatter interac- tion point. Their proper identification is important for the correct reconstruction of physics object. The PV are reconstructed by the usage of an adaptive primary vertex algorithm [24], which consists of three steps: vertex finding, vertex fitting and vertex 70 selection. The vertex finding is performed by clustering tracks according to their z—position. The selected tracks must have PT > 0.5 GeV and more than two SMT hits. The clustered tracks are fitted to a common vertex using a Kalman filter, whereby itera- tively removing tracks with the highest contribution to the x2 until the total vertex X2 per degree of freedom is reduced to less than 10. The tracks are then preselected according to the cluster distance to the closest approach to the beam spot (DCA), requiring the selected tracks to have a DCA significance (lDCAl/ODCA) < 5.0. Af- ter the preselection, the tracks are fitted using the adaptive vertex fitter algoritlnn, where each track receives a weight given by: 1 '.l 6(X2-Xgutoff)/(2T) (O ) 1+ where X? is the contribution of the ith track to the x2 and Xgut of f and T are fixed parameters that control the function. The reweighting procedure is repeated until the change in the weight with respect to the previous iteration is less than 0.1. Finally, the vertex is chosen as that with the lowest probability of being one which came from a minimum bias interaction [72]. 5.1.3 Electrons Electrons are defined as clusters of energy depositions in the calorimeter, together with a track confirmation from the Central Tracking System [73, 23]. The shower produced by an electron candidate must be. consistent with the shower of an electromagnetic object. The electrons are reconstructed mostly using the EM section of the calorimeter. Possible electron candidates are formed by clustering EM towers in a cone of AR < 0.4 near a seed tower with ET > 0.5 GeV. It is also required that at least 90% of the 71 0.4 Circlex Initial Cluster center of gravrty 0.2 Circle" FH+CH EisoTot = ' EM EisoCore = r: E‘— CPS (7 ISO = H/ij ‘ kThe interaction point Figure 5.2: Illustration of the isolation parameter. EisoTot is the energy in a cone of radius 0.4. EisoCore is the energy in a. cone of radius 0.2 (using EM layers). The numerator of iso subtracts EisoCore from EisoTot. energy deposited by cluster is located in the EM section of the calorimeter, a quantity known as the Electromagnetic Fraction. The EM objects deposit most of their energy in narrow regions of the EM layers, while hadronic objects have a much wider radius. This measurement is quantified by the isolation, defined as: Etotal(AR < 0.4) — [EEIU(AR < 0.2)] ' 1. t' 2 180 a mu EEM(AR < 0.2)) (5.2) where EtotallAR < 0.4) is the total energy in both the hadronic and electromagnetic part of the calorimeter within AR < 0.4. The isolation definition is illustrated in Figure 5.2. Additionally a covariance matrix is formed from the information of the shower energy fraction, cluster size, total energy shower and primary vertex position. A 7 x 7 H -matrix is then defined as the inverse of the covariance matrix, H : M ’1. Finally, a likelihood discriminant [74] is built in order to differentiate a cluster 72 coming from an Elmtromagnetic object from one of a Hadronic object with a large EM fractions: (5.3) where ’P Sig and ’P bkg are the probabilities of an EM object to be signal or backgrormd repectively. For the results presented in this dissertation the electrons must be within [ndetl < 1.1 (Only CC electrons), and they can be one of the following types: 0 Loose, isolated electron A loose, isolated electron is defined by: — Electron ID=10, ill; - EM fraction at least 00%; — The X2 from the H -matrix must be. less than 50; — The energy deposition in the calorimeter must be matched to a charged particle track from the tracking detectors with PT > 5 GeV and z(track, primary vertex) < 1 cm; - The isolation must be greater than 0.15; and - The transverse momentum pT(e) > 15 GeV. 0 Tight, isolated electron A tight, isolated electron must pass all the loose, isolated electron rer[nirenn-mts and have a value of EM-likelihood .C EM > 0.85. o Orthogonal electron An “orthogonal” electron is defined to have EM fraction > 0.9, H -1natrix x2 < 50, isolation < 0.15, pT(e) > 15 GeV, and £ EM 3 0.85. There are 73 no requirements for a matching track. The orthogonal electrons are used to define the multijet background sample. 5.1.4 Muons Muons are defined by using the hits information of the A, B and C layers of the muon detection system and by matching the tracks from the Central Tracking System to these hits [75, 20, 21]. Figure 5.3: Cartoon representation of the muon track segment algorithm. The Wire’s are represented by the black X’s, the MC track by the blue line, and the drift circles are red. The first step in the muon identification corresponds to the pattern study of the hits in the muons chambers [76]. A straight line called “segment” is fitted through the hits, followed by a fit of the segment to the scintillators hits consistent with the segment trajectory. Using the Toroid magnet, the W of the muon can be measm'ed by fitting the trajectories of the hits’ curvature. A muon defined with only the track from the muon system is known as “local” muon. The resolution of a local muon can be improved by matching the segment to a track in the Central Tracking System. Muons are described in terms of type and quality. The type is represented by 72369: A muon with segments in the A—layer has nseg = 1; one with segments in the 74 B and C layers, nseg = 2; and with segments in all layers has 'nseg = 3. nseg is positive for muons with central track matching and negative for no matching. The quality is described by the location and types of hits in the muon system and can be Loose, Medium or Tight. 0 Tight muons A Tight muon must satisfy: Insegl 2 3, at least two A layer wire hits, at least one A layer scintillator hit, at least three BC layer wire hits, at least one BC scintillator hit and a converged, local fit. 0 |nseg| =- 3 Medium/ Loose muons A Medilun |nseg| = 3 muon satisfies: lnsegl = 3, at least two A layer wire hits, at least one A layer scintillator hit, at least two BC layer wire hits, at least one BC scintillator. If one of the tests fails, the muon is considered Loose. o nseg + 2 Medium / Loose muons A Loose nseg+2 muon satisfies: nseg+2, at least one BC layer wire hit, at least one BC scintillator. If the muon is located in indetectorl < 1.6 it is considered Muon nseg + 3. o nseg + 1 Medium/ Loose muons A Loose nseg + 1 muon satisfies: nseg + 2, at least two A layer wire hits, and at least one scintillator hit. If the muon is located in lndetectorl < 1.6 it is considered Muon nseg + 1. The quality of the muon track can be one of the following: 0 Loose track: Ideal < 0.2 cm, 01' Ideal < 0.02 cm for muons with a SMT hit. 0 Medium track: fulfills loose track requirements and x2 / (1.0. f. < 4. 0 Tight track: fulfills medium track requirements and has SMT hits. Figure 5.4: A hollow cone in R, with the imler edge Ra and the outer edge Rb surrounding the muon. The transverse energy of the cells contained in the cone are added defining the cone Halo. The muon isolation variables are designed to separate W —> nu signal from heavy flavor background (B —> p). Based on the fact that muons from heavy flavor decays are usually inside the jet, these variables are: 0 TrackHalo: Izthks PTI in AR(track, muon. track) < 0.5. o CalorimeterHalo, see Figure 5.4: | Zceus ETl in 0.1 < AR(cal-—cells, muon cal — tmck) < 0.4. o ARM, jet): Distance to closest jet in 77 — d) space. 0 ScaledTrackHalo: lzthkS pT/pT(p)| in AR(track, muon track) < 0.5. o ScaledCalorimeterHalo: | Zcells ET/pt(p)| i110.1 < AR(cal —cells, muon cal - track) < 0.4. In order to discriminate muons coming from the collisions from cosmic rays, the muons candidates are to be registered within 10 ns from the bimeh crossing. This criteria is known as the “loose cosmic ray rejection”. 76 In this analysis, the following muon definitions are used: 0 Loose, isolated muon A Loose muon is defined by: — The quality of the muon must be medium |nseg : 3; — the muon must pass the loose cosmic ray rejection timing requirements; — the muon track quality must be “medium” and match to a track in the central tracker; — the ppm) of the muon must be greater than 15 GeV; and — AR(p,jet) > 0.5. 0 Tight, isolated muon Tight isolated muons are loose muons that must pass the additional isolation criterion called “TopScaledLoose,” which means the ScaledTrackHalo < 0.2 and ScaledCalorimeterHalo < 0.2. 5.1.5 Jets Jets are cone-like objects that represent the traces that strongly interacting particles, such as gluons and quarks, leave in the detector [18]. These traces are present in both electromagnetic and hadronic sections of the D0 calorimenter. It is important that the jet definitions comply with the following requirements [18]: 0 Fully specified: selection process, jet. variables and corrmtions must be uniquely defined. 0 Theoretically well-behaved: Infrared singularities should not appear in the per- turbative calculations. As well, the jet definition should not be sensitive to soft radiation in the event as seen in Figure 5.6. The algoritlnn should also be 77 CH1~.._ FH \ calorimeter jet Time parton jet Figure 5.5: Illustration of the evolution of hard-scatter parton in to a jet in the calorimeter. insensitive to collinear radiation which is illustrated in Figure 5.7. Jets should be also invariant under boosts, computationally easy to implement, and order independent, that is to say that the same jets should be found at either parton, particle or detector level. Experimentally specified: jets must be detector independent, not sensitive to angle or resolution smearing, stable with respect to the luminosity, easy to calibrate, and computing resource efficient. 78 Figure 5.6: Illustration of a jet being infrared safe, the jet clustering occurs near seeds represented by arrows of magnitude proportional to the energy. In the figure on the right, the case of two jets being merged into one due to the presence of soft radiation between them [18]. ‘V’ Figure 5.7: Illustration of problems due to collinear radiation on jet algorithms [18]. Before the jet reconstruction starts at DC, the T42 algoritlnn [77] is run to remove isolated small energy deposits that are likely due to noise. In order for a calorimeter cell to be considered as a signal cell it is required that the energy deposit on the cell must be at least 40, or 2.50 if the neighbor cell has 40 energy deposited on it. Here, a is defined as the RMS fluctuation on the signal in the cell. The next step in the jet reconstruction is to form energy pre-clusters from the calorimeter towers 1 by first selecting seed towers that have energy deposits greater than X GeV [18]. The seed towers are sorted by PT, then pre-clustered by adding those with PT > 1 MeV and within AR < 0.3. Pre-clusters with PT > 1 GeV are 1 A calorimeter tower is defined as the sum of all cells with common pseudo-rapidity and azimuthal angle 79 then added by an iterative process forming objects with AR < 0.5 and centroids calculated by using a weighted midpoint cone algorithm [18]. The last step in the jet definition is the splitting and merging of jets. Jets sharing a fraction of energy greater than 50% are merged otherwise they are split into two jets. In addition to the jet reconstruction, there is a set of criteria used to remove fake jets. These criteria follow the Jet-ID Algorithm Group’s recommendations [78] and [79]: 0 To remove electromagnetic particles from the list of jets, the jet el(~3(’:tromagnetic fraction is required to be 0.05 < EMF < 0.95. 0 To remove jets generated by calorimeter noise, at least 60% of the jet energy must be deposited in the fine hadronic part of the calorimeter since the noise level is higher in the coarse section. 0 To remove jets clusters from problematic cells, known as “hot cells”, the ratio of the highest to the next-to-highest energetic towers must be less than 10. a To remove jets coming from a single hot tower, jets for which one calorimeter tower contains more than 90% of the energy are removed. 0 To remove residual noise from readout, the jet PT is compared to the energy found by the level 1 trigger system. In addition to the previous requirements, this analysis requires that jets have PT > 15 GeV and be within lnl < 3.4. (The jet PT cut is made after all corrections have been applied). 5.1.5.1 Jet Energy Scale The energy in the calorimeter cells differs from the energy of stable particle jets before interacting with the detector. The jet energy scale purpose is to correct for these discrepancies [80]: 80 Euncorrected _ 0 139W": 3‘“ '.4 Jet FnXRXS (O ) where Eygcorrected is the jet energy determined by the reconstruction algorithm, 0 is the energy offset due to electronic noise, multiple interactions, underlying event, energy pile-up and noise from the Uranium absorber. F7, is the relative response correction to account for the calorimeter different 7) regions. R is the absolute response correction which represents non-instrumented and lower energy response regions of the calorimeter. S is the showering correction for the energy radiated outside the (30116. 5.1.6 Missing ET N eutrinos cannot directly be detected at DC, rather their presence is only inferred from the imbalance of the energy in the transverse plane [81, 82]. The sum of the transverse momenta of undetected neutrinos is therefore equal to the negative sum of the transverse momenta of all particles observed in the detector. In practice, the MET is defined as the vector sum of the electromagnetic and fine hadronic calorimeter cell energies, the cells in the coarse hadronic calorimeter are only added if they are part of a good jet. Finally, additional corrections are applied to the MET calculation to account for corrections applied to reconstructed objects and for the presence of 111110118. 5.1.7 b—tagging In the Single Top analysis, it is important to identify jets that. come from the decay of a b-quark, since the final state of the Single Top final involves at least one b—jet. After the b—quark hadronizes into a b—hadron, it will decay throughout the D0) detector. These b—hadrons have a longer lifetime than lighter hadrons resulting in a displaced decay vertex from the primary interaction point; this displacement is typically a few 81 Secondary Jet ’ Vertex Jet _ Figure 5.8: Illustration of the secondary vertex formed by the decay of a b- hadron. [17]. millimeters. The b—jets are identified by using this displacement, together with the the jet kinematical variables. A neural network b—jet tagger developed by the DC B—ID group is used to identify b—jets. First, the jets are required to be “taggable” and then the jets are “tagged.” For data, the tagging is done directly while for the simulated samples, a parameterization called tag-rate function (TRF) is used. The TRFs are derived on data to realistically estimate the b—tagging efficiency in the simulation because the simulated samples have a higher b-tag efficiency than data. Some quality requirements on the jet to be b—tagged are first imposed to reject different tracking efficiencies, badly reconstructed jets and detector effects in general. This quality selection is called “taggability” and it consists of requiring that the jets have at least two good quality tracks with SMT hits pointing to a common origin. 82 The details of the taggability calculation are found in the Appendix 6 of the Single Top selection note [19]. The “neural network (N N ) tagger” and its performance in data are described in detail in [83]. The NN tagger uses the following variables, ranked in order of separation power, to discriminate b jets from other jets: o decay length significzmce of the Secondary Vertex Tagger (SVT); 0 weighted combination of the tracks’ IP significances; 0 Jet LIfetime Probability (JLIP) (probability that the jet originates from the PV); 0 X2 per degree of freedom of the SVT secondary vertex; 0 number of tracks used to reconstruct the secondary vertex; 0 mass of the reconstructed secondary vertex; and 0 number of secondary vertices found inside the jet. There are 12 different operating points provided by b—tagger, each defined by a cut on the output of the NN tagger. For the analysis presented in this dissertation the following operating points were used: 0 one tag: Exactly one jet passes the TIGHT (NNoutput > 0.775) b—tagging cut and no other jet passes the OLDLOOSE cut (NNoutput > 0.5); and a two tags: Two jets pass the OLDLOOSE b—tagging cut. The vote of a second OLDLOOSE candidate in the one-tag definition ensures that. there is no overlap between the one tag and two tags samples. 83 Chapter 6 Data and Simulation Samples In this Chapter, the data sample used for the analysis is presented, as well as the simulation samples and their corrections. 6.1 Data Sample The data sample in this analysis corresponds to the data collected by the DC detector between April 2002 and August 2007. The events collected during this period of time are known as “RunII” as they correspond to the second phase of the Tevatron physics program. During the RunII there are two periods Run 11a and Run IIb which are differentiated by the upgrade made during the three month shutdown in 2006. Among the upgrades are the SMT, CFT, solenoidal magnet preshower detectors, forward muon detector and forward proton detector [15], which include the associated electronics, triggering [84] and data acquisition systems. The run numbers for the data collected range from 151,817 to 215,670 inclusive for the Run 11a, and sometimes labeled as p17, and from 222,028 to 234,913 sometimes labeled as p20. The data used have been reconstructed with production code versions p17.09.03 (refixed), p17.09.06 (unfixed, cable-swap), and p17.09.06 (unfixed, non- cable-swap) for Run Ila data, and p20.07.01 and p20.08.xx for Run IIb data; they 84 have been obtained from the DC Common Samples Group [85, 86]. There is a total of 2.3 fb-1 of good quality data in each of the electron and muon channels, as shown in Table 6.1 [87]. Integrated Luminosity [pb_1] Channel Trigger Version Delivered Recorded Good Quality Run IIa electron v8.00 ~ vl4.93 1,312 1,206 1,043 Run IIa muon v8.00 —~ vl4.93 1,349 1,240 1,055 Run IIb e and mu v15.00 -— v15.80 1,497 1,343 1,216 Total Run II Integrated Luminosity 2.3 fb'“1 Table 6.1: Integrated luminosities for the datasets used in this analysis. All the data are re uired to ass any “reasonable” tri rYer. See Section 6.5 for the ’(l . Eats definition of “reasonable” trigger and for the efficiencies obtained with it. 6.2 Simulation Samples In order to extract the final cross section measurement, one must properly model both the signal and backgrmmd for Single Top such that the sum of the background plus the signal simulated samples are equal to the data samples. All of the processes are simulated using Monte Carlo techniques, with the exception of multijet events, which are obtained directly from the data. 6.2. 1 Signal Modeling The Single Top events sample were generated with the CompHEP-SINGLETOP [88] Monte Carlo event generator which includes all the details of the current understand- ing of Single Top quark production. The kinematical distribution of events produced by SINGLETOP match those from NLO calculations [7, 6, 89]. The top quark mass used for the event generation corresponds to 170 GeV/c2 1, the parton distribution func- tions CTEQ6M are used [91] and the scales are m? for the s—chaimel and (mt/2)2 for the t-channel. The top quarks and the W bosons are decayed in CompHEP-SINGLETOP to ensure the spins are properly treated. PYTHIA [92] version 6.409 was used to add the underlying event and initial- and final-state radiation. TAUOLA [93] was used to decay tau leptons, and EVTGEN [94] to decay B hadrons. 6.2.2 Background Modeling The backgrounds for Single Top are W+jets, multijets, Z +jets, ti, and dibosons. The W+jets, Z +jets and tt were generated using ALPGEN [95] which is a leading order matrix element Monte Carlo generator similar to the CompHEP used for the signal generation. Version 2.11 of ALPGEN was used, which is comprised of a jet- matching algorithm following the MLM prescription [96] to match parton showers with the matrix elements. The matching algorithm ensures that each jet is generated by ALPGEN at the parton level and not filled in by PYTHIA, thus avoiding regions of AR and transverse momentum space for the radiated jets that used to be generated twice. For these samples, the parton-matching cluster threshold was set to 8 GeV, and the parton—matching cluster radius size was set to R = 0.4. For the tt samples, the top quark mass is set to 170 GeV/c2, the scale m? + Z p%(jets) used was along with the CTEQ6L1 pdf set. For the W+jets events, the pdf was the same as for the tt events, but the scale was ma, + E m%, where mT is the transverse mass defined as m% = m2 + p% and the sum 2: 771% extends to all final state partons (including the heavy quarks, excluding the W decay products) [95]. The W+light-parton (1p) jets samples must have parton-level cuts on the light partons to avoid divergences in the cross section. These cuts were pT(lp) > 8 GeV 1 At the moment of the event generation, the top quark mass average was close to 170 GeV/02. Although this mass differs from the the current top quark mass average, the effect on the final result is negligible as shown in References [19, 90]. 86 and AR(lp, 1p) > 0.4 for all massless partons (including the charm partons in these samples). For the W +heavy-flavor samples, there are no PT or AR cuts on the b or c partons, but additional light partons have the pT(lp) > 8 GeV and AR(lp, 1p) > 0.4 applied. I In addition, the dibosons WIV , W Z, and Z Z which represent only a small fraction of the total backgromld are also included in the analysis. These diboson samples were generated using PYTHIA with inclusive decays. 6.2.3 Additional Monte Carlo Treatments In all Monte Carlo event sets the duplicate events are removed. For the W+jets and Z +jets the events with heavy flavor jets added by PYTHIA are also removed to prevent duplication of the phase space of those generated already by ALPGEN [97]. The Wcj subprocesses are included in the W j j sample with massless charm. All the Monte Carlo events have DQ’S version of Time A for the lmderlying event2. The Single Top and Z +jets samples have the decays into electrons, muons, and taus as separate samples, whereas the W+jets and ti samples have them generated together in combined samples with approximately one third of each present (according to the branching fractions). The Monte Carlo event samples are processed through the the DC detector sim- ulator “DQgstar” [98] which is based on GEANT [99]. Next, all the events go through the same reconstruction process as the data. Table 6.2 shows the cross sections, branching fractions, and initial numbers of events of the Monte Carlo samples. The central values of the cross sections for Single Top [100] and tf pairs [101] are for 170 GeV top mass. The W+jets and Z +jets cross sections are from ALPGEN. The diboson cross sections were calculated using the NLO event generator MCFM [102]. 2 The “underlying event” corresponds to the partons (of the interacting protons and anti-protons) that did not participate in the hard interaction, and the resulting particles and measurements. 87 The Monte Carlo Event Sets Cross Section Branching No. of p17 No. of p20 Event Type [pb] Fraction Events Events Signals tb —+ Z+jets 1.12333); 0.3240 :t 0.0032 0.6M 0.8M tqb —+ €+jets 2.343;}? 0.3240 3: 0.0032 0.5M 0.8M Signal total 3.461333 0.3240 3: 0.0032 1.1M 1.6M Backgrounds tt —+ €+jets 7.91i‘1’;3} 0.4380 :1: 0.0044 2.6M 1.3M tt' —> (36 7.911533} 0.1050 :t 0.0010 1.3M 0.9M Top pairs total 7.91i‘1’;3} 0.5430 i 0.0054 3.9M 2.2M WbB —> eubb 93.8 0.3240 :s 0.0032 2.3M 2.5M WcE —» eyes 266 0.3240 3: 0.0032 2.3M 3.0M Wjj —+ my 24, 844 0.3240 :1: 0.0032 21.0M 18.3M W+jets total 25,205 0.3240 i 0.0032 25.6M 23.8M ZbE —. eebb 43.0 0.10098 :t 0.00006 1.0M 1.0M ZcE -. use 114 0.10098 :1: 0.00006 0.2M 1.0M ij —+ m j 7, 466 0.10098 :1: 0.00006 3.9M 7.0M Z+jets total 7, 624 0.03366 i 0.00002 5.1M 9.0M WW -» anything 12.0 :1: 0.7 1.0 i 0.0 2.9M 0.7M WZ -—> anything 3.68 i 0.25 1.0 :t 0.0 0.9M 0.6M ZZ —i anything 1.42 :1: 0.08 1.0 :1: 0.0 0.9M 0.5M Diboson total 17.1 :t 1.0 1.0 :t 0.0 4.7M 1.8M Table 6.2: The cross sections, branching fractions, and initial numbers of events in the Monte Carlo event samples. The symbol 8 stands for electron plus muon plus tau decays. 88 6.3 Multijets Background Modeling The multijet background is modeled using the data events that pass all the selection criteria, excluding the likelihood requirement for electrons and the isolation require- ment in the case of muons (see Chapter 7). Below is a more detailed explanation of the procedure to obtain the Multijets background for both muon and electron channels. 6.3.1 Electron Channel The electron multijets background is modeled using the “orthogonal” dataset. The orthogonal dataset corresponds to the events that pass all selection cuts (before b tag- ging) but where the EM object fails the electron likelihood cut and is not required to have a matching track. The kinematical distributions of this sample do not com- pletely correspond to those of a multijet background mainly due to the “not track match” requirement. This is solved by reweighting the distributions using the proce- dure explained below. The fake-electron probability comes from the “matrix method” of normaliza- tion [103, 104]. In this method, the tight data sample (events with a “tight” electron) is a subset of the ultraloose data sample (events with an “ultraloose” electron). The Nreal—e events with a real electron and N fake—e fake— uloose ultraloose sample contams uloose electron events. The efficiency for a real ultraloose electron to pass the tight electron selection is erea1_e, and the efficiency for a fake ultraloose electron to pass the tight electron criteria 1s Efake—e' Thereby Nuloose and Ntight are glven by: fak —e r: l—e . N1110059 : Nulogse + Nulgose (6.1) _ fake—e real—e _ fake—e real—e Ntight _ Ntight + Ntight — Efake—e Nuloose + Ereal—e Nuloose (6'2) 89 fake—e anc . 3‘ ) a ress». - s: ( thlght (anle(xp (d a. fake—e _ Efake—e N . _ Efake—e 1 - Ereal—e Nreal-e tight — 1 _ Efake—e uloose—tight 1 ‘ Efake—e Ereal—e tight (6.3) but the second term is small compared to the first term, which allows it to be rewritten as, Nfake—e _ Efake—e N tight — 1 _ efake—e uloose—tight (6'4) which represents the factor use for the re-weighting of the orthogonal data set. The Efake_e can be parametrized as a ftmction of PT of the electron as shown in Figure 6.1. The electron PT distributions before and after the re-weight is applied are shown in Figure 6.2, where the multijet. background is shown in brown. 13 E ‘0 Rlunlla '3 f . '- Runllb 7 L0 t 1 U) t Z 0.06 g— 7 . 0.04: ,, E I ] 0.03: 0'04: 3 LT ‘ ‘s g i i .- Z ”i , ; ~: : g ,- . _. 0.01.: , 0.029-... 3 5 ' ' ' ‘ ‘ : E i , 3 3 3 5 0.01 oELflglllzlllg 11 1 1: i t 1 .111 0:111l111l1111111l111 iiiliiiiiniliiiliii 0 200 0 40 80 120 160 200 lepton p-l-[GeV/c] lepton pT[GeV/c] Figure 6.1: Efake_e as a function of electron PT for Run IIa (p17) (left) and Run IIb (p20) data (right) [19]. 90 x103 D0 Run II Preliminag x103 D0 Run II Preliminag 25- - DATA 2-5 + - DATA m m E : - COD *5 - OCD ozo— - tt—>lep+jets 02.0 -tt-+ler+jets “>1 2 tt —>dilepton E - tt—e di epton : WW / WZ / ZZ : - WW / W2 / 22 1.5 5 Z + light jets 1.5 Z + light jets - ch + jets ch +j w be +jets ” - be + jets 1-0 p - W+llght jets 1-0 - W+llght jets — - ch + jets - ch +jets - Wbb + jets - Wbb + jets °~5 - — tqb (x100) 0-5 — tqb (X100) 7 tb (x100) — tb (x100) °‘° 20 so 100 140 $8 °'° 100 140 Lepton PT eV] Lepton P1- V] Figure 62: Electron transverse momentum distribution before (left) and after (right) multijet background reshaping [19]. 6.3.2 Muon Channel The muon multijets background is modeled using an orthogonal sample, whereby the events pass all selection cuts (before b tagging) however no isolation requirements are imposed to the muon. Events passing the muon charmel requirement are also removed to ensure the orthogonality of the samples. In past Single Top analysis [105], an isolation requirement of AR(muon, jet) > 0.5 was required, which led to a statistically limited sample. Removing the AR cut the sample size increased the sample size by a factor of ten. In order to make the jets in these events match those in the signal data, any jets close to the muon are removed from the. event and E T is recalculated to regain momentum balance. A comparison of kinematical distributions for the old and new multijets back- ground models is shown in Fig. 6.3. When looking at these plots one has to keep in mind that both the old sample (labeled “Reverse isolation”), and the new sample (labeled “Large QCD”) are only models of the true multijets background present in the signal sample, and do not precisely represent the background. The uncertainties on the multijets background normalization are of the order of (~30%), and the size 91 of the background is small compared to other more dominant backgrounds such as in the W+jets background. _ 6 __ 5 Large 000 Large 060 2.5_— Entries 18265 5 Entries 18265 2 :_ i Reverse lsolgtfl 4 * Reverse Isolation 5 + =F Entries 1498 W + Entrieé“‘1’498 ‘ 1.5:— -- 3 1f— 4: 2 E =F 0'5:— =1: *1:— : "" 0) 50 100 150 200 250 00 50 100 150 200 250 Jet 1 p1. Missing E1- 4 3 Large 000 Large oco 7 + Entries 18265 Entries 13255 3 ' *‘—— ". "“1 ‘— ______.___ fieyerse Isolation, 2 3_ Reverse isolation * Efltflssjm 2 ”amass? :— ++ 2 +** 1 ? _ -r" + i *++ + '1' 0 o E Au l l 1am I . . . . 0 50 1 150 200 250 300 I) 2 6 I! w Transverse Mass AR(Jefl , Jet2) Figure 6.3: Kinematic distributions comparing the old (red points) and new (black points) multijets background models. Upper row, pT(jet1) znid ET, lower row, AIT(W) and AR(jet1,jet2) [19]. 6.4 Corrections The description of the data by the simulated samples is not perfect. To rectify these differences, it is necessary to apply corrections to the Monte Carlo. One of the common mismodeling issues is the higher resolutions of the Monte Carlo simulation compared to data, which is corrected by the “smearing” of the event in one variable to better reproduce the data events. The number of events coming from the simulated samples is obtained by scaling 92 the Monte Carlo such that the reconstruction and selection efficiencies match those found in data, and by normalizing: s the tf, Z +jets, dibosons and Single Top samples to the integrated luminosity of the data-set using the cross sections and branching fractions listed in Table 6.2; and s the W+jets and multijet samples to data using an Iterative Kolmogorov-Smirnov (IKS) method explained in detail in Section 7.2). All of the corrections applied to the different objects in Monte Carlo are described in the following pages. 