SEARCHFORSTANDARDMODELTOPQUARKANDZBOSONASSOCIATEDPRODUCTIONATATLASByBradleyD.SchoenrockADISSERTATIONSubmittedtoMichiganStateUniversityinpartialful¯llmentoftherequirementsforthedegreeofPhysics-DoctorofPhilosophy2016ABSTRACTSEARCHFORSTANDARDMODELTOPQUARKANDZBOSONASSOCIATEDPRODUCTIONATATLASByBradleyD.SchoenrockThisdocumentreportsonthesearchfortheproductionofatopquarkinassociationwithaZbosonusingdatafromtheATLASdetector.Thedatawascollectedduring2015,fromproton-protoncollisionsatacenter-of-massenergyof13TeVdeliveredbytheLargeHadronCollider(LHC)atCERN.Toisolatethisproductionmode,selectionrequirementsaremadeonthethreeleptons,b-quarkjetandlightquarkjetthattZnaturallycontains.Apro¯lelikelihood¯tisperformedtoputanupperlimitontheStandardModelpredictedcross-section.TheresultingmeasurementisconsistentwiththeStandardModelprediction.Tomywonderful,beautiful,loving,attimesodd,butalwayssupportivewifeRachel.Iloveyou.iiiACKNOWLEDGMENTSIwouldliketothankthefollowingpeople. Myfamily,speci¯callymyparents.WithouttheirguidanceIwouldnotbethepersonIamtoday.Ioftenthinktheyshouldhavewrittenaparentingbookbecauseoftheremarkableexampletheyhavesetforme.ThemembersoftheWisconsinTrailblazers.Growinguparoundallofyoushowedmewhathardworkandkindnesscouldaccomplish.MywifeRachel,whohasinspiredmeeverydaytoaccomplishallthatIhave.Myhighschoolteacherswhotookaninterestintheeducationofeverystudenttheytaught.TheyinspiredmetobecreativeandinvestigativewhenIsolvedproblemswhichwereskillsthatservedmewellingraduateschoolandlife.Myundergraduateandgraduateprofessors,speci¯callyDr.TiremanandDr.Donovanwhoencouragedmetogetinvolvedwithresearchasanundergraduate.Mycommitteememberswhooversawthisresearch:Drs.ReinhardSchwienhorst,KirstenTollefson,CarlSchmidt,NormanBirge,andGerdKortemeyer.MyadviserReinhardSchwienhorstforhiscontinuedmentorship.AllofthepostdocsandotherstudentswhoIhavehadthepleasureofworkingwithatMSU.Someofyouhelpedmedebugcodewhileothersgavemesomethingtosmileateveryday.TheentireATLAScommunitywithoutwhichtherewouldbenoexperimentnorchanceatansweringthegreatquestions.ivTABLEOFCONTENTSLISTOFTABLES...................................viiLISTOFFIGURES..................................viiiChapter1Introduction...............................11.1TheStandardModel...............................1 1.2FeynmanDiagrams................................6 1.3TopQuarkPhysics................................7 1.4tZAssociatedProduction............................10Chapter2CERN,theLHC,andATLAS...................162.1TheAcceleratorChain..............................172.2TheLargeHadronCollider............................172.3ATLAS......................................232.3.1MagnetSystem..............................26 2.3.2InnerDetector...............................30 2.3.3Calorimeters................................33 2.3.4MuonSystems...............................36Chapter3TheTriggerSystemonATLAS...................403.1Level1TriggerandDataAcquisition(DAQ)..................423.2HighLevelTrigger(HLT)............................443.3TriggerChains..................................443.3.1SingleMuon................................45 3.3.2SingleElectron..............................45Chapter4EventSimulation............................484.1TheMonteCarloMethod............................494.2SignalSimulation.................................504.3DibosonProduction................................514.4Top-QuarkPairProduction...........................514.5Top-QuarkPair+BosonProduction......................524.6Zboson+jets...................................524.7SingleTopQuark.................................524.8Wboson+jetsandMultijet...........................534.9WeightingandCorrections............................53Chapter5Object&EventReconstruction...................555.1ElectronReconstruction.............................55v5.2MuonReconstruction...............................565.3JetReconstruction................................575.3.1Jetb-tagging...............................585.4Zboson......................................595.5MissingTransverseEnergy(EmissT)andtheWboson.............605.6Reconstructingthetopquark..........................61Chapter6Analysis.................................636.1Preselection....................................636.2ControlRegions..................................706.3CutFlow.....................................80Chapter7Results..................................887.1SystematicUncertainties.............................887.2StatisticalAnalysis................................947.3Outlook......................................95Chapter8Conclusion................................97BIBLIOGRAPHY...................................98viLISTOFTABLESTable1.1:Thecross-sectionfordi®erentmodesofsingletop-quarkproductionattheLHCatps=8TeV[1][2]...........................10Table4.1:Informationongeneratorsforeachprocessconsidered.Allcross-sectionsconsiderfulldecaysincludinghadronic....................49Table6.1:Eventyieldsforvariousstagesofanalysistocomparewithcontrolregion(CR)yields.The¯nalselectionisdescribedinSection6.3anduncer-taintiesprovidedonthe¯nalselectionaredescribedinChapter7takeninquadratureforeachsample.Theyareprovidedhereforreference......71Table6.2:Eventyieldsafterselectioncutsareapplied.Uncertaintiesprovidedonthe¯nalselectionaretheuncertaintiesdescribedinChapter7takeninquadratureforeachsample...........................81Table7.1:Systematicuncertaintiesrelatedtobackgroundnormalizationandtheorymodeling.OtherTopisthecombinationoft¹tVandsingletop.......92Table7.2:Systematicuncertaintiesrelatedtoobjectidenti¯cation,resolution,andscale.OtherTopisthecombinationoft¹tVandsingletop..........93viiLISTOFFIGURESFigure1.1:TheSMofhighenergyphysics[3]......................2Figure1.2:Historyofhighenergyphysicsillustratingthetimeittookfromtheorizingtheexistenceoftheparticlesuntildiscovery[4]..............4Figure1.3:RepresentativeFeynmandiagramforthet-channelsingletopquarkpro-cess[5].....................................9Figure1.4:RepresentativeFeynmandiagramsfortheWt-channelsingletopquarkpro-cess[5].....................................9Figure1.5:RepresentativeFeynmandiagramforthes-channelsingletopquarkpro-cess[5].....................................9Figure1.6:RepresentativeFeynmandiagramforthetZassociatedproductiondecay-ingtothreeleptonsviaaZbosonandaWboson[6]...........11Figure1.7:Top-Quarkpairandsingletopquarkcross-sectionswithandwithoutac-companyingZboson[7]...........................12Figure1.8:InformationdrawnfromsimulationoftZ.LightquarkpTand´aswellasb-quarkpTand´.ThissimulationisdescribedindetailinSection4.2withaddedsimulationstepstakenforamorecompleteanalysis.....13Figure1.9:InformationdrawnfromsimulationoftZ.ThepTofotherobjectsintZincludingtheleptonfromthedecayoftheZbosonandtheleptonfromthedecayoftheWboson.ThissimulationisdescribedindetailinSection4.2withaddedsimulationstepstakenforamorecompleteanalysis....................................14Figure2.1:DiagramoftheacceleratorcomplexforprotonstogettotheLHC[8]..18Figure2.2:ASegmentoftheLHCbeampipe[9]....................19Figure2.3:Peakinstantaneousluminosityovertime[10]................21Figure2.4:TotalLHCdeliveredintegratedluminosityovertimeforrun1[10]...21Figure2.5:TotalLHCdeliveredintegratedluminosityovertimeforrun2[10]...21viiiFigure2.6:Numberofinteractionsperbunchcrossingfor7and8TeV[10].....22Figure2.7:Numberofinteractionsperbunchcrossingfor13TeV2.6.........22Figure2.8:ATLASwithitsnamesaketoroidalmagnetsprominentlyvisible[11]...25Figure2.9:CutawaydiagramofATLAS[12]......................26Figure2.10:A¯gurediagramminghowparticleidenti¯cationcanbeachievedusingmultiplelayersofthedetector[13]......................27Figure2.11:IllustrationoftheATLASmagnetsystem,showingthebarrelsolenoid,barreltoroid,andendcaptoroidcoils[14]..................28Figure2.12:Amappingofthemagnetic¯eldsinATLAS[15]..............29Figure2.13:CutawaydiagramoftheATLASinnerdetector[16]............31Figure2.14:Trackreconstructione±cienciesfortheIDinATLAS[17]........33Figure2.15:CutawaydiagramoftheATLAScalorimetersystems[18].........34Figure2.16:CutawaydiagramoftheATLASmuonspectrometerandtoroidmagnetsystems[19]..................................37Figure2.17:TheTGCwheel[20].............................39Figure3.1:AZbosondecayingtoanelectronpositronpair..............42Figure3.2:Triggere±ciencyforthesinglemuontriggerin(a)thebarrelregionand(b)theendcapregion.[21].........................46Figure3.3:E±ciencyofthesingleelectrontriggerovertransverseenergyrangesintheATLASdetector[22]...........................47Figure5.1:Diagramillustratingadisplacedvertex.