6.4.1 Muons To study the muon corrections, events from the decay of a Z boson into a pair of muons is used, Z —> an. This procedure is known as the “tag-and-probe” method which uses the correlation between the two muons to measure efficiencies. The muon momentum resolution is estimated from the width and shape of the Z peak. The smeared variable is q/pT, which is proportional to the radius of curvature and where q is the muon charge and PT, the muon transverse momentum. The smearing can be expressed as: _q_ ——> £- + (A + 2) x Rnd ((5.5) PT PT pT where End is a Gaussian-distributed mnnber centered at. zero with width 1, and A and B are measured parameters determined from the Z —> an sample (See Refence [20] for more detail). In addition to the smearing, the muons are corrected by the following three factors: the muon ID efficiency, the track match, and the isolation. The ID scale factor is parametrized in ’7det and d), as shown in Figure 6.4; the track match is parametrized in track—z and "CFT, Figure 6.5; and the isolation in 77, as shown in Figure (5.6. All 93 the corrections applied follow the reconnnendation of the. D(/) Muon ID Group which are described in Ref. [20, 21]: Data Data Data _ EMediumID ETrackMatch ETlghtISOl (i (i fit-ID — MC x MC x ( ' ) E E 5 MC MediumID TrackMatch TightIsol 6.4.2 Electrons The electron corrections are derived by using Z —+ 66 data and Monte Carlo samples. The scale factor applied to the Monte Carlo accomlts for the differences in electron cluster-finding and identification efficiency. This scale factor is divided into two parts: “preselectien” and “post-selection.” Preselection refers to the basic electron criteria that are common among many electron quality definitions: ID, electromagnetic frac- tion, and isolation. The preselectien scale factor is parametrized in 17th as shown in Figure 6.7. The post-preselectien criteria, which are unique for our particular electron quality definition, consist of the H -matrix cut, the track-matching requirements, and the likelihood cut. The post-preselectien scale factor is parameterized in (ndet,¢). These follow the r an samples. r‘ to d s O ...................................................................................... o 4—....---..................-............-...... ............................................. Reco Efficiency 9 63 l n \ o . u u a n u I s s \ . a . s a I mmuzmm) Figure 6.8: Primary vertex reconstruction efficiency in data as a function of z[24]. w 6.4.5 Luminosity Reweighting Since the lmninosity distributions change over time, the MC events are reweighted using the vjets_cafe package to match the luminosity of Run 11a and Run IIb data. 6.4.6 Beam Position Reweighting The vertex-finding algorithms and reconstruction efficiencies depend on the 2 position of the vertex. The beam position reweighting corrects for the efficiencies, as a function of 2, by fitting the primary vertex distribution in zero bias events to a convolution of two Gaussian beams and the beam beta function. If then parametrizes the scale factor as a fimction of z for different instantaneous luminosities (See [109, 110] for more detail). 6.4.7 Z-pT Reweighting Since the Z boson spectrum is not properly reproduced by the Monte Carlo [111], it is required to reweight the MC such that the Z PT spectrum matches the theory [112]. 6.4.8 Taggability “Taggability” is defined as the probability of a jet to be taggable. A taggable jet is a calorimeter jet matched within AR < 0.5 of a track jet which consists of at least two tracks, with AR < 0.5 between them. Here, each track used to form the track jet must have at least one SMT hit and at least one of the tracks must have pT > 1 GeV. Since the tagger and tracking reconstruction are not perfectly modeled, the Monte Carlo can not be tagged directly. The TRFS must be applied to the MC in order to compensate for differences. The TRFs are parametrized in jet PT, jet 7], and primary vertex z zones. The details for the Single Top taggability measurements can be found in reference [19]. The results for the electrons channels for the Run IIb data can 100 be seen in Figure 6.9. The observed taggability and the predicted taggability are compatible within uncertainties. b—tagging Event Weights and b-Jet Assignment Combinations The probability to tag a jet of flavor a can be expressed as the product of the tagga- bility and the tagging efficiency: 730(PT’ 77) = Ptaggablc(pr, 77) X 8a(p.r, n). which can be used to predict that an event contains exactly a given number of tags. The probability equations for the b—tag definitions 011 page 83 herein are the following: N. jets Pevent(1 tag) = Z PE;GHT(ijy ”j) H(1 _ pgz-LDLOOSEU’TL 7%)) (6-9) 2:1 2%] N jets _ . Pevent(2 tag“) = Z Pai‘DLOObEWTj, 779') H P8,LDLOOSE(p:r.-, 772') 3:1 2%] (6.10) H <1 — PgfiDLOOSEm, m.» 1979951 Using the TRFS, the number of tagged jets per event can be estimated. However, individual jets cannot be tagged because the T RF returns a weight. This is solved by creating permutations of the same event for different scenarios of different number of b-tagged or non-b-tagged jets with a corresponding weight. Therefore, each event is taken into account several times, and the sum of weights for all possible combinations in each event returns the original probability for the event to be not-tagged, tagged once or tagged twice. This method allows the use of kinematic variables that rely the b-tagging information of the. jets. 101 $103 ..... _ ++ (5 .................... F103++H+ + N1 i i . O. ++Fff++++ + \ 5 \ 5" H#+*++ + a, 8 . + + .210 . ._ sees, it 3 . ++ +4.... C C _ a... '0' 1.1.1 1 IL! , a..." 100 150 m 011 0.5 1 1.5 .2 2 Jet p-r (GeV) mjetl Taggability 1 1:10 260 Jet p-r (GeV) ITijetl — observed — predicted Entries / 2 GeV o - Pred )/ Pred (Obs-Pred)/Pred PT Figure 6.9: The upper four plots show the fits for the derivation of the taggability. The lower four plots show the ratio of the predicted taggability rate fimction over the observed taggability. These plots are all for the electron channel in the Run IIb period in the central plus primary vertex zone. Results for other channels are found in [19]. 102 6.5 Trigger Efficiencies The data used in this analysis are selected using a so—called “Mega—OR” of triggers, which have a trigger efficiency close to 100% and thus no trigger MC efficiency cor- rection factors are needed. In the trigger Mega—OR, an event is said to have passed the trigger requirement if it was collected with any “reasonable” trigger in the D9 trigger list. Reasonable triggers are generally defined to be all triggers except b tagging, gap, and forward proton triggers, as well as EM triggers in the case of the muon channel, and muon triggers in the case of the EM channel. The total number of triggers used was: 788 triggers for the Run IIa electron channel, 358 triggers for the Run IIa muon channel, 492 triggers for the Run 111) electron channel, and 303 triggers for the Run IIb muon channel. Since the Mega-OR uses a large number of triggers, events that might have failed a certain requirement will be collected by another trigger. To show that the efficiency of the Mega-OR is 100%, the ratio of Single-Lepton-OR selected data, to Mega-OR selected data is compared with the ratio of MC simulation that has had the known Single-Lepton-OR turn-on curves applied to 100% efficient MC simulation. A ratio of these two ratios is then taken to represent the efficiency of the Mega-OR selection. Assuming that the Single-Lepton—OR is modeled correctly, then the ratio of ratios corresponds to the Mega-OR efficiency in data divided by the Mega-OR efficiency in Monte Carlo (100%). This ratio should be around 1.0 as long as the assumption of 100% trigger efficiency in the Mega-OR is correct. The ratio will be less than 1.0 if the trigger efficiency of the Mega-OR is less than 100%. Any value larger than 1.0 indicates imperfect modeling of the multijet backgromld or the Single-Lepton- OR trigger. These ratios are shown in Figure 6.10 with respect to the topological variables that are likely to be most sensitive to the trigger selection. In these plots, the vertical lines delineate the relevant region containing 90% of the data (with 5% 103 of the data on either side). A horizontal line is drawn at 100% efficiency (red), and at i5% (blue). Figure 6.10 shows that there is no indication of efficiency loss for the Mega-OR trigger set. For more detail on this study refer to [19]. 104 _L h .t A a 'ro I 31 _: a N 1T! d LeptonOR/MegaOR (Data - 000) + LeptonOR/MegaOR (Data - COD) 0 O O .s_- 0.8} .s't 0.6} A} 04} 02:— 0.2:- o:1. .l;.;41..all...l.... or. .nl-..l....l....l.... 0 50 100 150 200 250 0 50 100 150 200 250 Jet1 Pt [GeV] Lepton Pt [GeV] 31.4: $1.4: =12? :12:- “I < . E 1' uni-13:” E 1' -lljlllll o : kw ‘:-IT|]T||T|‘I % ' ""IIIIIII “0.8l 310.8. 3’ : : $0.6:- E05? 0 : 0 t- g0.4_— 30.4L fé. : § i o'....|r...i ...l....|.... 0'. ..|.. .I....|....|.... o 50 100 150 200 250 o 50 100 150 200 250 Jet1 Pt [GeV] Lepton Pt [GeV] 1-4: 1.4: A13:- i 0 s 8”; 11:31.2.- 0:212; O— I o: 'I “511'- a< :_ 3’s '- 9:“: 31: ' . A 3 .u. c . 0.9; 290.9:- + ' 2a - OS : 0.303- fad-6035' 39. D : 0.7" JVO.7E‘# 0'slllllLlll. .n-annnLnnnn 095' ..I.. 1].-1.] I 0 50 100 150 200 250 "’0 50 100 150 200 250 Jet1 Pt [GeV] Lepton Pt [GeV] Figure 6.10: Run IIa (p17) electron channel: Ratio of SingleLepton—OR. to Mega—OR in data—minus—multijets (top row); ratio of Single-Lepton—OR. to 100% in the sum of MC backgrounds (middle row); ratio of these “efficiencies” in data to MC (bottom row). The ratio is calculated for the leading jet PT (left) and electron PT (right) distributions. The corresponding plots for Run IIb, muon chamrel, and additional variables dependance can be found in Reference [10]. 105 Cl E\ 9‘? *7 .r. Hr: Chapter 7 Event Selection This Chapter presents the selection cuts applied to the data and Monte Carlo samples and the plots demonstrating the agreement between the model and the data. The purpose of the selection cuts is to reject events that have a similar final state signature with respect to the Single Top signal. Due to the complexity of this analysis and the overwhelming background, it is not possible to consider a cut-based—only study. Some other tools such as multi-variate techniques are required to accomplish the goal of separating the signal from the background. A brief presentation of the selection will be shown in this Chapter, for further details see [19]. 7 .1 Event Selection Cuts The purpose of selections cuts is to find W—like events containing an isolated lepton, missing transverse energy, and two to four jets with high transverse momentum. Most selection cuts are common to both muons and electron charmels and are listed in the following pages. In addition to all the quality and kinematical selections, there are also additional selection requirements related to the number of b—tagged jets per event. The b—tagging algorithm is applied after all the other selections and corrections are 100' O). performed. The events before the b-tagging stage are known as “pie-tagged” events. The pretagged samples are dominated by W+ jets events, with some tt contribu- tion that becomes more significant for higher jet multiplicities, and smaller contribu- tions from multijets, Z +jets and diboson events. Common selection for both electron and muon channels: 0 Good quality (for data); Instantaneous luminosity > 0; Remove duplicate events; Pass trigger requirement: at least one of the selected triggers has to fire; Good primary vertex: Iszl < 60 cm with at least three tracks attached; 0 Two, three, or four good jets with PT > 15 GeV and ln‘lm’l < 3.4; The leading jet is required to have PT > 25 GeV; Jet triangle cut |Ad>(leading jet, ET)| vs. 1;? T5 0 [Act] from 1.5 to 7r rad when E T = 0 GeV; 0 and E T from 0 to 35 GeV when IAQ'DI = 7r rad; Missing transverse energy 0 20 < E T < 200 GeV in events with exactly two good jets and o 25 < E T < 200 GeV in events with three or more good jets. Electron channel selection 0 Only one tight electron with (Udell < 1.1 and IT > 15 (20) GeV in events with 2 (3 or more) good jets; o No additional loose electron with pT > 15 GeV; 107 o No tight isolated muon with pT > 15 GeV and within Indetl < 2.0; 0 Electron coming from the primary vertex: |Az(e, PV)| < 1 cm; 0 Electron triangle cuts |A¢(e, ET)| vs. E T: o |A¢| from 2 to 0 rad when E T = 0 GeV, and E T from 0 to 40 GeV when |A¢| = 0 rad; o |A¢| from 1.5 to 0 rad when E T = 0 GeV, and E T from 0 to 50 GeV when |A¢| = 0 rad; o |A¢| from 2 to 7r rad when E T = 0 GeV, and E T from 0 to 24 GeV when IAqfil = 7r rad; o Scalar sum of the transverse energies of all good jets and the electron transverse momentum and the missing transverse energy: 0 HT(alljets, e, E T) > 120 GeV in events with exactly two good jets; o HT(alljets, c, E T) > 140 GeV in events with exactly three good jets and o HT(alljets, e, E T) > 160 GeV in events with exactly four good jets; Muon channel selection 0 Only one tight muon with pT > 15 GeV and Indetl < 2.0; o No additional loose muons with pT > 4 GeV; 0 No loose electron with pT > 15 GeV and within ln‘Ml < 2.5; o Muon coming from the primary vertex: |Az(p, PV)| < 1 cm; AMMETH VS- ET: 0 |A¢| from 1.2 to 0 rad when E T = 0 GeV, and E T from 0 to 85 GeV Muon triangle cuts when |A¢| = 0 rad; 108 o |A¢| from 2.5 to 7r rad when E T = 0 GeV, and E T from 0 to 30 GeV when lAqSl = 7r rad; o Muon track curvature significance cuts ITrackCurvSigl vs. |A¢(p, E T)|, where . - _ q/ . . _. , , , I’I‘rackCurv81g| — lfiT—fl’ and q and pT are the charge and transverse mo- mentum of the charged track associated with the muon: 0 IAqSI from 0.8757r to 7r rad when |TtackCurvSig| = 0, and |TrackCurvSig| from 0 to 4 (6) when [A45] : 7r rad for Run IIa (Run IIb) period; 0 |A¢| from 2 to 7r rad when [TmckCurvSigl = 0, and |TrackCurvSig| from 0 to 2 (3) when Mail 2 7r rad for Run IIa (Rim IIb) period; These cuts are needed to reject events with poorly measured muons that cause an excess in data over background model in the A45 distributions (See Sec- tion 7.1.1). 0 Transverse momentum of the leading jet within the ICD region of the detector: leading jet pT > 30 GeV when 1.0 < Ileading jet 77‘1“t| < 1.5; o Scalar sum of the transverse energies of all good jets, the electron transverse momentum, and the missing transverse energy: 0 HT(alljets, u, E T) > 110 GeV in events with exactly two good jets; o HT(alljets, p, E T) > 130 GeV in events with exactly three good jets and o HT(alljets, n, E T) > 160 GeV in events with exactly four good jets; Tables 7.1 and 7.3 show the number of events for data and MC signal samples as they pass through the selection chain of cuts as mentioned above. 109 Table 7.1: Numbers of data events after each selection cut is applied. 110 Selection cut - Electron Channel Run IIa Data (‘76) I Run IIb Data (‘70) Initial 335,220,509 (100) 207,299,315 (100) ZeroLumi, duplicate, DQ 206,288,032 (79) 178,635,715 (86) Trigger 239,165,711 (71) 169,252,679 (82) Tight lepton with 197‘ > 15 GeV 2,530,008 (0.70) 2,082,407 (1.0) Second-lepton veto 2,483,784 (0.74) 2,039,680 (0.98) Jet selection 1,200,082 (0.38) 1,024,900 (0.49) Leading jet [)7 > 25 GeV 508,850 (0.17) 408,752 (0.23) Veto opposite lepton type 568,619 (0.17) 408,488 (0.23) Vertex selection 536,045 (0.16) 429,777 (0.22) 15 GeV< ET < 200 GeV 200,025 (0.059) 109,597 (0.081) First lepton triangle cut 119,201 (0.035) 107,002 (0.051) Second lepton triangle cut 110,993 (0.034) 105,635 (0.050) Third lepton triangle cut 113,133 (0.033) 101,961 (0.049) Jet triangle cut 100,936 (0.030) 92,973 (0.044) Number of good jets cut 41,785 (0.012) 39,642 (0.019) Instantaneous luminosity > 0 41,600 (0.012) 39,640 (0.019) HT(alljets, e, 1;? 7) out 30,310 (0.0090) 29,070 (0.014) E T > 20/25/25 GeV 27,507 (0.0082) 20,291 (0.013) Lepton 127‘ > 15/20/20 GeV 20,847 (0.0080) 25,595 (0.012) Additional duplicate removal 24,662 (0.0074) 25,595 (0.012) Selection cut - Electron Channel Run IIa Data (‘76) Run IIb Data (‘76) Initial 330,306,915 (100) 352,185,449 (100) ZeroLumi, duplicate, DQ 270,187,161 (82) 303,612,026 (86) Trigger 247,589,750 (75) 205,892,437 (70) Jet selection 170,537,062 (52) 187,509,219 (53) Tight lepton with p'r > 15 GeV 919,420 (0.28) 774,158 (0.22) Second-lepton veto 906,444 (0.27) 761,494 (0.22) Veto opposite lepton type 903,054 (0.27) 758,603 (0.22) Leading jet m > 25 GeV 386,770 (0.13) 339,038 (0.090) Vertex selection 357,389 (0.12) 300,569 (0.085) 15 GeV< 1% < 200 GeV 192,933 (0.058) 109,904 (0.048) First lepton triangle cut (loose) 142,940 (0.043) 131,555 (0.037) Second lepton triangle cut 138,612 (0.041) 127,700 (0.036) Jet triangle cut 118,931 (0.030) 112,164 (0.031) Number of good jets out 49,649 (0.015) 48,903 (0.015) Instantaneous luminosity > 0 49,479 (0.015) 48,082 (0.015) HT(alljets, p, E T) cut 41,219 (0.013) 41,027 (0.012) ET > 20/25/25 GeV 38,291 (0.012) 38,170 (0.012) Leading jet m > 30 GeV if in 1CD 36,962 (0.011) 36,960 (0.011) First lepton triangle cut 34,297 (0.010) 34,357 (0.010) Track curvature significance cut 31,957 (0.0097) 32,939 (0.010) Additional duplicate removal 31,581 (0.0090) 32,939 (0.010) Selection cut - Electron Channel Run IIa tb (%) Run IIb tb (%) Initial 400,000 (100) 000,000 (100) ZeroLumi, duplicate, DQ 370,482 (94.1) 538,312 (89. 7) Jet selection 371,470 (92.9) 534,079 (89. 0) Leading jet m > 25 GeV 300,830 (90.2) 519,723 (86) 6) Tight lepton with pr > 15 GeV 96,728 (24.2) 119,434 (19. 9) Second-lepton veto 96,352 (24.1) 119,031 (19.8) Veto opposite lepton type 90,315 (24.1) 118,985 (19.8) Vertex selection 95,093 (23.8) 118,028 (19.7) 15 GeV< Er < 200 GeV 89,039 (22.3) 110,229 (18.4) First lepton triangle cut 85,403 (21.4) 105,926 (17.7) Second lepton triangle cut 84,017 (21.2) 104,905 (17.5) Third lepton triangle cut 83,892 (21.0) 103,910 (17.3) Jet triangle cut 81,900 (20.5) 101,291 (10.9) Number of good jets cut 60,412 (10.6) 81,330 (13.0) HT(alljets, 0, ET) cut 05,270 (16.3) 79,997 (13.3) ET > 20/25/25 GeV 02,425 (15.0) 70,371 (12.7) Lepton p7 > 15/20/20 GeV 60,439 (15.1) 73,914 (12.3) Selection cut - Muon Channel Run IIa tb (%) Run IIb tb (‘70) Initial 400,000 (100) 000,000 (100) ZeroLumi, duplicate, DQ 374,407 (93.0) 535,883 (89.3) Jet selection 370,388 (92.0) 531,898 (88.7) Tight lepton with 127' > 15 GeV 103,850 (20.0) 142,102 (23.7) Second-lepton veto 102,579 (25.6) 140,502 (23.4) Veto opposite lepton type 101,835 (25.5) 139,890 (23.3) Leading jet pr > 25 GeV 98,410 (24.0) 135,491 (22.6) Vertex selection 96,858 (24.2) 133,040 (22.2) 15 GeV< Er < 200 GeV 91,124 (22.8) 124,970 (20.8) First lepton triangle cut (loose) 88,967 (22.2) 121,997 (20.3) Second lepton triangle cut 87,994 (22.0) 120,008 (20.1) Jet triangle cut 85,024 (21.3) 116,697 (19.5) Number of good jets cut 70,870 (17.7) 97,375 (10. 2) HT(alljets, e, E T) out 70,342 (17.0) 90,713 (10.1) ET > 20/25/25 GeV 07,305 (10.8) 92,553 (15.4) Leading jet p7 > 30 GeV if in ICD 07,030 (10.8) 92,095 (15.4) First lepton triangle out 63,592 (15.9) 87,395 (14.0) Track curvature significance cut 02,406 (15.0) 86,426 (14.4) 111 Table 7.2: Numbers of MC tb channel signal events after each selection cut is applied Selection cut - Electron Channel Run IIa tqb (%) Run IIb tqb (%) Initial ZeroLumi, duplicate, DQ Jet selection Leading jet pT > 25 GeV Tight lepton with pr > 15 GeV Second-lepton veto Veto opposite lepton type Vertex selection 15 GeV< ET < 200 GeV First lepton triangle cut Second lepton triangle cut Third lepton triangle cut Jet triangle cut Number of good jets cut HT(alljets,e, ET) cut ET > 20/25/25 GeV Lepton 12:11 > 15/20/20 GeV Selection cut - Muon Channel 375,000 351,708 345,854 332,850 88,770 88,408 88,439 87,274 81,709 78,791 78,230 77,485 75,009 01,491 00,102 57,284 55,325 (100) (93.8) (92.2) (88.8) (23.7) (23.0) (23.0) (23.3) (21.8) (21.0) (20.9) (20.7) (20.2) (10.4) (10.0) (15.3) (14.8) Run IIa tqb ('70) 000,000 539,371 534,328 510,300 113,510 113,153 113,119 112,240 104,923 101,204 100,441 99,439 97,002 78,709 77,080 73,103 70,511 (100) (89.9) (89.1) (80.1) (18.9) (18.9) (18.9) (18.7) (17.5) (10.9) (10.7) (10.0) (10.2) (13.1) (12.9) (12.2) (11.8) Run IIb tqb (%) Initial ZeroLumi, duplicate, DQ Jet selection Tight lepton with pT > 15 GeV Second-lepton veto Veto opposite lepton type Leading jet p71 > 25 GeV Vertex selection 15 GeV< ET < 200 GeV First lepton triangle cut (loose) Second lepton triangle cut Jet triangle cut Number of good jets cut HT(alljets, e, E 7') cut ET > 20/25/25 GeV Leadingjet pT > 30 GeV ifin ICD First lepton triangle cut Track curvature significance cut 350,000 327,973 323,583 89,049 88,757 88,129 84,270 83,019 77,994 70,208 75,407 72,972 59,778 59,140 50,428 50,049 53,573 52,037 112 (100) (93.7) (92.5) 25.0) 25. ( ( 4 (2.2 ( .1 ( 0.7! 24 23.7 (22.3 (21.8) (21.0) (20.9) (17.1) ( 10.9) (10.1) (10.0) (15.3) (15.0) ) ) ) ) ) 599,250 540,250 535,007 141,100 139,030 138,793 132,902 130,531 122,023 119,893 118,504 114,509 93,745 92,903 88,522 87,923 84,103 83,411 (100) (90.2) (89.3) (23.0) (23.3) (23.2) (22.2) (21.8) (20.5) (20.0) Table 7.3: Numbers of MC tqb channel signal events after each selection cut is applied 7. 1.1 Triangular Cuts 3. A3. 7: 11’? 1112. 22. u '5 C 32. £2 E a .—'1. $1. 3 =1 e‘- e . < < A d)(Jot1.Missing ET) A G) (Lepton.Missing E'r) A <1) (Jot1,Miuing ET) A <1) (Lepton,Missing E1') 99 : a 0'1 ‘1 0 : I 1': I ~ I Missing E1- [GeV] Missing ET [GeV] Figure 7.1: A¢(jet1,E T) versus E T (left) and A¢(lepton,1;? T) versus ET (right) two-dimensional distributions for data (top), multijets (middle) and tb+tqb signal (bottom), in the electron channel in Run IIb data. Similar distributions for the Run 113. and muon channels can be found in [19]. The goal of the triangle cuts is to reduce the multijets background. Figure 7.1 shows the distributions of data, multijets and MC signal events in the two-dimensional planes of A¢(jetl,E T) versus E T and A¢(lepton,E T) versus E T- This is before any 113 triangular or ET cut is applied. The red lines illustrate the events removed by the triangular cuts; events inside the triangles fail the selection criteria. These rejected events correspond mostly to multijet events, however for the signal, the triangle cuts have a very little impact. For the muon channel, there is an additional triangular cut aimed to reject poorly measured muons in data that are not well modeled in MC. This cut uses the two— dimensional plane: “absolute value of the track curvature significance” vs. “A0501, E 71),” (see Figure 7.2). The need for this special cut can be seen in Figure 7.3 where the distribution A4501, E T) is plotted before and after the cut is applied. M 0| Fall-”Tldfi‘kl‘l‘“:Ill F! l I llllllli l 1,1 "v jji r“ «Lu abs(Muon track curvature signlf.) 2.5 M (111%) Figure 7.2: Absolute value of the muon track curvature significance versus A¢(n, ET). The cuts are shown as heavy black (blue) lines for Rim Ila (Run IIb). 7.1.2 Total Transverse Energy (HT) cut The purpose of the HT cut is to control the multijet background to levels below ~5% in the final selection. Figure 7.4 shows the HT distribution together with the MT(W) distribution before and after the cut is applied illustrating the motivation and use of this cut. 114 x1 0 3 9:” 4.0 o 3.5 > "J 3.0 0.5 0.5 11.522.53 11.522.53 ¢(Lepton, MET) [Rad] ¢(Lepton, MET) [Rad] Figure 7.3: A¢>(p, ET) distribution for the Run Ila before(after) the muon track curvature significance triangle cut left(right). 7 .2 W+jets and Multijets Background Normaliza- tion The W+jets background is taken from Monte Carlo samples and corrected for recon— struction efficiencies (as described in Sections 6.2.3 and 6.4). Unfortunately, some additional corrections are necessary because of some mismodeling associated ALPGEN. This mismodelling issue is solved by performing a reweighting ()f the W+jets sample to reproduce the jet 17 distributions in data (more in Section 7.2.1). The modeling of the multijets background is base on the data as explained in Section 6.3. The normalization of the multijets and the W+ jets backgromids is obtained using an iterative KS-test normalization method (IKS) that calculates two anti-correlated scale factors which are applied to the each one of the backgrotmds guaranteeing the proper normalization to data. The two normalization scale factors SW +jets and Smultijets are calculated during the pre b-tagging stage. 115 p17 e+jets pre-tag 2 jets HT > 120 GeV Event Yleld [counts/106°” “100 200 300 400 500 ' HT(jets,l,v) [GeV] Event Yleld [counts/aGeV] p17 e+jets pre-tag 2 jets .5 .1. N 23 23 E: O O O c? )— d 0| O lilclll Event Yleld [counts/36W] 50 so 100 150 "HONinGeVJ p17 e+jets pre-tag 2 jets 100 150 "H0N)F36V] Figure 7.4: Pretagged distributions for Run IIa events with 2—jet in the electron channel for for HT(lepton, ET, alljets) (left) and the W boson transverse mass be- fore(after) the HT cuts is applied - middle(bottom). Similar distributions for other jet multiplicity channel, leptons and reconstruction version can be found in [19] The total amormt of data (yield of data) can be expressed as: Y before—IKS pretagged data 2 SW+jetS * YW+jets + Y all other MC (7.1) * Ybefore—IKS + S'rnultijets multijets ’ where Ysample is the event yield of a sample (sample 2 pretagged data, W+ jets, all other MC, and multijets) after all the selection cuts and corrections have been applied. The SW+jets and Smultijets are determined simultaneously using an iterative KS-test normalization (IKS) method: 116 1. Select a kinematic variable (varl) that has noticeable differences on the distri- butions for W+ jets and multijets backgrmmds; 2. Initialize SW+jets = 1.0, KSmax : 0.0 and calculate a corresponding Smultijets from Equation 7.1; 3. For varl execute a Kolomogorov—Smirnov test (KS—test) between data and back- ground distributions; 4. If the new KS value is greater than KSm-dx, assign the new KS value to KSmax; 5. Increase SW +jets by 0.001; 6. Repeat the steps 3—5 until SW +jets is equal to 4.0 or when Smultijets becomes negative; and 7. Repeat the procedure for a group of varN kinematic variables. The final SW+jets and Smultijets are determined by doing a weighted average: varN i ’i Z SW+jets * Ksmax i=var1 SW+jets = varN i 2' Z Smultijcts * KSIIIHX 'izvarl Smultijets : For this analysis there were 3 variables chosen to calculate the normalization factors: 1271(6), ET, and MT(W). The weighted averages were calculated for each channel corresponding to a different jet multiplicity, lepton and reconstruction version. The results are summarized in Table 7.4. 117 IKS Normalization Scale Factors SW+jets Smultijets Run IIa (p17) R1u1 IIb (p20) Run Ila (p17) Run IIb (p20) 6 n e 11 e p e p 2jets 1.51 1.30 1.41 1.23 0.348 0.0490 0.388 0.0639 3jets 1.92 1.79 1.75 1.57 0.291 0.0291 0.308 0.0410 4jets 2.29 2.06 1.81 1.92 0.189 0.0244 0.424 0.0333 Table 7.4: W+jets and multijets scale factors calculated using the iterative KS-test normalization method. 7 .2.1 Reweighting for the W+Jets Sample The W+ jets sample must be reweighted before the b—tagging is applied. The purpose of this reweighting is to obtain a better data-backgrormd agreement by correcting the ALPGEN modeling discrepancies in the Monte Carlo. The distributions that need to be reweighted are (in order): 17(jet1), n(jet2), A¢(jet1,jet2), An(jet1,jet2), 77(jet3), and 17(jet4). For a given distribution, the reweighting function is calculated by obtaining the ratio: data — All Backgroundsexcept W +jcts 7.2 W + jets ( ) reweight function 2 Figure 7.5 shows the derivation of the reweighting function for 77(jet2) in the Run IIa sample set. The same procedure is followed to obtain the reweighting finiction for all other distributions, each reweighting is calculated after the previous reweighting is applied to the W+jets sample. The reweighting functions are combined in a bin—by—bin basis for the electrons and muons and for all jets multiplicity. The leptons combination is consistent with the motivation of the reweighting which is to correct jet quantities, and the jet combina- 118 - DATA - All bkgs — W+jets -— Multijets — tt, 2, Events m : 9 DATA-multijets—nonw "E - - W+Jets g 4 AM _ +h"..“ O I mm + . ‘0- _ ,. r — 4» EM — +z .1. M 7. -¢- ' _ +‘ 0+ 1 “ ‘* ‘ :1" '1‘... G I 1 I I I LJ_L I A I I -5 -4 -3 -2 -1 I) I 2 3 _ 4 ‘1 9090 ' Rmelghtlng factor = (Data-multljete-nonW) I (W+Jets) . .. In each bin " ' ) a.) I l ' 3am maid " "+’.Nm’¢’ OB -L y § r I l I r (Data-multijets-nonW)W+jets M nu IV A ~— Figure 7.5: ALPGEN W+jets reweighting factor derivation for 7}(jet2). The first plot shows the disagreement between data and all backgrounds, the middle plot illustrates the numerator and denominator of Equation 7.2 and the plot to the right presents the reweighting function. 119 tion is because there was no noticeable difference between the reweighting functions for different jet bins. The final reweighting functions for the Run 11a and Run IIb are. presented in Figure 7.6. Figure 7.7 shows the distributions of four jet-related parameters before and after the reweightings for Run IIb, muon and jets combined. Additional distributions can be fetmd in [19]. To achieve a good background-data agreement the W+ jets sample needs to be reweighted: the muon detector pseudorapidity ndetm). Figure 7 .8 shows the distri- butions before and after the reweighting is applied. Although all of the reweights presented in this subsections are small, they are necessary to ensure the final data- backgrmmd agreement. 7.2.2 W+Jets Heavy-Flavor Fraction The ALPGEN leading-log cross section for W06, W c5, and W j j are required to be scaled by the theoretical factors K’ and K3”; in order to account for the NLO effect. The DC V+Jets Group [113] calculated them by using comparisons of the LL and NLO calculations, and are presented in Table 7.5. NLO/ LL K’ and K 3,, F Factors for V+Jets Cross Sections Wjj Wcj ch WbB Zj j Zcé ZbB Run 118. 1.30 1.80 1.30 x 1.47 1.30 x 1.47 1.346 1.346 x 1.25 1.346 x 1.25 Run IIb 1.30 1.80 1.30 x 1.47 1.30 X 1.47 1.30 1.30 x 1.67 1.30 X 1.52 Table 7.5: NLO/ LL K ’ and K1,”; Theoretical Factors for V+Jets Cross Sections. In order to achieve better data-background agreement, an extra scale correctimi factor S H F for the heavy flavor W+jets samples is required. The procedure to 120 825% f 825: 5' : a ; g2}. 1 g2}, .. ‘21s} +++ ~ ++ gm:- fl... ++ g : fit flf _ .4 g : +3“. 443+ r a I ”no 1 r ' ' ""1""? . 3 : i 3 0.5, g 0.5 g 4 -'2' 0 2 i ' -4 '2 0 :2 4 now) noon) § 432.5%": E '2 . '5 'E- . '5 9 -' l 1 1 i 3 51.3L s g 1 W». _ WW}... g g IL ‘ .WH. 0'5" 'n -2 3 ' ' :2 ' *TL riietz) NW) §1.2: §1.2: 8 ~ ° . 9 Em: * ;' ~ 5 - gm} °’ ‘ f . i . : 9 . .. z . . . . + 3 '3 was + 3 ‘.+ 311188” i“ Ea": l ' $0331 ' “'0' '2"3 “"54 i ":2""3 Adidl .iet2) Afllofl .iet2) a _ a _ . 31.5 ' 31.9 1:» - 5’ ~ . é : i E H» § ' i §' ++++ . + 1-— 1— ~ 3 H—O—O— a 3; 4*“ i 5 i ‘ + O'EI)"':'*"4"'0' 0 o'5t1"'2"'i "t's'TTu Atflefl 4912) Arflefi ,jet2) Figure 7.6: The Run Ila (p17) left (2011mm and Run IIa (p20) W+jets reweighting factors for n(jet1), 17(jet2), Aq§(jet1,jct2), and An(jet1,jet2) ALPGEN. 121 II‘ S'CC-eCI‘h t-€—> hco>w U.®.> aim->mu 1H 3.0?! u C0>m 2 p17 (1+jets pre-tag 2—4 jets 5 Event Yleld [counts/0.4] N 231 n(jet1) n(jet1) p1711+jets p1711+jets pre-tag pre-tag 2-4 jets 2-4 jets Event Yleld [counts/0.4] -3 -2 -1 I pl 7 11+jets pre-tag 2-4 jets Event Yield [counts/0.4] 2 3 4 Event Yleld [counts/0.4] T1(iet2) E p1711+jets E p1711+jets >1500 pre-tag >1500 pre-tag ‘5 2-4 jets E o o 0’1 11’; 1000 1000 500 2 3 2 3 A¢(jet1,jet2) [Rad] A¢(jet1,jet2) [Rad] 3;, p17 u+jets % p1711+jeis ; pre-tag S pre-tag E 2-4 jets '5 2-4 jets o o > > III III 4 An(jet1,jet2) : 4 An(jet1 ,jet2) Figure 7.7: Distributions before (left) and after the reweighting (right) for the muon, Run IIb channels. 17(jet1), n(jet2), A¢(jet1,jet2) and An(jet1,jet2). 122 Q hll II: 1.." % p17 n+jets €9,000) p1711+jets ; pre-tag ; pre-tag E 2:: jets E ‘5 2-4 jets a: O a: L > > m Ill 2000 1000‘) 1 2 :l 1 2 3 1] det (lepton) '1 d et (lepton) Figure 7.8: Muon pseudorapidity for Run Ila before and after the reweightings are applied left and right, respectively. calculate S H F is explained in detail in [114]. Let us consider: D’ = X’ + S x (W’ + SHF x B’) (7.3) D” = X” + s x (W” + SHF x B”) (7.4) where D, W, B and X are the yields for the samples data, W+light-jets, W+heavy- flavor and the rest of the backgromid plus signal respectively. The method uses two ortogonal samples: one that passes the b—tagging requirements (’) and one orthogonal to it (”), thereby ensuring that the data-background agreement holds in both samples. Solving for S' H F: W/(Dl, _ x”) _ vvll * (DI __ xl) SHF : BI/(D/ _ XI) _ Bl * (DH _ x”). The final S H F applied to all channels is: SHF : 0.946 d: 0.082 (stat) which corresponds to a weighted average of all S H F presented in Table 7.6. 123 Heavy-Flavor Scale Factor Corrections S H F for 1V+Jets Events Run Ila Run 11b 6 n e )1 1 tag 1.04 :1: 0.19 1.15 :1: 0.20 0.95 :1: 0.20 0.65 :1: 0.18 2 tags 0.84 i 0.30 0.70 :t 0.29 1.23 :1: 0.40 1.17 :1: 0.40 Run IIa+b e + a Run IIa+b e 11 Run Ila Run 11b 6 + u k 1 tag 1.00 2‘: 0.14 0.90 :1: 0.13 1.10 i 0.14 0.79 :1: 0.13 0.95 :1: 0.10 2 tags 1.02 :1: 0.25 0.91 :t 0.17 0.77 :1: 0.21 1.20 i 0.28 0.97 :1: 0.17 Table 7.6: Heavy-flavor scale factor corrections for the two r1m periods and lepton types and combinations of each, calculated using two-jet events. 124 P: 7 .3 Number of Events After Selection Tables 7.7 and 7.8 show the number of events for each sample after the selection criteria, discussed previously, have been applied. These numbers are important as they represent the statistics available for training a Decision Tree and are also used to calculate statistical uncertainty of the measurement. Number of p17 Events after Selection Electron Channel Muon Channel 2 jets 3 jets 4 jets 2 jets 3 jets 4 jets Signal MC tb 42,407 14,339 3,093 42,295 10,181 3,990 tqb 30,508 14,273 4,484 33,744 14,503 4,330 tb+tqb 78,975 28,012 8,177 70,039 30,744 8,320 Background MC tf—vll 105,957 07,291 22,008 88,999 00,241 21,022 tf—rl-l-jets 34,183 110,291 128,273 23,000 103,952 140,513 W513 33,958 11,589 3,439 38,522 14,757 4,302 W05 29,781 11,105 3,202 34,801 14,112 3,925 Wcj 15,518 5,427 1,252 17,402 0,340 1,509 Wj j 214,395 74,244 18,417 200,022 98,177 24,348 255 2,827 1,202 432 7,371 2,077 591 ZcE 722 348 125 3,400 1,280 304 ij 9,192 3,510 1,353 35,374 11,000 2,729 Dibosons 92,882 25,720 5,897 113,327 33,989 7,037 PreTag data Multijets 241,173 105,002 40,458 18,281 8,083 2,827 Data 18,582 4,834 1,240 23,243 0,075 1,003 OneTag data Multijets 0,938 3,773 1,845 1,050 591 300 Signal data 508 202 103 027 259 131 Tonags data Multijets 451 417 285 07 08 38 Signal data 07 01 37 71 02 50 Table 7.7: Number of events for the elm-tron and muon channels after selection in the D17 sample. Signal MC tb tqb tb+tqb Background MC tit—>11 t{—+l+jets W115 Wcé W'cj Wjj Z bb ZcE ij Diboson PreTag data Multijets Data OneTag data Multijets Signal data Tonags data Multijets Signal data Table 7.8: Number of events for the electron and 11111011 (‘zhaln‘lels after selection in the p20 sample. Number of p20 Events after Selection Electron Channel 2 jets 51,228 44,803 90,091 01,042 15,401 50,850 37,524 0,590 91,201 3,200 2,185 9,193 25,373 229,208 19,048 6,838 547 505 79 3 jets 17,890 19,223 37,113 47,435 49,028 19,131 13,800 2,298 32,100 1,418 883 3,510 7,042 101,466 5,087 3,417 207 444 56 126 4 jets 4,790 0,425 11,221 15,473 57,044 5,572 4,001 507 8,335 009 347 1,353 2,001 47,660 1,460 1,773 124 287 51 Muon Channel 2 jets 55,557 50,861 106,418 57,435 11,787 03,500 48,043 8,010 120,751 12,124 9,454 35,387 30,480 21,416 23,972 3 jets 24,016 24,416 48,432 51,705 51,564 26,499 20,081 3,082 47,562 4,499 3,308 11,067 11,865 9,188 7,040 689 290 76 79 4 jets 6.853 8,134 14,987 17,108 09,033 7,730 5,588 724 11,711 1,280 804 2,730 3,001 3,233 1,927 271 142 29 80 7 .4 Event Yields In this section, the number of events after the event selection on the 2.3 fb—1 of data analyzed in this dissertation are presented. Tables 7.9 and 7.10 show these yields for all signals and backgrounds before the b tagging is applied. They are separated by data-taking period, lepton flavor and jet multiplicity within each table. Similarly Tables 7.11 and 7.12 show the yields after b—tagging algorithm is applied and the resulting selected events have one two b~tagged jets respectively. Figure 7.9 is a graphical representation of the or all yield tables for easy comparing the yields among the different backgrounds and the signal. Tables 7.13 and 7.14 sutmnarize the signals, summed backgrounds, and data from each channel, showing the uncertainties on the signals and backgrounds, and the signalzbackground ratios. 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Data Excess (+) or Deficit (—) Over SM-Signal+Background Model Run IIa (p17) Electron Channel Muon Channel 2 jets 3 jets 4 jets 2 jets 3 jets 4 jets 1 tag 0.260 -—0.600 0.100 0.350 —0.780 —0.160 2 tags —0.510 —0.070 ——2.040 —1.180 -l.350 —1.330 Run IIb (p20) Electron Channel Muon Channel 2 jets 3 jets 4 jets 2 jets 3 jets 4 jets 1 tag —0.030 -l.390 0.790 —1.110 —0.400 —0.200 2 tags 0.940 —0.740 —0.530 0.700 0.500 1.290 641, 2,3,4jets, 1,2tags p17,p20, 2,3,4jets, 1,2tags p17,p20, e,,u, 1,2tags All p17 p20 e u 2 jets 3 jets 4 jets channels —0.370 -0.310 —0.250 —().420 i —0.170 -—0.670 —().220 | —0.340 Table 7.15: Differences between the data and the predicted background (including SM Signals) shown as a factor times the uncertainty on the signa1+background predictions. 133 7 .5 Cross-Check Samples In order to ensure that the background model reproduces the data in regions were the biggest backgrounds dominate (“W+jets” and “tt—”), two cross-check samples of events for both the electron and the muon channels were prepared. The selection criteria for these samples are the same as for the all other samples (see Section 7.1), plus the following additional requirements: “W+jets” sample 0 Exactly two jets o HT(leptonJiI T,alljets) < 175 GeV 0 One b—tagged jet “tt—” sample a Exactly four jets o HT(lepton,E T,a.lljets) > 300 GeV 0 One or two b—tagged jets Table 7.16 shows the yields with backgrounds and channels combined for the cross-check samples. The agreement between the data and and background is shown in Figure 7.10, where the W transverse mass distribution is plotted for all channels combined (electron and muon, Run 11a and Run IIb). Plots for the individual channels together with other 12 significant variables can be found in in Appendix E. For the W+jets samples, W+jets events form 84% (electron channel) and 74% (muon channel) of the samples, and the tt- component forms only 1% of the samples. For the tt samples tf events form 85% (electron) and 82% (muon) of the samples, and the W+jets events form only 10% (electron) and 11% (11111011) of the samples. 134 ~>°9° 93.2300» .033) ut°>w Yields for the Cross— Check Samples W+Jets Samples tf Samples Signal tb+tqb 38 (3%) 8 (2%) Backgrounds ti 16 (1%) 311 (83%) W+jets 999 (78%) 40 (11%) Z+jets & dibosons 109 (9%) 7 (2%) Multijets 113 (9%) 7 (2%) Backgrounds+Signals 1,275 373 Data 1,311 368 Table 7.16: Yields after selection in the cross-check samples, for channels and back- grounds combined. The numbers in parentheses are the percentages of the total background+signal for each source. 400 p17+p20 e+n channel 1 b-tag + 2 jets w 8 8 o s Event Yleld [counts/10GeV] Event Yleld [counts/1OGeV] 6’ so 100 150 WW) [GeV] 80 p17+p20 e+n channel 1-2 b-tags 4 jets 0o 50 100 150 NW) [GeV] Figure 7.10: The W transverse mass distribution for the “W+jets” and “ti” cross- check samples, for all channels combined 7 .6 Variables Definition Table 7.17 lists the discriminating variables used in this analysis. The distributions of the variables are shown in Figs. 7.12 to 7.20 for all analysis channels combined. Jets are sorted in W where index 1 refers to the leading jet in a jet category. The jet categories are as follows: “jetn” (n=1,2,3,4) corresponds to each jet in the event, “tagn” refers to b—tagged jets, “untagn” signifies non-b—tagged jets, “bestn” relates to the best jet, and “notbestn” pertains to all but the best jet. The best jet is defined as the one for which the invariant mass 111(W, jet) is closest to mtop = 170 GeV/c2. The variables are separated into the following categories: 0 Object kinematics These are individual object transverse energy (ET) or momentum (pT) or pseu- dorapidity (7}) variables. 0 Event kinematics These are total transverse energy or invariant mass variables. 0 Angular correlations These are either AR, A05 angles between jets and leptons or top quark spin correlation variables. 0 Top quark reconstruction These are variables relating to reconstructing the top quark, identifying which jet to use, and which neutrino solution to pick. Neutrino 19;; solutions In order to estimate the neutrino’s pz the W boson mass is used, which results in a quadratic equation with two solutions for 192’. The smaller solution is denoted by the index “S1” and the other solution by “S2”. 136 T0p mass difference The top quark mass is reconstructed as: Mtop : \/(Elcp + EV + E jet)2 _(filep + fill + P3002 using all possible combinations of lepton, neutrino and jet. Mtop is then compared with 170 GeV defining the difference of these two-quantities as AMtop. The combination that gives the smallest difference in each event _ min . . is called AMt op , and the corresponding mass dlfference A M1333 Significance of top quark candidate. Assuming the top quark mass reso- lution function is a Gaussian distribution, the significance is calculated ‘dSI gRec0( Mtop— Mggc0) gRecthOp = 170 GeV)’ SignificanceIn in ( A! top ) = 111 where gRem is a Gaussian distribution centered at the reconstructed top quark mass with width 6Mt0p, given by: 5Mt0p = \/c% 52Ejet + c2 52 ET , where t t t C1 ___ (M1Ebmnkjepsum—kiepsmn_kiepsum) top 02 _ (1 k E Esum— ___psum_1 ____psum1 k upsum) _ u a: , Mtop 0S C¢ET$ sin ¢ET Esum : E191) ‘1' Eu + E'Ct , and psum 2 plep + p,- +17“t ,(2= cc, y, and z.) where jet jet . 0t ET cos d) -(,t ET sin (9 Jet smh y 1613;: —-—— y'= , and kg = ——-h— , piTt cosh y pji:—t——— (osh y ("0" y y is the jet rapidity, and 05 is its azimuthal angle. 137 The reconstructed top quark mass that gives the smallest significance in each event is called 11131g 'top’ and the corresponding significance is called Sigm'ficancem in ( 1” top) - 0 Jet reconstruction These variables include the jet width in 2] and d), the jet mass, and the relative PT with respect to the the leading jet. 7 .7 Data and Monte Carlo Agreement Figure 7.11 shows the color scheme used in the plots in this analysis. Key for Plots Data Signal: tb Signal: tqb Wb5+jets Wcé+jets W+1ight jets Zb5+jets Z cé+jets Z +light jets WW+WZ +Z Z t1? ——> ll tr? —> Z+jets Multijets flDDDDlIIIIfl|1° Figure 7.11: Illustration ()f the color scheme used in plots of signals and backgrormds in the Single Top analyses. Figures 7.12 to 7.20 demonstrate the agrmmeut between data and Monte Carlo 138 Decision Tree Input Variables Object kinematics pT(jet2) pr(jet3) pT(jet4) pfltagl) pT(light2) pT(notbest2) pT(lepton) E T Q(lepton) xn(jet1) Q(lepton) >< 77(jet2) Q(lepton) x 27(best) Q(lepton) x 27(light1) Q(lepton) x 77(light2) Jet Widths Width” (jet2) Width” (jet4) Width¢ (jet4) Widthn(tag1) Widthn (1ight2) Width (,5 (light2) Angular Correlations AR(jet1,jet2) AR(jetl,lepton) AR(tag1,lepton) AR(light1,lepton) A¢(lept0n,E T) cos(best,lept0n)besttop cos(best,notbest)besttop cos( jet1,1ept0n)btaggedtop COS(lept‘mbesttop’beSttOpCMframe) COS(leptonbtaggedtop imaggedtopCMframel cos(tag 1 ,lepton) btaggedtOp cos(lepton.Q(lept0n) X zlbesttop Event kinematics Centrality(alljets) HT(alljetS) HT(alljets—tagl) HT(alljets—best) HT(jetlJCt2) HT(jetl,jet2,lepton,E T) HT(alljets,lepton,E T) HT(E T,lepton) H (alljets—tagl) M (alljets) M (alljets—best) M (alljets—tag1) M(jet1,jet2) M(jet1,jet2,W) M ( jet3,jet4) MT(jet1,jet2) pT(jet1,iet2) x/E MT(W) Top quark reconstruction M (W, bestl) (“best” top mass) M (W, tagl) (“b-tagged” top mass) M(W,tag1, S2) (with second neutrino solution) M (W, jetl) M(W,jet1,82) M (W, jet2) M(W,jet2, S2) M (W, notbest2) M (W, notbest2, S2) .MAMmin top s1g 1Mt op ' 111111 Allftop Slgmficancemin (Jump) Table 7.17: Variables used with the decision trees in five categories: object kinematics, jet reconstruction, angular correlations, event kinematics, and top quark reconstruc— tion. For the angular variables, the subscript indicates the reference frame. Plots for these variables are shown in Figures 7.12 to 7.20. 139 for the variables in Table 7.17 for all the 24-channels combined. Figures 7.22 to 7.27 show the distribution of W transverse mass for data and the backgrormd model. The plots are separated by number of jets (2, 3, 4), number of b tags (1, 2), lepton type (6, ,u), and run period (Run IIa (p17) and Run IIb (p20)). Figure 7.28 shows the W transverse mass distribution with electron and muon and p17 and p20 combined. Additional plots can be found in Appendix B. 140 E p17+p20 e+n channel‘ %' p17+p20 e+jt channel 3 + 1-2 b-tags g 1-2 b-tags 3 + 2-4 jets 3 2-4 jets : E 2 2 ".1 a u 'u E E >- >- 50 100 150 100 150 men) [GeV] p,(I-ght1) [GeV] E _ p17+p20 my channel 50' p17+p20 e+j1 channel 3 -_ 1-2 b-tags g 1-2 b-tags g 300. 2-4 jets a 2-4 jets > ” E m ’ e H ” > g 200* 1!. e _ ; ; ‘:3 100* >' -2 o 4 50 190 150 O(Iepton)xn(jet1 p,(1et2) [GeV] % p17+p20 e+u channel 5' : p17+p20 e+11channe|j g 1—2 b-tags S r 1-2 b-tags a 600 24 jets 5 300C 2-4 jets E > i 2 a - 1!. 400 g 200_ o _ E 5" : >' 200 100_ 100 150 -2 o 2 4 p,(llght2) [GeV] Q(lepton)xEta(jet2) E p17+p20 e+n channel %' p17+p20 e+11 channel g 1-2 b-lags g 1-2 b-tags 3 2-4 jets B 2-4 jets E ‘E e e > > a a 2 E .2 2 >- >- 1 _ 150 50 100 150 pT(jet3) [GeV] pT(notbest2) [GeV] Figure 7.12: Individual object kinematic variables used in the BDT analysis for all channels combined (Part I). 141 E 300 p17+p20 e+n channelj E 400 p17+p20 e+u channel 3 1-2 b-tags 5.5, 1-2 b-tags a 200 E; U I“ § '5- 200 >- a 100 ; 100 -2 o 2 4 ‘b i 50 1110 150 Q(Iepton)xrj(best1) p,(1et4) [GeV] %' p17+p20 e+n channel 5 306 p17+p20 e+j1 channel g 1-2 b-tags 3 + 1-2 b-tags a + 2-4 jets ‘5 2-4 jets E 9 200— 0 LU > _ a 2 '0 2 E >' _ ; 100 100 150 -2 o 2 4 pT(Iepton) [GeV] Q(lepton)xrj(light1) %' p17+p20 e+u channel %‘ p17+p20 e+_u channel (5 1-2 b-tags g : 1-2 b-tags 3 2-4 jets a 2-4 jets E E 400 2 °>’ ‘ E E E E ' 2 .2 200 >- >- _ so 100 150 50 100 150 9,6391) [GeV] E [GeV] .a O O _ p17+p20 e+j1 channel _ 1-2 b-tags 2-4 jets Yield[Events/0.2] 01 .9. -2 0 2 4 O(lepton)xrj(llght2) Figure 7.13: Individual object kinematic variables used in the BDT analysis for all channels combined (Part II). 142 g p17+p20 e+jt channel g p17+p20 e+ll channel 3' 1-2 b-tags % _ 1-2 b-tags #9 2'4 jets o- _ 2-4 jets s 5 40 > > - a a E '2 — a: é ; 20— 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 o." Widthn(jet2) Widthnfiem) g p17+p20 e+n channel 3' 400? p17+p20 9+“ channel g 1-2 b-tags % ; 1-2 b-tags ‘5 2-4 jets E 300; 2-4 jets t» to - > > - a a : 2 E 200: .2 2 r >- >- : 100: 0.1 0.2 0.3 0.4 0.5 0.3 0.4 015 Width¢(jet4) Width¢(light1) g p17+p20 e+jt channel g p17+p20 e+jt channel a + 1-2 b-tags 3 + 1-2 b-tags ‘6 2—4 jets E 2-4 jets cu m > > E. E. E E 2 2 >- >- o.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 Widthn(light2) Width ¢(light2) Figure 7.14: Jet reconstruction variables used in the BDT analysis for all channels combined. 143 b O O p17+p20 e+tt channe? 1-2 b-tags 2-4 jets p17+p20 8+”. channel 1-2 b-tags 2-4 jets 0:) O O Yleld [Events/0.16] M E; Yleld [Events/0.16] .A O O 3 4 5 3 4 .5 AR(jet1,jet2) AR(lepton,jet1) p17+p20 e+n channel 400; p17+p20 e+n channell 1-2 b-tags : 1-2 b-tags b O 0 2-4 jets 2-4 jets Yleld [Events/0.16] Yleld [Events/0.1 6] no $ '0 O O 100} 2 3 4 t' 1 2 3 4 5 AR(lepton,tag1) AR(leptonJighfl) g p17+p20 e+_u Egannel —- 7, WW ~ , ,, ' 1- -tags 3 p17+p20 e+u channel a _ S 1-2 b-tags l 'E 2'4 Jets c 2-4 jets 2 o u: > h—I H E 1’ 2 g >- ‘b 1 2 3 -0.5 0 0.5 1 M(leptonfi ) [Rad] cos(lepton,best1)beSttop g 300', W m77P174F’267é3‘7053nrne" g p17+p20 e+ll channel 3 1-2 b-tags g 1-2 b-tags g 2-4 jets '5 2-4 jets > 2 E .“J. 3% :2 .. o >- :- -1 -05 0 05 1 -a5 0 Q5 1 cos(best1,notbect1)besnop cos(|epton,jet1)btaggedtop Figure 7.15: Angular correlation variables used in the BDT analysis for all channels C0111bined (Part I). 144 p17+p20 e+ll Chiannell p17¥52b e+ll chanhgl 1-2 b-tags 2-4 jets at o 9 Yield [Events/0.08] h 0 0 Yield [Events/0.08] M O O -o.5 o 0.5 I 91 -o.5 o 0.5 1 cos(lepton,tag1 )btaggedtop cOsl'eptonbesttop vbesnoPCMframe) 300 ' I V pt7+o20 e+jtchannel + 1-2 b-tags ' 2-4 jets p17+p20 e-rrijtichannel 1-2 b-tags + 2-4 jets Yield [Events/0.08] Yleld [Events/0.08] -o.5 u #05 1 1 .1 91 -o.5 o 0.5 cos(lepto . w . . w .bmrame) cos(lepton,()(lepton)xz)besuop Figure 7.16: Angular correlation variables used in the BDT analysis for all channels combined (Part II). '— "7j3-1?+n25e4nichannel 5' p17+p20 e+tl channel 3 300j o g ' 1-2 b-tags (3 1-2 b-tags ‘5' . 2-4 jets + j 2 2-4 jets . l L5. 200 ‘ El 2 H 2 s > 100’ ; 0.2 0.4 0.6 0.8 1 50 100 150 200 250 Centrality(alljets) HT(alljets) [GeV] 5' p17+p20 e+ll channel 5 p17+p20 €+ll channel é 1-2 b-tags g 1-2 b-tags .- 2-4 jets a 400» 2-4 jets 3 E 1: 9 5 a '5' E, 200 a .— ; >- 100 200 300 400 50 100 150 200 250 H(alljets-tag1) [GeV] H,(alljets-best1) [GeV] p17+p20 e+gt channel p17+p20 e+jl channell 1-2 b-tags 1-2 b-tags 2-4 jets 2-4 lets Yleld [Events/56W] Yleld [Events/569V] 50 100 150_ 200 250 300 400 HT(let1.let2) [GeV] H (lepton,E ,jet1,jet2) [GeV] p17+p20 e+jl channel 1-2 b-tags 2-4 jets p17+p20 e+ll channel 1-2 b-tags + 2-4 jets Yleld [Events/ZOGQV] Yleld [Events/569V] 200 400 600 50 100 150 200 250 H (lepton,E ,alljets) [GeV] H (lepton,E )[GeV] Figure 7.17: Event kinematic variables used in the BDT analysis for all channels combined (Part I). 146 p17+p20 e+ll channell p17+p20 e+ll channell 1-2 b-tags 1-2 b-tags 2-4 jets 2-4 jets Yleld [Events/269V] Yleld [Events/156W] 40 60 80 100 100 200 300 400 H,(alljets-tag1) [GeV] M(alljets) [GeV] E p17+p20 e+lt channel E p17+p20 e+ll channel (5 1-2 b-tags (5 1-2 b-tags 5 2—4 jets 5 2—4 jets E E 0 o > > .“J. E E '2 .2 2 >- >- 20 30 40 50 10 M(alljets-best1) [GeV] M(alljets-tag1) [GeV] p17+p20 e+jt channel 1-2 b-tags 2-4 jets p17+p20 8+!l channel“ + 1-2 b-tags 1 >— 2-4 jets 00- 50 Yield [Events/569V] Yield [Events/4GeV] 200 300 400 500 50 100 150 200 250 M(jet1,jet2) [GeV] M(W,jet1,jet2) [GeV] %' r p17+p20 e+ll channell %' p17+p20 e+gl channel (5 ‘ 1—2 b-tags (3 1-2 b-tags 3 2-4 jets 3 2-4 jets ‘E E 2 2 9.". E 2 2 .2 .2 >- >- ‘I 50 100 150 200 250 00 200 300 M(jet3,jet4) [GeV] M,(jet1,jet2) [GeV] Figure 7.18: Event kinematic variables used in the BDT analysis for all charmels combined (Part II). 147 %' p17+p20 e+tl channel %' p17+p20 e+jt channell (5 1-2 b-tags (5 1-2 b-tags 3 400 2—4 jets S 100 2-4 jets : E 2 2 2!. u...‘ 1: 1: 32 20° 5 50 >- >- 100 150 50 109 _150 200 M,(W) [GeV] pTUetLlet2) [GeV] %' p17+p20 6+.” channel ‘3 v- - e E l g 150 > E u 100 .13 >' so 400 600 800 \léjGeV] Figure 7.19: Event kinematic variables used in the BDT analysis for all channels combined (Part III). 148 %' p17+p20 e+n channel %' p17+p20 8+“ channel (5 1-2 b-tags (5 1—2 b-tags 3 2-4 jets 9 ' 2-4 jets 2 2 400 C c _ o o > > a a e u 1: 5; E 200 >- >- ' 00 3 0 200 300 40 M(W,best1) [GeV] M(W,jet1) [GeV] %' p17+p20 e+ll channel %' . p17+p20 e+jl channel g 1—2 b-tags g 400; 1-2 b-tags v- 2-4 'ets v- : 2-4 'ets 2 ' 2 ; ' c c 300 2 2 : E E. : 'U u 200- E :0 “ >- >- 100: 100 200 300 400 200 300 400 M(W,tag1,32) [GeV] M(W,jet1) [GeV] p17+p20 e+l| channel p17+p20 e+jt channel 1-2 b-tags 1-2 b-tags 2-4 jets 2-4 jets Yleld [Events/106W] Yield [Events/106W] 200 300 400 200 300 0 M(W,jet1,32) [GeV] M(W,jet2) [GeV] E p17+p20 8+“ channel %' I p17+p20 e+ll channell (5 1-2 b-tags (5 ; 1-2 b-tags S 2-4 ‘ets 3 300' 2-4 'ets E I E _ i t: c o a; > > E. .“J. 'u u E E >- >- 00 200 300 M(W,jet2,$2) [GeV] M(W,notbest2) [GeV] 100 200 300 400 Figure 7.20: Top quark reconstruction related variables used in the BDT analysis for all Channels combined. 149 p17¥p§6e+jl channel 1-2 b-tags 2-4 jets %' p17+p20 e+n channel 5 400 g 200 1-2 b-tags g L, 5 2‘4 jets E 300 , § 150 2 u>J L“. ';' 100 3 § >- >' 50 200 300 400 M(W,notbest2,$2) [GeV] p17+p20 e+u channel 1-2 b-tags 2-4 jets Yleld [Events/0.05] Yleld [Events/20] 4 i AM [35‘ p17+p20 e+u channel 1-2 b-tags 2-4 jets 500 1 000 1 500 A Yleld [Events/ZGeV] N O "f _I O 1 1 O l l l I 200 0 _ 150 Significance (Mtop min p17+p20 e+_u channel 1-2 b-lags 2-4 jets 250 ) [GeV] Figure 7.21: Top quark roconstructk)n related variables used in the BDT analysis for all Channels combined. 150 -,\a!1H\-.\ ?\uI§u~u .CLh tset~> hca>m €6000~ p17 e+jets $6000; p20 e+jets g * pre-tag (o5 _ pre—tag ‘— - 2 i v- — ' E _ jets E , 2 jets g 4000: g 4000— o o _ .2. 2. » E ‘ E ' 2 2000 g _ >_ _r >_ 200% E ‘E - a: o - I.I>.l . ii . 100 so ‘b 100 50 WW) [GeV] WW) [GeV] 1500 p17 e+jets p20 e+jets pre—tag 1500 pre-tag 3 jets 3 jets —| O 8 —l O O O a: 8 Event Yleld [counts/10GeV] 01 8 Event Yield [counts/1OGeV] ‘b 100 50 100 150 M70”) [GeV] WW) [GeV] l p17 e+jets : p20 e+jets ‘ pre—tag '_ pre—tag + 4 jets 300: 4 jets c» O .2. 200: 100: d ll'llll Event Yleld [counts/106W] N 8, Event Yleld [counts/1OGeV] 100 1r MT(W) [GeV] 50 50 100 50 WW) [GeV] Figure 7.22: The W boson transverse mass distributions in the electron channel for 2~jet (top row), 3-jet (middle row), and 4—jet events (bottom row), for p17 (left) and p20 (right) for events before the b-tagging is applied. p17 e+jets 1 b-tag 2 jets 150} Event Yleld [counts/1 OGeV] Event Yleld [counts/10GeV] p20 e+jets 1 b-tag 2 jets 100 150 100 50 WW) [GeV] MAW) [GeV] p17 e+jets 60“ p20 e+jets 1 b-tag - 1 b-tag 3 jets 3 jets Event Yleld [counts/1OGeV] Event Yleld [counts/1OGeV] 100 150 NkflflllGeV] 100 150 MHVDIGeV] (a) T C) p17 e+jets 1 b-tag 4 jets 20f 1o, Event Yleld [counts/1OGeV] Event Yleld [counts/10GeV] ‘b 50 1 00 1 50 WW) [Gen p20 e+jets 1 b-tag 4 jets 150 50 1 00 MW) [GeV] Figure 7.23: The W boson transverse mass distributions in the electron channel for 2-jet (top row), 3-jet (middle row), and 4-jet events (bottom row), for p17 (left) and p20 (right) for events with one b—tagged jet. 26: p17 e+jets 25 2 b-tags 2 jets p20 e+jets 2 b-tags 2 jets 15: Event Yleld [counts/1 OGeV] Event Yleld [counts/1OGeV] 5. 100 1!" 100 1? MW) [GeV] WW) [GeV] 15 p17 e+jets 20: p20 e+jets ' 2 b-tags I 2 b-tags 3 jets 155 3 jets Event Yleld [counts/1OGeV] Event Yleld [counts/106W] 100 150 100 150 MW) [GeV] MT(W) [GeV] 1° p17 e+jets p20 e+jets i 2 b-tags 2 b-tags F 4 jets 4 jets Event Yleld [counts/1 OGeV] Event Yleld [counts/1 OGeV] 1 00 1 50 50 1 00 1 50 WW) [GeV] MAW) [GeV] Figure 7.24: The W boson transverse mass distributions in the electron channel for 2—jet (top row), 3-jet (middle row), and 4-jet events (bottom row), for p17 (left) and p20 (right) for events with two b-tagged jets. F\“l(c ‘\1‘ll-ii&l l % p17 jig; % t p20 wag; g 6000: pre-tag g 6000- pre-tag .5; 2 jets E ' 2 jets :: I: g 4000_ g .2. .2. E 2 o _ .9.’ ; 2000) >_ E — E s “ E ‘h 100 150 100 150 Mr(W) [GeV] WW) [GeV] p17 jt+jets . p20 j.t+jets pre—tag : pre-tag 1 500 3 jets 1500: 3 jets Event Yleld [counts/106W] d 01 O O d: 1 00 150 M.(W) [GeV] Event Yleld [counts/106W] p17 e+jets pre—tag 4 jets 100 150 M.(W) [GeV] Event Yleld [counts/1OGeV] 01 3 o o . .°. . . .°, 100 150 NW) [GeV] p20 jt+jets pre-tag 4 jets Event Yleld [counts/10GeV] (b 50 100 150 M70”) [GeV] Fig‘urc 7 .25: The W boson transverse mass distributions in the electron channel for jet (top row), 3—jet (middle row), and 4—jet events (bottom row), for p17 (left) and p 0 (right) for events before the b—tagging is applied. 154 150 p17 e+jets 150 p20 e+jets 1 b-tag 1 b-tag 2 jets 2 jets —l 8 —l O O 01 O at o Event Yleld [counts/1OGeV] Event Yleld [counts/106W] ‘b 100 150 Q) 100 150 MW) [GeV] WW) [GeV] p17 tt+jets p20 e+jets 1 b-tag 1 b-tag 3 jets 3 jets Event Yleld [counts/106W] Event Yleld [counts/1OGeV] 100 150 100 150 MT(W) [GeV] MT(W) [GeV] p17 e+jets — p20 e+jets 1 b-tag 30'. 1 b-tag : 4 jets 4 jets 20: Event Yleld [counts/106W] Event Yleld [counts/1OGeV] ‘1) so 100 150 ‘h ,50 100 150 Mm) [GeV] MW) [GeV] gigure 7.26: The W boson transverse mass distributions in the electron channel for ‘Jet (top row), 3-jet (middle row), and 4—jet events (bottom row), for p17 (left) and p20 (right) for events with one b—tagged jet. 25 p17 jt+jets 2 b-tags 2 jets 30 p20 e+jets 2 b-tags 2 jets 20 Event Yleld [counts/10GeV] Event Yleld [counts/10GeV] 100 150 100 150 NW) [GeV] M.(W) [GeV] p17 e+jets 20: p20 e+jets 2 b-tags I 2 b-tags 3 jets 15: 3 jets 1o: Event Yleld [counts/106W] Event Yleld [counts/10GeV] 100 150 100 150 HT(W) [GeV] WW) [GeV] . p17 e+jets p20 e+jets 15: 2 b-tags 2 b-tags j 4 jets 15 4 jets 10h Event Yleld [counts/106W] Event Yleld [counts/10GeV] 50 1 00 150 50 100 1 50 W) [GeV] Mr(W) [GeV] Figure 7.27: The W boson transverse mass distributions in the electron channel for ‘Jet (top row), 3-jet (middle row), and 4—jet events (bottom row), for p17 (left) and p 20 (right) for events with two b—tagged jets. Event Yleld [counts/1OGeV] Event Yleld [counts/1 OGeV] Event Yleld [counts/1OGeV] 600— 400 200 p17+p20 9+“ channel 1 b-tag 2 jets 50 100 150 MW) [GeV] p17+p20 9+“ channel 1 b-tag 3 jets 100L ‘b 50 100 150 MW) [GeV] p17+p20 e+jt channel 1 b-tag 4 jets 50 1 00 150 NW) [GeV] Event Yleld [counts/10GeV] Event Yleld [counts/1OGeV] Event Yield [counts/1OGeV] p17+p20 e+jt channel 2 b-tags 2 jets 60 50 100 150 NM [GeV] p17+p20 e+jt channel 2 b-tags 3 jets 50 100 150 MW) [GeV] p17+p20 8+“ channel 2 b-tags 4 jets 50 1 00 150 MW) [GeV] Figure 7.28: The W boson transverse mass distributions in the electron and muon channels and Run 11?. and Run IIb datasets combined, for 2-jet (top row), 3-jet (middle row), and 4—jet events. Single-tagged (left), and double—tagged (right) events. Chapter 8 Decision Trees A Decision Tree (DT) [115, 116, 117] is an algorithm that can be used to classify events as signal or background. The structure of a DT resembles a tree, hence the name. It is built by splitting a sample recursively into two disjointed subsets mitil the ratio of signal-to—background reaches a predefined threshold or the number of events reaches a minimum. Each split is based on a selection cut that maximizes the signal-to-background ratio. The result is many subsets of the main sample based on the principle “divide and conquer.” However, one Decision Tree is not enough to separate the Single Top signal from the background, rather some additional tools are required such as Boosting. Boosting is a technique that increases the separation performance for a multi- variate technique. In particular, Boosting for Decision Trees creates a series of trees that give increasing importance to the harder to classify events. The final result is a discriminant output that is used to perform a measurement of the Single Top cross section. This chapter presents an overview of Decision Tress and Boosting. Signal 3kg Bkg Signal Bkg Y2 Y Bkg L2 R2 yl Bkg y 162 GeV, the final discriminant out put will be D(§;) = 0.82, progressing along one path until it reaches the final leaf. Sinlilarly other events with different 3; will follow unique paths. The Decision Trees have many advantages compared to other multivariate tech- niques. If an event fails one of the node cuts, the event is still considered in subsequent nodes and, in principle, it may pass the classification criteria; this is in contrast to a purely cut-based analysis. In addition, DTs are also easy to understand as they have a hlIlium-readable structure making it possible to follow a particular event through the full tree. Lastly, any final result can be explained by Boolean logic. The process in which a Decision Tree is built is known as training, which is ex- p lai 118d in the following Section. The training of a Decision Tree is fast compared to otller multivariate techniques such as Neural Networks, that is to say large ammmts 0f data can be processed in much shorter amount of time. For this analysis, all the tra‘iIlillg is done using the background models, and the data is used only at the end whell performing the measurements. Also adding more variables to the DT does not affect the DT performance as 1011 g as the variables are well-modelled, an extra variable can only do good to the Cla‘ 8‘ “ - b n o e o o - SIflcatlon problem. Neither is 1t necessary to preprocess the input files as 111 other 160 Figllre 8.2: Graphical representation of a DT. Nodes with their associated splitting test, are shown as (blue) circles and terminal nodes with their purity values are shown fi-S (green) leaves. All nodes continue to be split until they become leaves. Note that if One event fails a cut, it does not necessarily follow that the event will fail to pass as t118$ event can be recuperated and pass later down the tree chain [25]. mllltiVai-iate techniques. Any monotonic transformation to the input variables will yield the exact same tree, which is due to the principle used to split nodes (explained in the next Section). Lastly, another implication is that discrete variables can be directly used in the list of variables. some of the draw-backs of a DT are the intrinsic instability of the tree structure With respect to the training sample composition. This means that any small changes are I)l‘opagated to the whole tree due to the hierarchical nature of the process, and in $0an occasions producing very different trees but still with similar separation power. one additional issue with DTs is that the final output has a discrete nature, this is be 1139, the discrnmnant output 18 defined based 011 the purity of the leaves but the 161 nunlber of leaves is finite. 8 .2 Training Algorithm Let us consider a sample of known content of signal and background events where . u . ——) . o 0 each event 18 defined by an event. welght and a set of variables 13,. Using th1s “tranmg” sample, the following algorithm can be employed to build a Decision Tree: 1. Normalize the signal training sample and the background training sample to the same value, such that Z 3,,- = 2 b2- (3 z b); 2. Create the first node, containing the full training sample 3 + b; 3. For each variable: order the events by the value of the variable and select the variable value (cut value) that gives the best signal-background separation. More about this in Section 8.2.1; 4. From the list of variables and cuts from the previous step, choose the one that gives the best signal-background separation. If no further improvement in the separation is possible, the node becomes a leaf; 5. Using the selected variable and cut value, split the node into two subsamples one passing the selection cut and one failing it. The two subsamplcs are now child nodes of the original node; 6. If the number of events on the node reaches a minimmn, the node becomes a leaf. This minimum is one of the DT parameters (see Section 8.2.3); and 7. Apply the algorithm rectu'sively from Step 3 until all nodes are leaves. 162 8.2.1 Splitting a Node The most critical part in the Decision Tree training process is the splitting of a node, as the structure of the tree can be dramatically changed if the splitting criterion is Inodified. The determination of the splitting of a node is based on the quantity degra- dation, D, which is constructed from the weight of the events in the node, including both signal and background events. For any split, the change in the degradation can be expressed as, AD: AD = D — DL — DR = De. b) — Beam — Deg, b3) (82) where L and R are indiccs corresponding to the right and left daughter nodes, and by construction 3 = s L + s R and b = b L + b E This quantity AD sometimes is referred as the “goodness of the split.” The goal with each split is to find the one that best separates signal from background. This can be accomplished by finding the cut that reduces the most of the degradation or equivalently the split that gives the maximum AD. As such, finding the optimal split can be seen as a minimization problem. The Part of the algorithm that split the node can be expressed as the following steps: 1. For each variable: 0 Sort all the events in the node according to the current variable; 0 Go through the events in order and calculate AD for the split correspond- ing to cutting between the current and the next event; and 9 Select the cut value for which AD is maximum. 2. Out of all combinations (variable, cut value), select the one that gives the maximum separation. There are many possible degradation measm‘es that have been used in the past. For example, the lVlisclassificat-ion Error, the Gini Index [118] and the Cross En- 163 tropy [116]. Each degradation measurement is defined in terms of the node purity p as follows: Misclassification Error : D = 1 — max(p, 1 — p) Gini Index : D = 2p(1 — p) Cross Entropy : D = —plogp — (1 — p) log(1 — p). where p is defined as in Equation 8.1. —— Cross Entropy Gini Index 0.5 :— — Misclassificatlon Error .. 