[23]................59Figure6.1:DistributionsofLeptonpTfor(a)leading,(b)second,and(c)thirdlep-tonsaswellas(d)leadingjetpTwithpreselectionappliedexceptthecutsonminimumpTthresholdsshownwhichare40GeVfortheleadinglepton,20GeVforthesecondlepton,10GeVforthethirdlepton,or40GeVfortheleadingjet.ThereareminimumpTreconstructionthresholdsfortheseobjectswhichare25GeVfortheleadingleptonandleadingjet,and10GeVforthesecondandthirdleptons................67ixFigure6.2:Distributionsof(a)numberofjets,(b)numberofb-jets,(c)mW T,(d)EmissT.Atleastonejetisrequiredatthislevelinallcases,butthecutonthevariableshownisomittedinordertoassessthefulldistribution.Thedistributionofthenumberofjetsdoesnotincludethecutonthenumberofjets,thedistributionofthenumberofb-jetsdoesnotincludethecutonthenumberofb-jets,andthemW TandEmissTdistributionsdonotcontaintheEmissTorthenotchcuts.........................68Figure6.3:Distributionsof(a)two-dimentionalmapofmW TvsEmissTforthesignal,(b)twodimentionalmapofmW TvsEmissTforthedata,and(c)invariantmassoftheZboson.Forboth(a)and(b)theEmissTcutandthenotchcutarenotappliedandfor(c)theZ-bosonmasswindowcutisnotappliedinordertoshowthefulldistribution....................69Figure6.4:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthecontrolregionfort¹t..................................72Figure6.5:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthecontrolregionfort¹t......................73Figure6.6:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetintheinter-mediatecontrolregionforDibosonandZ+jets..............74Figure6.7:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTintheintermediatecontrolregionforDibosonandZ+jets.....75Figure6.8:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthecontrolregionforDiboson..............................76Figure6.9:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthecontrolregionforDiboson...................77Figure6.10:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthecontrolregionforZ+jets...............................78Figure6.11:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthecontrolregionforZ+jets....................79xFigure6.12:Distributionsof(a)mW Twhichisrequiredtobe>50GeV,(b)the´oftheleadingnonb-taggedjetwhichisrequiredtobe>1.5,and(c)the¢Rbetweentheb-jetandleadingnon-b-jetwhichisrequiredtobe>2.5.Eachhastheentireselectionappliedexceptthevariableplottedtoviewthefulldistribution..............................82Figure6.13:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthesignalregion.....................................84Figure6.14:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthesignalregion..........................85Figure6.15:(a)Numberofelectronsand(b)numberofmuons.............86Figure6.16:Distributionsofthetop-quarkpolarizationinthe(a)Optimalbasisand(b)thehelicitybasis,(c)theW-bosonhelicity,and(d)themassofthetopquark...................................87xiChapter1 Introduction Ifyouhaveknowledge,letotherslighttheircandlesinit.-MargaretFullerHighenergyphysicsisconcernedwithobtainingthemostfundamentalunderstandingoftheuniverse.Inpracticethismeanscategorizingallfundamentalparticlesandtheirinteractionsinordertounderstandwhattheworldismadeof.Assortedscienti¯c¯eldsquestionwhattheworldismadeofinvariousdetail.Chemistryaskswhichatomsandmoleculescomprisethethingsaroundus,nuclearphysicsinvestigateswhatmakesupthenucleiofatomsandhownucleiareformed,andhighenergyphysicsstudieswhatwecurrentlythinkarethemostfundamentalparticlesinexistence.Inordertounderstandhighenergyphysicsweneedaframeworktodescribetheelementaryparticlesandtheirinteractions.ThisframeworkisreferredtoastheStandardModel(SM). 1.1TheStandardModel TheSMofhighenergyphysicshasbeenamongthemostsuccessfultheoriesofthepastcentury.Ithasbeentestedagainandagainandhasencounteredfewunexplainedanomalies.Itstartedasane®orttocombinethefundamentalforcesweknowintooneoverarchingtheory.ElectricityandmagnetismhadbeencombinedintoelectromagnetismlongagoandinthelastcenturytheSMwasdeveloped.Electromagnetismwascombinedwithweakinteractions,1followedbytheinclusionoftheHiggsmechanismandstronginteractionstoformtheSMweknowtoday[24,25,26].Figure1.1:TheSMofhighenergyphysics[3].TheSMparticlesareclassi¯edbasedontheirpropertiesandinteractionsandareshowninFigure1.1.Onewaywecanclassifyparticlesisbytheirspin.Aparticlewithhalfintegerspiniscalledafermion(coloredredorgreeninFigure1.1)whileaparticlewithintegerspinisaboson(coloredblueorblackinFigure1.1).Alldiscoveredfundamentalparticlesareeitherspin0,spin12orspin1.Wefurtherbreakdownthefermionsintotwocategories,the¯rstsetaretheleptonswhichhaveanelectriccharge§1(electron,muon,andtau)tointeractwiththeelectroweakforce,andthreeneutralneutrinoswhichonlyinteractviatheweakforce.Theothertypeoffermionisthequark.Quarksinteractviatheweak,electromagnetic,andstrongforcescarryinghalfintegerspins,§13or§23electricalcharges,andcolorcharges.The2strongforce,atlowenergies,impartscolorcon¯nementontoindividualquarkswhichbindsthemtogetherinmesons(quarkantiquarkpairs)orbaryons(threequarksystemssuchastheprotonorneutron).Ifquarksarehighenoughenergytheyundergoaprocessknownashadronizationwherenewquark-antiquarkpairsarecreatedfromthatenergyuntilallthatremainaremanymesonsandbaryons.Quarksalsointeractelectromagneticallyandweaklyliketheirchargedleptoniccounterparts.Thevectorbosons(spin1)moderatetheforcesinvolvedintheStandardModel.Thegluoninteractsviathestrongforce,thephotonandtheW§interactelectromagnetically,andtheW§andZbosonsinteractweakly.The¯nalparticlewehaveistherecentlydiscoveredHiggsboson[27]whichtooknearly50yearstodiscover.AhistoryofparticlediscoverycanbeseeninFigure1.2.AdeeperunderstandingoftheSMcanbeobtainedthroughtheLagrangedensity[25],L=¡12tr[G¹ºG¹º]¡12tr[W¹ºW¹º]¡14B¹ºB¹º+i¹Ã[¡¡D¡m]Ã+¹ÃiLyijÃjRÁ+h:c:+jD¹Áj2¡V(Á)(1.1)whereÃistheDirac¯eldwithasumoverthematterparticleswithLdenotingleft-handedparticlesandRdenotingright-handedparticles,ÁistheHiggs¯eld,yijaretheYukawacouplings,¡¡Disthecovariantderivativede¯nedthroughDiracslashnotationas¡¡D=°¹D¹(1.2)D¹=@¹¡igSTaGa¹¡iYgYB¹¡igL2¾aWa¹(1.3)whereYisthehyperchargeofaparticle.Hyperchargeforleft-handedparticlesare¡12for3Figure1.2:Historyofhighenergyphysicsillustratingthetimeittookfromtheorizingtheexistenceoftheparticlesuntildiscovery[4].4leptonsand16forquarkswhileforright-handedparticleshyperchargeistheelectricchargeoftheparticle.ThetensorTaisde¯nedashalfof¸a(whicharethe8GellMannmatrices)forquarks,andiszeroforleptons.The¾amatricesarethe3Paulimatrices.ThecovariantderivativealsoappliestotheHiggsboson,withTa=0(nocouplingtostrongforce)andY=¡12.Thegauge¯eldstrengthtensorisdenotedbyB¹ºandisde¯nedbyB¹º=@Bº@¹¡@B¹@º(1.4)whereBºisthehyperchargegaugepotential.TheQCD¯eldtensorG¹ºde¯nesthegluon¯eldsandarede¯nedasG¹º=¸a2Ga ¹º=igs[D¹;Dº](1.5)Ga ¹º=@¹Ga º¡@ºGa ¹+gsfabcG¹bGºc(1.6)whereGºisthestronggaugepotential.TheweaktensorW¹ºisde¯nedasW¹º=¾a2Wa¹º=ig[D¹;Dº](1.7)Wa¹º=@¹Waº¡@ºWa¹+gfabcW¹bWºc(1.8)whereWºistheweakgaugepotential.NotethattheWa¹terminequation1.3onlycouplestoleft-handedparticles.TheSMLagrangianinequation1.1containsalotofinformationontheSMinoneconciseequation.The¯rstthreetermsintheLagrangedensityformulacontainsthestrongandelectroweakforces,thefourthtermdescribeshowtheparticlesinteractwiththese¯elds,5the¯fthtermanditsHermitianconjugate(h:c:)describeshowthefermionsgettheirmasses(notetheÁdependencemeansthattheHiggscontributesbutdoesnotdeterminethevalueoftheirmasses),thenexttolasttermdescribeshowtheHiggsgivesmasstothebosons,andthe¯naltermistheHiggspotential[24,25,26].ThisformulationrepresentsagroupwithaSU(3)£SU(2)£U(1)symmetry.TheSU(3)representsthestrongforce,withthethreefoldsymmetryincolorcharge.TheeightgeneratorsofthisSU(3)symmetrycorrespondtothevariouscolorcombinationsofthegluonwhichcanbemathematicallyrepresentedbytheGell-Mannmatrices.TheSU(2)£U(1)representstheelectroweakforcewhichuni¯edelectricity,magnetism,andtheweakforceswhosegeneratorscanberepresentedbythePaulimatrices.TheHiggsmechanismbreaksthissymmetryandthisphenomenonisknownaselectroweaksymmetrybreaking.Bybreakingthissymmetrythemasslesselectroweakbosons(W1,W2,W3),andthehyperchargeboson(B)arerecombinedasthemassiveW+,W¡(whicharelinearcombinationsofW1andW2),themassiveZ0(whichisalinearcombinationofW3andB)andthemasslessphoton(whichisacombinationofW3andBaswell).TheHiggsdoublethas4degreesoffreedom,threeofwhichareconsumedbythelongitudinalcomponentsofthemassiveW+,W¡,andZ0.Theremainingdegreeoffreedomisaneutralscalarparticle,theHiggsboson[28,29].1.2FeynmanDiagrams ThankstoRichardFeynmanwecanobtainanintuitiveunderstandingofparticlesandtheirinteractionsthroughFeynmandiagrams[25].Wecanviewthesepicturesashavingdirectcorrelationwiththeprocessesinvolvedandevensetuptherelevantequationstocomputethescatteringamplitudeofaparticularprocess.Inthesediagramswecompactthespacial6dimensionsintooneverticalaxiswhiletimeisrepresentedonthehorizontalaxis.Thecross-sectionforaparticularscatteringprocessisde¯nedastheratioofnumberofparticlesscatteredperunittime(dN(t))tonumberofparticlespassingthroughade¯nedareaperunittime(n),seeequation1.9.d¾=dN(t)=n(1.9)Nevents=¾ZL(t)dt(1.10)L(t)=n1n24¼¾x¾y(1.11)Informallythisishowprobablethatprocessistooccurineachinteraction.Thestan-dardunitforcross-section(¾)istheBarn(10¡24cm2)butwecommonlyusepicobarnorfemtobarntodescribecross-sections.Consequentlywede¯nethebeamintensity,orlumi-nosity(L),ininversepicobarnsorinversefemtobarns.Thatwaywecaneasilycalculatetheexpectednumberofeventsfromequation1.10.Luminositycanbecalculatedfromthebeamparametersoftheacceleratorbyequation1.11wheren1andn2arethenumberofparticlesineachbeam,and¾xand¾yaretheGaussianRMSbeamsizesintheirrespectivedirections[25]. 1.3TopQuarkPhysics Thetopquarkisofspeci¯cinteresttohighenergyphysicsandinparticularthisthesis.Ithasamassthatmakesittheheaviestfundamentalparticlethatweknowtoday,173.2GeV,7whichisaboutthemassofagoldatom[30].Duetothetopquark'slargenaturalwidth,whichisde¯nedastheprobabilityperunittimethataparticledecays,itistheonlyquarkwithanobserveddecaylifetime(10¡25s)shorterthanthetimescaleforstronginteractions(10¡24s)[31,32,33,34].Becauseofthis,andthattheCKMmatrixelementVtb(Vtbcorrespondstothestrengthofthetopquark°avorchangingtobottomquarkthroughaweakdecay)isapproximatelyequalto1,thetopquarkalmostalwaysdecaysintoaWbosonandabquarkbeforeithadronizesintoajet[35,25].ThetopquarkwasoriginallydiscoveredthroughpairproductionattheTevatronin1995[36,37].LatertheproductionofasingletopquarkwasdiscoveredattheTeva-tron[38,39]anditswidthmeasured[32,33,34].TheseproductionchannelshavealsobeeninvestigatedattheLHC[40,41,42,43,44].TherearethreechannelsofsingletopquarkphysicsthathavebeenstudiedattheLHC.Theyaret-channel,s-channel,andassociatedproduction(alsoreferredtoasWt-channel).ThelargestcontributiontosingletopattheLHCist-channel,followedbyWt-channel,withs-channelbeingthesmallestofthethree.Beingthelargest,t-channelwasobserved¯rstandhasbeenobservedindependentoftheothersingletop-quarkproductionmodes[45].Wt-channelhasalsobeenobservedinATLAS[46]andCMS[47].Cross-sectionsforthedi®erentsingletop-quarkprocessesataproton-protoncolliderwithps=8TeVaregiveninTable1.3.Thecenter-of-massenergyisdenotedaspsfortheproton-protoncollision.TheLHC'shighbeamenergiesmakegluonsintheprotonmoreprevalentthenwhencomparedtoenergeticquarkssoalookintotheinitialstatesoftheseprocessesshowninFigures1.3,1.4,and1.5revealthehierarchicalnatureoftheircross-sections.Thet-channelprocesshasaninitialstateofanenergeticgluonaswellasalightquark,8Figure1.3:Representative Feynmandiagramforthe t-channelsingletopquarkpro-cess[5].Figure1.4:Representative Feynmandiagramsforthe Wt-channelsingletopquarkpro-cess[5].Figure1.5:Representative Feynmandiagramforthe s-channelsingletopquarkpro-cess[5].9Wt-channelhasaninitialstateofanenergeticgluonaswellasanenergeticbquark(whichwillbehardertogetfromaprotonwhencomparedtoalightquarkwhichisnaturallyinaproton),ands-channelhasanenergeticantiquarkinitsinitialstatemakingitdi±culttoproduceattheLHC.Whiles-channelhasacomparativelysmallcross-sectionattheLHCitwasnotsodisfavoredattheTevatronbecausetheTevatronwasaprotonanti-protoncollider,makingenergeticanti-quarksmoreprevalent.t-channel216.99+9.04-7.71pbWt-channel84.4+5.00-6.80pbs-channel10.32+0.40-0.36pbTable1.1:Thecross-sectionfordi®erentmodesofsingletop-quarkproductionattheLHCatps=8TeV[1][2].1.4tZAssociatedProduction TheproductionofatopquarkinassociationwithaZbosonhasnotbeenconsideredattheLHCuntilnow.TheFeynmandiagramfortZcanbeseeninFigure1.6.Therelatedt¹tZcross-sectionhasbeenmeasured,andalthoughtheuncertaintyisquitehigh,thetopquark+Zbosonprocessesareapotentiallyfruitfulonetoinvestigate[48].TherateofthetZprocesssuggeststhatitshouldbevisibleinthe8TeVdatasetasseeninFigure1.7whichshowsNLOcross-sectionsfortheprocessesshownatvariousenergies.ThetZsignatureinvestigatedincludesthreechargedleptons,missingtransverseenergy,andtwojets,oneofwhichmaybeidenti¯edasabquark[7].SeveralhistogramscanbeseeninFigures1.8and1.9whichshowsimulationsofparticlesbeforeanydetectorinteractionordecays.SomenotablefeaturesoftZarethedisparitybetweenthe´(´isde¯nedinSection2.3)ofthelightjetvs.bquark,thehighertransverse10momentum(pT)ofthelightjetcomparedtothebquark,thesimilarityinpTofleptonsfromtheZbosonandWboson,andthepToftheneutrinowhichwillmanifestasEmissT.ThevariableEmissTisdiscussedinmoredetailinSection5.5.Figure1.6:RepresentativeFeynmandiagramforthetZassociatedpro-ductiondecayingtothreeleptonsviaaZbosonandaWboson[6].StandardmodeltZisimportanttomeasurebecauseitisabletoprobethecouplingofthetopquarkwithaZboson[7].StandardmodeltZisalsoabackgroundtoseveralSMprocessesandBeyondtheSMprocesses.AnomaloustZcouplingsareonemodelthatareofinterest[49].Monotop-quarkproductionisoneoftheseinvolvingatopquarkandlargemissingtransverseenergycomingfromtheorizeddarkmatercandidates.SingletopquarkproductioninassociationwithaHiggsbosonisimportanttolookfortoprobethecouplingofaHiggsbosontothetopquark.OnecanalsoconsidertZasabackgroundtoFlavorChangingNeutralCurrent(FCNC)decaysfromt¹twhereoneofthetopquarksdecaystoaZbosonandalightquarkwhichwouldenhancethecrosssectionforthisanalysis.Forthisanalysisacutandcountmethodisused.Byexaminingthekinematicproperties11Figure1.7:Top-Quarkpairandsingletopquarkcross-sectionswithandwithoutaccompanyingZboson[7].12TLIght Quark P050100150200250300350400Events/10GeV020406080100120140hLight Quark 012345Events20406080100T050100150200250300350400Events/10GeV050100150200250h012345Events20406080100120140Figure1.8:InformationdrawnfromsimulationoftZ.LightquarkpTand´aswellasb-quarkpTand´.ThissimulationisdescribedindetailinSection4.2withaddedsimulationstepstakenforamorecompleteanalysis.13TZ lepton P050100150200250300350400Events/10GeV05101520253035TW lepton P050100150200250300350400Events/10GeV01020304050T050100150200250300350400Events/10GeV01020304050TWboson P050100150200250300350400Events/10GeV0102030405060TTopQuark P050100150200250300350400Events/10GeV0510152025303540TNeutrino P050100150200250300350400Events/10GeV05101520253035Figure1.9:InformationdrawnfromsimulationoftZ.ThepTofotherobjectsintZin-cludingtheleptonfromthedecayoftheZbosonandtheleptonfromthedecayoftheWboson.ThissimulationisdescribedindetailinSection4.2withaddedsimulationstepstakenforamorecompleteanalysis.14oftheparticles,aswehavebeguntodoinFigures1.8and1.9,regionsofphasespacecanbecreatedtoisolatebackgroundstoensureproperdatamodelingthroughsimulationaswellasisolatingthetZsignaltoimprovesensitivityforastatisticalanalysis.15Chapter2 CERN,theLHC,andATLAS Whenonetugsatasinglethinginnature,he¯ndsitattachedtotherestoftheworld-JohnMuir.In1954theConseilEuropenpourlaRechercheNuclaire(CERN)formedanuclearphysicslaboratoryjustoutsideofGeneva,Switzerland.CERNhassincedeliveredontheirpromisetogiveusdozensofexperimentsthatstudyeverythingfrommeteorologytobiology.Someofthelabsaccomplishmentsinclude:thediscoveryoftheWboson[50]andZboson[51];thedeterminationofthenumberoflightneutrinofamilies[52];thecreationoftheworldwideweb[53];thecreation,isolation,andstabilizationofanti-hydrogenforupto15minutes[54];andthediscoveryoftheHiggsboson[55,56].OverthepastfewdecadesCERNhasfocusedonacceleratorphysics,housingtheLargeElectron-PositronCollider(LEP)[57]whichranfrom1989until2000.LEPwasthenreplacedwiththeLargeHadronCollider(LHC)[58]startingoperationsin2009afterafaultystartin2008duetoafailureinanelectricalconnectionleadingtoaruptureoftheliquidheliumenclosureofoneofthesuperconductingmagnets.TheLHCandLEPareoftenthoughtofhandinhandbecausetheybothusedthesame27kmtunnel.162.1TheAcceleratorChain TheLHCiscapableofcollidingprotonsaswellasheavyions,althoughwefocusontheprotonacceleratorchainshowninFigure2.1.TheprotonsusedintheLHCstartfromahydrogenbottlewhereamagnetic¯eldstripstheelectronsfromH2andtheresultingprotonsaresentthroughlinearaccelerator3(Linac3).Linac3usesradio-frequencycavitiesthatchargecylindricalconductorswhicharealternatelypositivelyandnegativelycharged.Theconductorsdirectlybehindtheprotonsarepositivelychargedwhiletheconductorsinfrontoftheprotonsarenegativelycharged,withbothworkingtoacceleratetheprotons.OncetheprotonsarethroughLinac3theywillbebunchedwith100msbunchspacingandwillbeupto50MeVinenergy[59].Fromheretheyaresentthroughthe157mcircumferenceProtonSynchrotronBoosterwhichacceleratetheprotonstoanenergyof1.4GeVinonly530ms[60].Fromtheretheprotonsgotothe628mcircumferenceProtonSynchrotron(PS)fortighterbunchingof25ns,andareacceleratedto25GeV[61].The¯nalstepbeforetheLHCistheSuperProtonSynchrotron(SPS)whichis7kmincircumference.TheSPScanaccelerateprotonsto450GeVin4.3seconds[62].TheSPSisnotableforthe1984NobelprizewinningdiscoveryoftheWbosonandZboson[63].FinallytheprotonsmakeittotheLHCtoberampeduptothedesiredenergyforcollision.AsegmentoftheLHCcanbeseeninFigure2.2whichshowsthehousingforthemagnetswiththebeampipelocatedinside. 