0.4 _— D I c : 3 0.3—— a _ u _ E : g 0.2 _— o.1 :— oi ’— I 1 4 1 l 1 I I 1 1 1 I 1 l 1 1 L4 1 0 0.2 0.4 0.6 0.8 1 purity [D] Figure 8.3: Degradation measures comparison as a function of the purity p. The Cross Entropy has been scaled down to compare the 3 cases. Figure 8.3 shows a comparison of these three degradation measm'es. The measures are similar as they are maximal for equal amounts of signal and background (p = 0.5), symmetric and concave. The exception to the similarity ais that. the h’Iisclassification Error is not differentiable with respect to p. Alternately, these measures are often defined in terms of the sum of weights of signal and background in the node, 5 and b 164 Missclassification Error : D = max(s, b) (8.3) 3b G' ' I '1 £2 : = 8.4 mi nux s+b ( ) Cross Entropy : D = —slog 3:1) — blog :6 (8.5) A preference among the definitions is a matter of taste, but they do differ from each other by a factor of (s + b). The second set of quantities is easier to handle as they are additive. From this point on, the definition of degradation measure will correspond to Equations 8.3, 8.4, and 8.5, which is also used in [119]. For the analysis presented in this dissertation, the degradation measure used is the Gini Index (Equation 8.4). It was found that for the set of samples used (see Chapter 6) it had better performance when classifying Single Top events. Detail 011 the degradation measure selection can be found in Section 8.3. 8.2.2 Boosting Boosting was introduced into machine learning over ten years ago [120] and is a powerful technique to improve the performance of any weak classifier 1. Boosting has been widely used in several scientific fields including high energy physics: the MiniBooN E experiment used it together with Decision Trees [119, 121] and similarly the Single Top group at DD [56, 105]. The D(/) work on Boosting led to the evidence of Single Top in 2006. In the case of Decision Trees, the Boosting technique is based 011 three principles. First, creating a initial tree, second, calculating an associated error function, and third, generating a second tree with a smaller error function. The third step is done by re-weighting the events 011 the first tree such that the misclassified events will have 1 Weak classifier: A classifier that performs just above random classification. a. higher weight than properly classified events. There are many Boosting algoritlnns available. For the results presented in this dissertation, the AdaBoost algorithm was chosen. Formulated by Y. Freund, and R. Schapire [122, 123, 124] (AdaBoost is short for Adaptive Boosting). Adaptative refers to subsequent decision tress that are tweaked in favor of the misclassified events by previous trees. The Boosting algorithm consist of the following steps for the nth tree in the Boosting chain: 1. rIi'ain the nth Decision Tree; 2. Calculate the error en associated the the tree. en is equal to the weighted fraction of misclassified 2 events; 3. Calculate the tree weight according to: 1 ._._. an 2 a x 111 6" (8.6) 6n where [3 is parameter of the algorithm known as the Boosting parameter; and 4. Modify the weight of each event by: Boosted Decision Tree w,- ——> w, x exp (an) (8.7) thus the (n + 1)th tree will be one that better identifies the events that the previous tree failed to properly classify. The above procedure is repeated N times, where N is the number of Boosting cycles, to be defined by the user. The final N M Boosted Decision Tree discriminant 2 An event is consider misclassified if [Dn(E,-’) — yil > 0.5 where Dn(f{) is the discriminant associated with the nth tree, and y is 1 for a. signal and 0 for background. 166 output for the event 2' is N Deg?) = ——N—1——— Z aware» (8.8) anO an 7220 During the process of training, it was found that Decision Trees always improve their performance with the number of Boosting cycles. This overall improvement is about 20% with respect to the no-Boosting case. In addition, the Boosting produces a smoother discriminant output D(E;). The increase in the performance reaches a plateau at approximately 30 Boosting cycles, and does not degrade after that. In Figure 8.4, some quantities are plotted as a function of the number of Boosting cycles: 3 the tree weight with respect to the first tree, Cross Section Significance and the number of leaves. 8.2.3 Boosted Decision Tree (BDT) Parameters There are several parameters that can influence the final result of a Boosting Decision Tree, some have been explicitly defined in previous sections: 0 Initial normalization. Step 1 in Sec. 8.2. In this analysis, both the signal and the background are normalized to s = Z s,- = b = Z bi = 0.5. 0 Criteria for deciding when a node becomes a leaf. This parameter is known as minimum leaf size and represents the minimum number of events allowed in a leaf. (Step 6 in Sec. 8.2). This value was set to 100. 0 Degradation function used to find the best split. Sec. 8.2.1. The Gini Index was used as degradation measure. a Number of Boosting cycles. 50 Boosting cycles provided the best separation. 3 Cross Section Significance (CSS) is defined as \/( Z (Si/(s,- + bill) 167 Boosting Tree W. relative to first tree for each tree Boosting Tree w. relative to first tree 2 .. .2. 9 '3‘ as 2. “u ‘ 1 ' . . .. 0e 111L111?.T.I.103‘l'559gffg_[ 20 30 40 50 Tree Number Cross Sectlon Slgnlflcance vs number 01‘ trees Included 0 2.05:— ,'£”'..... .‘ g : S’N‘fi."~.. C's-00 00000-0... 3 2 3— '“ ' E : 5" c r- 2135} f a) - ,« c I ' O 1.9: .0. "'7' : .' 3 1.8533' g 1.8:3' 0 :5 1.753 b 1 1 1 1 l 1 1 1 1 I 1 1 1 1 l 1 1 1 1 l 1 1 1 1 J O 10 20 30 . 4O 50 Number of trees Included Number of Leaves for each tree 500— 3 -'. M. > ems..- ‘: 8 400:— - as ': r -| t t E .’-: '5 t is h 300— ' :- 51’- 3 : ‘-..-’=sa ., 22:2 E — 2533'. 9.33:! 3200:- “‘35... z : i 13.}: .. 3" 100_— Q .2. 6'. .— ' , a. .1 '. " ““ ‘y‘uéa ,’.-' .3 0'.11.111 .L..1.1.?°.'.1 O 10 20 30 4O 50 Tree Number Figure 8.4: Relative weight, Cross Section Significance; and number of leaves as a function of the number of Boosting cycles for one of the 24-channels in the analysis. 168 0 Value of the Boosting parameter fl. 3 = 2 gave the best performance. A more detailed discussion on the choice of values for these parameters is in Section 8.3. 8.2.4 Decision Tree Implementation To build and evaluate the decision trees we use the code package classifier which is in the D0 CVS code repository 4. This code has been used before by the Single Top group at DD, and corresponds with the code used for the Single Top evidence publication [56, 105]. There are some differences with the code currently used, but these are mainly improvements and additional options which were implemented. 8.3 BDT optimization It is very important to have good list of well-modelled variables when training a BDT. In addition, an appropriate fine tuning of the BDT paramenters (8.2.3) can guarantee an optimal BDT. 8.3. 1 Variable Selection A list of sensitive variables has been derived based on an analysis of the signal and background Feynman diagrams [125, 126] and on a study of Single Top quark produc- tion at next-to—leading order [6, 7]. The variables fall into five categories: individual object kinematics, jet widths (RMS width of the jet energy cluster), global event kinematics, top quark reconstruction variables, and variables based 011 angular corre- lations. The number of initial variables is about 600, but not all are used as those with unsatisfactory data-background agreement are directly removed. Each variable is 4 http: / /cdcvs0.fnal. gov /cgi-bin/p1lblic-cvs/cvsweb-public.cgi / 169 required to have a Kolmogorov-Smirnov test value of at least 0.1 calculated from comparing the variable distribution for data with the sum of backgrounds. The KS implementation in ROOT [172] is used, together with histograms with many bins [0(1000)] in order to get an accurate estimate. The addition of well-modelled variables in Decision "Iree training does not degrade the performance. Indeed, if new variables have even some discriminating power, they will improve the performance of the tree even by a small quantity. If they are not discriminating enough, they will be ignored and the tree unchanged. However, having more variables also increases the computation power required to train a BDT, there- fore all the variables that have no or little discriminating power have been removed from the list. The variable selection process is done by following the subsequent procedure of: 0 train several decision trees with the full list of well modeled variables; 0 using the decision tree variable ranking5 to judge which variables were more important during the decision tree training; 0 next, out of the 24—cham1els available: the 50 highest (best) ranked variables are selected from the {2-jets,1-b-tag} channels, the 30 best from the {3—jets,1— b-tag} channels, the 20 best from the {2-jets,2-b—tag} channels, and the 10 best from each of the other three jets / tags combinations; 0 All the sublists are combined and then reduced by removing duplicated vari- ables. The number of variables selected for each channel varies according to the im— portance of the channel in the whole analysis. For channels with a smaller signal- background, a larger number of variables are taken to be part of the common list of 5 The decision tree variable ranking for a variable is the sum of degradation im- provement AD for each split in which the variable is used. 170 variables, such as the 2-jet,1-b-tag. The final number of variables after all the variable selection is performed is 64 (see Table 7.17). 8.3.2 Parameters Optimization As described in Section 8.2.3, there are many parameters that can impact the perfor- mance of a Decision Tree. In order to study their impact in the final result, several Decision Trees were trained (using the first subset of events) and figure of merit was used to compare each case performance in a second (independent) subset. The figure of merit used to determine which parameters to choose was the erpected Cross Section Significance calculated in the second subset. The Cross Section Significance is defined as: (:38 = \/Z sg/(s, + b,) (8.9) where s,- and bi are the signal and background yields in bin 2' of a histogram of the decision tree output with 100 equal-sized bins. To choose the optimal set of decision tree parameters, an initial value for each parameter is chosen based on previous results from the Decision Tree analysis in the Single Top evidence paper [56]. Ideally, one could give each parameter a range of val- ues and then with all possible combinations of parameters settings, perform a scan of the parameters phase-space and select the optimal selection of parameters. However, this procedure would require too much computation due to the many possible combi- nations and high probability of introducing hlnnan error. Instead, the strategy used for the optimization was to “smarten up” the possible values given to each parameter still covering its full range, and concentrating 011 near zones, where the fine tuning of a parameter can make a significant impact on the final result. Finally, one parameter is varied at a time combining the setting of a few well-perfonning points and then 171 run all possible combinations for this reduced set. Out of the 24—cha1mels available in the analysis, only the most significant charmels were included in the parameter optimization. Such events have exactly two jets, of which one of them b-tagged. There were also additional cross checks performed in other channels to ensure there was no bias by only considering few channels in the optimization. The BDT parameter phase-space is complex to interpret because there are several nonlinearities and several dimensions which could cause some difficulties at the mo- ment of interpreting the final result. It is often the case that the trends observed in the optimizations do not follow a particular pattern as one moves along the parameter range. The initial set of parameters for all the scans is: e AdaBoost Parameter: 0.20 0 Minimal Leaf Size: 100 o degradation Measure: Gini The BDT parameter with the biggest impact in the final optimization is the number of Boosting cycles. There is a clear improvement when going from zero to twenty Boosting cycles. For each one of the parameters to be scanned, the following Boosting cycles are used: 20, 30, 50 and 70. Next, the results of the study are sulmnarized in a plot of the figure of merit as a function of number of Boosting cycles and different parameter values. 8.3.3 The AdaBoost Parameter The following values were given to the AdaBoost parameter: c 0.05, 0.15, 0.18, 0.20, 0.22, 0.25, 0.30 and 0.50. 172 Ada_0.05 2. L1 Ada__0.15 o g A Ada_0.18 3 2. E 1» Ada_0.20 : .9 e Ada_0.22 m 2 5 ' + Ada_0.25 g x Ada_0.30 g 2' o Ada_0.50 h 0 x Zero Boosting 2. Ada 0.20 Glnl LeafSlze 100 0 10203040506070 NBoost Figure 8.5: Cross section Significance as a function of the number of Boosting cycles for different values of the AdaBoost parameter. The uncertainty on the points is estimated to be i005. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. Note the zero suppressed vertical scale. Note that most points are close to the previous analysis [56] value 0.2. In Figure 8.5, one can see that for most AdaBoost values a plateau is reached after 50 Boosting cycles. 111 most cases, the improvement can be seen up to approximately 30 cycles, after which the performance fluctuates up and down, demonstrating that no real improvement occm's when going beyond 50. In addition, the AdaBoost values near 0.2 perform similarly, giving us no reason why to change this paramenter value from 0.2, thereby confirming the previous analysis optimization studies. 8.3.4 Degradation Measures The following degradation measures were contemplated in the study: 173 2- Merlt_Glnl o o 1: g2 * MerrLSovequrtSplusB 'E .9 (I) c 2. .2 A Merlt_Entropy g 2. 2 x Zero Boosting Glnl 0 2, Ada 0.20 LeafSlze 100 0 10203040506070 NBoost Figure 8.6: Excess significance as a function of the number of Boosting cycles for different purity measures. The uncertainty on the points is estimated to be :l:0.05. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. o Gini, Entropy, s/Vs + b and s/x/b. The result from the scan is presented in Figlu'e 8.6. s/ \/b is not shown since it performed significantly worse than the other measures. The Gini Index was chosen as optimal point for this parameter. 8.3.5 Minimal Leaf Size The following values for minimal leaf sizes were. used in this scan: 0 50, 75, 90, 100, 110, 125, 150, 200 and 500. In Figure 8.7 there is no clear trend when varying the minimal leaf size parameter, and again, it is clear that after 50 Boosting cycles, there is no improvement in the. 174 LeafSlze_50 2. Li LeafSIze_75 o g A LeafSlze_90 3 2 E ‘ * LeafSlze_1 00 1: ('12; e LeatSlze_110 52' + LeafSlze_150 g x LeafSlze_200 ' §2. o LeafSlze_500 L 0 are Zero Boostlng LeafSlze 100 2. Ada 0.20 Glnl 0 10203040506070 NBoost Figure 8.7: Excess significance as a fmrction of the number of Boosting cycles for different Minimum leaf size. The uncertainty on the points is estimated to be 21:0.05. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. performance. The value of this parameter is very important because a leaf size too small will create overly large trees which then degrades the tree performance. The final value for the leaf size is 100. 8.3.6 Parameters Summary After scanning the parameter phase space and performing many studies using different parameter combinations, we arrive at the following optimal set of parameters: 0 Number of Boosting cycles: 50 o AdaBoost parameter: 0.20 0 Minimal leaf size: 100 0 Degradation measure: Gilli This list of parameter settings gives the best separation for the studied chalmels (e+2jets/ 1tag, p+2jets/1tag). In addition, the same set of values can be used in other analysis channels since the other channels have less impact on the final measurement; therefore, no further optimization is critical. As an additional cross check, the AdaBoost parameter scan was also performed for the following chamiels: events with exactly three jets, where one jet is b—tagged, and events with exactly two jets, two of them b-tagged. In Figures 8.8 and 8.9, the selected point (0.2) lies right in the middle of a small spread in the CSS for both cases, confirming the results of the optimization. It is also reassuring that the dependance with the number of Boosting cycles remains the same and that after 50 Boosting cycles no clear improvement occurs. 8.4 Discriminant Output Transformation A Boosted decision tree output given by the Equation 8.8, the possible values for D(E:) range from 0 to 1. As the nmnber of Boosting cycles increases the aver- age BDT output gets more central for both signal and background distributions, as shown in Figure 8.10 before the transformation. This effect produces an output dis— tribution that is scarcely populated in the high (low) discriminant output regions. When performing the final measurements this behavior can cause irregularities, as some bins can contain signal but no background or vice-versa producing undefined results. In order to solve this problem, a monotonic transformation is applied to the BDT output: 176 Variables Scan - 3-jet 1-tag 1. .~ Ada_0.05 L} A f: g ,5 g _ Ada_0.15 O x x X x 2 A Ada_0.18 a 0 %1 , o o o * Ada_0.20 % e Ada_0.22 5 + Ada_0.25 g x Ada_0.30 §‘- 0 Ada_0.50 b 0 x Zero Boosting Ada 0.20 C’ Glnl LeafSlze1OO pilllllllllllllllllllllllllllllllllllll 0 10 20 30 40 50 60 70 NBoost Figure 8.8: CSS as a function of the number of Boosting cycles for different values of the AdaBoost parameter for the 3-jet 1-tag case. The uncertainty on the points is estimated to be :l:0.05. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. :1:_<_0.8 HIP? y 2 f M — Kx, 0.8 < a: < 0.95 (8-10) 1, :r 2 0.95 \ where the constants are determined such that the total normalization of the BDT output is the same after and before the transformation is applied and by ensuring continuity of f (cc) in the full range 0 to 1. The constants are determined to be: it = 0.346, K = 2.88 and M 2 0.2.74. In addition to the function f (a), it is also required that at least 40 background events are present in each bin of width 0.02, in 177 Variables Scan 2-iets 2-tag 1. L) Ada_0.05 1. A E a '9 m Ada_0.15 o * 3, + Q + g x 0 A Ada_0.18 81 ' X X x — o ‘k Ada_o.2o 2'. o o 0 '=1.4 g e Ada_0.22 g 1.4 + Ada_0.25 3.1 31 x Ada_0.30 3 o Ada_0.50 91. 0 a: Zero Boosting Ada 0.20 1, Glnl LeafSlze 100 0 10 20 30 40 50 60 70 NBoost Figure 8.9: CSS as a function of the number of Boosting cycles for different values of the AdaBoost parameter for the 2-jet 2-tag case. The uncertainty on the points is estimated to be i005. As a reference, the zero Boosts point is added to the plot to show the importance of Boosting. order ensure that there are no empty bins when measuring the cross section (more in Section 9.3). The transformation is applied from the high discriminant region down to zero. Figure 8.10 shows the BDT discriminant output before and after the transformation. 8.5 Removal Of One Variable From The Training One additional study was performed to confirm that. the right variables were used while training the BDTs. The performance of the BDTs were evaluated after one variable from the initial list of 64 variables is removed from the training. The figure of merit used for this study is the same used when selecting the BDT parameters CSS. 178 - 0.1 0.“ - - 0.00} 0.08 - : _ 0.06 .— 0'“ ' 0.04:— 0.02 — 0.02 '— o I...1...i.. .1 of 1 | l I l 1. 1. .1 . l 0.2 0.4 0.6 0.0 0 0.2 0.4 0.6 0.8 1 Orlglnel BDT Discrlmlnant Output Orlglnel BDT Discrlmlnent Output Transformation Function P D A l P a 1 o b Transformed BDT Output 0 h 1111 1 111 l o o. 02 “0.3” ‘ ‘ oil; o‘s” ” '1 Original BDT Discriminant Output Figure 8.10: BDT discriminant output before (top left) and after (top right) the transformation, for both signal (blue) and background (red). The monotone transfor- mation f (x) is shown in the bottom. The plots correspond to one of the 24-channels in the analysis, similar results are obtained for other charmels. The total number of bins is 50. A summary of the results is presented in Figure 8.11, where the ratio of the CSS for the decision tree trained with one variable less than the. nominal case (all variables). The statistical uncertainty associated with the calculation of the CSS is the cause of any fluctuation above 1. It is found that no single variable alone can cause an abrupt change in the final performance, as there is no CSS change greater 0.7%. This derives from the nature of the DTs, for which the full set of variables gives the classification power rather than individual contributions. 179 866 O |- ZOO'I. None LeadingBTaggedJetPt Cos_L htOuarkJetLegtoana edTo .9 HT_ IlJets gt%nME‘P H _METIep LeadirtigBTaggedJetTo Mass Leadln Ligh uarkJetLepton ltaR — os_ BactJetLeptonfiBestTop _ Cos_BestJetNotB&ctJet_B$tTop Cos_BT edJetLepton _BTa edTOp agjefl Lepton_BTag§edT op - Cos_LeptonBestTopFrame__,BestToqu Frame n Cos LeptonBTaggedTopFrame BTaggedTopCMFrame Cos_LeptonClZw BestTop Centrali AllJets — Chi opMass — DeflaPhlLeptonMET DeltaRJet1Jet2 H AllJets MinusBTaggedJet ' HT_ "Jets _ HT_AIIJets_MInusBestJet _ HT_AIIJets_MInusBTaggedJet HT_Jet1Jet2 " HT _ _Jet1Jet2LeptonMET - lnvariantMassiAllJets _ InvariantMass_AllJets_MinusB&ctJet InvariantMass_AllJets_MinusBTaggedJet InvariantMass__Jet1Jet2 - lnvarlantMass_Jet1Jet2W _ lnvariantMass_Jets3_ 4 Jet1L tonDelta Jet10 imosEta - Jet1T0pMass — Jet1TopMass_Sz _, Jet2Etaw Jet2Pt ' JeflQfimaEta - Jet2TopMass .. Jet2TopMass__Sz L— Jet3Pt Jet4EtaW - Jet4Phiw - Jet4Pt BestJetO‘l'imesEta BactJetTopMass ' LadingBTag edJetEtaW — LudingBTaggedJet onDelta LeadingBTaggedJetTopMass__S NotBestZPt NotBest2TopMass NotBestZTopMass_32 Pt_Jet1Jet2 QfimesEta SecondngthuarkJetEtaW SecondlgghtouarkJetPhlw Seco ngthuarkJetPt SeoondngthuarkJetQfimesEta Shat '- Si To Mas — TapMassM nC iSqr TopMassMinag TransverseMasskJefiJ LeptonPt - METPt ._ WTransverseMass Figure 8.11: Relative changes in CSS after removing each variable compared to the all variables included case (first bin). The CSS for the all variable case is 5.465. The statistical uncertainty is estimated to be 1—2%. pauiquioo slauuauo-vz one: aouaomufiis uonoas 99013 T l Tl 180 Chapter 9 Analysis In this Chapter, the full Single Top analysis is outlined. Starting from the systematics used in the analysis, followed by the process used to split the samples, and finally presenting the final measurements and their significances. 9.1 Systematic Uncertainties There are two types of systematic uncertainties included in this analysis: uncertainties 011 the normalization of the signal and background samples, and those related to distributions shape-changing systematics (summarized in Tables 9.1 and 9.2). The uncertainties for each of the 24 chaimels is presented in Appendix C. Below are listed all of the uncertainties contributions in the analysis: 0 Integrated luminosity Corresponds to the :l:6.1% uncertainty on the luminosity estimate, and affects the signal, tt_, Z +jets, and diboson yields. This systematic has an impact. on the normalization only. 0 Theory cross sections The uncertainties 011 the Single Top and ti cross sections have the following 181 contributions: scale, PDF, kinematics, and top quark mass dioice [53, 128]. The mass uncertainty is taken as the difference between the cross section at 170 GeV and the current quark top mass world average (172.4 GeV [43]). The uncertainties values are +4.3%, -11.2% for s—channel tb, +55%, —7.4% for t- channel tqb, and +7.7%, —12.7% for tf. For tb+tqb combined, the uncertainty is +52%, —8.4%. The diboson cross section uncertainties were calculated using the N LO MCFM generator [102]: the imcertainty for WW is +56%, for WZ it is +68%, and for Z Z it is +55%, and on the sum of the three processes it is +58%. This average value is used as uncertainty for the Z +jets background. Branching fractions The branching fractions for a W boson to decay to an electron, muon, or tau lepton, have an average uncertainty of +15% [1]. Parton distribution functions The effect of changing the parton distribution fmlctions is evaluated by reweight- ing signal events according to the 40 CTEQ error PDFs and by measuring the signal acceptance in each case. This evaluation corresponds to a systematic uncertainty of +3%. Trigger efficiency The trigger used for the Single Top analysis corresponds to the OR of many trigger conditions which gives a trigger efficiency close to 100% (see Section 6.5). The corresponding uncertainty is +10% for all the p20 muon charmels and +5% for others. The uncertainties for muons and electrons and Run Na and Run 111) are treated as uncorrelated. Instantaneous luminosity reweighting All the MC luminosity distributions are reweighted to match the Run Ila or 182 Run IIb data distributions. The uncertainty on this reweighting is +10%. Primary vertex modeling and selection The MC primary vertex distributions along the z-axis are reweighted to match the data distributions [129, 130]. The uncertainty 011 this reweighting is +0.05%, and the imcertainty on the difference in primary vertex selection efficiency be- tween data and MC is +14%. Electron reconstruction and identification efficiency The electron scale factor lmcertainty includes the dependence of the electron ID scale factor on the variables not included in the parameterization: jet multiplic- ity dependence, track match and likelihood scale factor. The dependences on (b and W of the electron are included in the systematic error as well as the limited statistics in each bin of the parametrization. The assigned total uncertainty +is 2.5%. Muon reconstruction and identification efficiency The MC scale factor uncertainties for muon reconstruction and identification, including isolation requirements, are estimated by the muon ID group. The assigned total uncertainty is +25%. Jet fragmentation The Jet fragmentation sytematic uncertainty is measured by comparing the ac- ceptance of ti events generated with ALPGEN+PYTHIA with the ones generated by ALPGEN+HERWIG. The resulting uncertainty is about 1% to 8%, and is applied to all MC samples in the analysis. Initial-state and final-state radiation This uncertainty is evaluated using tt_ samples with the generation of these effects varied within expectations [75]. The uncertainty ranges from 0.6% to 12.6%. 183 o b-jet fragmentation The b—jet fragmentation micertainty comes from the difference between the frag- mentation parametrizations preferred by SLD (SLAC Large Detector) vs. LEP (Large Electron Positrion collider) data, and it is evaluated in the tf pairs cross section [131]. The uncertainty is measured to be +20%. 0 Jet reconstruction and identification The efficiency to reconstruct and identify jets has an imcertaiuty of +1%. This uncertainty is related to the fact that jets reconstructed in MC have a higher efficiency than those in data. 0 Jet energy resolution It was found that the shape changing variations due to J ES are smaller than 4% for all signals and backgrounds, therefore it was safe to assign a flat JES uncertainty of +4%. 0 W+jets and multijets normalization The W+jets and multijets backgromlds are normalized to the data using a fit as described in Section 7.2. The uncertainties related to this normalization vary from cha1mel to cha1mel (see Appendix C), and range from 30% to 54% for the multijets backgrormds and from 1.8% to 5.0% for the W+jets backgrounds. o W+jets heavy-flavor scale factor correction The heavy-flavor scale factor correction, S H F, for W bf) and Wcé is measurml in data in several channels, as shown in Section 7.2.2. The Monte Carlo TRF uncertainty induces fluctuations in the effective scale factor that are at least as large as the chamrel-to—channel variations in the measurement. Therefore, any additional systematic can be considered as double-counting. However, a +13.7% uncertainty on the scale factor is assigned. 184 o Z+jets heavy-flavor scale factor correction The heavy-flavor scale factor K f] F for Z bf) and Z CE is determined from NLO calculations, with an uncertainty of +13.7% taken from the S H F of W+jets events. 0 Sample statistics This uncertainty is due. to the finite size of the samples. Tables 7.7 and 7.8 show the number of events on each sample. All of the samples statistics are taken into accomit for each bin of the final discriminant distribution. 0 Jet energy scale The JES uncertainty is evaluated by increasing/ decreasing the J ES correction by one standard deviation on each MC sample and then repeating the whole analysis with the shifted samples. The result is a shape-changing uncertainty, and an overall normalization uncertainty, see Appendix D. The normalization part ranges from 1.1% to 13.1% on the signal acceptance and from 0.1% to 2.1% on the combined background. 0 Taggability and tag-rate functions for MC events The uncertainty associated with b—tagging in MC events is evaluated by adding the taggability and the tag rate components of the uncertainty in quadrature. The TRF values are raised and lowered by one standard deviation on each MC sample. The entire analysis is then repeated. This raising and lowering is done simultaneously for heavy flavor and light jets which causes the uncertainties for heavy flavor TRFs and light jets TRFs to be correlated. The result is an overestimation of the total TRF micertainties. These uncertainties affect both shape and normalization of the MC samples. The normalization of the uncertainty is shown for each analysis channel in Appendix C and the shape changing systematics part is shown in Appendix D. The values range from 2.3% to 11.4%. o ALPGEN reweighting Some W+jets background distributions are reweighted based on several pretagged data distributions (see Section 7.2.1). The uncer- tainty from these reweightings affects the shapes of the W+jets background components but not its normalization (more detail can be found in Appendix D). Relative Systematic Uncertainties Components for Normalization and Shape Jet energy scale for signal (1.1 413.1)% Jet energy scale for total background (0.1~2.1)% (not shape for Z +jets or dibosons) b tagging, singletagged (2.1-7.0)"0 b tagging, double-tagged (9.0—11.4)% Component for Shape Only ALPGEN reweighting W Table 9.1: A surmnary of the relative systematic uncertainties for each of the correc- tion factors or normalizations. The micertainty shown is the error on the correction or the efficiency, before it has been applied to the MC or data samples. 186 Relative Systematic Uncertainties Components for Normalization Integrated luminosity 6.1% tf cross section 12.7% Z +jets cross section 5.8% Diboson cross sections 5.8% Branching fractions 1.5% Parton distribution functions 3.0% (signal acceptances only) rIriggers 5.0% Instantaneous luminosity reweighting 1.0% Primary vertex selection 1.4% Lepton identification 2.5% Jet fragmentation (0.7— 4.0)% Initial-and final-state radiation (0.6-12.6)% b—jet fragmentation 2.0% Jet reconstruction and identification 1.0% Jet energ resolution 4.0% W+jets heavy-flavor correction 13.7% Z +jets heavy—flavor correction 13.7% W+jets normalization to data (1.87‘45.0)% Multijets normalization to data (30+54)% MC and multijets statistics (0.5‘—16)% Table 9.2: A smnmary of the relative systematic uncertainties for each of the correc- tion factors or normalizations. The micertainty shown is the error on the correction or the efliciency, before it has been applied to the MC or data samples (Part II). 