2.2TheLargeHadronCollider Ittakesafewminutesto¯lleachLHCring(oneineachdirection)formingthebeamswiththousandsofbunchesofprotonswhichgetacceleratedtogether.Aftera20minutewaittime17Figure2.1:DiagramoftheacceleratorcomplexforprotonstogettotheLHC[8].18Figure2.2:ASegmentoftheLHCbeampipe[9].afterinjectiontostabilizeandtightenthebeamstheyareacceleratedoverhalfanhourtogetuptofullenergy.Intotalittakesbetween5and20secondstogettheprotonsfromLinac3totheLHC,thenalittlelessthananhourtogetthemuptoenergy.Oncesetuptheycanbestoredforcollisionsforaround10hours.Thelifetimeoftheusablebeamislimitedmostlybyprotonsinthebeamexchangingmomentumbetweenthetransverseandlongitudinaldirections.ThisisknownastheTouscheke®ect[64].ParticlesarelostfromthebeamiftheirlongitudinalmomentumdeviationisgreatenoughforthemtoescapetheRFbucket(thelongitudinalspacethatde¯nesbunches)orthemomentumaperture(thetransversespacethatde¯neshowlargeabunchcanbeinthetransverseplane).Afterapproximately10hoursofbeamcollisionsthebeamisexhaustedandisdumpedandtheinjectionprocessisrepeated[65].19Giventhatthenecessaryconditionsforthediscoveryofnewphysicsweresoextreme,theLHCwasdesignedwithunprecedentedcapabilities.WhilemostpeoplethinkoftheLHCasthehighestenergycolliderintheworld,whichitis,therearemoreconsiderationswhenbuildinganaccelerator.Inordertodiscoverrareprocessesweconsiderinstantaneousluminosityinordertocollectasmanyinterestingeventsascanbeproducedasquicklyaspossible.PeakATLASonlineluminosityisaround5¤1033cm¡2s¡1(asseeninFigure2.3)whichisaround20timesthepeakTevatronluminosity[66,67].Agreaterinstantaneousluminosityleadstoagreaterintegratedluminosity,whichisameasureofhowmuchdatahasbeencollectedovertime,asseeninFigure2.4forpreviousthe7TeVand8TeVrun(Run1)andFigure2.5forthe13TeVrun(run2).Asrun2wentoninstantaneousluminositywasincreasedtomaximizedatacollectionshowingthedramaticincreaseindatacollectioninAugustandSeptember[10].Thegenerictermluminositywillusuallyrefertointegratedluminosityinthisthesisunlessotherwisestated.Inordertokeepthebeamsontrackandtogether,theLHChas1232dipolemagnetstosteerthebeamand392quadrupolemagnetsforfocusingandatotalofaround9600superconductingmagnets.Thebeamsaresegmentedinto2808bucketswhichcanbe¯lledwithbunchesofprotonsornot.TheLHCwasdesignedtodeliverbunchesthatarespacedsothattheresultingcollisionsare25nsapart(correspondingtoapproximately10metersbetweenbunches).In2015theLHCoperatedat50nsbunchspacing(leavingeveryotherbucketempty)tohelpwithpileup.Pileupiswhentwoseparateprotonprotoncollisionsarereadinatthesametimeandcancomeintwoforms.The¯rstisout-of-timepileupandreferstotwodi®erentbunchcrossingsinteractingwiththedetectormorequicklythanthedetectorsresponsetime.Runningwith50nsbunchspacinghelpswithout-of-timepileup20Figure2.3:Peakinstantaneousluminosityovertime[10].Month in YearJanAprJulOct]Delivered Luminosity [fb05101520253035 = 7 TeVs2010 pp = 7 TeVs2011 pp = 8 TeVs2012 pp ATLASOnline LuminosityFigure2.4:TotalLHCdeliveredinte- gratedluminosityovertimeforrun1[10]Figure2.5:TotalLHCdeliveredinte- gratedluminosityovertimeforrun2[10]21whilerunningwith25nsbunchspacinghelpswiththeothertypeofpileup,in-timepileup.In-timepileupiswhentwopartoncollisionshappenwithinthesamebunchcrossingandbothinteractwiththedetectoratthesametime.Ourdatacollectiontechniquesaredesignedaroundsomedegreeofpileup.Raisingthepileupallowsustocollectmoredata,potentiallyatthecostofdataqualityifitisnotcarefullymonitored.Withthisinmindpileupwasincreasedfromthe7TeVrunwithanaverageof9.1interactionsperbunchcrossingtothe8TeVrunwith20.7interactionsperbunchcrossingasseeninFigure2.6.Inrun2amoreconservative13.7interactionsperbunchcrossingwasusedasseeninFigure2.7.Pileupisanimportantconsiderationintriggeringandisdiscussedinthiscapacityinchapter3[65].Mean Number of Interactions per Crossing051015202530354045/0.1]Recorded Luminosity [pb020406080100120140160180Online LuminosityATLAS> = 20.7m, = 9.1m, = 13.7m15GeVandj´j<2.5OR¸2leptonswithpT>10GeVand¸1leptonwithpT>20GeVwhichhasj´j<2.5.ThisrequirementalongwiththeleptontriggermatchingrequirementdescribedinChapter5andtheelectronormuonselectiondescribedinChapter6meanthattheelectronandmuontriggerchainsarethemostrelevant.443.3.1SingleMuon Thesinglemuontriggerisoneofthelargestcontributionstothisanalysis.ThisbeginswiththemuoninteractingwiththevariouscomponentsofthedetectorasdescribedinChapter2.ThemostusefulinteractionformuontriggeringpurposesistheResistivePlateChamber(RPC)hits.IftherearecoincidenthitsinmultiplelayersoftheRPC,amuoncandidateis°aggedandpassedtotheHLT.TheHLTthenusestheRoItomakeafewrequirementsonthequalityofpossiblemuoncandidates.OneoftherequirementsoftheHLTisthathitsintheRPC,TGC,MDT,andIDlineupin´¡Áforamuoncandidate.AnotheristhatthemuonsbeisolatedfromhadronicactivitytoimprovetheselectionofmuonsoriginatingfromWbosonorZbosondecayswhilemitigatingmuonsfrompionorheavyquarkdecayswhichareputintoB-physicsstreams.Cosmicmuonsarerejectedwhenthemuonhitsdonotpointbacktotheinteractionpoint.Oncetheaboverequirementshavebeenmet,furtherchecksareperformedtoensurethequalityofmuonstheymustbewhollyreconstructedbyeverylayerofthedetector,andverifythattherequirementsareaccuratelymet.Theeventisthenstoredwithinformationonthevarioustriggerspassedorfailed,andobjectsarereconstructedo²ine[97].Thee±ciencyofthesinglemuontriggerisassessedseparatelyinthebarrelandforwardregions,andissigni¯cantlybetterintheforwardregionsasshowninFigure3.2[21].Thedi®erenceine±ciencyislargelyduetothecrackregionaround´=0.3.3.2SingleElectron Oneofthemostrelevanttriggersthatappliestothisanalysisisthesingleelectrontrig-ger.ThisbeginswiththeelectroninteractingwiththevariouscomponentsofthedetectorasdescribedinChapter2.AtL1,energydepositionsintheelectromagneticandhadronic45(a)(b)Figure3.2:Triggere±ciencyforthesinglemuontriggerin(a)thebarrelregionand(b)theendcapregion.[21] calorimetersareconsidered,andaRoIisbuiltaroundhighenergydepositions.ForelectronstheelectromagneticdepositionsareusedtobuildtheRoI.ThisRoIclustermustbehighenoughinenergyaswellasbeingisolatedfromotheractivityintheelectromagneticcalorime-terandthehadroniccalorimeter.AtthispointtheROIispassedtotheHLT.Notethattheobjectpassedisnotanelectronyet,becausephotonsexhibitverysimilarbehaviorwithitsinteractionsintheelectromagneticcalorimeter.OnceanRoIhasbeenpassedtotheHLTwecantakeinnerdetectorinteractionsintoaccount.Energyclustersintheelectromagneticcalorimeterarematchedin´¡Áanditsenergyarecomparedtothemomentummeasuredbytheinnerdetectortracks.Isolationrequirementsintheelectromagneticcalorimeterandhadroniccalorimeterarere-assessedaftercorrectionsareapplied,andisolationontracksareappliedtoensuretheentireenergydepositcamefromoneproton-protoninteraction.Oncetheserequirementsaremettheeventisstoredwithinformationonthevarioustriggerspassedorfailedandtheelectron(andotherobjectsintheevent)isreconstructedo²ine[97].Overallthee±ciencyofthesingleelectrontriggerisquitegoodatover90%forallenergiesusedforthisanalysisasseeninFigure3.3[22].46 [GeV]TE2040608010012014010´Trigger Efficiency00.20.40.60.811.21.4Data ee MC®Z HLT e12_lhloose_L1EM10VHATLAS PreliminaryL dt = 3.34 fbò=13 TeV, sFigure3.3:E±ciencyofthesingleelectrontriggerovertransverseenergyrangesintheATLASdetector[22].Multileptontriggersareusedthatworkonsimilarprinciplesasthesingleelectronandsinglemuontriggers.Thesetriggerchainshavevariedthresholdstoacceptpairsofobjectsthatareindividuallymorelooselyde¯ned(bothinenergy/momentumthresholdsaswellasisolation)comparedtotheirsinglecounterparts[98].47Chapter4 EventSimulation Alllawsaresimulationsofreality.-JohnC.LillyTheabilitytodiscoveranythinginhighenergyphysicshingesonourabilitytoaccuratelymodeloursignalandbackgroundsinordertodistinguishthekinematicpropertiesofthebackgroundeventsfromthekinematicpropertiesofthesignalbeingsearchedfor.Thesimulationcomesinseveralsteps.Firstwesimulatethepartonlevelinteractionswithoneofseveraldi®erentMonteCarlogenerators.Thenwegothroughapartonshoweringprocesstotakebarequarksandhadronizethemintojets,whichisperformedbyoneofseveraldi®erentpartonshoweringprograms.NextwegothroughadetectorsimulationinordertomimichowparticlesinteractwithATLASusingtheGEANT4[99]packageforallprocesses.LastlywerunoursimulationsthroughthesamesoftwarethatisusedtoprocessdatatoreconstructobjectsasdescribedinChapter5.Backgroundsconsideredinthisanalysisare:²DibosonprocessesincludingWW,WZ,andZZ.²Top-quarkpairproduction,t¹t.²Top-quarkpair+bosonproductionwhichisthesameasTop-QuarkPairProductionbutwitharadiatedWbosonorZboson,t¹tZort¹tW.48²Zboson+jets.²SingleTop-QuarkProductionincludings-channel,t-channel,andWt-channelasde-scribedinChapter1.²Wboson+jetsandMultijetwhicharesingleleptonbackgrounds.andfurtherdetailsabouthowtheyweresimulatedcanbefoundinTable4.1.processgeneratorpartonshowerpdfordercross-section(pb)t¹tPowhegPythia6CT10/CTEQ6L1NLO(0extrapartons)/LO(>0extrapartons)451.6Single-TopPowhegPythia8CT10/CTEQ6L1NLO(0extrapartons)/LO(>0extrapartons)t-channel:70.3Wt-channel:35.8s-channel:3.44ttVMadgraph5Pythia8CTEQ6L1LOttZ:0:471ttW:0:567Z+jetsSherpa2.2.1Sherpa2.2.1CT10NLO(<2extrapartons)/LO(3or4extrapartons)17486.7DibosonPowhegPythia6CT10/CTEQ6L1NLO(0extrapartons)/LO(>0extrapartons)WW:101:3WZ:137:7ZZ:124:5tZMadgraph5Pythia8CTEQ6L1LO0.240Table4.1:Informationongeneratorsforeachprocessconsidered.Allcross-sectionsconsiderfulldecaysincludinghadronic. 4.1TheMonteCarloMethod SimulatingthedatabeginswithStandardModelpredictions,whichinanidealworldcouldbecalculatedexactly.WeemploytheMonteCarlomethodtoperformintegrationsthatarecumbersometoperformbyhandandwherenumericalmethodsaremoreappropriateinordertocalculaterelativeratesatwhichparticlesinteractwitheachother.Fromthis,fundamentalpropertiesofoutgoingpartonscanbepredicted.Thereareaplethoraofgeneratorsandpartonshoweringprogramswhichexcelatsimu-latingvariousprocesses.TheATLAStopgrouprecommendswhichMonteCarloprograms49touseforeverysampleexcepttZforwhichthereisnorecommendation.4.2SignalSimulation SeveralMonteCarlogeneratorsareconsideredtomodelthetZprocess.Madgraph[100]isusedtogeneratesamplesandPythia[101]isusedtoperformpartonshowering.Mad-graph5+Pythia8ischosenbecausethisisthesamegeneratorandshoweringsetupusedtosimulatet¹t+X.AnotherreasonMadgraph5+Pythia8ischosenisthatMadgraphandPythiahavebeenwidelyusedtoolsforquiteawhileinhighenergyphysicsandasaresulttheyareverywellunderstoodgeneratorswithgoodsimulationofawidevarietyofphysicsprocesses.OneofthelimitationsofMadgraphisthatitisaleadingorder(LO)generator.OneconsiderationwhengeneratingtZiswhatdecaymodesoftheZbosonandWbo-sonshouldbegenerated.ForthisanalysisweareinterestedintheallleptonicmodewiththeZbosonandtheWbosondecayingtoleptons.OtheranalyseswithinATLASareinterestedindi®erentleptonmultiplicitieswhichcanbevariedbyeithertheWbosondecayinghadron-ically,theZbosondecayinghadronically,ortheZbosondecayingtoapairofneutrinoswhichisknownastheinvisiblemode.ThefullyhadronicmodefortZhasalargebranchingratioandisnotofinteresttoATLASanalysesduetothelackofadistinctsignatureinthedetectortotriggeron,sotosaveoncomputingtimeitisnotincludedintheMonteCarlosample.Everyothercombinationisproduced.Anotherconsiderationishowweparametrizetheincomingpartons.ThisisdescribedbyPartonDistributionFunctions(PDFs)andthePDFthatisusedforthisMonteCarlosampleisCTEQ6L1fromtheLHAPDFinterfaceaspersingletopgrouprecommendations[102,103,104].Atechniquewhereonlylightquarksareincludedinthepartondistributionfunction50oftheincomingprotons(the4°avorscheme)isusedsotheincomingbquarkshowninFigure1.6mustcomefromgluonsplittingwheretheb-antibquarkpairareproducedfromaninitialstategluon.Thetop-quarkmassusedforMadgraphsingletopquarksamplesis172.5GeV. 4.3DibosonProduction AmongthemostprominentbackgroundsisDibosonwhichisalargenon-topbackgroundinthisanalysis.ItsrelativecontributionisnotsurprisingconsideringthemostprominentDibosoncontributionisWZ,whichcontainsarealZboson,threeleptons,andEmissT(whichisdescribedinChapter5.5).AdditionaljetscancomefromInitialStateRadiation(ISR)orFinalStateRadiation(FSR)whereagluonisradiatedo®andisconstructedasanotherobjectentirely.Dibosonproductionismodeledwiththenexttoleadingorder(NLO)generatorPOWHEGandshoweredinPYTHIA6[105,101]. 4.4Top-QuarkPairProduction Top-quarkpairproductionisadominantbackgroundforalmostanysearchinvolvingatopquark.Itslargecross-sectionmeansthatitisdi±culttoremoveevenifdistinctkinematicdi®erencesexist.Thisprocesscanhave0,1,or2leptons,meaningthateveryt¹teventthatpassesselectionbyde¯nitionhasatleastonejetwhichismis-reconstructedasalepton.Beyondhavingajetmis-reconstructedasaleptontwoofthoseleptons(atleastoneofwhichisnotatruelepton)willhavetobemis-reconstructedasaZbosonwithintheconstraintsoutlinedinChapter6.Powhegisusedtomodelt¹tanditisshoweredwithPythia6[105,101].514.5Top-QuarkPair+BosonProduction Thet¹t+XisaprocessthathasbeenunderstudywithinATLASandindicationsarethatthisprocesswillbeobservedsoon[48].TheXint¹t+XcanbeaZboson,aWboson,oraHiggsboson.Thet¹t+Zcontributesmuchmorestronglywhencomparedwitht¹t+WduetotheZboson.Thisprocesshas0,1,2,3,or4realleptons,andonlythe3leptoncontributioncontributestoour¯nalstateasselectioncutsinChapter6describe.Thet¹t+Zmatchesoursignalfairlyclosely.Madgraph5isusedtomodelt¹t+XanditisshoweredwithPythia8[100,101]. 4.6Zboson+jetsZboson+jetsisanotherlargebackgroundbecauseithasarealZboson.Despitenothavingatopquarkandonlyhavingtworealleptons,itstillremainsanimportantbackgroundtoconsiderduetoitslargecross-section.Zboson+jetstakenincombinationwitht¹tconstitutesamajorityofmis-reconstructedleptonsthatcomeupinthisanalysisduetothesesamplesnaturallycontainingfewerthanthreeleptons.Zboson+jetsismodeledandshoweredwithSherpa[106]. 4.7SingleTopQuark Botht-channelands-channelhaveonlyonelepton,andwhileconsideredforthisanaly-sis,theycontributenoevents.However,Wt-channelhastworealleptonsandarealtopquarkwhichleavesitcloseenoughtotZtoaddtotheeventyieldinasmallway.Singletop-quarksimulationisperformedwithPowheg+Pythia8[105,101].524.8Wboson+jetsandMultijetAlsoconsideredforthisanalysisisWboson+jetsproduction.Thisprocess,despitehavingalargecross-sectionincomparisontotheotherbackgroundsconsidered,iscompletelyelimi-natedbypreselectioncutsdescribedinChapter6becauseithasnoZboson,notopquark,andonlyonelepton.Thismeansitwouldrequire2jetstobemis-reconstructedasleptons.GiventhattheWboson+jetsprocesshasnocontributionduetothecombinatoricsofrequiringsomanymis-reconstructedleptonsandbosons,multijetswillalsohavenocontributionasitrequiresthreemis-reconstructionsthatmatchthekinematicpropertiesoftheWbosonandZboson.BothSherpaandPowheg+PythiaareconsideredforW+jetssimulationsandforbothzeroeventspassedtheeventpreselection(seeSection6.1)[106,105,101].4.9WeightingandCorrections WhengeneratingMCevents,wemustgenerateasu±cientlylargesampletogetavarietyofpotentialkinematicpropertiesandtoensurealowstatisticaluncertainty.InordertocomparethisgeneratedMonteCarlotodatawemustweightthesampleappropriately.FirstlythenumberofgeneratedMonteCarloeventsdoesnotmatchthenumberofdataeventssotheMonteCarlogetsscaledbythecross-section(XS)oftheprocess.ThisincludestheK-factor(K)whichscalesittohigherordercalculations,thebranchingratio(BR)fordecaysspeci¯edbytheprocessgenerated,theintegratedluminosity(L)ofthedatacollected,andthenumberofgeneratedevents(NMC)calculatedasshowninEquation4.1.XS¢BR¢K¢L¢PUSF¢LepSF¢BtagSFNMC(4.1)53Anotherweightusedisthepile-upscalefactor(PUSF)whichscalestheMonteCarlotoaccountforbothin-timeandout-of-timepileupwhichisdiscussedinChapter2.Theleptonscalefactor(LepSF)adjustsfordi®erencesbetweensimulationanddataofleptons.Lastlythereisab-taggingscalefactor(BtagSF)whichaccountsfordataMonteCarlodis-agreement.Thesescalefactorsareallbetween0and2.TheassesmentofthesescalefactorsaresystematicuncertaintiesdescribedinChapter7.54Chapter5 Object&EventReconstruction Iwasalwaysinterestedin¯guringthingsout.I'ddoexperiments,likecombiningthingsIfoundaroundthehousetoseewhatwouldhappenifIputthemtogether.-AlanAldaInpractice,highenergyphysicsismessy.Havingparticlesthatinteractwithseveraldi®erentlayersofthedetectormakesourparticleidenti¯cationandreconstructioncomplexbutpossible.Byusingtrackingfromtheinnerdetector,energymeasurementsfromthecalorimeters,moretrackingfromthemuonspectrometers,andbylookingatglobalvariablesthathavetodowitheventkinematicpropertieswecanensurequalityphysicsobjectsforanalysis.Thisanalysisinparticularusesawidevarietyofobjectsincludingelectrons,muons,jets,b-jets,EmissT,reconstructedWbosonsandZbosons,andtheheaviestofallfundamentalparticleswithoneofthemostuniquesignatures,thetopquark. 5.1ElectronReconstruction Electronsuseinformationfromtheinnerdetectorandtheelectromagneticcalorimeter.Elec-tronsareamongthemorescrutinizedreconstructedobjectsbecausehadronicjets,photons,andtauscanfakeelectronsheighteningtheimportanceofqualitycontrol.Electroncandi-datesarerequiredtobewithinj´j<2:47asmeasuredbythetracksintheinnerdetectorwithpT>7GeVasmeasuredbyanenergycluster(energydepositswithindRof0.4)inthe55calorimeter.Requirementsonthetransverseimpactparameter(d0)andthelongitudinalimpactparameter(z0)constrainthedegreetowhichtracksintheIDareallowedtovaryfromtheinteractionpointwhilestillbeingcountedaspartoftheelectronobject.Ratiosofenergymeasuredintheelectromagneticcalorimeterandthehadroniccalorimeterarealsousedtorejectjetsthatinteractwithintheelectromagneticcalorimeterandcouldfakeelec-trons.Ratiosofenergyinvaryingwindowsizesintheelectromagneticcalorimeterarealsousedtohelpdistinguishotheractivitysuchaspionsfromelectrons.ThesereconstructedelectronsarerequiredtohavepT>25GeV,thentriggermatchedwithL1EMobjectsandHLTelectronsandrequiredtobeisolatedfromhadronicactivity[107,108,109].5.2MuonReconstruction Muonsuseinformationfromtheinnerdetector,themuonsystems,andtoalesserextentthecalorimeters.Muonsarenotstoppedbythedetector,makingfullcalorimetryimpossible,sotheirenergymustbedeterminedbytheircurvatureinthemagnetic¯eldsetupbyATLAS'snamesaketoroidalmagnetsystem.Therearefouralgorithmsthatareusedinmuonreconstructionandde¯netherequire-mentsforvariouslevelsofthemuonreconstructionprovidedtoanalyzers.Onemethodusedstartsfromhitsinthemuonspectrometerandtracesthembacktoaprimaryvertextocreateastandalonemuon.Anothermethodcombinesaninnerdetectortrackwithamuonspectrometertracktoproduceacombinedmuon.Yetanothermethodperformsasearchforsegmentsandtracksinthemuonspectrometerusinganinnerdetectortrackasaseed,andifthere¯tperformedissuccessful,thenaCombinedmuonismade,ifnotthenataggedmuonismade.Thefourthmethodidenti¯esmuonsbyassociatinganinnerdetectortrack56withastandalonemuoninasimilarwaytothe¯rstmethodtoproduceataggedmuon.Muonsfromallofthesealgorithmsareaddedafteroverlappingde¯nitionsareaccountedfor[110,111]. 