187 9.2 Sample Preparation The signal and background model samples are split into three independent and non- overlaping subsets. The first subset is used for the training of the BDTs; the sec- ond subset is used for the combination of the BDTs with other multivariate analy- ses [132, 133]; and the third subset is used to perform all the final measurements. It is important to note that only the Monte Carlo samples are split and that the data remains unaltered. The data is only used at the point where the final cross section measurement is performed. The procedure to split the samples is based on the EventN umber, where the Eventhl umber is a unique identifier for each MC event. The motivation for its usage is to have all of the b—tagged permuted events in the same subset, which avoids possible correlations among the sets. The splitting criteria are outlined in Table 9.3. All the subsets are normalized such that each subset has the same sum-of-weights as the original sample. Sample Subset Splitting Procedure Subset Splitting Criterion Training subset, “first third” EventNumber mod 3 = 0 Testing subset, “second third” EventNumber mod 3 = 1 Yield subset, “third third” EventNumber mod 3 = 2 Table 9.3: Splitting procedure of the samples. The event number is given to a MC event during generation and is the same for all permutations of an event. 9.3 Measuring a Cross Section The Single Top cross section is determined by using signal and background binned dis- tributions (BDT discriminant outputs). The cross section calculations are performed 188 employing Bayesian statistics with the top-statistics [135, 136] package. 9.3.1 Bayesian Approach For a given histogram bin, the number of expected events d, is determined by: N N d=aLU+Zbi=a0+Zbi (9.1) k=1 k=1 where a is the signal acceptance, L =f£dt is the integrated luminosity, a is the signal cross section, b,- is the yield for the background 2', and a E all is the effective luminosity for the signal. In that bin, the likelihood to observe a data count D, given the number of expected events (1, is determined by the Poisson distribution: e—ddD P(D|d) = m mm Furthermore, since the probability to observe a count is independent on the counts in other bins, the combined likelihood for M bins corresponds to the product of all of bins’ likelihoods: M ummaJMawzflumm) ma j=1 where D and d represent vectors of the observed and expected counts, and a and b are the corresponding vectors of effective lmninosity and background yields. From Bayes’ theorem, the posterior probability p(a, a, le) [137] can be written p(0|D) = fif/L(D|0,a,b)7r(a, a, b) dadb (9.4) where 7r(a, a, b) is the prior probability density, N the overall normalization, and the the posterior density integration over a and b is to remove the dependence on the 189 nuisance parameters. The prior density contains the knowledge of all parameters, including all systematic m1certainties and their correlations. In addition, the prior can be factorized as [135]: 7r(0,0,1?) = 7r(at, b)7T(0), (9-5) where the cross section prior can be assumed to be flat in 0: 77(0) : l/Umax, 0 < 0 < Omax (9.6) = 0, otherwise. (9.7) Hence, the posterior probability for the signal cross section is: p(0’[D) Z m//L(D[0, a, b)7r(a, b) dadb (9.8) where the integral can be estimated numerically by sampling the prior density 7r(a, b) by a large number K of points (ak, bk) K f/L(D|a,a,b)7r(a, b) dadb ~ i Z L(D|a,ak,bk). (9.9) K [:21 The cross section central value is determined by the peak of the posterior density distribution and its uncertainty is established by the 68% interval around the peak. Figure 9.1 illustrates the peak of the posterior density distribution and its peak. 9.3.2 Systematic Uncertainties To determine the effect of the shape-changing systematics, three separate distributions are required namely, the nominal distribution, and the 11p and down one standard 100 999 0.0! Tllll'llIIII—Ill Posterior Density 9 .5 oIllllllll l J J I l I I gl l 6 8 1o 12 Single Top Cross Section O Figure 9.1: Example of a 1D posterior density distribution for the Single Top cross section. deviation systematic shift distributions (See Figure 9.2). The uncertainty of a given bin is modeled by sampling a Gaussian distribution with mean 0 and width 1, which results a shift for yin-n: :l: i Ayibin = Stat >< 9(0, 1) X 5am (9.10) where Sikot = -—Zyr for shape-only shifts, and 1 otherwise. 2 yibz'n 015 Red: + l 0 Black: nominal value : 0,2 _Green: -1 o 0.235: t 5;“! 0'15 0.23:— y,” I: _ 1? [_E 0.1 I I 0.225 0.05 [FITTIIIIIIIIIII Figure 9.2: Example of a kinematic variable showing the nominal distribution and the up—shifted and down-shifted histograms of the shape-changing systematics. The plot on the right corresponds the the same distribution for only bin only. 191 The uncertainties that affect only the normalization are computed using a multi- variate Gaussian approach in which a correlation matrix encodes all the correlations. Details of this procedure can be found in Reference [135]. 9.4 Results 9.4.1 Expected Results no Run II Preliminary, 2.3 lb" Z: t “a 0.45 g g o 4 E— 3 g 0.35 E- Peak/Half—Wldth .3 0.3 E— = 4.07 n. o 25:— Expected : Cross Section 0'2 E— = 3.61 +0-95pb 0.15 I- [0'89 E . 0.1 :— o.05 f:- E , , , , l . a 4% . . a I “o 2 4 6 8 1o 12 tb+tqb Cross Sectlon [pb] Figure 9.3: Expected posterior density distributions from Decision Tree outputs trained with s + t-channel tb+tqb as signal for all 24 channels combined—i.e., Run 11a and Run IIb, e and ,u, 2-4 jets and l or 2 are b-tagged. All systematic uncertainties are taken into account in this measurement. The theoretical cross section is 3.46 pb. The Decision Tree discriminants histograms shown in Appendix A were used as input to measured the Single Top cross section. This result is called “expected” because instead of using the data for the measurement, the sum of all backgrounds plus the Standard Model amormt of Single Top is used. All of the 24-channels are combined by multiplying the likelihoods. More details of this procedure are given in [135]. 192 The cross section measurements are presented in Table 9.4. The measurements are all consistent with the Standard Model cross section of 3.46 pb which was used during the calculation. As expected, the more channels that are combined, the smaller the uncertainty on the measurement. The Bayesian Posterior for the all-channels— combined cross section is shown in Figure 9.3. The ratio of posterior peak position over the lower 68.3% confidence bound (“peak over half-width”) is given in Table 9.5. The purpose of this quantity is to provide a rough estimate of the measurement sensitivity. Expected Cross Section lVleasurements 1,2tags + 2,3,4jets e,p + 2,3,4jets e-chan p—chan 1 tag 2 tags Run IIa 3.60:};ggpb 3.63+[;§§pb 3.61+{;§§pb 353333131) Run IIb 3.6s+1;3§’pb 3.713%; pb 3.74333 pb 3.62333 pb R,unIIa+b[[ 3.64flggpb 3.(51:};§3pb 3.64:5;3gpb 3.61t};$‘,‘pb eat + 1,2tags All 2 jets 3 jets 4 jets channels Run Ila 3593331)}; 369+§§gpb 3.76:§;;g pb 3.601171% pb Run IIb ascrigipb 3.79+§;§3pb 3.73:3;33pb 3.70:1;ggpb Run IIa+b 3.78i};(1,§1)b 3.74+§;g3 pb 3.324353 pb 3.61+3;33 pb Table 9.4: Expected cross section measurements for many combinations of analysis channels with all systematic uncertainties taken into account. In Table 9.5, the Bayes Ratio Significance (BRS) and Bayes Factor Significances (BFS) for the measurements are presented. These quantities are. Bayesian measures of the sensitivity. The BFS is calculated according to the procedure described in [138] integrating over the full posterior. And the BBS is an estimate of the same value 193 calculated using the posterior density at only two points (zero and the peak). For all the channels, BF S and BRS are consistent with each other within 0.5%. The measurements for all individual channels are presented in Table 9.6. Expected Posterior Peak Over Half-Width 1,2tags + 2,3,4jets e,p + 2,3,4jets e,u + 1,2tags All e-chan p-chan 1 tag 2 tags 2 jets 3 jets 4 jets channels Run IIa 2.1 2.4 2.7 1.6 2.7 1.5 1.0 3.1 Run IIb 2.2 2.3 2.7 1.6 2.5 1.6 1.0 3.0 Run IIa+b 3.0 3.2 3.7 2.1 3.5 2.0 1.2 4.1 Expected Bayes Ratio Significance 1,2tags + 2,3,4jets 3,}; + 2,3,4jets e,;u + 1,2tags All e-chan p—chan 1 tag 2 tags 2 jets 3 jets 4 jets channels Run IIa 2.3 2.6 3.0 1.6 3.0 1.5 0.7 3.4 Run IIb 2.3 2.5 2.9 1.6 2.8 1.7 0.8 3.3 Run IIa+b 3.2 3.5 4.2 2.3 4.1 2.2 1.0 4.7 Expected Bayes Factor Significance 1,2tags + 2,3,4jets 8,/.L + 2,3,4jets an + 1,2tags All e-chan p-chan 1 tag 2 tags 2 jets 3 jets 4 jets channels Run IIa 2.3 2.6 3.0 1.6 3.0 1.5 0.7 3.4 Run IIb 2.3 2.5 2.9 1.6 2.8 1.7 0.8 3.3 Run IIa+b 3.2 3.5 4.2 2.3 4.1 2.2 1.0 4.7 Table 9.5: Expected significance estimators for many combinations of analysis chan- nels: posterior peak over half-width (top Table), Bayes Ratio Significance (middle Table), and Bayes Factor Significance (bottom Table). All systematic uncertainties are taken into account in the calculations. The best values from all chamlels combined systematics are shown in bold type. 104 Expected Results in Individual Channels Channel 0 :t A0 P / HW BFS BRS e / p17 / 1tag / 2jets 3.577333 pb 1.8 1.9 1.9 e / p17 / 1tag / 3jets 4.16:§;g$ pb 1.1 0.9 0.9 e/p17/1tag /4jets 3.803334 pb 1.0 0.4 0.4 e / p17 / 2tags / 2jets 3.73:3;33 pb 1.1 1.0 1.0 e / p17 / 2tags / 3jets 3.74i§;$3 pb 1.0 0.6 0.6 e / p17 / 2tags / 4jets 3.9633158 pb 1.0 0.4 0.4 e / p20 / 1tag / 2jets 3.81333 pb 1.7 1.8 1.8 e / p20 / 1tag /3jets 3.81tggg pb 1.1 1.0 1.0 e/p20/1tag /4jets 4.2839230 pb 1.0 0.6 0.6 e / p20 / 2tags / 2jets 3.753;]; pb 1.1 1.0 1.0 e / p20 / 2tags / 3jets 3.65:3;3; pb 1.0 0.7 0.7 e / p20 / 2tags / 4jets 3.763337 pb 1.0 0.4 0.4 p / p17 / 1tag / 23m 3.71i§;§3 pb 2.0 2.1 2.1 [1 / p17 / 1tag /3jets 3.755;}; pb 1.2 1.0 1.0 ,u / p17 / Itag /4jets 4.4331,? pb 1.0 0.5 0.5 [1 / p17 / 2tags / 2jets 3851?? pb 1.2 1.1 1.1 p / p17 / 2tags / 3jets 3.66:3;32 pb 1.0 0.7 0.7 p. / p17 / 2tags / 4jets 3.613333 pb 1.0 0.3 0.3 p / p20 / 1tag / 2.16:... 38235;; pb 1.8 1.9 1.9 u / p20 / 1tag, / 3jets 4:31:33? pb 1.3 1.2 1.2 p / p20 / 1tag /4jets 4.5339532 pb 1.0 0.6 0.6 p / p20 / 2tags / 2jets 4.191333 pb 1.2 1.1 1.1 ,u / p20 / 2tags / 3jets 4.36:3;32 pb 1.0 0.8 0.8 p / p20 / 2tags / 4jets 3831”},f’gg‘3 pb 1.0 0.4 0.4 Table 9.6: Expected cross section, peak over half-width, Bayes factor significance and Bayes ratio significance, with all systematic uncertainties taken into account, for the 24 analysis channels. 9.4.2 Observed Results 'u 3. D0 Runll prelim. 2.3m1 aw : D0 Runll Prelim. 2.3 fb“ p17+p20 6+“ channel '>'- ' p17+p20 e+_u channel 1-2 b-tags E 1-2 b-tags 2-4 jets 3 2-4 jets _t O M l 0.2 0.4 0.6 0.8 1 . . 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output 3;, D0 Runll Prelim. 2.3m1 Key for P10“ ; p17+p20 e+uchannel“ 0 Data ‘3' 1-2 b-tags = 21$ :bb _ - l : q r. 2 4,... - was... - Wc5+jets - W+1ight jets - be+jets + [:1 ZcE+jets D Z+light jets - WW+WZ+ZZ - tE—rll 0.85 0.9 0.95 1 l t;_,1+je,, tb+tqb DT Output - Multijets Figure 9.4: Decision tree discrin‘iinant outputs for all 24 channels combined. The histograms are obtained by stacking each one of the 24 DT outputs on top of each other. The Single Top contribution in this plot is normalized to the measured cross section. The three plots correspond to the same distribution: linear scale (top left), log scale (top right) and a. zoom in the signal region (bottom). The color key is shown in the bottom right-hand corner. This section contains the decision tree observed Single Top cross section results using the 2.3 fb‘l dataset. The. decision tree discriminant distributions used for this measurement are shown in Appendix A. The decision tree output for all 24 channels combined 1 is shown in Figure 9.4. The measured cross sections are presented in Tables 9.7 and 9.8, and the cor- 1 The histograms are combined by stacking the individual decision tree individual outputs. 196 responding peak over half-width and BRS are found in Table 9.9. The BFS is not presented as it is not possible to be calculated in real data. Figure 9.5 shows the posterior density for the all combined measurement. The measurements for all of the 24 individual channels are given in Table 9.10. DO Run II Preliminary, 2.3m1 0.5—- =2 : C c. 8 0.: 2 3 ' - Peak/HaIf-Width E : =4.73 3 o.3_— “- - Observed 2 Cross Section 0'2:— = 3.74 3979ng 0.1:— " l l . l . l . . . El . . . l 00 2 4 6 8 1o 12 tb+tqb Cross Section [pb] Figure 9.5: Observed posterior density from s + t-channel Single Top cross section measurement using boosted Decision Trees. This is for 24 channels combined—mic. Run 11a and Run IIb, e+jets and e+jets, 2—4 jets and 1 or 2 are b—tagged. All systematic uncertainties are taken into account in this measurement. Observed Cross Section Measurements [ 1,2tags + 2,3,4jets 6,11 + 2,3,4jets e—cllan p-chan 1 tag 2 tags Run IIa 2.323;? pb 2.73333 pb 1.86332 pb 3.65332 pb Run IIb 620333116 3.933;;3 pb 5.80333 pb 3.793;§§pb Run IIa+b [[ 4.40332 pb 3323;33pb 3.84+3;$§pb 3.72333 pb Table 9.7: Observed cross section measurements for many combinations of analysis channels with all systematic tmcertainties taken into account. 197 Observed Cross Section Measurements 8,” + 1,2tags All 2 jets 3 jets 4 jets channels Run IIa 1.23fl:5§ pb 4.713%? pb 5.82:??3 pb 2.501“;ng pb Run IIb 4.253;: pb 5.573% pb 9.25tg;§3 pb 4.923;? pb Run IIa+b 2.62353 pb 5.24ifggi pb 7.003%; pb 3.74i3;$3 pb Table 9.8: Observed cross section measlu'ements for many combinations of analysis channels with all systematic uncertainties taken into account. Observed Posterior Peak Over Half-Width 1,2tags + 2,3,4jets e,u + 2,3,4jets e,u + 1,2tags All e-chan p-chan 1 tag 2 tags 2 jets 3 jets 4 jets channels Run Ha 1.4 1.9 1.6 1.6 1.2 1.8 1.3 2.2 Run IIb 3.2 2.6 3.7 1.7 2.8 2.3 1.8 4.1 Run IIa+b 3.6 3.2 4.1 2.2 2.6 2.9 1.8 4.7 Observed Bayes Ratio Significance 1,2tags + 2,3,4jets 8,” + 2,3,4jets 6,11 + 1,2tags All e-chan p-chan 1 tag 2 tags 2 jets 3 jets 4 jets channels Run IIa 1.3 1.9 1.5 1.6 1.0 1.8 1.3 2.2 Run IIb 3.6 2.9 4.4 1.8 3.2 2.6 2.0 4.6 Run IIa+b 3.7 3.5 4.4 2.4 2.9 3.2 2.1 5.0 Table 9.9: Observed posterior peak over half-width and Bayes ratio significance for many combinations of analysis chainiels. All systematic unmrtainties are taken into account in the calculation. The best values from all channels combined with system- atics are shown in bold type. 198 Observed Results in Individual Channels Channel 0‘ :1: A0 P/HW BRS e / p17 / Itag / 2jets 0.911:3;3°1 pb 1.0 0.5 e / p17 / 1tag / 3jets 9. 0;;+3_p3‘11 b 1.7 1.8 e / p17 / 1tag / 4jets 8. 151531132 pb 1.0 0.9 e / p17 / 2tags / 2jets 0. 00130316 pb 0.0 0.0 e / p17 / 2tags / 3jets 9 27+3 33 pb 1.5 1.5 e / p17 / 2tags / 4jets 0. 0013530 5-1 pb 0.0 0.0 e/p20/1tag /2jets 0.001333 pb 0.0 0.0 e / p20 / 1tag / 3jets 5.65:3;33 pb 1.6 1.7 e / p20 / 1tag / 4jets 14. 1'11? 53 pb 1.5 1.0 e / p20 / 2tags / 2jets 4. 2433 pb 1.2 1.1 e /p20/2tags/3jets 50415333111) 1.0 0.9 e /p20/2tags/4jets 21.37+3333 pb 1.6 1.9 u / p17 / 1tag / 23.21.»; 2. 53333 pb 1.5 1.4 p / p17 / 1tag / 3jets 0.817333 pb 1.0 0,2 [1 / p17 / ltag / 4jets 0. 003305 pb 0.0 0.0 ,1/ p17/ 2tags/ 2jets 1.. 56333 pb 1.0 0.5 u / p17 / 2tags / 3jets 1.001531 33 pb 1.0 0.2 p / p17 / 2tags / 4jets 12. (55+331'g5 pb 1.4 1.7 a / p20 / 1tag /2jets 5.051333 pb 2.3 2.0 u / p20 / 1tag / 3jets 5 .191“; 28 pb 1.4 1.4 p / p20 / 1tag / 4jets 3.62+§0638 pb 1.0 0.4 u / p20 / 2tag‘s / 2314.3 2. 0215333 pb 1.0 0.0 u / p20 / 2tags / 3jets 4 ”+2317, pb 1.1 1.0 ,1 / p20 / 2tags / 4jets 8. 08+31338 pl) 1.1 1.1 Table 9.10: Observed cross section, peak over half-width and Bayes ratio significance, with all systematic uncertainties taken into account, for the 24 analysis channels. 199 9.5 Significance 9.5.1 Ensemble Tests To verify the cross section measurement procedure, several ensembles of pseudo- datasets were generated by using the final discriminant output distributions, The generation is done by randomly drawing a Poissondistributed number in each bin, taking into account all systematic uncertainties. First one set of random system- atic shifts is generated for each systematic uncertainty, then the bin contents for all sources in all cha1mels are adjusted accordingly, and finally a Poisson random number is drawn in each bin. The ensemble generation was done using the package top_statistics and is described in detail in Reference [134, 135]. There were several ensembles generated, each one with different amounts of Single Top: 2, 3, 3.46 , 4.2, 5, 7, 8 and 10 pb. In each case, the cross section was measured using the same method as with the real data. Figure 9.6 shows the results, where each ensemble has its corresponding cross section measurement as well as a fitted Gaussian around the peak of the distribution. In addition, a linear fit from the means and their errors can be seen in Figure 9.7. The measured cross sections are consistent with the Single Top cross sections used in the ensemble generation. Furthennore, there was one more ensemble generated which had no Single Top. This ensemble was used to measure the final senSitivity of the analysis, see Section 9.5.2 below. 200 Measured cross section Meesured cross section ‘ In ensembles In ensembles MLM—POI" "’W ' Entries 7580 Mean 2.984 000 mas o 7 600 Meen:1.96:o.02 400 “film 200 0 . 0 123456789 0123456789 tb+tqb Cross Section [pb] tb+tqb CrossSectionmb] Measured cross section Meeeured cross section "' MN“ - .LNLM 1 2 3 4 5 6 7 8 9 tb+tqb Cross Section [pb] Meesured cross section In ensembles ME... Meen:4.9410.02 Entries 7580 tb+tqb Cross Measured cross section Measured cross section In ensembles in ensembles tb+tqb Cross Section [pb] Figure 9.6: Measured Single Top cross sections in ensembles with various amounts of Single Top. 201 BDT Ensemble Linearity Test _L O :- lntercept: -0.016 4.- 0.016 Slope: 0.994 1 0.003 ‘5 Q lfliIllTllllrilllll Measured Single Top Cross Section [pb] N c» xxiiiLugilJmllliriijnji ch 2 4 6 8 10 Input Single Top Cross Section [pb] Figure 9.7: Linear fit through the means from the Gaussian fits (Figure 9.6) of the measured cross sections in ensembles 9.5.2 Significance To measure the Single Top cross section significance, a very large number of zero-signal ensemble pseudo-datasets was used, where each dataset corresponds to 2.3 fl)_1 data without any Single Top. The measured cross section distribution for the zero—signal ensemble can be seen in Figure 9.8, together with the expected and observed cross sections. From the measured cross sections in the ensemble, one can calculate the probabil- ity that data containing no Single Top quark events could fluctuate enough to produce a cross section measurement of at least the observed cross section. This probability is referred to as the “p-value”, and is widely used to estimate the significance of a measurement. The number of standard deviations equivalence N0 can be calculated in terms of 202 49.4M pseudo experiments 10,, 374 above SM p-value: (7.6:0.4) x 1045 105 Expected Significance: 10‘ 4.3333311 sigma 4 5 tb+tqb Cross Section [pb] 49.4M pseudo experiments 95 above obs. measurement p-value: (1 3:02) x 1043 Observed Significance: 4.62232" sigma 4 . 5 ‘ tb+tqb Cross Section [pb] Figure 9.8: Measured cross section from a large ensemble of pseudo-datasets contain— ing no Single Top. The significance of a particular cross section is calculated from the number of pseudo-datasets measuring a cross section higher than the given cross section (green line). The plot above uses the Single Top Standard Model cross section and corresponds to the expected significance. The plot below the bottom uses the measured cross section and therefore corresponds to the observed cross section. 203 a p—value a as: N0 = \/§ - erf_1(1 — 2a) (9.11) which fulfills Na Gauss(x) dx = 1 — a. (9.12) —00 where the normal distribution Gauss(:v) is normalized to unity. The p-value and the corresponding number of standard deviations for the expected and observed excess of signal over background are shown in Figure 9.8. 9.6 Gross Check samples The cross check samples are defined in Section 7.5. In this Section, the results from evaluating these samples through the final BDTs are presented. Figure 9.9 shows the Decision Tree output distributions in these cross-check samples for Run IIa—b, e and p, 1-2 tags combined. In Appendix E all the distributions are shown separately for Run 11a and Run IIb, for e+jets and e+jets, and for 1 and 2 tags. 3200 D0 Run II Prelim. 2.3 fb" 1:3 no Run II Prelim. 2.3m-1 >- p17+p20 e+u channel >- p17+p20 e+u channel 2:; 1 b-tags ‘5' 60; 1-2 b-tags $150— 2 jets u): : 4 jets ‘b 0.2 0.4 0.6 0.8 1 (l) 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output Figure 9.9: Combined Decision Tree outputs for the “W+jets” sample (left) and the “ti” sample (right) cross-check samples. From the information in these histograms, one can conclude that there is no 204 obvious bias in the decision tree measurement from the composition of the different backgrounds components. For these subsamples dominated by W+jets and ti, the background model describes the data within uncertainties. 9.7 14;, measurement As outlined in Section 2.3.2.1, the magnitude of the CKM matrix element th can be inferred from the Single Top cross section measurement [57]. This is direct mea- surement that does not assume the unitarity of the CKM matrix nor the existence of three quark families. In addition to the systematics included in the Single Top cross section, there are theoretical uncertainties that must be considered in the th measurement. These uncertainties are applied to the s— and t-channels separately, and are summarized in Table 9.11. s-chalmel t—channcl Top quark mass [‘70] 5.56 3.48 Factorizatioin scale [%] 3.7 1.74 PDF [‘70] 3.0 3.0 a S [0/0] 1.4 _ 0.01 Table 9.11: Systematic uncertainties in percentage on the cross section factor required in the measurement of V”). A Bayesian posterior for Ith|2 is obtained in the closed interval [0,1]. The resulting limit for the CKM matrix element th is: |an > 0.78 (9.13) at 95% CL. within the Standard Model, (flL = 1). When the upper limit constraint. on the Ithl2 posterior is removed, the V — A coupling strength is meassured to be: 205 |th flLI = 1.05 8;}3, (9.14) where flL is the left-handed Wtb coupling. Figure 9.10 shows the posterior probability densities for IthI2 and thbflLl2- De Run II, 2.3m-1 A hdlllllilIll]llllllilllllllllllTlllllllllITl 2 35 thbI > 0.59 IVI >0.77 tb Posterior Density at 95% CL fiat prior < 1 0.4 0.5 0.6 0.7 0 .8 0.9 1 2 "L vtbl De Run II, 2.3 fb“ 1 2 +0.28 "Lva = 1.09 .1124 1 +0.13 IfLV,bI = 1.05 .1112 d 'AllllllI)!lllllllllllllll'Tlllllll Posterior Density 0.8 0.6 0.6 0.8 ’ 0.2 0.4 Figure 9.10: Posterior probability densities for [thl2 (left) and thbf1Ll2 (right). The color bands represent different confidence bounds: 68.3 %, 95.4 % and 99.7 %. 206 9.8 Event Display Figures 9.11 and 9.12 presents a possible Single Top event candidate. This event is identified as having three jets, of which two are considered b—tagged, a muon, and a neutrino in the form of MET. In XY view, the SMT barrel hits are represented by red dots and the CFT axial fiber hits by blue dots. The outer part represents the calorimeter energy deposits, where the red portion corresponds to EM deposits and the blue to Hadronic. The lego view, represents the calorimeter (77, (1)) space. The circles correspond to the cone radius and the jet widths. Muons are represented in green, the corrected MET is represented in yellow, and the calorimeter deposits follow the same convention as in the XY view. Run 223473 5373179543 _Sun Jul 23 19:21 :41 gpoe Tfigfiéréim il‘TITATET 7 7 7 I EM JT2_3JT12L*MM3_V . JT2 3JT15L |P_VX I 1 mu partlcle I '00 JT2_ACO_MHT_BDV ~ & MG JT2_ACO_MHT_HT ” I HAD JT2_ACO_MHT_LM - . l CH JT2_MHT25_HI, / - "11., , v‘h ‘ —A\. r" ././ 0 Bins: 171 . _. ‘ , if; y -1 eta Mean: 0.856 {"f * Q -2 Rms: 1.96 o "_4 7 '3 mu particle et: 43.46 Mi": 0-00916 ' MET et: 53.63 Max: 16.2 Figure 9.11: Possible candidate event display. The event contains three jets out of wich two are b—tagged, a muon, and a neutrino. Lego view of the DD detector. 207 Flun 223473 Evt 27278544 Sun Jul 23 19:21 :41 2006 bjet ET scale: 28 GeV .\ rnuon neutnno Figure 9.12: Possible candidate event display. The event contains three jets out of wich two are b—tagged, a muon, and a neutrino. XY View of the D0 detector. 208 Chapter 10 Results and Conclusions This dissertation presents the results of the observation of Single Top using 2.3 fb‘1 of Data collected with the D0) detector at the Fermilab Tevatron collider. The analysis includes the Single Top muon+jets and electron+jets final states for events with two to four jets with at least one jet b—tagged. Furthermore, Boosted Decision Trees are employed as a method to separate the Single Top signal from the overwhelming background. The resulting Single Top cross section measurement is: _ . .9." U(pp —+ tb + X, tqb + X) = 3.74 i873 pb, (10.1) where the errors include both statistical and systematic uncertainties. The probability to measure a cross section at this value or higher in the absence of signal is p = 1.9 x 10-6. This corresponds to a standard deviation Gaussian equivalence of 4.0. When combining this result with two other analysis methods, the resulting cross section measurement is: U(pp ——> tb + X, tqb + X) = 3.04 :1: 0.88 pb, (10.2) and the corresponding measurement significance is 5.0 standard deviations. In addition, using the cross section measurement, a Bayesian posterior for thbl2 209 is obtained in the closed interval [0,1]. The measm'ement does not assume unitarity of the CKM matrix or the existence of three quark generations. The resulting limit for the CKM matrix element th is: leI > 0-78 (10.3) at 95% CL. within the Standard Model. When the upper limit constraint 011 the IthI2 posterior is removed, the V — A coupling strength is meassured to be: L r . |th f1 | :10.) i813 (10.4) where flL is the left-handed Wtb coupling. 210 Appendix A Decision Tree Outputs In this Appendix, the boosted decision tree discriminant outputs are shown. First. for all the 24 channels combined (Figure A.1); second, combining reconstruction ver- sions and leptons but separated by number of jets and nmnber of b—taggcd jets (Fig— ure A2); third, separately for each of the 24 chalmels (separated by jet multiplicity Figures A.3, AA, and A5; and finally considering only the high discriminant region, DToutput > 0.8 where mostly signal is expected to be found (Figures A.6 to A8). ‘211 D0 Runll Prelim. 2.31‘b‘1 p17+p20 9+“ channel 2 o >- E 1-2 b-tags 51300 2—4 jets 0.2 0.4 0.6 0.8 1 tb+tqb DT Output D0 Runll Prelim. 2.310" p17+p20 e+11 channel 1-2 b-tags 2-4 jets Event Yield ‘ 55. 10: 0 0.2 0.4 0.6 0.8 1 tb+tqb DT Output ”$154520 élfihéfinél’ 1-2 b-tags 2-4 jets Event Yield .h O 0.9 0.95 1 tb+tqb DT Output Figure A.1: Decision trees discriminant output for all 24 channels combined. The Single Top contribution in this plot is normalized to the measured cross section. Same distribution on linear scale (above), log scale (middle) and a zoom in to the signal region (below). 212 u I." 1, DO Runll Prelim. 2.3 m‘ E W DO Runll Prelim. 2.3m1 >- - p17+p20 e+jl channel >- p17+p20 e+_u channeli :00- ‘b::%: “is: u: . j I“ _ je s 2°°_ 2. ++ 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output E200_ DO Runll Prelim. 2.3 fb" % DO Runll Prelim. 2.3 fb‘1 >- p17+p20 e+jl channel ; _ p17+p20 e+ji channel ‘5 1 b-tags E _ 2 b-tags 9150* 3 jets 5 4°_ 3 jets 100 20 50 ’ 0.2 0.4 0.6 0.3 1 °( 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output Emu" D0 Runll Prelim. 2.3 fb“ Em" D0 Runll Prelim. 2.3 1b" >- p17+p20 e+_ii channel >- p17+p20 e+ll channell E - 1 b-tags ‘3' t 1 b-tags u>l 4 jets I.I>.l 4 jets 50* 50* 0.2 0.4 0.6 0.8 1 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output Figure A.2: Decision trees discriminant output for the e.n+jet.s combination in RunIIa+b data. The total Single Top contribution in this plots is normalized to the measured cross section. [Rowsz top =2 jets, center :3 jets, bottom =4 jets, columns: left :1 b—tag, right :2 b—tagsj 213 DO Runlla Prelim. 1.1 tb“ 60 DO Runlla Prelim. 1.1 fb" p17 e+jets 10 p17 e+jets 1 b-tag 2 b-tags 2 jets 2 jets Event Yleld Event Yleld S M O 0.2 0.4 0.6 0.8 1 . 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output % DO Runlla Prelim. 1.1 tb" % DO Runlla Prelim. 1.1 fb" ; p17 e+jets ; p17 e+jets § ‘32:: ”Sits I“ l I.” ]e S 0.2 . 0.6 0.8 1 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output 3 60 DO Runllb Prelim. 1.2m1 % DO Runllb Prelim. 1.2m1 >- p20 e+jets ; p20 e+jets E 1 b-tag E ‘ 2 b-tags a 40 2 jets E 2 jets l 0.2 0.4 0.5 0.8 1 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb 01' Output % oo Runllb Prelim. 1.2 1b“ % '" DO Runllb Prelim. 1.2m-1 ; p20 ii+jets ; p20 ji+jets E 1 b-tag E 8 2 b-tags «>1 2 jets g 2 jets Iu "1 6 *T‘l—T-I—r—r—l—rr ‘1' ‘r‘r‘r—v—rj—T—rfi— 0.2 0.4 1 0.2 0.4 0. . 1 tb+tqb DT Output 0.6 0.8 tb+tqb DT Output Figure A.3: Decision trees discriminant. output for event with exactly two jets in the final state. One b—jet (left) two b—jet (right). 214 Event Yleld M O 10 DO Runlla Prelim. 1.1 fb'1 p17 e+jets 1 b-tag 3 jets Event Yleld 0.2 0.4 0.6 0.8 1 tb+tqb DT Output DO Runlla Prelim. 1.1 fb‘1 p17 ll+jets 1 b-tag 3 jets 0.2 0.4 0.6 0.8 1 tb+tqb DT Output Event Yleld DO Runllb Prelim. 1.2 fb“ p20 e+jets 1 b-tag 3 jets Event Yleld Figure A.4: Decision trees discriminant output for event with exactly two jets in the 0.2 0.4 0.6 0.8 1 tb+tqb DT Output DO Runllb Prelim. 1.2_tb‘1 p20 e+jets 0.2 0.4 0.6 0.8 1 tb+tqb DT Output Event Yleld Event Yleld Event Yleld Event Yleld final state. One b—jet (left) two b-jet (right). DO Runlla Prelim. 1.1 fb‘1 p17 e+jets 2 b-tags 3 jets 0.2 0.4 0.6 0.8 1 tb+tqb DT Output 00 Runlla Prelim. 1.1 tb“ p17 e+jets 2 b-tags 3 jets 0.2 0.6 0.8 1 tb+tqb DT Output D0 Runllb Prelim. 1.2 fb“ p20 e+jets 2 b-tags 3 jets 0.4 0.2 0.4 0.6 0.8 1 tb+tqb DT Output DO Runllb Prelim. 1.2 tb’1 p20 _u+jets 2 b-tags 3 jets 0.8 tb+tqb DT Output 0.2 0.4 0.6 1 % DO Runlla Prelim. 1.1 fb‘1 % D0 Runlia Prelim. 1.1 fb‘1 ; p17 e+jets ; p17 e+jets E 1 b-tag E 5 2 b-tags 2 4 'ets g 4 'ets 0.2 0.4 0.6 0.8 ‘l 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output 2 15 . .1 E . .1 0 DO Runlla Prelim. 1.1 fb 0 DO Runlla Prelim. 1.1 fb ; p17 il+jets ; p17 e+jets E 1 b—tag E 2 b-tags 2 1o 4 'ets 9 4 'ets I" I m l 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 ‘I tb+tqb DT Output tb+tqb DT Output % DO Runllb Prelim. 1.2 ft)‘1 % 01 DO Runllb Prelim. 1.2 fb'1 ; p20 e+jets >_- p20 e+jets E * 1 b—tag E 5 2 b-tags 2 1° 4 jets ‘3 4 jets in u: 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output % 15- DO Runllb Prelim. 1.2m1 % I DO Runllb Prelim. 1.2m1 ; p20 ll+jets ; 10 p20 e+jets E 1 b-tag E 2 b-tags ‘>’ 4 'ets 2 4 jets m 10- I in 0.2 0.4 ‘b 0.2 0.4 0.6 0.8 1 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output Figure A.5: Decision trees discriminant output for event with exactly two jets in the final state. One b—jet (left) two b—jet (right). 216 .0 . __ ,! , __ ,. -, E 10 p17 e+jets E 2 p17 e+jets t 1 b-tag >- 2 b-tags 5 2 jets ‘ 5 1.5 2 jets > > In |.l.l 0.85 0.9 0.95 1 . 0.85 0.9 0. 1 tb+tqb DT Output tb+tqb DT Output 3 W W 7 7 p717 jl+jetsfl E 4 if? Vp17éli-t-jets : 1 b-tag : 2 b-tags 5 2 jets j 5 3 ~ 2 jets > > i [ll lu ' 0.9 0.95 1 0.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output 3 W i 7 p20 e+jets 3 5 ' i" {320 e+jets : 1 b-tag : 4 2 b-tags g 2 jets 5 2 jets > > m l“ 3 2i 1 0.9 0.95 1 8.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output 3 1O HipZOjHjets 7 t E 51* _____ 7 A7 Vp20jll+jetsj : 1 b-tag >- 4 j 2 b-taqs. 5 2 jets . g 2 jets > > u: I tu 0.8 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output Figure A.6: Decision trees discriminant output for event with exactly two jets in the final state. One b—jet (left) two b—jet (right). Signal region only, ODT > 0.8. 217 E 5 —_—_""p1_7e+fi? 3 5 ‘g 7* ‘ ’pTr‘EErQ >- 1 b-tag >- 47 2 b—tags E 3 jets g 3 jets > l > m l 11.1 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output 3 F p17li+jets % 4 V W mitt-jets j 3'. 