5.3JetReconstruction Hadronizingquarksandgluonsinteractwiththeinnerdetector,theelectromagneticcalorime-ter,andthehadroniccalorimeter.Weusethisinformationtoreconstructthelocationandenergyofthejets.Thereareseveraljetreconstructionalgorithmsbutthemostcommonaredescribedbyequations5.1and5.2,dij=min(p2pT;i;p2pT;j)¢´2ij+¢Á2 ijR2;(5.1)di=p2pT;(5.2)wherepTisthetransversemomentumtothepowerof2pwhichiseither1,0,or-1.Thesethreevaluescorrespondtothekt,CambridgeAchen,oranti-ktalgorithm[112].Thesealgorithmsworkbyconsideringeverycellofthedetectorasanobjectinalistenumeratedbyiandjandconsideringpairsofthesecellsforcombinationbythisequation.Iftheminimumdijissmallerthandithenthetwoobjectsarecombinedintooneobject.Ifadiissmallerthenthatobjectisremovedandconsideredajet.Thiscontinuesuntilallobjectsareremovedfromthelist.TheparameterRsetstheseparationdistancebetweentwojets.The¯rstofthesethreealgorithmsisthektalgorithmwhichgivesirregularjets,but57ismoretheoreticallysoundthansimpleconedrawing.TheCambridgeAachenalgorithmgivesjetsthatareslightlymoreregularbutarelargerthantheirktcounterparts,whiletheanti-ktalgorithmgivesjetsthataremoreregularthanthekt.Theanti-ktalgorithmistheonechosenforATLASandthisanalysisconsidersanti-ktjetswithanRparameterof0.4,andforhighpTjets(greaterthan50GeV)theJetVertexTagger(JVT)outputvariableisrequiredtobegreaterthan0.64[113].Aftertheselectionofjetswiththeanti-ktalgorithm,correctionsareappliedtoeachjetbasedonthejet'spositionandpTtocorrectforspeci¯cdetectore®ects.ThesecorrectedjetshaveaseriesofqualitycutsappliedincludingaminimumpTthresholdof30GeV,acheckforunphysicalnegativeenergyjets,anetarangej´j<4:5andelectronisolationrequirementstoensurethatanelectronisnotbeingdoublecountedasajet. 5.3.1Jetb-taggingJetsthatareb-tagedareuniquebecausethebquarkdecaysafterthehadronizationprocessbeginsbutbeforeitinteractswiththedetector.Thiscreatesasecondaryvertex(displacedbyafewmillimeters)whichcanbefoundbylookingatthetrackinginformationfromtheinnerdetector[23].ThiscanbeseendiagrammaticallyinFigure5.1.Theb-taggingalgorithmusedinATLASforRun2istheMV2c20algorithm[114].Whenthisalgorithmisappliedtoanti-ktjetswithanRparameterof0.4thepTofthejetisrequiredtobegreaterthan20GeV,the´isrequiredtobelessthan2.5.TheMV2c20algorithmisaneuralnetworkanalysisofb-taggingalgorithmsusedinATLAStocreateasinglediscriminatingvariablethatcandistinguishbetweenjetsoriginatingfromabquarkandallotherjets.[115].58Figure5.1:Diagramillustratingadisplacedvertex.[23].5.4ZbosonNowthatwehavetheleptonsde¯nedwecanreconstructtheintermediateZboson.WerequirethattheZbosonbeconstructedfromanOpposite-SignSame-Flavor(OSSF)leptonpair.Withthreeleptons(whichcanbeelectronsormuons)wecanhave0,1,or2OSSFpairs.TherearetwofundamentalcutswemakeinSection6.1.WhenthereisoneOSSFpair,theZbosonisreconstructedwiththose,andtheremainingleptonisusedtoreconstructtheWboson.WhentherearetwoOSSFpairs,thentheOSSFpairwhichreconstructstheZ-bosonmassmorecloselyisconsidered,andtheremainingleptonreconstructstheWboson.ThelastcasewithnoOSSFpairrepresentseitherachargemisidenti¯cationofaleptonorajetmis-reconstructedasaleptonwhosechargecouldn'tbeproperlyreconstructed.Inthiscasetheeventisrejected.595.5MissingTransverseEnergy(EmissT)andtheWbosonForeacheventweapplyconservationofmomentuminthetransverseplaneofthedetectortoobtainwhatisknownasmissingtransverseenergy(EmissT).WeoftenuseEmissTasasastandinforsomeinformationonneutrinos.Whilewecannotapplythesamemethodto¯ndtheneutrinopz,becausethecollidingpartonsdonotnecessarilyhavebalancedzmomenta,wecanmaketheassumptionthatitcamefromaWbosonandbeginwithconservationoffour-momentumoftheWbosondecayvertexwiththemomentumoftheWbosonp¹ w,themomentumoftheneutrinop¹ º,andthemomentumoftheleptonp¹ l.p¹ w=p¹ º+p¹ l(5.3)TheleptonupforconsiderationistheonethatdidnotcomefromtheZboson.Solvingforthepzoftheneutrinoweobtainthefollowingquadratic:pzº=®pzlp2 tl§v u u t®2p2 zlp4 tl¡E2lp2 tº¡®2p2 tl(5.4)®=m2 w2+cos(¢Á)ptºptl:(5.5)Equation5.4canhavetwo,one,ornorealsolutions.Ifithastworealsolutions,theonewithlowerpzischosen.InthecasewheretherearenorealsolutionsthemeasuredEmissTisscaledtothepointwhereonerealsolutionisfound.ThemeasuredEmissTandazimuthalangle(Á)oftheEmissTandthereconstructedpz,andbecauseneutrinosarefunctionallymassless,de¯netheneutrinofourvector.Nowthattheneutrinoisde¯ned,wehavereconstructedthefourvectorsforallofour60¯nalstateparticles.WecanreconstructtheWboson,butthemasswillalreadybede¯nedbecauseweassumedtheW-bosonmassinreconstructingtheneutrino.Forthisreason,andtoremainindependentofanyassumptionsregardingzmomenta,theexperimentalvariablemW Tisused.ThisisthetransversemassoftheWboson,whichasde¯nedbytheenergiesoftheleptonandneutrino(ETl;ETv)andtheanglebetweenthem(¢Á)inequation5.6.ItisusedtohelpdistinguisheventsthathavearealWbosonfromeventsthatdon't[116,117].mW2T=2ETlETv(1¡cos(¢Á))(5.6)ThehelicityoftheWbosonisanothervariablewhichcanbeusedtodistinguisheventswitharealWbosonfromonesthatdonot.Furthermore,Wbosonsfromtopdecayshavecorrelationswiththeb-jetbecausetheycarryforwardinformationaboutthespinofthetopquark.Helicityisde¯nedastheprojectionofthespinvector(s)ontothemomentumvector(p)asde¯nedinequation5.7.H=s¢pjs¢pj(5.7)5.6Reconstructingthetopquark OncetheWbosonisreconstructedandtheb-jetselected,thereconstructionofthetopquarkissimplytheresultoftheadditionofthefourvectorsofthetwoobjects.Thetopquarkdecayhaspropertiesthatareusedtohelpdistinguishsignalandbackgrounds,eventhoughthisanalysishasalargebackgroundcontributionfromtop-quarkpairproductionasseeninChapter6.Oneofthosepropertiesisthetop-quarkpolarization,whichisuniquebecausethetopquarkdecaysbeforeitsspincanbe°ippedbythestronginteractionallowing61thistobemeasuredinsingletopproduction.Thetop-quarkpolarizationisevaluatedastheanglebetweentheleptonfromthetopquarkdecayandthepolarizationaxis,inthetopquarkrestframe[118].Thepolarizationofthetopquarkisdependentonwhatreferenceframeyouaremeasuringfrom.TwocommonreferenceframesforthisaretheOptimalBasisandtheHelicityBasis.TheHelicityBasis,whichisthemostcommonbasisofconsideration,takesthetopquarkrestframe.TheOptimalbasisisthehelicitybasismeasurementboostedintothereferenceframeofthejetthatdoesnotcomefromthetopdecayinthecaseofsingletopt-channel.62Chapter6 Analysis Let'sthinktheunthinkable,let'sdotheundoable.Letuspreparetograpplewiththeine®ableitself,andseeifwemaynote®itafterall.-DouglasAdamsAftertheZboson,thetopquark,theWbosonfromthetopquarkdecay,andtheneutrinofromtheWbosondecayarereconstructedasdescribedinChapter5,theyareusedtohelpseparatetZfromthevariousbackgrounds.Theenergiesandmomentaofeachoftheseobjectsinourdetector,aswellasthemultiplicityoftheobjects,areusedtoachievethisseperation.Thedecisionsmadeinthepreselectionandcut°owareinformedbythekinematicpropertiesofthetZprocess.ThetZFeynmandiagramisshowninFigure1.6.6.1Preselection Onegoalinsettingupananalysisistounderstandthebackgroundmodelinrelationtotheobserveddata.Toaccomplishthis,de¯ningcharacteristicsofthesignalregionaredeterminedinordertolimitthenumberofMonteCarlosamplesneeded.BecausethesignalhasthreeleptonsandaZboson,cutsonthenumberofleptonsandZ-bosonmass(forinstance)areappliedtolimitanycontributionfromcertainlowleptonmultiplicitynon-Z-bosonsourcessuchasWboson+jetsandmultijets.ThefollowingcutsareoptimizedbymaximizingS=pBwhereSisthetotalexpected63signalcontributionandBisthetotalexpectedbackgroundcontribution.Thisisdonetoimproveagreementbetweendataandthebackgroundmodelwhilemaintainingasmuchsignalstatisticsaspossible.²Exactly3leptonswithpT>10GeV.Exactly3leptonsisade¯ningfeatureofthisanalysis.TwooftheleptonscomefromtheZbosondecay,whilethethirdcomesfromthetopquarkdecay.Becausetheseleptonsarerequiredtobeelectronsormuonstheirdistributionsaremirrorsofeachotherbyde¯nitionwhichcanbeseeninFigure6.15.²AtleastoneOSSFpair.BecauseweareconcernedwithprocessesthatcontainarealZboson,thisrequirementensuresthatwecanalwaysattempttoreconstructavalidZbosoncandidateevenifitisaneventthatismis-identi¯edascontainingaZboson.²LeadingleptonpT>40GeV.Theleadinglepton'sthresholdishigherthanthesecondandthirdduetobeingmorelikelythatitisthecandidatethatisrequiredtopassthesingleleptontriggeroracandidateinthecaseofamulti-leptontrigger.Figure6.1showsthatthiscutremovessomebackground,butlittlesignalislost.²SecondleptonpT>20GeV.Thisleptonisnotrequiredtohavepassedasingleleptontrigger,butmayhavebeenrequiredtopassthedi-electrontriggerthreshold.Figure6.1showsthatthiscutremovessomebackground,butlittlesignalislost.TighteningthiscutisalsoinvestigatedbecauseZ+jetsandt¹tpeakatalowermomentumthanthesignal,butintheinterestofmaintainingstatisticsalowerpTthresholdischosen.²ThirdleptonpT>10GeV.ThepTofthisleptonissigni¯cantlylowerthantherest.10GeVischosenduetothethresholdsthatde¯nehowelectronsarereconstructed.Figure6.1showsthatthesignalpeaksathigherpTthanZ+jetsandt¹t,andtightening64thiscutisinvestigated,butintheinterestofmaintainingstatistics,alowerpTthresholdischosen.