1 b-tag E 2 b-tags 5 3 jets 5 3 jets > > tu in 0.9 0.95 1 . 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output 3 ”*M" " p720 e+jets” 3 pEerets — i t 1 b-tag >- 2 b-tags 5 3 jets . E . 3 jets > I > In 1.11 0.85 0.9 0.95 1 . 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output E p20jl+jets ‘ ‘73 5 7 p20tl+jets ; 1 b-tag ; 4 2 b-tags E 3 jets E 3 jets > > It] ul 3‘ 2" 1 . 0 0.8 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output Figure A.7: Decision trees (hscriminant output for event with exactly two jets in the final state. One b—jet (left) two b—jet (right). Signal region only, ODT > 0.8. 218 4i i.__‘ h) g In 71. is; 3 p17 are: :- 1 b-tag l >- 2 b~tags 5 3‘ 4 jets * E 1.57 4 jets > > it: in 2 1 1 0.5 0 0 0.8 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output 1:: 5 a __- * ' , u 2 * * E l— pl7ll+jel5j E P17U+jet$ : 1 b-‘tag i", 2 b-tags 5 4 jets 5 . i' 4 jets > > 11.1 tu p— i.J 0.9 0.95 1 . 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb,DT Output 11 . 'O 2 ‘- E 920 9+let5 E) I7 {120 e+jets a: 1 b-tag : 2 b—tags ‘ 5 4 jets j 5 1.5 4 jets > . > in . in 1 D— 0.5 I 0 0 H 0.8 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output 1% 4 -— — if _p20jl+jets l 3;; 4 FF ”7 ip20ll+jetsl 5': 1 b-tag ‘ ; 2 b-taqs 5 ‘g 3t 4 jets > > in 11.1 1 2 1 0 0.8 0.85 0.9 0.95 1 0.8 0.85 0.9 0.95 1 tb+tqb DT Output tb+tqb DT Output Figure A.8: Decision trees discriminant output for event with exactly two jets in the final state. One b—jet (left) two b—jet (right). Signal region only. ODT > 0.8. 219 Appendix B Plots of Discriminating Variables Figures B.1 to B21 show various kinematic distributions in the final samples: 0 transverse momentum of the lepton (Figures B.1, B2, and B3) 0 missing transverse energy (Figures B4, 8.5, and B.6), o transverse energy of the leading jet (Figures B7, 8.8, and B9), c transverse energy of the second leading jet (Figures B.10, B.11, and B.12), o scalar transverse energy sum (Figures B.13, EM, and B.15), a reconstructed top quark mass (Figures 8.16, B.17, and B.18); and o pseudorapidity of the light quark jet times lepton charge (Figures B.19, B20, and B21). Each figure corresponds to a given jet multiplicity, the left column correspond the the Runn IIa period and the right colunm to the R111] IIb period. 220 %' p17 e+jets E p20 e+jets 0 1 b-tag <5 1 b-tag Eu 2 jets g 2 jets : I: 3 3 o o .2. 2. u 'c E E >- >- E ‘E o o > > m In 50 100 150 200 50 100 150 200 pT(lepton) [GeV] pT(Iepton) [GeV] p17 e+jets p20 e+jets 2 b-tags 2 b-tags 2 jets 2 jets Event Yleld [counts/106W] Event Yleld [counts/1OGeV] 50 100 150 200 50 100 150 200 pT(lepton) [GeV] pT(Iepton) [GeV] 5 : p17 e+jets 5 p20 e+jets g 150j 1 b-tag g 1 b-tag E 2 jets E 2 jets C ’ C 3 100: g .2. » .2. 2 I '2 o b .2 S'- 50. >- ‘E ' E o o > > In In 50 100 150 200 50 100 150 200 pT(lepton) [GeV] pT(lepton) [GeV] 305 p17 jt+jets p20 tt+jets| 2 b-tags 2 b-tags. 2 jets 2 jets! I 1 Event Yleld [counts/106W] Event Yleld [counts/1OGeV] 50 100 150 200 100 150 200 pT(lepton) [GeV] pT(Iepton) [GeV] Figure B.1: The transverse momentum of the lepton for channels with exactly two jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-l)tag. 221 Event Yleld [counts/1 OGeV] 50 100 150 200 pT(|epton) [GeV] Event Yleld [counts/1OGeV] %' p17 e+jets 5 p20 e+jets g - 1 b-tag g 1 b-tag S 3 jets 5 3 jets E 40” E 3 - 3 o o .2. .2. u ' '3 1) 20% E >- ~ >- 5 I 5 > > ul Ill 50 100 150 200 100 150 200 pT(Iepton) [GeV] pt(lepton) [GeV] % p17 e+jets % p20 e+jets g _ 2 b-tags g 2 b-tags S 20L 3 jets S 3 jets ‘E * E 3 3 o o .9. F 2. 1: _ '3 E 1°. E >- >- ‘E ‘E o o u’. .3 100 150 200 100 150 200 pT(Iepton) [GeV] pT(lepton) [GeV] %' p17 e+jets %' p20 e+jets (5 1 b-tag <5 1 b-tag g 3 jets g 3 jets ‘E E 3 3 o o .2. 8. E E 2 2 >- >- ‘E E o o u’. u’. 100 150 200 100 150 200 pT(lepton) [GeV] pT(|epton) [GeV] 20; p17 e+jets p20 e+jets ' 2 b—tags 2 b-tags 3 jets 3 jets 50 100 150 200 pT( lepton) [GeV] Figure B2: The transverse momentum of the lepton for channels with exactly three jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. 222 %' 30 p17 e+jets %' 40 p20 e+jets 121:: 12:: E ’ 2 I t: c 3 3 o o .2. 2. E 2 2 2 >- >- E E m o I: u’. 100 150 200 100 150 200 pT(Iepton) [GeV] pT(lepton) [GeV] %' 15F p17 e+jets E p20 e+jets g : 2 b-tags (of! 2 b-tags E : 4 jets E 4 jets 5 1°.“ 5 o _ o 2. - .2. E ‘ E 2 5* 2 >- > >- E E 3 ..>. 100 150 200 100 150 200 p,( lepton) [GeV] p,(|epton) [GeV] %' p17 e+jets %' p20 e+jets ‘3 ‘3‘? 8 ‘21“? E je s E je s c t: 3 3 o o .2. .2. E 2 2 2 >- >- E E o o .z u’. 100 150 200 100 150 200 pT(|epton) [GeV] p,(|epton) [GeV] %' p17 e+jets E p20 e+jets g 2 b-tags 0 2 b-tags . o . 5 4 jets 5 4 jets E E 3 3 o o .2. .2. 2 2 2 2 > >- E E u o > > m m 50 100 150 200 100 150 200 pT(Iepton) [GeV] pT(Iepton) [GeV] Figure B3: The transverse momentum of the lepton for channels with exactly four jets in the final state. Run 113. (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2—btag. 223 (E5; 150 p171egjfts (s3. p201egjfts - ag - ag o . o . i 2 lets i 2 jets C C 2 3 o o .2. .9. 2 E 2 2 >- >- E E 2 2 l.l.l u: 50 100 150 200 100 150 200 Missing ET [GeV] Missing ET [GeV] %' F p17 e+jets E p20 e+jets 0 2 b-tags (5 2 b-tags 9 15- ' 2 - E 21ets E 20_ 2 jets C C 3 10 3 .9. .9. 'D 1: _ >- 5 >- E E 2 2 m 100 150 200 '" 100 150 200 Missing ET [GeV] Missing ET [GeV] 5' p17g1+jets 5' 20 p+jets 3 1.. .2 p 1... - ag - ag o . c . E 2 jets E 2 Jets C C 3 3 o o .2. .2. 2 2 2 2 >- >- E E 2 2 u m 50 100 15 200 50 100 15 Missing ET [GeV] Missing ET [GeV] 5 20 p17 u+jets E p20 u+jets g 2 bitegts g 2 bétags :2? 15_ 1e 5 3 1e 5 C _ C 3 :l o o .2. 10* .2. 2 — 2 2 2 >- 5— >- E _ E 2 2 m m 100 150 200 100 150 200 Missing ET [GeV] Missing ET [GeV] Figure B4: The missing transverse energy for channels with exactly two jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 224 %' 60 p17 e+jets % p20 e+jets g 1 b-tag g 1 b-tag i 3 jets E 3 jets C C 3 a o o 2. 2. '2 ‘2 .2 2 >- >- E E > + > In in 100 150 200 100 150 200 Missing ET [GeV] Misslng ET [GeV] 50' 15» p17 e+jets % 152 p20 e+jets g 2 b-tags 0 2 b-tags 1- 3 jets S 3 jets E E g 10* g 10— o o .2. ~ 2. 2 '2 .2 5' 2 5* >- >- E E on 0 > > In in 100 150 200 50 100 150 200 Missing ET [GeV] Missing ET [GeV] %' p17 _u+jets % 80} p20 u+jets (‘35 1 5:23:95 3 : 32 ' 2 60~ : c " :1 3 - O o _ .2. .9. 40* 'o 1: ; E E - >' >' 20L ‘5 E ’ o o * .3 E 100 150 200 100 150 200 Missing ET [GeV] Missing ET [GeV] 26 p17 gx+jetS p20 _u+jets 2 b—tags 15_ 2 b-tags 15— 3 jets 3 jets Event Yleld [counts/1OGeV] 8 i 100 150 200 Misslng ET [GeV] Event Yleld [counts/1OGeV] 8 i 50 100 150 200 Missing ET [GeV] Figure BS: The missing transverse energy for channels with exactly three jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 225 E E p20 e+jets 8 ‘3 30- ‘ fi‘fig E 20 E )9 S C C 3 3 20s 2. 8.. ‘O ”O _ 1o _ ¥ é’ 1o- E E 2 2 III In 50 100 150 200 100 150 200 Missing ET [GeV] Misslng ET [GeV] E p17 e+jets %' 15 p20 e+jets <5 2 b-tags (5 2 b-tags 2 10+ 4 jets 3 4 jets E E 10" C C 3 3 9.. .2. '0 s '0 E 5 E 5- >- >- 5 5 > > m m 50 100 150 200 100 150 200 Missing ET [GeV] Missing ET [GeV] % p1711+jets 5' p2011+jets d) g 30 1 b-tag <5 1 b-tag .- 4 jets 53 4 jets :«2 2 § 20— 5 o o .2. .2. 2 E 0 _ 0 >1 1° ; E E > 2 I.“ u: 50 100 150 200 100 150 200 Missing ET [GeV] Missing ET [GeV] %‘ 15 p17 _u+jets %' .8. ”:21: 2 ‘ 2 5 ‘0’ 5 o o 2. 2. ‘2 2 2 5* 2 >- >- E L ‘E a m E u” 50 50 100 150 200 100 150 200 Missing ET [GeV] Missing ET [GeV] Figure 8.6: The missing transverse energy for channels with exactly four jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 226 %' : p17 e+jets %' 150 p20 e+jets g - 1 b-tag (5 1 b-tag .— - + 2 jets 9 2 jets 2 100— E I: ' C 3 - a .2. ‘ .2. '0 H u E 5°- 5 >- >- ‘E ‘E d) 0 > > ill ILI 00 150 200 100 _150 200 pT(jet1) [GeV] p T(jet1) [GeV] p17 e+jets 2 b-tags 2 jets p20 e+jets 2 b-tags 2 jets Event Yield [counts/1OGeV] Event Yleld [counts/1 OGeV] 50 00 150 200 100 _150 200 p,(iet1) [GeV] 910°“) [GeV] %' p17 gu+jets E p20 jn+jets g 1 b-tag g I 1 b-tag v- 2 ' t 1- 150” ' E 19 3 E : 2 jets I: : ~ : 3 - g L0,. 100: E E 3 2 2 _ >- >- 50: E E - o o > > m tu 50 100 _150 200 50 100 .150 200 910m) [GeV] pToefi) [GeV] p20 ti+jetS 2 b-tags 2 jets Event Yield [counts/1OGeV] Event Yleld [counts/10GeV] 50 50 100 .150 200 100 .150 200 Me“) [GeV] Me“) [GeV] Figure B7: The transverse energy of the leading jet for channels with exactly two jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1—btag and 2—btag. 227 p17 e+jets 1 b-tag + 3 jets Event Yleld [counts/106W] Event Yleld [counts/1OGeV] 100 .150 200 so we“) [GeV] Event Yleld [counts/1OGeV] Event Yleld [counts/1OGeV] 50 00 150 men) [GeV] Event Yleld [counts/106W] Event Yleld [counts/1OGeV] - %' _ E p20 tt+jets ‘3 8 22:3: 5 I 5 E E a - a o _ o 2. .2. u 5” u E ’ E >- r >- ‘E t E o _ o > > In I.“ 50 1 0 50 o _150 200 00 150 200 we“) [GeV] 910°") [GeV] Figure B8: The transverse energy of the leading jet for channels with exactly three jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l—btag and 2—lttag. 228 Event Yleld [counts/1 OGeV] Event Yleld [counts/106W] 50 Event Yleld [counts/1 OGeV] Event Yleld [counts/106W] 10 Event Yleld [counts/1 OGeV] Event Yleld [counts/1 OGeV] 00 .150 200 men) [GeV] % » g ‘93 1o! 3 E - E C — C 3 3 O ' O .2. - .9. 2 5* 'g 2 - 2 >- >- ‘E E 0 - O I7: 5 ‘l 50 100 _150 200 so 100 150 200 men) [GeV] wen) [GeV] Figure B9: The transverse energy of the leading jet for channels with exactly four jets in the final state. Run 113 (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-l)tag and 2—btag. 229 % p17 e+jets E p20 e+jets <5 1 b-tag 0 1 b—tag o o 2 ‘ t v- ' E 1e 3 E 2 jets : c 8 8 .2. .2. u '0 E E >- >- E 2.5. E , fi 1Q 50 190 150 pToet2) [GeV] pTOetZ) [GeV] % p17 e+jets E p20 e+jets <5 2 b-tags 0 2 b-tacs o c E 19 S E + 21ets : c 8 3 .2. 2. 1: 1: E E > >- ‘E E m a: u>.t . E: . 100 150 1Q0 150 PTtlet2) [GeV] pTUet2) [GeV] 5 t p17 u+jets "3" 300~ p20 ..+jets‘; * I g 1 2b-Latgs; (é) . 1 b-tagl to ‘ 33 - E c 200“ 3 3 _ o o 8. .9. '2 E ” 2 2 100— >- >. - E E o c > > In In me 150 1Q 150 pTuet2) [GeV] pTuetZ) [GeV] (E5; 30‘ p127 g+jets g pZSE-zjets j -tags - ags g — 2 jets g 2 jets g 20f g 0 _ O .2. . 2. 2 - 2 a 1°: ,2. E _ E 0 0 IE ’ . u’; . q 100 150 100 150 P (jet2) [GeV] P (jet2) [GeV] T T Figure B.10: The transverse energy of the second leading jet for channels with exactly two jets in the final state. Run Ila (left) and Run 111) (right). Electron (top four) muon (bottom four). Alternating rows l—btag and 2-l)tag. 230 %' 66 p17 e+jets %' p20 e+jets (5 1 b-tag (5 1 b-tag % 3 jets % 3 jets E E E E 1: 'o E E >- >- E; E a. , E 1Q0 150 1Q0 150 pT(jet2) [GeV] pT(1et2) [GeV] p17 e+jets p20 e+jets 2 b-tags 2 b-tags 3 jets 3 jets Event Yleld [counts/1 OGeV] Event Yleld [counts/10GeV] 50 190 150 up 150 pT(jet2) [GeV] pTuet2) [GeV] p17 h+jets p20 jt+jets 100.” 1 b-tag 1 b-tag 3 jets 3 jets 50— Event Yleld [counts/106w] Event Yleld [counts/1OGeV] 50 190 150 Mm) [GeV] p20 h+jets 2 b-tags 3 jets 1qo 150 pTuetz) [GeV] p17 gu+jets 2 b-tags 3 jets Event Yleld [counts/1OGeV] Event Yleld [counts/1 OGeV] 50 50 1qo 150 1qo 150 p,0et2) [GeV] pToetZ) [GeV] Figure B.11: The transverse energy of the second leading jct for channels with exactly three jets in the final state. Run IIa (left) and Rim Ill) (right). Electron (top fom') muon (bottom four). Alternating rows l—btag and 2—btag. 231 p20 e+jets p17 e+jets 30:— 1 b-tag _ 4 jets Event Yleld [countd1 OGeV] 3. Event Yleld [counts/1 OGeV] 1Q0 150 10_0 150 pTOeIZ) [GeV] pTuetZ) [GeV] %' p17 e+jets %' p20 e+jets g 2 b-tags (of) 2 b-tags E 4 jets .5:- 4 jets c c :1 = o o .2. .2. E E 2 2 >- >- E E o o a u>.| . 100 150 100 150 pTUet2) [GeV] PT(iet2) [GeV] p17 e+jets p20 jt+jets 1 b-tag 4 jets 1 b-tag 4 jets Event Yleld [counts/1OGeV] Event Yleld [counts/1 OGeV] 190 150 190 150 pT(jet2) [GeV] p,(1et2) [GeV] p20 e+jets 2 b-tags 4 jets Event Yleld [counts/1OGeV] Event Yleld [counts/1 OGeV] ‘b 50 50 1Q0 150 men) [GeV] mp 150 pTuetZ) [GeV] Figure B.12: The transverse energy of the second leading jet for channels with exactly four jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2—btag. 232 Event Yleld [counts/25GeV] 100 200 300 400 no |-|T(jets,l,v) [GeV] p17 e+jets p20 e+jetsI 2 b-tags 2 b-tags 2 jets 2 jets t 100 200 300 400 500 HT(ietalw) [GeV] Event Yleld [counts/256W] %' p17 e+jets E 200‘ p20 e+jets (D 1 b-tag <5 I 1 b-tag g 2 jets § 150' 2 jets E ‘E 3 3 3 i 2. g 100_ E E i 2 2 — >- >- 50_ E E - o a: E u’: ' 100 200 300 400 500 100 200 300 400 500 l-lr(jets,l,v) [GeV] H,(jets,|,v) [GeV] 5 p17 e+jets % 30: p20 e+jets g 2 b-tags g — 2 b—tags % 2 jets % j 2 jets E E 20- + 3 3 _ o o - .2. 2. - 2 E ’ 2 2 10“ >- >. > E E e e I?! E 100 200 300 400 500 300 400 500 HT(jets,l,v) [GeV] H,(jets,l,v) [GeV] % p17 jt+jeIS % 200; p20 jt+jets (5 1 b-tag 3 1 b-tag g + 2 jets g 1503 2 jets E E T 3 3 o o 2. 2. E 2 2 2 >- >- E E to e > > u.| u.| 100 200 300 400 500 H,(jets,l,v) [GeV] 100 200 300 400 500 l-l,(jets,l,v) [GeV] Figure B.13: The scalar transverse energy sumfor channels with exactly two jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 233 p17 e+jets p20 e+jets 1 b-tag ' 1 b-tag 3 jets 40‘ 3 jets Event Yleld [counts/256W] Event Yleld [counts/256W] 100 200 300 400 500 HruetsJ .v) [6er H,(jets,l,v) [GeV] 100 200 300 400 E p17 e+jets %' 10_ p20 e+jets g 2 b-tags g , 2 b-tags % 3 jets is 3 jets E E 8 8 .2. 2. u '3 E E >- >- E E e o E E 100 200 300 400 500 100 200 300 400 500 HT(jets,l,v) [GeV] HT(jets,I,v) [GeV] 5 60- p17 _t.+jets %' L p20 e+jets <5 ' 1 b-tag 0 5°_ 1 b-tag tn . In . g 3 jets s; 3 jets S S 40— O o _ 2. 2. - E 2 - e t» _ E ; 2°- E E o tn > > In W 0 100 200 300 400 500100 200 300 400 H,(jets,l,v) [GeV] I-l,(jets, I,v) [GeV] . p17 e+jets 15. p20 e+jets - 2 b-tags : 2 b-tags 10 3 jets . 3 jets Event Yleld [counts/256eV] Event Yleld [counts/25GeV] 100 200 300 400 500 HT(jets,l,v) [GeV] HT(jets,I,v) [GeV] 100 200 300 400 506? Figure B.14: The scalar transverse energy sum for channels with exactly three jets in the final state. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l—btag and 2-btag. 234 1.4 %' p17 e+jets %' 20; p20 e+jets 3 1 b-tag g : 1 b-tag g 4 jets g 4 jets : c a a o o .2. .2. E 2 2 2 >- >- E E o o E a 100 200 300 400 500 300 400 500 H,(jets,|,v) [GeV] H,(jets,l,v) [GeV] 16 . -—- , a I p17 e+jets 3 10* p20 e+jets (5 » 2 b-tags (5 _ 2 b-tags In 3— . In . % ~ 4 jets % 4 jets E E = 3 33 ea 2 E 2 2 >- >- E E o o .7. > s 100 200 300 400 500 300 400 500 H1(jets,l,v) [GeV] HT(jets,l,v) [GeV] %' 20; p17 jl+jets %. 30? p20 jl+jets <5 3 1 b-tag g » 1 b-tag g : 4 jets g 4 jets - 15_ _ _+ c _ c a _ :s o , o .2. 1o_ .9. 2 - 2 2 2 >- >- E E 0 c» > - > _ |.I.l |.I.l .242. 100 200 300 400 500 100 200 300 400 500 H1(jets,l,v) [GeV] H,(jets,l,v) [GeV] 5 , p17 j1+jets % t p20 _u+jets g - 2 b-tags g _ 2 b-tags g 10‘ 4 jets % 10 4 jets E E * 3 a o o .2. .9. E E 2 2 >- >- E E c» a) > > m u: ‘100 200 300 400 500 HT(jets,|,v) [GeV] H,(jets,l,v) [GeV] 100 200 300 400 500 Figure B.15: The scalar transverse energy sum for channels with exactly four jets in the final state. Run 113. (left) and le IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 235 p17 e+jets 1 b-tag 2 jets _n O ‘1’ Yleld [Events/zoGeV] S ‘l) 100 200 300 400 500 M(W,jet1)(leading jet top mass) [GeV] %' 15— p17e+jets (g 2b-tags % 2jets 3:; 10 > E 1: E )- ‘l 100 200300 400 500 M(W,jet1)(leading jet top mass) [GeV] %' p17u+jets (85 150 1b—tag 2' t E je s C 2 100 EL‘ 2 a: ; 50 100 200 300 400 500 M(W,jet1)(leadlng jet top mass) [GeV] __ p17 jt+jets 20 2 b-tags ' 2 jets Yleld [Events/206W] ‘lt 100 200 300 400 500 M(W,jet1)(leadlng jet top mass) [GeV] p20 e+jets 1 b-tag + 2 jets 8 6‘. o o Yleld [Events/20GeV] 01 O 100 200 300 400 500 M(W,jet1 )(leadlng jet top mass) [GeV] E 25_ p20 e+jets <5 _ 2 b-tags 3% 20_ 2jets 5 15~ > . EL‘ '2 10— 2 - >' 5 (l) 100 200 500 M(W,jet1)(leadlng jet top mass) [GeV] % p20u+jet—l 0 § 150 § E. 100 E o ; 50 100 200 300 400 500 M(W,jet1ledlng jet top mass) [GeV] p20 jt+jetS 2 b-tags 2 jets Yleld [Events/ZOGeV] 100 200 300 400 500 M(W,jet1 )(leading jet top mass) [GeV] Figure B.16: The top quark mass for channels with exactly two jets in the final state. Run 1121. (left) and Run IIb (right). Alternating rows 1—btag and 2-btag. Electron (top four) muon (bottom four). 236 %' p17 e+jets %' 60 p20 e+jets (5 1 b—tag (5 1 b-tag g 40 3 jets § 3 jets 8 5 > > LI 3 13 13 :6 2° 15 >- >- 100200 300100 00500 M(W,jet1)(leadlng jet top mass) [GeV] M(W,jet1)(|eadlng jet top mass) [GeV] %' p17 e+jets a“ p20 e+jets (5 15_ 2 b- -tags (5 2 b— —tags § 3 jets § 3 jets 8 5 > > E. L”. '0 u E E >- >- Q) 100 200 300 400 500 100 200 300 400 500 M(W,jet1)(leadlng jet top mass) [GeV] M(W,jet1)(leadlng jet top mass) [GeV] %‘ 60_ p17 jt+jets E p20 u+jets 0 - 1 b-tag (5 g 3 jets g 5 5 > > a a E E o 2 ; >- ‘1 010200 300 100 200 00400500 M(W,jet1)(leadlng jet top mass) [G-eV]0 M(W,jet1)(leadlng jet top mass) [GeV] p17 ~111-jets 2" p2051+jets 2 b-tags ‘ 2 b-tags 3 jets 15— 3 jets Yleld [Events/206W] Yleld [Events/ZOGeV] 100 200 300 400 500 (1)100 200 300 400 500 M(W,jet1)(leadlng jet top mass) [GeV] M(W,jet1)(leadlng jet top mass) [GeV] Figure B.17: The top quark mass for channels with exactly three jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l—btag and 2-btag. 237 %' p17 e+jets %' p20 e+jets L89 1 b—tag (85 40* 1 b-tag 4 . _ . B 20_ jets B 30— 4 jets "' E s 0 r E 11>: :- 3- 20* E 10f— § . >' >- 10.. 100 200 300 400 500 ‘1) Q) 100 200 300 400 500 M(W,.jet1)(leadlng jet top mass) [GeV] M(W,jet1)(leadlng jet top mass) [GeV] p17 e+jets 15_ p20 e+jets 2 b- -tags 2 b-tags 4 jets 4 l9t3 —l 9 U1 Yleld [Events/206W] 3 U! Yleld [Events/206W] 100 200 300 400500 Q) 100200300400 M(W,jet1)(|eadlng jet top mass) [GeV] M(W,jet1)(leadlng jet top mass) [GeV] %' 40 p17 u+jets %‘ p20 jn+jets O 1 b-tag 0 1 b-tag g 4 jets 5% 30— 4 jets 30 E '5: L": 20 i 20— 2 2 o 0) >_- 1 ; 10 ’ 00 200 300 400 500 (0100 200 300 400 500 M(W,jet1)(leading jet top mass) [GeV] M(W,jet1)(leadlng jet top mass) [GeV] an (U p17 jt+jet5 20_ p20 n+jets 2 b-tags > 2 b-tags 4 jets 4 jets Yleld [Events/206W] a l 3 ' j Yleld [Events/2OGeV] a | ‘ 0| q) 100 200300400500 ‘11 100 200 300 400 500 M(W,jet1)(leadlng jet top mass) [GeV] M(W,jet1 )(Ieadlng jet top mass) [GeV] Figure B.18: The top quark mass for channels with exactly four jets in the final state. Run 113 (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l—btag and 2-btag. 238 p17 e+jets 80.— p20 e+jets 1 b-tag : 1 b-tag 2 jets 50 + 2 jets Event Yleld [counts/0.4] Event Yleld [counts/0.4] 20 2 ll 2 l O x n O x n 5:. p17 e+jets 5.. 20 p20 e+jets 3 15' 2 b—tags S 2 b-tags g . 2 jets g 15 2 jets o o .9. 2. - E g 10 >- F- E ‘E o o > > m In 2 l 2 4 an an 53' 80; p17 u+jets 5: 80* p20 u+jets S : 1 b-tag % l 1 b-tag E - 2 'ets E - 2 ‘ets g 60_ ' g 60_— ’ .2. - 2, - U ‘ u _ 3; 40_ § 40— >. _ > Z > 20L > 20“ III III _ I 2 2 l 4 O x n G x 1] '5: p17 u+jets "7.. 25_ p20 jl+jetS S 15’ 2 b-tags % 20 2 b-tags g 2 jets g F 2 jets o o .2. 1o .2. 2 '2 2 2 >- >- ‘E ‘E o 0 > > In in .2 “7| 4 an 0x1] Figure B.19: The pseudorapidity of the light quark jet times lepton charge for channels with exactly two jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2—btag. 239 "72' p17 e+jets g 40— p20 e+jets g 1 b-tag a - 1 b-tag g 30 3 jets g 30* 3 jets o o .2. .9. - 2 20 2 2 2 >- >- 5 1o 5 > > In In 2 4 2 I 0 x n O x n p17 e+jets p20 e+jets 15_ 2 b-tags 15‘ 2 b-tags 3 jets 3 jets Event Yleld [counts/0.4] 3 Event Yleld [counts/0.4] 2 ll 2 I O x n 0 x n G: 66, p17 n+jets "T: 50 p20 jl+jetS % 1 b-tag 3 40s 1 b-tag g 3 jets g _ 3 jets o o .9. .2. 30 u 1: - :1 7: >- ; 20 7.5. 75‘ ' a. a 1°» 2 l -2 0 2 4 O x n O x n 5" p17 jl+jets g F p20 j1+jets S. 15‘ 2 b-tags E 15f 2 b-t_ags g 3 jets g _ 3 jets 8 8 I; 10* I; 10 E E j >- >- E 5‘ E 5‘ m ll] -2 2 4 2 4 Q x 1] 0 x I] Figure B20: The pseudorapidity of the light quark jet times lepton charge for channels with exactly three jets in the final state. Run Ila (left) and Run 111) (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2-btag. 240 "72‘ p17 e+jets ? 30— p20 e+jets g 1 b-tag g 1 b—Itag fig: 4 jets g 4 jets .2. 2:, 20 15 '0 E E >- >- ‘E E 10 t» o > > In ll] 2 4 2 4 an Oxn "72' p17 e+jets 3 15 p20 e+jets 3 2 b-tags 3 L 2 b-tags : 10 4 jets 1: L 4 jets : 3 o o 8 3 g '0 2 E >- >- e l e o . d) > » > In tn 2 t 2 I Q X T] Q x 7] 5: p17 u+jets "7.. p20 jt+jets 3 1 b-tag i 1 b-tag c 4 jets : 4 jets g 20 g 20 8 2 'o u E E 3; 1o 3: 10 t: c t» o > > 11.1 In 2 4 2 4 an an 3? p17 tt+jets '3.‘ p20 u+jets s 15‘ 2 b-tags % ”T 2 b-tags E _ 4 jets E 4 jets : :1 o o 3 1o .2. 2 2 2 2 >- >- 5 5 s > > 1.1: u: -2 2 4 -2 2 4 an an Figure B21: The pseudorapidity of the light quark jet times lepton charge. for channels with exactly four jets in the final state. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1-btag and 2—btag. 241 Appendix C Systematic Uncertainty Tables Tables C.1—C.24 show the flat systematic uncertainties on the signal and background samples for the all of the 24 channels in the analysis. All of the shape changing systematics are treated separately in the calculation and are presented in Appendix D. Note that due to the normalization to data before b tagging, the Wbfi, W05, and W j j tagged yield estimates are not affected by any of the systematic uncertainties that affect the overall yield. The exception to this is b tagging, which is applied after normalization. There is still an effect on the shapes of distributions from the uncertainty components that depend on event kinematics. The row “WQCD” in each Table includes the uncertainty on the W+ jets normal- ization and on the multijets normalization. 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S a: O.v O4 ON ONH 5v mN “v4 OA Ob ON m4 3: HO 3 0.0m| 8.32:8 Ogv OA ONH Ev mN v4 OA Oh Oh HO O6 O4 O.w O6 mN v4 OA Ob wd fiO 288% 3N 0.0N 0.0N O6 O6 O4 O4 I ON O.w O.w O6 O6 ON ON a; «A OA OA Ob O.m. Wm Oh HO HO 8N 3N w; “OI at: w; w; O.m| Oh Nam: N22 033 3x: @8th $350th 35:30 £022 $750k wwwwfibéwfim O6 O4 ON 0.0 NO ON vA O4 Oh 3 5.2 S 3.: O6 OA ON 0.0 NO mN v; O4 O.m. ma NNH HO 2.3 mvz N mam 033 “Em 3 5cm .8.“ eon A: awn .mg 8.3 grime .wwa awn n: c895 xmfig dim .332 .255 muowwtrfi mam dab maEQcfim €me biofifisq 263 Appendix D JES, TRF, and RWT Systematic Uncertainties Table D.1 shows the normalization part of the uncertainty from the jet energy scale and the taggability plus tag-rate functions, for the signal acceptances and for the combined backgrounds. These values are not included in the tables in Appendix C because they are not treated separately as flat systematics, but are included at the same time as the shape-changing part of the uncertainty is included. The J ES normal- ization uncertainties are included on the t5, Z +jets, and diboson backgrounds as well as the signal uncertainties, and the shape part is in addition applied to the W+jets, tt_, Z +jets, and diboson backgrounds. The TRF normalization and shape uncertain- ties are applied to all MC samples. Figure 7.6 shows the size of the reweighting uncertainties (error bars 011 points). The JES uncertainties as used in the analysis are shown in Figs. D.1- D.3 for the signal boosted decision tree discriminant output. The signal TRF uncertainties are shown in Figs. D.1~D.3, and the ALPGEN reweighting function uncertainties in for the backgrounds is shown in Figs. D7 and DE). Similar distributions for J ES and TRF background uncertainties can be found in Reference [90]. 267 oamd oamd ARNOH AXE: mafia mac; 053w oafiw 3% a mafia “NovOH KYOH $0.3 “New; “Nam; 05: cam: 3% m mwmuN $2: find 05?: RON can? cams 0am? oawN case 05: ca: ca; o\oo.v 0&3: oawh 0564.9 3% m 3% v a: cam mama“. ombb “REM 05m; AWAUNO o\om.o Rood came. 3%. m 33; find 05o.» “NRA. 056v AKOO capo “KEN mafia much N oaod wand “Rad “ROS sac; cam; oaww cam: 3% v mama 05:: flNVNOH 05min: 05mg 05v; “New; ANLN 3% m mmfiN .3585 33328 :38 .8“ 328:8 39mg 93 sand came Ram 053%” 05v...“ fish oxymé 0&3” fizfiewwg 2: 98 2.8m $.55 8% m5 8on $5383er 8:388 98 Emma 23 so mosfiefimog dogmazwahoz HQ .3an A3 casewvfimm A3 punchy—3m 3 est: A3 33% 935055 euflmuwflfi tam huzmn—wwwmfl “RNA: AKLN AXES cavN can? $3 $3: same name $3 $3 fixed o\ofim 055.: $3 can: 3% m 3% a QHH 35m mmmucmduhmuch# GOSSNSOHCHOZ Emu—L UGO mam. de oafio 05mg.“ 05mg“. 3% m 33; cameo cane can; «New; 3% m A3 pascamxowm Amv cascaqumm 3 set: 3 flat: 2.3m Quwcfl awn. 268 1.6 : —!b!qb nominal _ 7 T 1 —!b!qb nominal 1.4 ;— tbtqb JES plus 1.4 l— tbtqb JES plus — tbtqb JES minus — !b!qb JES minus 12: L25 1 :— W—E 1 :‘ as— on: 0.6} p17 cc EqueTag EquoJe! 0.6 }~ p20 cc EqueTag 15quon 0.4L ..1....1 llllllllllllllllllllllllllllllll 0.4» ..L....1....1. ......11 .1. 61.8.1.1. 0 0.2 0 0.2 D?! Result, maxi! binned DT_ Result, maxi! binned 1'6; —!b!qb nominal ’ _- "6 _ tbtqb nominal 1.4 ;— tbtqb JES plus 1.4 — tbtqb JES plus — tbtqb JES minus — tbtqb JES minus 1.2: ‘L W W W ~ W 0.3’ 0.6 p17 CC EquoTag EquoJe! E p20 CC EquoTag EquoJe! 0.40 .1....oli.L.JLLL.1.. 1. o .1...61.2...l ........ l ........ 1....01....l....‘l ' Di; Result, maxi! ”binned ' Dsi'4 _Result,l maxi! binned 1'6: — tbtqb nominal j 1'6 ; — !b!qb nominal E —!b!qb JES minus :_ tbtqb JES minus 12; 12} 0.8 ‘ 0.8:; M 0.6 p17 MU EqueTag EquoJe! 0.6; p20 MU EqueTag EquoJe! 1 0'4, ..1... .1...-.1 .1. 01.6 .1. é11144.1... 0'4“ ..1....1... .1 .1L...1.... 0 0 0.2 0 8 Dsi’f Result, maxi! binned @Dsi‘f Result, maxi! binned 1'6: —tb!qb nominal “fl 1'6 — tbtqb nominal 1A;_!btqb JES plus 1.4 — tbtqb JES plus E _ tbtqb JES minus _ tbtqb JES minus 1.2 f 1 .2 1:— W 1 W on“ as 0.5 p17 MU EquoTag EquoJe! 0.6 92° W EqTWTaG Equ-‘e‘ 0.4, .1....1 ................................ 0'4 .1....l.s.. .LL ....... l ............ 0 0.2 O 0.2 I D9; Resulii'6 maxi! binned Dsii‘ _Result, maxi! binned Figure D.1: Systematic shift when varying the JES signal distributions by :l:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 209 1'6: — !b!qb nominal fl — _ 1'6 En— !b!qb nominal 1.4 ;— !b!qb JES plus 1.4 “_— !b!qb JES plus —!b!qb JES minus — !b!qb JES minus 1 .2 L— 1'2 T ”W 13% 0.8} 0.8% 0.6} p17 cc EqueTag Eq'l'ilreeJe! 0.6} p20 CC EqueTag EthreeJe! . L. L L. 0.4 ..1....1....1....1....1....1...Au..1....1.... 0.4 LLLL41111L4111111WWW 0.2 .4 0.6 o s o 0.2 .4 . o s | D¥_Resu|!, maxi! binned ‘l'_Resuii), inaxi! binned 1'6_ —!bt_qb nominal i 13t —!b!qb nominal 1.4 ;— !b!qb JES plus 1.4 L— !b!qb JES plus —!b!qb JES minus —!b!qb JES minus 1.2 T 1.2: t i 1 C 1 5 W 0.8“ 0.3} 0.6 p17 CC EquoTag EthreeJe! 0.6 p20 CC Eq‘l'onag EqTilreeJe! 0.40 .mdmhb.2 ¢EWE§W1 0.40 ..L...61..2...1..”$1.4“.1....016...J...bl.8...1....‘ D _Result, maxi! binned D _Result, maxi! binned 1'6 —!b!qb nominal __ 1'6 —!b!qb nominal _ l 1.4 —-!b!qb JES plus 1.4 — !b!qb JES plus : — !b!qb JES minus ’ — !b!qb JES minus 1.2: 1.2 0.81} 0.8 0.6;— p17 MU EqueTag EqTi'lreeJe! 0.6 p20 uu EqueTag EthreeJe! 0.46 .1...61..2...1....¥1j.4.1....1l.6.._._L 0'8 1.4...._ 0.4 0.2 .¥.|.4....|...0.1.6.. 08 D _Resuli), maxi! b n D _Resui!. maxi! binned "6 —!b!qb nominal “i "6: —!b!qb nominal 1.4 _ !b!qb JES plus 1.4 ;_ !b!qb JES plus — !b!qb JES minus — !b!qb JES minus 1.2 1.2 j 1 W 1 L W 0.8 g 0.8 :— o.o p17 MU Equo‘i'ag EthreeJe! 0.6} P2° M” EqW°TaQ 50mm“ 0.4 .._L._..4.L.._._._L MLMALLMLMQLAJ 0.4: .14 . .4 lawmwmufi o 0.2 0.4 0.6 o e o 0.2 .4 0.6 o 8 | DT_Result, maxi! binned Di'_ResuI!, maxi! binned Figure D.2: Systematic shift when varying the JES signal distributions by :lzlo for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l—btag and 2-btag. 270 — !b!qb JES plus _4: — !b!qb JES plus — !b!qb JES minus —!b!qb JES minus EM 1-2: W ‘I 7 J 1 ; anJ—H'FL 03,7 W 0.8: W as 15E — !b!qb nominal _— E 'u: —-!btqb nominal 0.6 p17 CC EqueTag EqFourJe! 0.6 ;- p20 cc EqueTag EqFourJe! 9.4; 1 0‘2 .l oI4 l 016. l 0I3.l 0'4‘; .1....ol.2..1. “01:4...11...ol.6...l ...ol.8...l.... ' DT'_Resul!,' maxi! binned ' DT_Resuit,'maxit binned 1-5 . 1.6 efi , , : — !b!qb nominal ; — tbtqb nominal 1_4;— !b!qb JES plus 1_4_—!btqb JES plus —tbtqb JES minus —!b!qb JES minus 1w... .. ”2...... W 0.8;J WW WU h earlwng -a .A C 0.6} p17 CC EquoTag EqFourJe! 0.61 p20 cc EquoTag EqFourJe! 0.4‘; i.l...(.)[.2...i1. loiaALJlAlLbjélAlijl 08 14.441 ”'4‘; .l1. 6|21l .......... ' DT_Result,' maxi! binned ' Dsi'f Result, maxi! binned 1'6 :— !b!qb nominal 1'6; — !b!qb nominal 1.4 :— !b!qb JES plus 1_4;— tbtqb JES plus i —tb!qb JE us » —!b!qb JES minus 1.21 1.25 ‘i WWI—l ‘; 0.8 "- w m “~33 0.6} p17 MU EqueTag EqFourJe! 0.6} p20 MU EqueTag EqFourJe! 0.4‘; .1.. 01.2 1. .014..| 016 I oléwa 0.46 .1 612 1 014 1 0'6 1 018..1. ' D1"_Result,’ maxi! binned ' DT'_Resuli,'maxil binned 1.6 —!b!qb nominal _ !b!qb JES minus 1.4 r—tbtqb JES plus 0.87 0.6 p17 MU EquoTag EqFourJe! 0.6 g p20 MU EquoTag EqFourJe! o 4 Joiwwm. 1M.._._1,.J ._._L.._L._L._._L. L“. 0.4 LLL. Luisa; 1 1 1 1 1 1 l . 0.2 .4 0.6 0.8 0 ° 2 $3.5m, maxlt binned Dsi'fResulg'glaxi! girsined Figure D.3: Systematic shift when varying the J ES signal distributions by :lzla for the BDT discriminant outputs of events with exactly two jets. Run Ila (left) and Run IIb (right). Electron (top four) 11111011 (bottom four). Alternating rows l-btag and 2—l)tag. 271 1.5 m—tbtqb nominal " ff" 7 ; -—!btqb nominal — !btqb TRF plus " ——!btqb TRF plus 125 — !btqb TRF minus 12 _~— !btqb TRF minus 1 ...—...: __ ....” ...—... ‘— — *— ‘ fi——- -..__— ——_—_1 0.75 _ 0.8 p17 CC EqueTag EquoJe! 3_ p20 CC EqueTag EquoJe! 050' 02 4-.. ..16....|...o.18... 0.6; ..1....01.2...1....1.4...1....01.6...1....o1.8...1....‘ ' Dimosulg' maxi! binned ' Di“_nosult,' maxi! binned 1"; —!btqb nominal “ "4E —tb!qb nominal r— !btqb TRF plus r _ !b!qb TRF plus 12 E—— !b!qb TRF minus 12 f— !btqb TRF minus C I 0.8:: 0.8;— :_ p17 CC EquoTag EquoJet :_ p20 CC EquoTag EquoJet : E 0.6* .L....1.... ...................... 0.6' ..1...-.1....1 0 0.2 0 0.2 D51; I‘Resuii)6 maxi! binned Diiij Resuiii'é” maxi! binned 1'45 — !b!qb nominal 1'4g — !btqb nominal “:‘-— !btqb TRF plus r— !b!qb TRF plus 1,2;_ !b!qb TRF minus 1.2;... !btqb TRF minus 5.... _ _ .....— é.____.__._ .... 1 E 1 . :mf ‘ ‘— .3. fl____ - a 0.83 0.8“ p17 MU EqueTag EquoJe! p20 MU EqueTag EquoJet 0.6; ..1....1....1....1.-..1....1....1....1....1....i 0.6 ..1.1-..1.63...1.b1.6.-..1-..1. o 0.2 .4 .6 o 8 i o 0.2 Dii'_Resuli), maxi! binned DT _Resuit, maxi! binned 1'4E —tbtqb nominal 1 1'4: —tb!qb nominal r— !btqb TRF plus E -—!btqb TRF plus 1.2 E— !btqb TRF minus 1,2':-— !btqb TRF minus 5 E i 1 F 03 - 0.8:- p17 MU EquoTag EquoJet g p20 MU EquoTag EquoJe! 0.60 .1....0112...1.J. in...- 0.60- .1....01é11.1.-LLL.l.o.6l....1.01.-.-1-L.. Dig” Result, maxlt binned Di: Result, maxi! binned Figure D.4: Systematic shift when varying the TRF signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run Ila (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l—btag and 2-btag. 272 5L ' E —!btqb nominal E —-tbtqb nominal E'— !btqb TRF plus ” —!b!qb TRF plus 12;— !btqb TRF minus 1.2 :—_ !b!qb TRF minus 'I r 1 r : MW ; 0.8 E— 0.8} ;_ p17 cc EqueTag EqTilreeJe! 3 p20 cc EqueTag EthreeJe! 0.6,:— ..1....1... 1. 1.. l ..1 .1.u.1....1.... 0.6E .1..-.1 ................................ 0 0.2 .4 0.6 0 8 0 0.2 D‘i'_Result, maxit binned Di; Result, maxi! binned 1" —!btqb nominal 1"; _ !b!qb nominal E — !btqb TRF plus E — !b!qb TRF plus 1_2§—— —!b!qb TRF minus 1.2 g— tbtqb TRF minus 0.3:— o.sE- :_ p17 CC EquoTag EthreeJet g_ p20 CC EquoTag EqTilreeJe! 0.65. ..l....1....1....l....1. ...1 “Lolé ... 0.6: ..1....l....1....l....l....i....1-.-.l....1#...' 0 0.2 .4 0 0.2 .4 .6 0 8 Dsi'_Resui!,l"6l maxi! binned Dsi'_Resuii,, maxit binned "4E —tbtqb nominal “F ”g —tbtqb nominal ;— !btqb TRF plus ?— !b!qb TRF plus 12 :—— !btqb TRF minus 1.2 T.—— tbtqb TRF minus ; _.,.._..__——-— E i ‘ _; _j; 1 E“ _ #_ 0.8 ' 0.8 1 p17 MU EqueTag EthreeJet p20 MU EqueTag EthreeJet 0.6‘ 1..-.1....1. .01...-1. .-.Lu. .1U-61.8.-.1. .... 0'6 .1....1... .1--..1-...ol ..1-.. 0 0.2 0 0.2 DT_ 4Result, maxi! binned Di: Result, maxi! binned 1.4 — — 1 .‘ E — !btqb nominal — !btqb nominal §_ !b!qb TRF plus —. !b!qb TRF plus 1.2 -—— tbtqb TRF minus 1, if—tbtqb TRF minus 1% 1 _ 0.8? 0.8 _ :_ p17 MU EquoTag EqTilreeJe! p20 MU EquoTag EthreeJet 0.6E .1....J.. . . .1.L.41.8...L.-... 0.6 .1....1.L..1....1....14...l....1....1....lL... 0 0.2 O 0.2 0.4 0.6 0 8 1595 Result, maxi! binned DT_Resuit, maxi! binned Figure D.5: Systematic shift when varying the TRF signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Rim IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 273 1.4 *“mw' “— E — tbtqb nominal E — tbtqb nominal 5 — !b!qb TRF plus ?— tbtqb TRF plus 1.2 g— tbtqb TRF minus 1.2 ;—— !b!qb TRF minus 1;» W 1?: 0.8E- 0.8»: 5 p17 CC EqueTag EqFourJe! :_ p20 CC EqueTag EqFourJe! 0.6h ..1....1.....1.1..01.6L..JJ-.LL§.LLL.... 0.6; LLL_LJ_L1_LL_L_LJ_L.A_L 0 0.2 0 0.2 .4 . 111'? Result, maxi! binned Di'_Resuli), tinaxi! gigned "4E —!btqb nominal '7 "4 —!b!qb nominal E — !btqb TRF plus —!btqb TRF plus 1-2E"_ tbtqb TRF minus 12 — !btqb TRF minus 12‘ 1 ~ 1. 0.3: 0.8 s i— p17 CC EquoTag EqFourJe! p20 CC EquoTag EqFourJe! 0.66 ..1....012....I....|.a_.._.|....o|6....|....oL§J_‘_._L “-1 0.60 ..1....0121 ................... 1 ............ . ' Di_Result, maxit binned ' Di; Resuli’,"5 maxi! binned ‘°‘ _ !b!qb nominal 1"; —!b!qb nominal — !btqb TRF plus ;— !b!qb TRF plus 1_2 — !b!qb TRF minus Lari—!b!qb TRF minus Y1iniliili‘iTYTTT—T‘ Ill lT'TlTT 0.8 ,- 0.8: p17 MU EqueTag EqFourJe! E p20 MU EqueTag EqFourJe! 0.60 0201.._LLLLM_LL1.8..LLL1._L.. 0.6‘; _.L...blé...1--.-13...1....016..-LL...01.8.4.1-... ' Di: Result, maxi! binned ' DsiiResuit; maxi! binned 1 '4E — tbtqb nominal _ 1'4 ' — !b!qb nominal f— !btqb TRF plus ;‘— !b!qb TRF plus 1.2 E—— tbtqb TRF minus 0.8’ p17 MU EquoTag EqFourJe! irjrrvrw r 0.60: 4‘11 “aléWLzL-L‘L‘J WM; 1 ' DiiResuitfmaxi! binned iiiiii YTTIII T'TY i 1.25—.4111“ TRF minus ,_ . L a- . L ._ r- , s- . 08t . iv L p20 MU EquoTag EqFourJe! 06 All]AL411L1ll)ALLlAJ.ALLAJ__LLJJ,H_A_L‘_‘_LL.L.L—l—l—l—LJ—I—L—LJ ' 0 0.2 . 0.6 0 8 Di'_Resul!, maxi! binned Figure D.6: Systematic shift when varying the TRF signal distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom fom'). Alternating rows l-btag and 2-btag. 274 E — bkg nominal E — bkg nominal :— — bkg RWT plus E’ — bkg RWT plus 12} — bkg RWT minus 1.2} — bkg RWT minus 5 E 0.85 0.3? g p17 CC EqueTag Eq'l'woJet 5 p20 CC EqueTag EquoJet E '5 0.6” -.1....1....1.. .44 L...1....1_... 0.6 .LLL..1....1....1....1....1....l....1....1.... 0 0.2 0 0.2 .4 0.6 0 8 Dig“ Result, maxit binned Dsi'_Result, maxit binned 1'4E — bkg nominal 1'4E — bkg nominal ; — bkg RWT plus 5 — bkg RWT plus 1.2;— — bkg RWT minus 12’;— — bkg RWT minus 1:— —— k _— 1H 1; f _ W‘ 0.8% 0.83 E p17 CC EquoTag EquoJet : p20 CC EquoTag EquoJet 0.6: .1....1-.-.1....1....1....1....1..._.1.“.1.... 0.6'; .1....1... ..1 01.. ABW' 0 0.2 .4 .6 0 8 0 0.2 D!l'_Resuli), maxit binned Dgi’jm Result, maxit binned 1'4E — bkg nominal 1'45. — bkg nominal :— — bkg RWT plus :— — bkg RWT plus 1,2;— — bkg RWT minus 1,23— — bkg RWT minus 0-39 0.834 5 p17 MU Eque‘l'ag EquoJet : p20 MU EqueTag EquoJei 0.6:-..1....1...1.1..4. .1. 614+..1.L.4 0'6" ..1....1 ................................ 0 0. 2 0 0.2 Di; 4Resul£léu maxit binned Di; Result, maxit binned ME — bkg nominal ME — bkg nominal F _ bkg RWT plus ? — bkg RWT plus 1. .. 1.2? — bkg RWT minus 1,2;— — bkg RWT minus 1? _4 Q -- :aa-a-E 1 i 4- *“- : .fin E— EE 0.8% 0.8? g p17 MU EquoTag EquoJet 5 p20 MU EquoTag EquoJet 0.6; .1....01é...1....1....1....l....1....1....1.... as; .1-...01.2.L.1...,14_._..|....l....l..,.|....|....‘ Dsi'fResula'?naxit gigned Dgi'fResulg'giaxit gigned Figure D.7: Systematic shift when varying the RWT background distributions by ilo for the BDT discriminant outputs of events with exactly two jets. Run 113. (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. "4g — bkg nominal ”E ... bkg nominal E‘ — bkg RWT plus 5 — bkg RWT plus 12; _ bkg RWT minus 1.29 . bkg RWT minus 0.85 0,3; 5 p17 CC EqueTag EthreeJet ; p20 CC EqueTag EthreeJet 0.6:-“1““l ................ o1.6...1 ........ 1..... 0.6: _.1....1 ............................ 1.... 0 0.2 0 0.2 Di": Result, maxit binned D9; Result, maxit binned 1.4% — bkg “OMIMI 1'4E — bkg nominal ; — bkg RWT plus 3‘ — bkg RWT plus 1,25— _ bkg RWT minus 1,2 g _ bkg RWT minus 0.8 i 0.8 E :_ p17 CC EquoTag EthreeJet E p20 CC EquoTag EthreeJet 0.6;. H1,L“J ,,,,,,,,,,,,,,,,,,,,,,,,,,, 4L4. 0.6::- .-1....1 ................................ . 0 0.2 0 0.2 Di; Result, maxit binned Dsl'l': Result, maxit binned ”E — bkg nominal 1"; _ bkg nominal : _ bkg nwr plus F — bkg RWT plus 1,2? — bkg nwr minus 12:— _ bkg nwr minus ir E— 03 E- 0.3 : 5 p17 MU EaneTag EthreeJet g p20 MU EqueTag Ethl'eeJet 0.6; ,.1..L.1.-..1 “1.0.1.1.035 _.L....1..L.1.... .1.1....1....1....1..... 0 0. 2 0 0.20.6 0 8 Di: Resul? maxit binned Dig“ Result, maxit binned 1 4E — bkg nominal fl 1 4E — bkg nominal F g _ bkg RWT plus *5 — bkg RWT plus 1,2 E- — bkg RWT minus 12} — bkg RWT minus I t 1 13— ...—“066% c : L :— 0 8E 0 8E ' p17 MU EquoTag EthreeJet ' é p20 MU Eq‘nvoTag EthreeJet 0.6E W.Wu1..uw 0.6E .1..--1....1....|....I....|....l..............‘ o 0.2 0.4 .6 o a ‘TI 0 .4 0.6 o a DT_Resulg maxit binned Dgi'_Result, maxit binned Figure D.8: Systematic shift when varying the RWT background distributions by $10 for the BDT discriminant outputs of events with exactly two jets. Run 1121 (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows 1—btag and 2-btag. 276 1'4E — bkg nominal - a 1'4E — bkg nominal 3 — bkg RWT plus r — bkg RWT plus 1,2:L — bkg RWT minus 125-- — bkg RWT minus 0.8 E 0.8: E p17 cc EqueTag EqFourJet g p20 CC EqueTag EqFourJet 0.6; ..1...(.)1.2 ............... 6..1...i:’118...1....1 0.65 .1...61.2...1....1.4...1-...1.6...1...bié...1....‘ ' Dsi'f Result, maxit binned ' DeiResulg' maxit binned "4:: — bkg nominal ‘ ‘ ”E — bkg nominal ‘ F — bkg RWT plus 5‘ —- bkg RWT plus 1.2} —- bkg RWT minus 1,23- — bkg RWT minus 1 1: W 0.8 0.8 : p17 CC Eq‘l‘onag EqFourJet 5 p20 cc EquoTag EqFourJet 0.6: .J....J....1....1....1....1....1....1....1....' 0.6:...1....1.... .6..-144461.8 ..1- o 0.2 .4 0.6 0.8 I 0 0.2 Dgl'_Result, maxit binned Def“ Result, maxit binned 1"1E — bkg nominal _— _ 1'4 — bkg nominal ? —— bkg RWT plus - — bkg RWT plus 1.2} — bkg RWT minus 12 , — bkg RWT minus 1 2 WW 1 .. W E C 0.8:— 0.8 - 5 p17 MU EqueTag EqFourJet p20 MU EqueTag EqFourJet E . o.6* .1..._.]....1....1...-1....1....1....LL....LL...‘ 0.6 ..1 .ALLWWWL o 0.2 .4 0.6 0,8 0 0.2 .4 0.6 o a I DSLResu , maxit binned DSLResult, maxit binned ”E _ bkg nominal "4:. _ bkg nominal ; _ bkg RWT plus — bkg RWT plus 12:— — bkg RWT minus L23 — bkg RWT minus E E- 1; k 1-333399% 0.11L 0.8? g p17 MU EquoTag EqFourJet ; p20 MU EquoTag EqFourJet 0.6!; . .1 . . ..oié... .1. .. .-1. 01.6 -._uL. ..1. 8... 1.444 0.60 LL. . .LLLwLu ._._1_. .._._1_._._.._1....._._1_._....._1_._L._._LL..._.1 D‘i':rm Result, maxit binned .4 . D’i'_Resuli), inaxit gigned Figure D.9: Systematic shift when varying the RWT background distributions by :1:10 for the BDT discriminant outputs of events with exactly two jets. Run IIa (left) and Run IIb (right). Electron (top four) muon (bottom four). Alternating rows l-btag and 2-btag. 277 Appendix E Cross Check Samples In this Appendix, 6 variable distributions are shown for the W+jets and ti? cross- check samples. The background model reproduces the data in each channel within the uncertainties confirming the validity of the samples in regions dominated by back- grounds. The cross-check samples defined in Section 7.5, have all the same selection as the main sample, plus the following cuts: a “W+jets” (2 jets, 1 tag, HT < 175 GeV). 0 “ti” (4 jets, 1—-—-2 tags, HT > 300 GeV). Figures E7 and ES show the BDTs discriminant output for the the cross check samples in both linear and log scale. 278 %' 100 p17 e+jets % p17 e+jets (5 1 b-tag (5 1 b-tag 5’ 2 jets 3 2 jets 2 2 c i: = 3 .§ 50 .9. 2 2 .2 g >- >- m ‘11 100 11' m 100 150 200 M,(W) [GeV] pT(lepton) [GeV] p20 e+jets - p20 e+jets 1 b-tag 100— 1 b-tag + 2 jets - 2 jets Event Yield [counts/106W] Event Yield [counts/106W] 100 11' 100 150 200 M,(W) [GeV] p,(|epton) [GeV] %' 100 p17 n+jets % _ p17 n+jets 8 1:119 8 100- 1,5119 1- v- - s E les 2 le S c 8 3 o g. ' 2 5°. 2 5o 2 2 ' >- >- "‘ 100 11" m 100 150 200 M,(W) [GeV p11Iepton) [GeV] 5 100— p20u+jets %' p20u+jets c; - 1 b-t - c a 'ag (OD 100 1 blt'ag 5 2jets 5 2jets <3. 50 § 2 - 2 50 s 2 >- >- '" so 100 15 I” ‘li so 100 150 200 MT(W) [GeV] pT(lepton) [GeV] Figure E.1: Cross-check plots for several variables in the W+jets cross-check sample. 279 Event Yleld [counts/106W] Event Yleld [counts/106W] Event Yield [counts/1 OGeV] Event Yleld [counts/106W] 50 p17 e+jets 1 b-tag 2 jets Event Yleld [counts/0.35] p17 e+jets 1 b-tag 2 jets 100 150 200 6 Missing ET [GeV] AR(jet1,jet2) . p20e+jets 51"” p20e+jets + 1 b-tag % 1 b-tag 100 2jets E 1 2jets 3 o .2. 2 so 5 ‘E o > ll! ‘1 50 100 150 200 4 6 Missing ET [GeV] AR(jet1,jet2) p17u+jets g p17gi+jets 1b-tag g 100 1b-tag + 2jets ‘E 2jets 100 3 o .2. 1:1 3. 50 50 >' . E 0 > m ‘l 100 150 200 4 5 ' Misslng ET [GeV] AR(jet1,jet2) p20..+jets g p20u+jets 1b-tag g 100” 113-tag 2jets E 2jets 3 o 2. E .2 >. ‘E 2 in so 100 150 200 (l 4 6 Missing ET [GeV] AR(jet1,jet2) 280 Figure E2: Cross—check plots for several variables in the W+jets cross-check sample. %' p17 e+jets '5: 40* p17 e+jets g 150 1 b-tag g " 1 b-tag g 2 jets § 30 + + 2 jets E o , 3 100 " .§ 3 20 2 >- 0 o-I 5 u u’; 100 200 300 400 500 2 4 H,(jets,l,v) [GeV] 0 x Y] E 200 p20 e+jets ?. 20 e+jets g 1 b-tag g 40‘ 1 b-tag g 150 2 jets E ' 2 jets g 53, 30 o 1: ' 3 10° 2 20 E >- e . ' : 50 § 10 5 1.11 > I” J—k—L‘ 100 200 300 400 500 2 4 HT(jets,l,v) [GeV] O x 1] %' p17 114-jets g 56_ 17 e+jets <5 1 b-tag 1 b-tag § + 2 jets E 4o? 2 jets 0- 0 § .2. 30 § 3 3 >- 20 Q 0‘ .. s 5 e- > 10 E I" , u’: 100 200 300 400 500 2 4 H,(jets,l,v) [GeV] 0 x n 5 p20 tl+jet$ 5' L- p20 gl+jets g 1 b-tag 3 4° 1 b-tag g 2 jets g ‘ 2 jets ..g. .10" 30 o u .2 E 20 2 >- 1» - ' — 1: 2', 2 1o 5 ... - E 100 200 300 400 500 -2 2 4 H,(jets,l,v) [GeV] 0 x TI Figure E.3: More cross—check plots for variables in the W'+ jets cross-check sample. 281 an AU E p17 e+jets E ~ p17 e+jets g 1-2 bét-agts g 15: 1-2 bAt‘agts 1- 1- E 19 S E _ 1e 5 5 5 O o 10: .2. .2. - E E ' o o ' ; 5 5.— 15 E - o o u’. 11>: 1 00 150 50 1 00 1 50 200 NW) [GeV] pT(lepton) [GeV] E p20 e+jets E : p20 e+jets e _ E . a : . g g 15.’ o o : a a - 2 2 ‘07 .2 .9 : >' >- L E ‘E 5: + o c a u’: 100 150 50 100 150 200 M,(W) [GeV] pT(|ept0n) [GeV] %‘ p17 jt+jets %' p17 u+jets g 1-2 b-tags (OD - 1-2 b-tags E 4 jets E 207 4 jets : c = a g a E E 10 .2 2 >- >- ‘E E o o u>.| E 1 00 1 50 50 100 150 200 M,(W) [GeV] pT(|epton) [GeV] p20 e+jets p20 j1+jets 1-2 b-tags 1-2 b-tags 4 jets 4 jets Event Yleld [counts/106W] Event Yleld [counts/1OGeV] .0 50 100 1'5 100 150 200 MT(W) [GeV] pT(Iepton) [GeV] Figure E4: Cross—check plots for several variables in the t5 cross-check sample. 282 %' 152 p17 e+jets '5' j p17 e+jets g 1-2 b-tags % 1-2 b-tags 5 4 jets E 20 4 jets ed 3 g 104 3 o u 2- 2 'o 2 E 5— 3'. >- I: It; 5 > m (b 109 150 200 4 6 Missing ET [GeV] AR(jet1,jet2) %' 20_ p20 e+jets g j 1320 e+jets g ~ 1-2 b-tags g 1—2 b-tags S 4 jets E j 4 jets rev 15_ 3 zoj 1: o 3 . 0 8 3' E- 10‘ E, .2 ’ 3: :1 5e 5 5 - u>.t I: . q 100 150 200 4 6 Missing ET [GeV] AR(jet1,jet2) 2“ p17 114-jets p17 u+iets 1-2 b-tags 30_ 1-2 b-tags 15 4 jets 4 jets 01 Event Yleld [counts/0.35] 8 1 Event Yield [counts/106W] 8 100 150 200 4 6 ' Mlsslng ET [GeV] AR(jet1 ,jet2) 5.. p20 u+jets “MIT p20 tl+jelS g 20, 1-2 b-tegs % 30* 1-2 b-tags S _ 4 jets E 4 jets ... 3 g 15- 3 O _ _ g 2 10* a u - :2 - t 1'. 5— 5 5 - E > '" q 50 100 150 200 ‘l 6 Misslng ET [GeV] AR(jet1,jet2) Figure E.5: Cross-check plots for several variables in the tt_ cross-check sample. 283 p17 e+jets _ p17 e+jets 1-2 b-tags 20E 1-2 b-tags 4 jets 4 jets Event Yleld [counts/0.4] + + Event Yield [counts/ZOGeV] 100 200 300 400 50 2 4 M(l,v,b) [GeV] Q x 11 p20 e+jets 20_ p20 e+jets 1-2 b-tags 1-2 b-tags 4 jets _ 4 jets Event Yleld [counts/0.4] Event Yield [counts/206W] 100 200 300 400 500 2 4 M(I,v,b) [GeV] 0 x n E p17 lH-jetS '5: p17 u+jets g 1-2 b-tags S 1-2 b-tags % 4 jets g 20 4 jets 0- O C 0 3 lu—nl 2 38 u ; E E 10 >- o E ii 0 u’: l 100 200 300 400 500 2 A M(l,v,b) [GeV] 0 x n E p20 jl+jetS '3' 30— p20 gl+jets g 1-2 b-tags 3 1-2 b-tags g 4 jets g 4 jets ‘g’ _c°_» 20 g g g F 0 4- ; 5 1o 4- > c m 0 fl . 100 200 300 400 500 -2 2 4 M(|,v,b) [GeV] 0 x 1] Figure E.6: More cross-check plots for variables in the t? cross-check sample. 284 2 ~ »1 2100~ -1 2 80 DO Run lla Prch. 1.1 lb 0 DO Run IIb Prelim. 1.2 fb >- p17 e+jets ; p20 e+jets ‘5’ 1 b-tag ‘3’ 1 b-tag a 60 2 jets a 2 jets 40 5° 20 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output 3.? DO Run Ila Prelim. 1.1 try1 3; DO Run llb Prelim. 1.2 1b" ;100— p17 11+jets '>- p2011+jets ‘5' 1 b-tag E1 1 b-tag a 2 jets 11>: 2 jets 50 0.2 0.4 0.6 0.8 1 (b . . 0.6 0.8 1 tb+tqb or Output tb+tqb DT Output 3;, 5 DO Run Ila Prelim. 1.1 ib" %‘°‘ ; 2 p17 e+jets ; E ’ E g - 2 I” I“ "’5 10 1 0.2 0.4 0.6 0.8 1 o 0.2 0.4 0.6 0.3 1 tb+tqb DT Output tb+tqb DT Output % DO Run lla Prelim. 1.1 fb“ 3.31 D0 Run llb Prelim. 1.2 in"! '>'- p17 n+jets ; p2011+jetsj E E 1 b-tag «>3 2 2 jets I” I” _t O _L O 1 0 0.2 0.4 0. . 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output Figure 13.7: Decision tree outputs for the cross-check sample “W+jets” 011 a linear scale. Upper row: electron channel; second row: muon channel. Left column: Run 113.; right column: Run 111). The last two rows are the same plots that are in first and second row but in log scale 0 0.2 0.4 E - .1 E - 1 2 30 DO Run Ila Prelim.1.1 lb 0 DO Run llb Prellm.1.2fb '>- p17 e channel ; 30} p20 9 channel. ‘dé; ” 1-2 b-tags E _ 1-2 b-tags‘ fi 20* 4 jets E 4 jets 10 0.2 0.4 0.6 0.8 1 q) 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output % 00 Run Ila Prelim.1.1l‘b‘1 % DO Run lib Prelim. 1 21b‘ ; p17 ll channel ; 40 p20 ll channel E 1-2 b-tags E _ 1-2 b-tags E 4 jets “>1 30_ 4 jets 20 10 0.2 0.4 0.6 0.8 1 . 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output 2 .1 E .1 2 00 Run Ila Prelim. 1.1 lb 0 L DO Run IIb Prelim. 1.21‘b >- p17 e channel ; p20 e channel E’ 10 1-2 bétaegt: E 10? 1-2 bilagts In J In E ]e S 1 1 r 0.2 0.4 0.6 0.8 1 ) 0.2 . 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output % ” DO Run Ila Prelim. 1.1 lb"1 % I+ DO Run IIb Prelim. 1.2 lb’1 5: ‘ p17 ll channel ; , p20 ll channell "c‘ _ 1-2 b-tags ‘5 1-2 b-tags 510g 4jets 31o:— 4jets * l (i 0.2 0.4 0.6 0.8 1 (l 0.2 0.4 0.6 0.8 1 tb+tqb DT Output tb+tqb DT Output Figure E.8: Decision tree outputs for the cross-check sample “it?" on a linear scale. Upper row: electron channel; second row: muon channel. Left column: Run IIa; right column: Run Ill). The last two rows are the same plots that are in first and second row but in log scale 286 Appendix F Combination of Single Top Measurements This Appendix presents the combination result of the three DQ) Single Top analysis methods: Boosted Decision Trees (BDT) [90], Bayesian Neural Networks (BNN) [132] and Matrix Element (ME) [133]. These three analyses measure the Single Top cross section individually; however, these analyses are not fully correlated (as such, see Figure F .1 which shows 2—D plots comparing the individual analysis pseudo-datasets cross sections, and their correlations). As a consequence, a combination of these three measurements would produce an increase in the measurement sensitivity. The combination uses a Bayesian Neural Network (CBNN) [139], which is trained using the discriminant outputs from each analysis as inputs, and the second subset sample (see Section 9.2) for the training. Similar to the Boosted Decision Trees (Chapter 9), the CBNN is trained for each of the 24 channels (2,3, and 4 jets - 1 and 2 b—jets - muons and leptons — Run 118. and Run IIb). After the CBNN is trained, the measuring subset sample is evaluated, which produces a discriminant output. Figure F .2 presents the resulting CBN N discriminant for all chamlels combined and the discriminant outputs from all the three Single Top analyses. Following the same procedure outlined in Section 9.3, the CBNN discriminant 287 DE 2.3 fb"l _10 g 93. 74% correlation C i O 8; 'f'é 7:— ' g, L x g; Q ? U' : :7 4;” 5 3: z 2%- 2 1&- m _ O 0 ME tb+tqb Xsection [pb] O-‘NCO-§UIO>NGDCDO O Pseudo datasets wth t rttg. ound and S "I urge al .:LL1L._1_L_Llu_LLLu_l.L rim A‘LLLLLIMJ- wwnL 1 2 3 4 5 6 7 8 9 10 BDT tb+tqb Xsection [pb] ME tb+tqb Xsection [pb] 0 -¥ N o: b 01 O) \I co to o_,...,.... _I o i r D9 2.3 fb‘1 60% correlation ' Pseudo-datasets with background and SM signal 1 2 3 4 5 6 7 8 910 BDT tb+tqb Xsection [pb] 0% 2.3 fb‘1 Ill HIV]: '1.” I Itlll 57% correlation ill... ' Pseudo—datasets with background andSMsignal 1....1. .....l ill I. A 12345678910 BNN tb+tqb Xsection [pb] Figure F.1: Correlations among the three Single Top analyses pseudo-datasets: (BNN vs BDT), (ME vs. BDT), and (ME vs. BNN). 288 500 ,fi, 0'! O O 1 1: W W 1: "WW1 W” " "WW” 3 - t Data on 2.3 fb“ .11 I lies on 2.3 fb" >- 400_ - tb+tqb >- 400 7 I tt—m g - Wbb A7 , E - tt'—)l+jets a > h - ch ; > - Multijets “’ 30°— - Wjj+Wcj L" 300 200 — 200 100 _ 100 o o o 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Boosted Decision Trees Output Bayesian Neural Networks Output 2 300'" " "“ "L1" 2 w" -1: .2 DD 2.3 fb .2 DD 2.3 fb . >- . >- ‘ a a 100 *‘ 3 5 5 H > 175 GeV . .3 200" H,<175 GeV “>1 T i l i 50 i ‘ 0 0L 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Matrix Elements Output Matrix Elements Output Final Discriminant Signal Region 3 K on 2.3 fb" S _ on 2.3 fb-‘i o \. o l E 600 E 40 + i g > } Didi? ‘ 5 L . 1.1+ ti; ;= i I: 400_ V‘s/+1933 - I: ‘ "" t n‘ I "‘ , 2 Manger; I 3 20 i + ‘1’ .9 . 0.2 0.4 0.6 0.8 1 38 0.85 0.9 0.95 1 Ranked Combination Output Ranked Combination Output Figure F.2: Discriminant output for the three analyses methods. The bottom row corresponds to the combined BNN output discriminant, and a zoom into the signal region (BNN discriminant > 0.8). 289 output is used to build a posterior density from which the Single Top cross section measurement is obtained. The measured cross section is U(pp —> tb + X, tqb + X) = 3.94 :l: 0.88 pb, (1311) where the errors include both statistical and systematic micertainties. This measure- ment has a p—value of 2.5 x 10’7, corresponding to a significance of 5.0 standard deviations. Table F.1 shows the individual analyses measurements and sensitivities together with the combined result. Figure F .3 shows the measurements posterior densities, and the corresponding pseudo-datasets ensembles. Single Top Results with DU.) 2.3 fl)‘1 of data Significance Analysis Method Cross Section Expected Observed Boosted Decision Trms 3.74 i833 pb 4.3 a 4.6 a Bayesian Neural Networks 4.70 111,33 pb 4.1 a 5.4 0 Matrix Element 4.30 i933 pb 4.1 a 4.9 0 Combination 3.94 :l: 0.88 pb 4.5 a 5.0 a Table F.1: Single Top cross section measurements. Using the Single Top cross section measurement from the CBN N, a Bayesian posterior for thb|2 is built in the closed interval zero to one, [0, 1]. H0111 this posterior, the limit th > 0.78 is extracted at 95% CL. within the Standard Model. If the upper limit constrain on the interval is removed, the resulting measurement for |th f IL | is: L +0.11 |th f1 I z 1.07 -012 (F.2) which corresponds to the strength of the electroweak V — A coupling. The full details of the measurement can be found in Reference [57]. Figure F.4 shows the posterior 290 tb+tqb Cross Section [pb] '5" : l 3 ' VEEo'st’ed’becisionfiees ‘8. : Boosted ; a 49.4M pseudo-datasets (background-only) ; 0.4g Decision Trees i g 95 above measured cross section ._ l -6 o l o - 5 0'3 Observed g zg'ue: 1.9.: 10 0 cross section i g erve 3'9" an“ " 02 = +0.95 1 n. T: t 3'74-0719 DD; ‘7 3 o 1 E. i e E ': EI'CS' ”fh' } 2 o: ,, H - '6_ , 0 2 4 6 O 10 12 o 2 3 4 5 0 tb+ tqb Cross Section [pb] 2 117+ tqb Cross Section [pb] -- 0.5 A ,_ , ~ We , _ E Bayesian ‘3 Bayesran Neural Networks : °-‘ Neural Networks 3 62'“ 2.6:: mlmwml'i “? '2 0.3 erved g p-value = 3.2 x 10'8 8 cross section 3 Observed significance} . _ +1.13 V’ = ‘ -8 0.2 4.70433 pb ‘70- 5-41 O 2 _ e - é 0-1 to 2.3 ib g I o» . . .‘; in 1..“. l . .6 ,Mml o 2 4 6 6 1o 12 o' 2 3 6 tb+ tqb Cross Section [pb] z tb+ tqb Cross Section [pb] "F M m 7 Tm“ 7'. W T ' ' 13 , Matrix Elements .3 _ Matnx Elements n 10 emu pceudo-datasou (background-only) "" 0-4: a 10‘ 25 above measured cross section %’ t Observed 3 106 p-value = 4.0 x 10‘7 c 0.3‘ cross section 1: _ , .0 99 a 104 Observed Significance 3 4.:I.o_1'20 pb% g h ‘ . J O 0.2 i F9- 10 g t to z 31 ‘ 1‘3 10’ o 0'11 ""- 10 fl. ; l 2 o - 1 , . ,l o 1 o 2 4 6 6 1o 12 o' 2 3 4 5 6 tb+tqb Cross Section [pb] z tb+tqb Cross Section [pb] —~ , ,, .--, a "“*”De"ca'rasi’nataon’ h D“ 2.3 fly1 3: 67.8M psoudo-daMpmkground-onm & 0.4 a 17 above measured cross °mmum o p-value = 2 5 x 10'7 g 0.3 = 3.94 30.88 pb '3 Observed significance 0 E 0,, a = 5.03 o l I. '7 i .g 0.1 E ‘ +3 2 0 1° ° .5 2 3 4 5 6 z tb+ tqb Cross Section [pb] Figure F.3z Posterior probability densities (left colunm) and significance measure- ments (right colunm) for the BDT, BNN, ME, and the combination of the three analyses methods. 291 probability densities for inbi2 and Ithf1Li2- l i i l 3‘ 5‘ ‘ ’ “a — D0 2.3 fb'1 1: - o 4 0 i l- _ .2 — I— 3_ .3 : we > 0.78 O , n. 2; : at 95% CL _ 0 S flat prior 3 1 1 r- V Di“ . . l . 0 0.2 0.4 0.6 - 0.8 1 2 thbI z. _ “a DD 2.3 fb'1 ‘3 1.5-- o - D ‘6 -— ' L 3 |v,,,r1 |= 1.07 t 0.12 1;; 1.0r O .. 0. flat prior 2 O 0.5 - 00 0.5 A 1 1‘5 2 2.5 3 lvtbfi'l2 Figure F4: Posterior probability densities for Ith|2 (left) and thbf1L|2 (right). The color bands represent different confidence bounds: 68.3 %, 95.4 % and 99.7 %. 292 Appendix G Design and Implementation of the New D0 Level-1 Calorimeter Trigger In this Appendix, the upgrades of the DQchel 1 Calorimeter trigger are presented. Special focus is put on the ADF (Analog to Digital Filters) cards with which I worked as part of my service work for the DC experiment. Some of my hardware related task included the development of a work bench to test over 100 ADF-cards. The testing avoided any complications and /or malfunctions of the cards during the installation process of the system at Did and current performance on the trigger system. The full report on the Level-1 Calorimeter trigger was published in Nuclear In- struments and Methods in Physics Research. A 584, 75 (2008). Excerpts from the original paper are presented below. G. 1 Introduction Increasing luminosity at the Fermilab Tevatron collider has led the D0 collaboration to make improvements to its detector beyond those already in place for Run IIa, 293 which began in March 2001. One of the cornerstones of this Run IIb upgrade is a completely redesigned level-1 calorimeter trigger system. The new system employs novel architecture and algorithms to retain high efficiency for interesting events while substantially increasing rejection of background. We describe the design and imple- mentation of the new level-1 calorimeter trigger hardware and discuss its performance during Run IIb data taking. In addition to strengthening the physics capabilities of D0, this trigger system will provide valuable insight into the operation of analogous devices to be used at LHC experiments. In the following we describe the Level-1 Calorimeter Trigger System (LlCal) de- signed for operation during Run IIb. Section G2 discusses the motivation for replac- ing the LlCal trigger, which was used in Run I and Run IIa. Algorithms used in the new system and their simulation are described in Section G.3, while the hardware designed to implement these algorithms is detailed in Sections G.4, G5, G6, and G7. Mechanisms for online control and monitoring of the new LlCal are outlined in Sec- tions G8 and (3.9. This article then concludes with a discussion of early calibration and performance results in Sections G.10. G.2 Motivation for the LlCal Upgrade By the time of the start of Run 1121 in 2001, there was already a tentative plan in place for an extension to the run with accompanying upgrades to the accelerator complex [142], leading to an additional 2—6 fb-1 of integrated luminosity beyond the original goal of 2 fb_1. This large increase in statistical power opens new possibilities for physics at the Tevatron such as greater precision in critical measurements like the top quark mass and W boson mass, the possibility of detecting or excluding very rare Standard Model processes (including production of the Higgs boson), and greater sensitivity for beyond the Standard Model processes like supersymmetry. At a hadron collider like the Tevatron, however, only a small fraction of the 294 collisions can be recorded, and it is the trigger that dictates what physics processes can be studied and what is left unexplored. The trigger for the D0 experiment in Run Ila had been designed for a maximum luminosity of 1x1032 cm-2s_1, while the peak luminosities in Run IIb are expected to go as high as 3x1032 (7111—28—1. In the three-level trigger system employed by D0, only the L3 trigger can be modified to increase its throughput; the maximum output rates at L1 and L2 are imposed by fundamental features of the subdetector electronics. Thus, fitting L1 and L2 triggers into the bandwidth limitations of the system can only be accomplished by increasing their rejection power. While an increase in the transverse energy thresholds at Ll would have been a simple way to achieve higher rejection, such a threshold increase would be too costly in efficiency for the physics processes of interest. The D0 Run IIb Trigger Upgrade [144] was designed to achieve the necessary rate reduction through greater selectivity, particularly at the level of individual L1 trigger elements. The LlCal trigger used in Run I and in Run IIa [147] was based on counting individual trigger towers above thresholds in transverse energy (ET). Because the energy from electrons / photons and especially from jets tends to spread over multiple TTs, the thresholds on tower ET had to be set low relative to the desired electron or jet ET- For example, an EM trigger tower threshold of 5 GeV is fully efficient only for electrons with ET greater than about 10 GeV, and a 5 GeV threshold for EM+HD tower ET only becomes 90% efficient for jet transverse energies above 50 GeV. The primary strategy of the Run IIb upgrade of LlCal is therefore to improve the sharpness of the thresholds for electrons, photons and jets by forming clusters of TTs and comparing the transverse energies of these clusters, rather than individual tower ETs, to thresholds. The design of clustering using sliding windows (see Section G3) in Field Pro- grammable Gate Arrays (FPGAs) meets the requirements of this strategy, and also opens new possibilities for LlCal, including sophisticated use of shower shape and isolation; algorithms to find hadronic decays of tau leptons through their character- istic transverse profile; and requirements on the topology of the electrons, jets, taus, and missing transverse energy in an event. G.3 Algorithms for the Run IIb LlCal Clustering of individual TTs into EM and Jet objects is accomplished in the Run IIb LlCal by the use of a sliding windows (SW) algorithm. This algorithm performs a highly parallel cluster search in which groups of contiguous TTs are compared to nearby groups to determine the location of local maxima in ET deposition. Variants of the SW algoritlnn have been studied extensively at different HEP experiments [148], and have been found to be highly efficient at triggering on EM and Jet objects, while not having the latency drawbacks of iterative clustering algorithms. For a full discussion of the merits of the sliding windows algoritlnn, see [149]. The implementation of the sliding windows algorithm in the D0 calorimeter trigger occurs in three phases. In the first phase, the digitized transverse energies of several TTs are summed into Trigger Tower Clusters (TTCL). These TTCL sums, based on the size of the EM or Jet sliding window, are constructed for every point in trigger tower space, and are indexed by the n, (b coordinate of one of the contributing T Ts, with different conventions being used for different algorithms (see Sections ?? and ??). This process, which yields a grid of TTCLs that share energy with their close neighbors, is shown in the first and second panels of Fig. G.1. ' In the second phase, the TTCLs are analyzed to determine locations of large en- ergy deposits called local maxima (LM). These LM are chosen based on a comparison of the magnitude of the ET of a TTCL with that of its adjacent TTCLs. Multiple counting of Jet or EM objects is avoided by requiring a spatial separation between adjacent local maxima as illustrated in the third panel of Fig. G.1. 296 In the third phase, additional information is added to define an output object. In the case of Jet objects, shown in the fourth panel of Fig. G.1, energy of surrounding TTs is added to the TTCL energy to give the total Jet object energy. EM and Tau objects are also refined in this phase using isolation information (see Sections ?? and ??). Results for the entire calorimeter can be obtained very quickly using this type of algorithm by performing the LM finding and object refinement phases of the algorithm in parallel for each TTCL. 11' Space TTCL Space 11 _> LM Space Jet Space Figure G.1: The stages of algorithm flow for the sliding windows algoritlnn. In this example, which corresponds to the Run IIb Jet algorithm, a 2x2 TT TTCL is used, indexed by the position of its smallest n, ()5 TT. Baseline subtracted TT energies are indicated by numbers, and local maxima are required to be separated by at least 1 TT. Jet objects are defined as the ET sum of the 4x4 TTs centered on the TTCL. Light gray regions in the diagrams indicate areas for which the object in question cannot be constructed because of boundary effects. G.4 Hardware Overview The algoritlnns described previously are implemented in several custom electronics boards designed for the new LlCal. An overview of the main hardware elements of the Run IIb LlCal system is given in Fig. G2. Broadly, these elements are divided into three groups. 1. The ADF System, containing those elements that receive and digitize analog 297 SCLD ADF Timing , r Trans.Syst. x8 ppcogao) 16 EM ‘ ' f PFCables(x160) 16 HD _" (x1152) ”c (m) ADF ADC + Dlgl'lal Flltor (130) VME/SCL work TAB/GAB ch flmlng/Ctrl me/etl/vrne B-blt obl's E“ era ’ TAB cums GAB m .' Trlg 7 Sum: + . x90 Alcoa x8 Trlo 7'" , Q... _~_, Tom: IlEt 0(8) (X1) Jet Ell L1 CalTrk ‘ ... Figure G2: A block diagram of the main hardware elements of the Run IIb LlCal system and their interconnections. TT signals from the BLS cards, and perform TT-based signal processing. 2. The TAB/CAB System, where algorithms are run on the digitized T T signals to produce trigger terms. 3. The Readout System, which inserts LlCal information into the D0 data path for permanent storage. The L1Cal also connnunicates with other elements of the DO trigger and data acquisition (DAQ) system, including the following. o The Trigger Framework (TF W), which delivers trigger decisions and synchro— nizes the entire D0 DAQ. From the LlCal point of view, the TFW sends global timing and control signals (see Table G1) to the system over Serial Command Links (SCL) and receives the LlCal and / or terms. 0 The LlCal Trigger Control Computer (LlCal TCC), which configures and men- 298 itors the system. 