²2,3,or4jetswithpT>25GeV.Figure6.2showsthattheonejetregioncontainsvirtuallynosignal,soremovingiteliminatesbackgroundatnocost,whileeventswith>=5jetshavelittlesignalandarenotaswellmodeled.²LeadingjetpT>40GeV.Figure6.1showsthatbelow40GeV,thereislessthan1expectedsignalevents,soverylittleisremoved.²Exactly1b-jet.Figure6.2showsthatthereislittlesignaloutsidetheoneb-jetregion.Thesignalandtopbackgroundshaveoneb-jetfromthetopdecaywhilenon-topbackgroundsareunlikelytohaveone.²80GeV20GeV.Thiscutde¯nesprocessesthathavearealsourceofEmissTsuchastheneutrinofromtop-quarkdecays.Figure6.2showsthatthelowEmissTregionispopulatedheavilybyZ+jetswithlittlesignal.²IfmW T<40GeVthenEmissT>40GeVisrequired.Ifviewedinthetwodimentionalplane,caseswherejetsaremis-reconstructedasleptonsareexpectedtohavelowmW TandlowEmissT.DistributionsformW TandEmissTcanbeseenindependentlyinFigure6.2.The2DplaneofmW Tvs.EmissTisshownforbothsignalanddatain65Figure6.3.Herewecanseethatthesignalpeaksabove20GeVinEmissTandabove40GeVinmW TwhiledatapreferentiallyresidesintheregionwherebothmW TandEmissTarebelow40GeV.ThiscutisprimarilytargetedatZ+jetsevents(aswellaspotentialbackgroundswithmis-identi¯edWbosons)whichheavilypopulatethelowmW Tregion.Thiscutisreferredtoasthenotchcutbecauseofitsuniqueshape.66 (GeV)TLeading Lepton P020406080100120140160180200Events/20GeV0102030405060DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a) (GeV)TSecond Lepton P020406080100120140160180200Events/20GeV020406080100DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b) (GeV)TThird Lepton P020406080100120140160180200Events/20GeV0102030405060708090DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c) (GeV)TLeading Jet P020406080100120140160180200Events/20GeV051015202530354045DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.1:DistributionsofLeptonpTfor(a)leading,(b)second,and(c)thirdleptonsaswellas(d)leadingjetpTwithpreselectionappliedexceptthecutsonminimumpTthresholdsshownwhichare40GeVfortheleadinglepton,20GeVforthesecondlepton,10GeVforthethirdlepton,or40GeVfortheleadingjet.ThereareminimumpTreconstructionthresholdsfortheseobjectswhichare25GeVfortheleadingleptonandleadingjet,and10GeVforthesecondandthirdleptons.67Number of Jets01234567Events0102030405060708090DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)012345Events050100150200250300350400DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)W transverse mass (GeV)050100150200250Events/10GeV01020304050607080DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)miss TE020406080100120140160180200Events/20GeV020406080100120140160DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.2:Distributionsof(a)numberofjets,(b)numberofb-jets,(c)mW T,(d)EmissT.Atleastonejetisrequiredatthislevelinallcases,butthecutonthevariableshownisomittedinordertoassessthefulldistribution.Thedistributionofthenumberofjetsdoesnotincludethecutonthenumberofjets,thedistributionofthenumberofb-jetsdoesnotincludethecutonthenumberofb-jets,andthemW TandEmissTdistributionsdonotcontaintheEmissTorthenotchcuts.68 (GeV)miss TE050100150200250W Transverse Mass (GeV)05010015020025000.0050.010.0150.020.0250.030.0350.04ATLAS Work In Progress=13TeV, 3.2 fbs(a) (GEV)miss TE050100150200250W Transverse Mass (GeV)05010015020025000.511.522.533.54ATLAS Work In Progress=13TeV, 3.2 fbs(b)020406080100120140160180200Events/10GeV020406080100DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)Figure6.3:Distributionsof(a)two-dimentionalmapofmW TvsEmissTforthesignal,(b)twodimentionalmapofmW TvsEmissTforthedata,and(c)invariantmassoftheZboson.Forboth(a)and(b)theEmissTcutandthenotchcutarenotappliedandfor(c)theZ-bosonmasswindowcutisnotappliedinordertoshowthefulldistribution.696.2ControlRegions Threecontrolregionsareconsideredforthethreeprimarybackgroundstoensurethatthebackgroundmodeldescribesthedatawell.Thecontrolregionsarefort¹t,Diboson,andZ+jetsandtheiryieldsaresummarizedinTable6.1whereitcanbeseenthattZcontami-nationissmallandthatthecontrolregionsarefairlypureintheirrespectivebackgrounds.Thecontrolregionfort¹tisde¯nedbythepreselectioncutswiththeexceptionoftheZ-bosonmasswindowwhichisinverted.Thishasthee®ectofcuttingoutlargecontributionswhichcontainarealZboson,leavingprimarilyt¹t.IneverydistributionshowninFig-ures6.4and6.5,thereisgoodagreementbetweendataandsimulatedeventswithaquitepuresampleoft¹t.InordertoisolateDibosonandZ+jets,webeginwiththepreselectionagain,butinsteadofrequiringexactly1b-jet,werequireexactly0b-jetsinordertoelimi-natetop-quarkcontributions.Thisde¯nesanintermediatecontrolregionwithDibosonandZ+jetsmixedasshowninFigures6.6and6.7.ThisisexpectedbecausebothDibosonandZ+jetshavearealZbosonanddonothaveabquarkthatwouldcomefromatop-quarkde-cay.ToisolateDibosonmoreprecisely,acutisplacedonmW Ttoconstrainittohigherthan80GeVasshowninFigures6.8and6.9.ThisprovidesaregionwithhighDibosonpuritytoevaluatethequalityofitsmodeling.InordertoisolateZ+jetsfromtheintermediatecontrolregionacutonEmissTismadetoconstrainittolowerthan60GeVasshowninFigures6.10and6.11.ThisregionhaslowerpurityinZ+jetswhencomparedtothet¹tcontrolregionandtheDibosoncontrolregion,andshowsareasofmis-modelinginlowtomidmW T(lessthan70GeV).LowleptonpTalsoseemstobepoorlymodeled(20-40GeVforeachofthethreeleptons).Thisislikelybecausethethirdleptonmustbeamis-reconstructedone.Despitealsohavingamis-reconstructedlepton,duetoonlyhavingtworealleptons,t¹tdoesnotshow70similarmis-modelingfortwoprimaryreasons.The¯rstreasonisthatt¹tMCstatisticsismuchbetterthanZ+jets.Thesecondreasonisthatt¹thasmorehardobjects(extrajets)stemmingfromtheprimaryinteractions,whileZ+jetshasextrahardobjectscomefrominitial-stateor¯nal-stateradiation.Thismis-modelingismitigatedbycutsonpT,mW T,andEmissTaswellascutsmadetothesignalregion.Evenwiththesemeasurestakenthemis-modelingre°ectsitselfaslargeuncertaintiesonZ+jetswhichisshowninChapter7.Collectivelythesecontrolregionsgiveinsighttothecontributionofthelargestbackgroundstothisanalysis.EventYieldsPreselectiont¹tCRintermediateCRDibosonCRZ+jetsCR¯nalselectiont¹t45196164.05.710§45%singletopquark1.47.70.850.260.300.34§66%ttV4.42.71.00.380.300.61§66%Z+jets32101104.0781.7§413%Diboson185.010031483.3§32%tZ5.70.631.60.40.682.9§11%TotalExpected1082232324113419§71%DataObserved1082372145213122S/B0.060.000.010.010.010.18S/pB0.570.040.100.070.060.71Table6.1:Eventyieldsforvariousstagesofanalysistocomparewithcontrolregion(CR)yields.The¯nalselectionisdescribedinSection6.3anduncertaintiesprovidedonthe¯nalselectionaredescribedinChapter7takeninquadratureforeachsample.Theyareprovidedhereforreference.71 (GeV)TLeading Lepton P020406080100120140160180200Events/20GeV020406080100120140DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a) (GeV)TSecond Lepton P020406080100120140160180200Events/20GeV020406080100120140160180200220DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b) (GeV)TThird Lepton P020406080100120140160180200Events/20GeV050100150200250DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c) (GeV)TLeading Jet P020406080100120140160180200Events/20GeV020406080100DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.4:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthecontrolregionfort¹t.72Number of Jets01234567Events020406080100120140160180200DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)012345Events050100150200250300350400DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)W transverse mass (GeV)050100150200250Events/10GeV01020304050DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)miss TE020406080100120140160180200Events/20GeV020406080100DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.5:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthecontrolregionfort¹t.73 (GeV)TLeading Lepton P020406080100120140160180200Events/20GeV020406080100120DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a) (GeV)TSecond Lepton P020406080100120140160180200Events/20GeV020406080100120140160180DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b) (GeV)TThird Lepton P020406080100120140160180200Events/20GeV020406080100120140160180200220DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c) (GeV)TLeading Jet P020406080100120140160180200Events/20GeV020406080100120DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.6:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetintheintermediatecontrolregionforDibosonandZ+jets.74Number of Jets01234567Events050100150200250DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)012345Events050100150200250300350400DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)W transverse mass (GeV)050100150200250Events/10GeV0102030405060DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)miss TE020406080100120140160180200Events/20GeV020406080100120140DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.7:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTintheintermediatecontrolregionforDibosonandZ+jets.75 (GeV)TLeading Lepton P020406080100120140160180200Events/20GeV0246810121416DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a) (GeV)TSecond