0 The Level-1 Cal- Track Match trigger system (L1CalTrk), another L1 trigger system that performs azimuthal matching between LICTT tracks and L1Cal EM and Jet objects. Within the L1Cal, the ADF system consists of the Transition System, the Analog and Digital Filter cards (ADF), and the Serial Command Link Distributor (SCLD). The Transition System, consisting of Patch Panels, Patch Panel Cards (PPC), ADF Transition Cards (ATC), and connecting cables, adapts the incoming BLS signal cables to the higher density required by the ADFs. These ADF cards, which reside in four 6U VME—64x crates [150], filter, digitize and process individual TT signals, forming the building blocks of all further algorithms. They receive timing and control signals from the SCL via a Serial Command Link Distributor card (SCLD). Trigger algoritlnns are implemented in the L1Cal in two sets of cards: the Trigger Algorithm Boards (TAB) and the Global Algorithm Board (GAB), which are housed in a single 9U crate with a custom backplane. The TABS identify EM, Jet and Tan objects in specific regions of the calorimeter using the algoritlnns described in Section G.3 and also calculate partial global energy sums. The GAB uses these objects and energy sums to calculate and / or terms, which the TFW uses to make trigger decisions. Finally, the VME/SCL card, located in the L1Cal Control Crate, distributes timing and control signals to the TABs and GAB and provides a communication path for their readout. The architecture of the L1Cal system and the number of custom elements required, sunmiarized in Table G2, is driven by the large amount of overlapping data required by the sliding windows algoritlnn. In total, more than 700 Gbits of data per second are transmitted within the system. Of this, each local maximum calculation requires 4.4 Gbits/s from 72 separate TTs. The most cost effective solution to this problem, which still results in acceptable trigger decision latency, is to deal with all data as serial 299 SCL ADF TAB / GAB Description INIT yes initialize the system CLK'I yes yes 132 ns Tevatron RF clock TURN yes yes marks the first crossing of an accelerator turn REALBX yes . flags clock periods containing real beam crossings BX_NO yes counts the 159 bmlch crossings in a turn L1ACCEPT yes yes indicates that an L1 Accept has been is- sued by the TF W MONITOR yes initiates collection of ADF monitoring data L1ERROR yes a TAB/ GAB error condition transmitted to the SCL hub LIBUSY , yes asserted by the TABs/ GAB until an ob— served error is cleared ADF MON allows T CC to freeze ADF circular buffers 7, ADF TRIG — ~ allows TCC to fake a MONITOR signal on the next L1 Accept 7 TAB RUN TAB/ GAB data path synchronization sig- nal I, TAB TRIG pulse to force writing to TAB / GAB diag- nostic memories TAB FRM used for synchronization of TAB/ GAB VME data under VME/SCL control TAB ADDR internal address for TAB/ GAB VME read / write operations TAB DATA data for TAB/ GAB VME read/write op— erations Table G.1: Timing and control signals used in the L1Cal system. Included are DO global timing and control signals (SCL) used by the ADFs and the TAB / GAB system, as well as intra-system communication and synchronization flags described later in the text. 300 Board Input TT Region Output TT Region Total Number PPC 4 x 4 4 x 4 80 ATC 4 x 4 4 x 4 80 ADF 4 x 4 4 x 4 80 SOLD all all 1 TAB 40 x 12 3 1 x 4 8 GAB all all 1 VME / SC L all all 1 Table G2: A summary of the main custom electronics elements of the LlCal system. For each board, the TT region (in 77 x (b) that the board receives as input and sends on as output is given as well as the total number of each board type required in the system. bit-streams. Thus, all infra-system data transmission is done bit-serially using the Low Voltage Differential Signal (LVDS) protocol and nearly all algorithm arithmetic is performed bit-serially as well, at clock speeds such that all bits of a data word are examined in the 132 ns Tevatron bunch crossing interval. Examples of a bit-serial adder and comparator are shown in Fig. G.3. The only exception to this bit-serial arithmetic rule is in the calculation of Tau object isolation, which requires a true divide operation (see Section G.3) and thus introduces an extra 132 ns of latency to the trigger term calculation. Even with this extra latency, the L1Cal results arrive at the TFW well within the global L1 decision time budget. 301 SYNC (a) CARRY sun I (b) svuc D .8 :Brer-a am :D—flAxs D Q CA>B *4} .. Figure G.3: Logic diagrams for a Bit-serial adder (a) and a bit-serial comparator (b). G.5 The ADF System G.5. 1 Transition System Trigger pick—off signals from the BLS cards of the EM and HD calorimeters are trans- mitted to the L1Cal trigger system, located in the Movable Counting House (MCH), through 4&50 1n long coaxial ribbon cables. Four adjacent coaxial cables in a rib- bon carry the differential signals from the EM and HD components of a single TT. Since there are 1280 BLS trigger cables distributed among ten racks of the original 302 L1Cal trigger electronics, the L1Cal upgrade was constrained to reuse these cables. However, because the ADF input signal density is much larger than that in the old system (only four crates are used to house the ADFs as opposed to 10 racks for the old system’s electronics) the cables could not be plugged directly into the upgraded L1Cal trigger electronics; a transition system was needed. The transition system is composed of passive electronics cards and cables that route signals from the BLS trigger cables to the backplane of the ADF crates (see Section G.5.2). It was designed to allow the trigger cables to remain within the same Run I / Ila rack locations. It consists of the following elements. 0 Patch Panels and Patch Panel Cards (PPC): A PPC receives the input signals from 16 BLS trigger cables and transmits the output through a pair of Pleated Foil Cables. A PPC also contains four connectors which allow the monitoring of the signals. Eight PPCs are mounted two to a Patch Panel in each of the 10 racks originally used for Run I / Ila L1Cal electronics. 0 Pleated Foil Cables: Three meter long Pleated Foil Shielded Cables (PFC), made by the 3M corporation [151], are used to transfer the analog TT output signals from the PPC to the ADF cards via the ADF Transition Card. There are two PFCs for each PPC for a total of 160 cables. The unbalanced characteristic impedance specification of the PFC is 72 O, which provides a good impedance match to the BLS trigger cables. 0 ADF Transition Card (ATC): The ATCs are passive cards cormected to the ADF crate backplane. These cards receive the analog TT signals from two PF Cs and transmit them to the ADF card. There are 80 ATCs that correspond to the 80 ADF cards. Each ATC also transmits the three output LVDS cables of an ADF card to the TAB crate —- a total of 240 LVDS cables. 303 G.5.2 ADF Cards The Analog and Digital Filter cards (ADF) are responsible for sending the best esti- mate of the transverse energy (ET) in the EM and HD sections of each of the 1280 TTs to the eight TAB cards for each Tevatron beam crossing. The calculation of these ET values by the 80 ADF cards is based upon the 2560 analog trigger signals that the ADF cards receive from the BLS cards, and upon the timing and control signals that are distributed throughout the D0 data acquisition system by the Se- rial Command Links (SCL). The ADF cards themselves are 6U x 160 mm, 12-layer boards designed to connect to a VME64x backplane using P0, P1 and P2 connectors. The ADF system is set up and monitored, over VME, by a Trigger Control Computer (TCC), described in Section G.8. G.5.3 Signal Processing in the ADFs Each ADF card, as shown schematically in Fig. G.4, uses 32 analog trigger signals corresponding to the EM and HD components of a 4x4 array of Trigger Towers. Each differential, AC coupled analog trigger signal is received by a passive circuit that terminates and compensates for some of the characteristics of the long cable that brought the signal out of the collision hall. Following this passive circuit the active part of the analog receiver circuit rejects common mode noise on the differential trigger signal, provides filtering to select the frequency range of the signal caused by a real Tevatron energy deposit in the Calorimeter, and provides additional scaling and a level shift to match the subsequent ADC circuit. The analog level shift in the trigger signal receiver circuit is controlled, separately for each of the 32 cha1mels on an ADF card, by a 12 bit pedestal control DAC, which can swing the output of the ADC that follows it from slightly below zero to approximately the middle of its full range. This DAC is used both to set the pedestal of the signal coming out of the ADC that follows the receiver circuit and 304 CHO * ‘° ADC ‘ I , 18 Et‘s ‘ Data Path 7 CHO FPGAO 3““ ’ Data Clock 16(3hannels 4st : , BTTS —-7‘— 7 : ' b ,7 ’ Data I : f i J 42 Clock : —7"-. 7 , 7 : . DataPath 16Et's "' Data CH 15%—ADC . ! FPGA1 3Rsrv 42 Clock EM ._. 160hannels % Ha l as An 3 778 BX_x8 cu .i ‘l w clocksstat s __ Conrol U Registers Maestro ADF only ‘ cur/cu 6 sum: from '° Registers sou) Wm TURN Crate “80:33:! pm ,, mm m ane ADF_TRIG VME VME Conflo saw 2 3‘” Interface on-card Bus Figure G.4: ADF card block diagram. as an independent way to test the full signal path on the ADF card. During normal operation, we set the pedestal at the ADC output to 50 counts which is a little less than 5% of its full scale range. This offset allows us to accommodate negative fluctuations in the response of the BLS circuit to a zero-energy signal. The 10 bit sampling ADCs [152] that follow the receiver circuit make conversions every 33 ns -— four times faster than the Tevatron BX period of 132 us. This conversion rate is used to reduce the latency going through the pipeline ADCs and to provide the raw data necessary to associate the rather slow rise-time trigger signals (250 ns typical risetime) with the correct Tevatron beam crossing. Although associating energy deposits in the Calorimeter with the correct beam crossing is not currently an 305 1Tl' ADC Latch 0“" E" °' ”D 4, TCC Filter E to E: to mm "' Lookup Channel _Wonitor Da U _ . MADE: ‘ Memory ' ' Link Mon/Slut Simulation Da; x I DP" Constant ; U l [I Data gum = X "m" Output _TSim ;. on-cardBu __D!il___l I mm, Data I DP" Figure G.5: Block diagram of signal processing for a single TT in the ADF. issue since actual proton-antiproton collisions only occur every 396 ns, rather than every 132 us as originally plaimed, the oversampling feature has been retained for the flexibility it provides in digital filtering. On each ADF card the 10 bit outputs from the 32 ADCs flow into a pair of FPGAs [153], called the Data Path FPCAs, where the bulk of the signal processing takes place. This signal processing task, shown schematically in Fig. G.5, is split over two FPGAs with each FPGA handling all of the steps in the signal processing for 16 channels. Two FPGAs were used because it simplified the circuit board layout and provided an economical way to obtain the required number of I / O pins. The first step in the signal processing is to align in time all of the 2560 trigger signals. The peak of the trigger signals from a given beam crossing arrive at the LlCal at different times because of different cable lengths and different channel capacitances. These signals are made isochronous using variable length shift registers that can be set individually for each channel by the TCC. Once the trigger signals have been aligned in time, they are sent to both the Raw ADC Data Circular Buffers where monitoring data is recorded and to the input of the Digital Filter stage. The Raw ADC Data Circular Buffers are typically set up to record all 636 of the ADC samples registered in a full turn of the accelerator. This writing operation can be stopped by a signal from the TCC, when an L1 Accept flagged with a special 306 Collect Status flag is received by the system 011 the SCL, or in a self-trigger mode where any TT above a progrannnable threshold causes writing of all Circular Buffers to stop. Once writing has stopped, all data in the buffers can be read out using the TCC, providing valuable monitoring information on the system’s input signals. The Raw ADC Data Circular Buffers can also be loaded by the TCC with simulated data, which can be inserted into the ADF data path instead of real signals for testing purposes. The Digital Filter in the signal processing path can be used to remove high fre- quency noise from the trigger signals and to remove low frequency shifts in the base- line. This filter is currently configured to select the ADC sample at the peak of each analog TT signal. This mode of operation allows the most direct comparison with data taken with the previous L1Cal and appears to be adequate for the physics goals of the experiment. The 10 bit output from the Digital Filter stage has the same scale and offset as the output from the ADCs. It is used as an address to an E to ET Lookup Memory, the output of which is an eight bit data word corresponding to the ET seen in that TT. This E to ET conversion is normally programmed such that one output count corresponds to 0.25 GeV of ET and includes an eight count pedestal, corresponding to zero ET from that TT. The eight bit TT ET is one of four sources of data that can be sent from the ADF to the TABs under control of a multiplexer (011 a channel by channel and cycle by cycle basis). The other three multiplexer inputs are a fixed eight-bit value read from a programmable register, simulation data from the Output Data Circular Buffer, and data from a pseudo-random number generator. The latter two of these sources are used for system testing purposes. During normal operation, the multiplexers are set up such that TT ET data is sent to the TABs on those bunch crossing corresponding to real proton-antiproton collisions, 307 while the fixed pedestal value (eight counts) is sent 011 all other accelerator clock periods. If noise on a channel reaches a level where it significantly impacts the D0 trigger rate, then this chamiel can be disabled, until the problem can be resolved, by forcing it to send the fixed pedestal on all accelerator clock periods, regardless of whether they contain a real crossing or not. Typically, less than 10 (of 2560) T Ts are excluded in this manner at any time. Data is sent from the ADF system to the TAB cards using a National Semicon- ductor Channel Link chip set with LVDS signal levels between the transmitter and receiver [154]. Each Channel Link output from an ADF card carries the ET data for all 32 channels serviced by that card. A new frame of ET data is sent every 132 us. All 80 ADF cards begin sending their frame of data for a given Tevatron beam crossing at the same point in time. Each ADF card sends out three identical copies of its data to three separate TABS, accommodating the data sharing requirements of the sliding windows algorithm. G.5.4 Timing and Control in the ADF System The ADF system receives timing and control signals listed in Table G.l over one of the Serial Command Links [141]. Distribution of these signals from the SCL to the 80 ADF cards is accomplished by the SCL Distributor (SCLD) card. The SCLD card receives a copy of the SCL information using a D0—standard SCL Receiver mezzanine card and fans out the signals mentioned in Table G.1 to the four VME-64x crates that hold the 80 ADF cards using LVDS level signals. In addition, each ADF crate sends two LVDS level signals (ADFJVION and ADF_TRIG) back to the SCLD card, allowing TCC to cause synchronous readout of the ADFs. Within an ADF crate, the ADF card at the mid-point of the backplane (referred to as the Maestro) receives the SCLD signals and places them onto spare, bused VME-64x backplane lines at TTL open collector signal levels. All 20 of the ADF 308 cards in a crate pick up their timing and control signals from these backplane lines. To ensure a clean clock, the CLK7 signal is sent differentially across the backplane and is used as the reference for a PLL on the ADFs. This PLL provides the jitter-free clock signal needed for LVDS data transmission to the TABs and for ADC sampling timing. G.5.5 Configuring and Programming the ADF System The ADF cards are controlled over a VME bus using a VME-slave interface im— plemented in a PAL that is automatically configured at power-up. Once the VME interface is running, the TCC simultaneously loads identical logic files into the two data path FPGAs on each card. Since each data path FPGA uses slightly different logic (e.g., the output check sum generation), the F PGA flavor is chosen by a single ID pin. After TCC has configured all of the data path FPGAs, it then programs all control-status registers and memory blocks in the ADFs. Information that is held on the ADF cards that is critical to their Physics triggering operation is protected by making those programmable features “read only” during normal operation. TCC must explicitly unlock the write access to these features to change their control values. In this way no single failed or mis-addressed VME cycle can overwrite these critical data. G.6 ADF to TAB Data Transfer Digitized TT data from each ADF’s 4x4, 77 x 43 region are sent to the TABs for further processing, as shown in Fig. G.6. To acconnnodate the high density of input on the TABs, the 8—bit serial trigger-tower data are transmit.th using the cha1mel-link LVDS chipset [154], which serializes 48 CMOS/TTL inputs and the transmission clock onto seven LVDS channels plus a clock channel. In the L1Cal system, the input to the 309 ADF : TAB mm 12mm I wean—u : —1eeu1'r —>16I5u1'1' 16 HDTT—u» "I ADF-to-TAB cm“ — 16l-ID1'T —. —>16HDTI' park! —W cm" “N. r- parfly —- “m D“ —>par|tv Link Link Dual Port spore —u VDS _ LVDS — spore -u —>opon Bc—uv '- ac _- "°"‘°'V —>ADF BC tram—u 7mm“ M" from r —>Am=trama ' moor road ‘— 7¢Itl+ meet-tram W‘W 1 Clock welt Md" coutucIk—a> LVDS — 6(3de —a> («comet Figure G.6: ADF to TAB data transmission, reception and the dual-port-memory transition from 8-bit to 12-bit data. transmitter is 60 MHz T TL (eight times the bunch crossing rate), which is stepped up to 420 MHz for LVDS transmission. Each ADF sends three identical copies of 36 8-bit words to three different TABs on each bunch crossing. This data transmission uses eight LVDS channels — seven data channels containing six serialized data words each, and one clock ~ on Gore cables with 2mm HM connectors [155]. The 36 data words consist of the digitized ET of 16 EM and 16 HD TTs and four control words. The bunch crossing number control word indicates which accelerator crossing produced the ADF data being transmitted, and is used throughout the system for synchronization. The frame-bit control word is 'used to help align the least significant bits of the other data words. The parity control word is the logical XOR of every other word and is used to check the integrity of the data transmission. Finally, one control word is reserved for future use. While the ADF logic is 8—bit serial (60 MHz) the TAB logic is 12-bit serial (90 MHz). To cross the clock domains, the data passes through a dual-port memory with the upper four bits padded with zeros. The additional bit space is required to accommodate the sliding windows algorithm smns. The dual port memory write address is calculated from the frame and bunch crossing words of the ADF data. The least significant address bits are a data word 310 bit count, which is reset by the frame signal, while the most significant address bits are the first three-bits of the bunch crossing number. This means that the memory is large enough to contain eight events of eight-bit serial data. By calculating the read address in the same fashion, but from the TAB frame and bunch crossing words, the dual-port memory crosses 60 MHz / 90 MHz clock domains, maintains the correct phase of the data, and synchronizes the data to within eight crossings all at the same time. This means the TAB timing can range between a minimal latency setting where the data is retrieved just after it is written and a maximal latency setting where the data is retrieved just before it is overwritten. If the TAB timing is outside this range, the data from eight previous or following crossings will be retrieved. Although off-the-shelf components were used within their specifications, operating 240 such links reliably was found to be challenging. Several techniques were employed to stabilize the data transmission. Different cable lengths (between 2.5 and 5.0 m) wer used to match the different distances between ADF crates and the TAB / GAB crate. The DC-balance and pre—emphasis features of the cha1mel-link chipset [154] were also used, but (leskewing, which was found to be unreliable, was not. G.7 The TAB / GAB System G.7 .1 Trigger Algorithm Board The Trigger Algorithm Boards (TABs) find EM, Jet and Tan candidates using the sliding windows algorithm and perform preliminary sums for total and missing ET calculations. Each TAB is a double—wide 9U x 400 111111, 12-layer card designed for a custom backplane. The main functional elements of the TAB are shown in Fig. G.7. In the TAB’s main trigger data path, LVDS cables from 30 ADFs are received at the back of the card using feedthrough connectors on the backplane. The data from 311 Fuses _l E A Cyclone Power Regulators 9 B E FPGA . ——D— c 3 —l:l’ l (0 g ,_ Serializer+ Fiber T D— ‘_" Optic Transmitter 5 £43]:— I 43 "i 2 Global | $E—ED_ a c FPGA l 4 5 J :52? E 3 ——D‘ a - 2 £343— '-'- J 4: fl _. g B T i -' l— o ——D‘DD— C MUON SLDBs SWA LVDS FPGAs Recvs Figure G.7: Block diagram of the TAB. these cables are extracted using Channel Link receivers[154] and sent, as individual bit-streams for each TT, to ten TAB sliding windows algorithm (SWA) FPGAs [156] for processing. These chips also pass some of their data to their nearest neighbors to acconunodate the data sharing requirements of the sliding windows algorithms. The algorithm output from each SWA is sent to a single TAB global FPGA [156]. The global FPGA calculates regional sums and sends the results out the front of the board to the GAB, over the same type of cables used for ADF to TAB data transmission (see Section G.6) using embedded LVDS functionality in the FPGA. This data transmission occurs at a clock rate of 636 MHz. 312 The global FPGA also sends three copies of Jet and EM object information for each bunch crossing to the L1CalTrk system for processing using Gbit/s serial link transmitter daughter cards (MUON SLDB) [141]. Upon receiving an L1 accept from the D0 TFW, the TAB global chip also sends data out on a serial fiber—optic link [157] for use by the L2 trigger and for inclusion in the D0 event data written to permanent storage on an L3 accept. Low-level board services are provided by the TAB Cyclone chip [158], which is configured by an on-board serial configuration device [159] on TAB power-up. These services include providing the path for power-up and configuration of the other FPGAs on the board, under the direction of the VME/SCL card; communicating with VME and the D0 SCL over the specialized VME/SCL serial link; and fanning out the 132 ns detector clock using an on—board clock distribution device [160]. G.7 .2 Global Algorithm Board The global algorithm board (GAB) receives data containing regional counts of Jet, EM, and Tau physics objects calculated by the TABs and produces a menu of and/ or terms, which is sent to the D0 trigger framework. Like the TAB, the GAB is a double— wide 9U x 400 mm, 12-layer circuit board designed for a custom backplane. Its main functional elements are shown in Fig. G.8. LVDS receivers, embedded in four Altera Stratix FPGAs (LVDS F PGAs) [156] each receive the output of two TABs, synchronizing the data to the GAB 90 MHz clock using a dual-port memory. The synchronized TAB data from all four LVDS FPGAS is sent to a single GAB S30 F PGA [156], which calculates and/or terms, and sends them to the trigger framework through TTL-to—ECL converters [161]. There are five 16-bit outputs on the GAB, although only four are used by the framework. Much like the TABs, upon receiving an L1 accept, the GAB S30 sends data to L2 and L3 on a serialized fiber-optic link [157]. Also as on the TABs, a Cyclone FPGA 313 Fuses ...l 0 fi Cyclone Power Regulator E FPGA fl x 8 "’ ,——. a g .1 Serializer + Fiber 1 , E, l Optic Transmitter E T ,_.__.l o — ._. .8 — I: 3 mm 8 3. __ c — _ l—J E T“ L Fisaac.0 < — TI‘L—to-ECL LVDS FPGAs Translators Figure G.8: Block diagram of the GAB. [158] provides low-level board services. G.8 Online Control Most components of the D0 trigger and data acquisition system are programmable. The Online System allows this large set of resources and parameters to be configured to support diverse operational modes — broadly speaking, those used during proton- antiproton collisions in the Tevatron (physics modes) and those used in the absence of colliding beams (calibration/testing modes), forming a large set of resources and parameters needing to be configured before collecting data. The L1Cal fits seamlessly into this Online System, with its online control software 314 11—0 VISlave ‘J VI Slave ADF #1 8 ADF #20 ADFCrotot VME-6U. f ADF#1 ADF #20 ADF Crate 4 VME-6U L1CalTCC t f g POI-VME E: I a 6‘ E D G? < r: g m < o l- > g a g 8 < :53. g 0 3 W _ '5 g 5‘, E E “5 ' E 8 2 E 8 > > > IS Monitoring 1 fl [ a L3 , ti 1 control Clients { _ I II I My I VI Slave VHS #1 TAB #1 AB #8 GAB TAB/GAB Crate Custom-9U van #3 vnac sec Readout Crate VME—9U I I Q f * , , > L2 L1 CalTrk w/ splitters Figure G.9: Connmmications in the L1Cal system. hiding the complexity of the underlying hardware, while making the run time pro- gramming of the L1Cal Trigger accessible to all D0 users in simple and logical terms. A diagram of the L1Cal, from an online data and control point of view, is shown in Fig. G9. The main elements of L1Cal online control are listed below, with those aspects specific to L1Cal described in more detail in the following sections. For more information on DO—wide components see [141]. o The Trigger Framework (TFW) delivers global D0 timing and control signals to the L1Cal and collects and/ or terms from the GAB as described in Section G.4. COOR [141], a central D0 application, coordinates all trigger configuration and programming requests. Global trigger lists, containing requirements and param- eters for all triggers used by the experiment, are specified using this application as are more specific trigger configurations (several of which may operate simul- taneously) used for calibration and testing. The L1Cal Trigger Control Computer (TCC), a PC running the Linux operating system, provides a high level interface between COOR and the L1Cal hardware and allows independent expert control of the system. The Communication Crate contains cards that provide an interface between the L1Cal custom hardware in the ADF and TAB / GAB crates, and the L1Cal TCC and SCL. The L1Cal Readout Crate allows transmission of L1Cal data to the L3 trigger system. Monitoring Clients, consisting of software that may run 011 a number of local or remote computers, display information useful for tracking L1Cal operational status. G.9 Managing Monitoring Information The monitoring resources available in the ADF, TAB and GAB cards are described in Sections G.5.3.This information is collected by the TCC Control Software and is made available to Monitoring Clients via the Monitoring Interface. During normal operation, monitoring data are collected approximately every five seconds when the Collect Status qualifier is asserted on the SCL along with LlACCEPT. If data flow has 316 stopped, monitoring data are still collected from the L1Cal, initiated by the TCS, which times out after six seconds of inactivity. Monitored data include the following. o The ADF output ET of all TTs for all 36 active bunch crossings of the ac- celerator turn containing the L1ACCEPT for which the Collect Status signal is asserted. o The bunch crossing number within this turn that identifies the LIACCEPT. o The contents of all error and status registers in the TABs and GAB (associated with each SWA and Global chip on the TABs and with the LVDS and 830 chips 011 the GAB). These registers indicate, among other information, syn- chronization errors on data transfer links, parity errors on each transfer, and bunch crossing number mismatches at various points in the TAB / GAB signal processing chain. Monitoring information is displayed in the D0 control room and remotely using Monitoring Client GUIs. This application, written in Python [168] with Tkinter [169], requests and receives data from the TCS via calls to ITC. It displays average pedestal values and RMSs for each TT, to aid in the identification of noisy or dead channels, as well as system status information. Another tool for monitoring data quality in the control room is a suite of Root- based [172] software packages called Eramine. The L1Cal Examine package receives a stream of data from L3 and displays histograms of various quantities related to L1Cal performance, including comparisons between L1Cal and calorimeter precision readout estimates of TT energies. Data distributions can be compared directly to reference curves provided on the plots, which can be obtained either from an earlier sample of data or from simulation. 317 G.1O Calibration of the L1Cal Several methods are employed to ensure that the ET of individual trigger towers, used in the system, is correctly calibrated —— i.e., that one output cormt corresponds to 0.25 GeV of ET and that the zero-ET baseline is set to eight counts. G.10.1 Online Pedestal Adjustment and Noise The most frequently used of these procedures is a tool, run as part of the TCS, which samples ADC-level data from the ADFs when no true energy is expected to be deposited in the calorimeter. Based on this data, corrections to the DAC values used to set each channel’s zero—energy baseline are calculated and can be downloaded to the system. This online pedestal adjustment is performed every few days because of periodic pedestal shifts that occur in a small mnnber of channels ~ typically less than ten. These pedestal shifts arise because of synchronous noise, with a period of 132 ns, ob- served in the system due largely to pickup from the readout of other, nearby detector systems. Although the amplitude of this noise varies from cha1mel to chamrel (it is largest in only a handful of TTs), its phase is stable over periods of several stores of particle beams in the Tevatron, which sets the timescale for pedestal readjustment. G.10.2 Calorimeter Pulser The calorimeter pulser system [141], which injects carefully calibrated charge pulses onto the calorimeter preamps, is also used by the L1Cal to aid in the identification of dead and noisy channels. Special software compares ET values observed in the ADFs with expectations based on the pattern of preamps pulsed and the pulse amplitudes used. Results are displayed graphically to allow easy identification of problematic channels. In addition to its utility in flagging bad channels, this system also provides 318 F_' '-T~_— fl T' V W WT TV »'-—~ '—'“.— "T T 'a' ’’’’’’ — sog— .- 60:— e 5 : (a) i : (b) 9 50;- 1 9 so} l- : t ‘ l“ ’ l.l.l [- : 40E 5 . t: 40?- .9 : : 49"" .9 : .2 307* ' 3 ..s‘" _g 30:— §20E ff :3 20E 1:. r' gr“ ’ a. : ‘ 10;» as” 7 1o; : a” s : ~ , _ ofltiifiid“ 430 T“ 50 610‘j ° 3 “lb“‘TSLoT‘T‘iioT ° n51 (GeV) ° TTE (GeV) Figure G.10: Precision versus TT ET for one EM (a) and one HD (b) trigger tower. The linear relationship with slope=1 indicates the good calibration of the tower. The excursion away from an absolute correlation is an indication of the inherent noise of the system. a quick way to check that the L1Cal signal path is properly cabled. G.10.3 Offline Gain Calibration The desired TT response of the L1Cal, 0.25 GeV per output count, is determined by comparing offline TT ET’s to the corresponding sums of precision readout channels in the calorimeter, which have already been calibrated against physics signals. For this purpose, data taken during normal physics running of the detector are used. An example can be seen in Fig. G.10. Gain calibration constants, for use in the ADF ET Lookup Memories, are derived from the means of distributions of the ratio of TT to precision readout channel sums for each EM and HD TT. Gain coefficients derived in this way have been determined to be stable to within ~2% over periods of months. 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