Lepton P020406080100120140160180200Events/20GeV05101520253035DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b) (GeV)TThird Lepton P020406080100120140160180200Events/20GeV01020304050DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c) (GeV)TLeading Jet P020406080100120140160180200Events/20GeV051015202530DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.8:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthecontrolregionforDiboson.76Number of Jets01234567Events051015202530354045DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)012345Events0102030405060708090DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)W transverse mass (GeV)050100150200250Events/10GeV051015202530DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)miss TE020406080100120140160180200Events/20GeV0510152025DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.9:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthecontrolregionforDiboson.77 (GeV)TLeading Lepton P020406080100120140160180200Events/20GeV010203040506070DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a) (GeV)TSecond Lepton P020406080100120140160180200Events/20GeV020406080100DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b) (GeV)TThird Lepton P020406080100120140160180200Events/20GeV020406080100120DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c) (GeV)TLeading Jet P020406080100120140160180200Events/20GeV01020304050607080DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.10:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthecontrolregionforZ+jets.78Number of Jets01234567Events020406080100120140160DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)012345Events020406080100120140160180200220DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)W transverse mass (GeV)050100150200250Events/10GeV051015202530354045DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)miss TE020406080100120140160180200Events/20GeV020406080100120140DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.11:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthecontrolregionforZ+jets.796.3CutFlow Oncethepreselectionregionisde¯ned,ourgoalistoimprovethesensitivityoftheanalysis.Wedothisbysearchingforkinematicvariableswheretheshapeofthesignaldistributionsigni¯cantlydi®ersfromtheshapeofoneorallofthebackgrounddistributionsandevaluatingitse®ectonthevalueS=pB.ThevariableS=pBisusedtooptimizebecauseitensuresbothstrongsignaltobackgroundratioswhilealsoensuringthatwelimitthecontributionofstatisticalerrors.Manydistributionsareconsideredfortheirbackgroundrejection,and/orphysicalmotivationsbutdistributionsofspecialinterestaretheangularvariablesandtop-quarkmassshowninFigure6.16becausetheydisplaythepropertiesofthetopquark.ThepolarizationofthetopquarkismostnotableinFigure6.16wheretheoptimalbasisshowsbotht¹tandtZhaveadistributionfavoringvaluescloserto1,whileDibosoniscomparatively°at.Inprinciplethesevariablescouldbeusedtodistinguishbackgroundswithoutatopquarkfromthesignalwhichdoes.Inpracticethediscriminationpowerofthesevariablesisnotasstrongasthatofothers.ThevariableswiththebestdiscriminatingpowerareshowninTable6.2andare,²mW T>50GeV.ThisselectsforeventswithhigherenergyWbosons.²Leadingnon-b-jet|´|>1.5.Thisselectsforeventswithaforwardjetasisthecasewithsingletopt-channelandtZ.²¢Rbetweentheb-jetandLeadingnon-b-jet>2.5.¢Riscalculatedasthe¢´andthe¢Áaddedinquadrature.Thesetwoobjectsareexpectedtonotbeneareachotherinthesignalselectingforeventswherethejetsdonotbothcomefromthesamesource.80ThedistributionsofthesevariablesareshowninFigure6.12andarere-optimizedse-quentiallytoshowthatanycorrelationsareminor,andtoensureoptimalsensitivity.Ta-ble6.2alsoshowswhatbackgroundeachcutispreferentiallyremoving.ThemW TcuttargetsZ+jets,whilealsoeliminatingt¹tandsomeDiboson.Thecutontheleadingnon-b-jet´islessobviouslytargetedataspeci¯cbackground,butisremovingapproximatelyhalfofallbackgroundswhileremovingcomparativelylittlesignal.Thisisduetotheforwardjet,acharacteristickinematicpropertyofsingletop-quarkproduction.Thecutonthe¢Rbetweentheb-jetandleadingnon-b-jetperformswellbecausetheb-jetandtheleadingnon-b-jetarecomingfromoppositelegsofthehardinteraction.Thiscreatesadistributionwherethetopquarkanditsdecayproducts(inthiscasetheb-jet)comeoutpreferentiallyfarapartin¢Rinthesignalcomparedtothebackgrounds.ProcessPreselectionmW TLeading-nonb-jet´fullselectiont¹t45281510§45%singletopquark1.41.00.490.34§66%ttV4.43.11.00.61§66%Z+jets325.32.31.7§413%Diboson18135.23.3§32%tZ5.74.33.22.9§11%TotalExpected108552719§71%DataObserved108622922S/B0.060.080.130.18S/pB0.570.600.660.71Table6.2:Eventyieldsafterselectioncutsareapplied.Uncertaintiesprovidedonthe¯nalselectionaretheuncertaintiesdescribedinChapter7takeninquadratureforeachsample.Oncewehaveappliedthefullcut°ow,weareleftwiththeremainingdistributionstoanalyze.TheserepresentthekinematicpropertiesofeventsselectedbythisanalysiswhichareshowninFigures6.13and6.14.TheapplicationofthefullselectiontakesusfromanS=Bof0.06to0.18.Thesee®ortsaretoimprovethesensitivityofouranalysisasshowninthenextchapter.Thereisreasonableagreementthroughoutthesignalregion,andinpTdistributions81W transverse mass (GeV)050100150200250Events/10GeV02468101214DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)h012345Events05101520253035DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)01234567Events024681001234567Events0246810DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)Figure6.12:Distributionsof(a)mW Twhichisrequiredtobe>50GeV,(b)the´oftheleadingnonb-taggedjetwhichisrequiredtobe>1.5,and(c)the¢Rbetweentheb-jetandleadingnon-b-jetwhichisrequiredtobe>2.5.Eachhastheentireselectionappliedexceptthevariableplottedtoviewthefulldistribution.82itcanbeseenthatthesignalpeakshigherwhenthecutsareplaced.ThesecutswerechosenbecausetheyoptimizedS=pBwhichinthiscaseprioritizedpreservingstatisticsoverimprovingsignalpurity.WithmoredatacollectedthesecutscouldbetightenedtofurtherimproveS=pB.83 (GeV)TLeading Lepton P020406080100120140160180200Events/20GeV0246810121416DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a) (GeV)TSecond Lepton P020406080100120140160180200Events/20GeV02468101214DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b) (GeV)TThird Lepton P020406080100120140160180200Events/20GeV0246810121416DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c) (GeV)TLeading Jet P020406080100120140160180200Events/20GeV0510152025DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.13:Distributionsoftransversemomentafor(a)theleadinglepton,(b)thesecondlepton,(c)thethirdlepton,and(d)theleadingjetinthesignalregion.84Number of Jets01234567Events02468101214161820DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)012345Events05101520253035DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)W transverse mass (GeV)050100150200250Events/10GeV0246810DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)miss TE020406080100120140160180200Events/20GeV0246810DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.14:Distributionsof(a)jetmultiplicity,(b)b-jetmultiplicity,(c)mW T,and(d)EmissTinthesignalregion.85Number of Electrons0123456789Events0246810121416DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)Number of Muons0123456789Events0246810121416DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)Figure6.15:(a)Numberofelectronsand(b)numberofmuons.86TopQuark Polarization Optimal Basis00.511.5Events02468101214DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(a)TopQuark Polarization Helicity Basis00.511.5Events0246810DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(b)Wboson helicity00.511.5Events02468101214161820DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(c)TopQuark mass (GeV)050100150200250300350400450500Events/20GeV012345678DatatZttZ+jetsDibosonVttSingleToptZx5ATLAS Work In Progress=13TeV, 3.2 fbs(d)Figure6.16:Distributionsofthetop-quarkpolarizationinthe(a)Optimalbasisand(b)thehelicitybasis,(c)theW-bosonhelicity,and(d)themassofthetopquark.87Chapter7 Results Bayesianaddressthequestioneveryoneisinterestedinbyusingassumptionsnoonebelieves.Frequentestuseimpeccablelogictodealwithanissueofnointeresttoanyone.-L.LyonsAsinglebinpro¯lelikelihoodcalculationisperformedtoextractlimitsonthetZcross-sectionatthe95%con¯dencelimitusingroostats[119].Pro¯lelikelihoodcalculationscanproducecon¯denceintervalsonnon-normaldistributionsmoreaccuratelythanmaximumorpartiallikelihoodfunctions[120]andforthisreasontheyhavebecomeapopularstatisticalmethodforhighenergyphysics.However,beforewecandothisevaluation,aseriesofsystematicuncertaintiesmustbeadressedandevaluated.Theexpectedsensitivitytolargerdata-setsfromtheLHCisalsoevaluated. 7.1SystematicUncertainties Systematicuncertaintiesontheobjectreconstruction,eventreconstruction,normalization,andtheoreticalmodelinga®ecttheacceptanceandexpectedeventyieldforeachsource.Tables7.1and7.2containevaluateduncertainties.Someuncertaintiesaresymmetricinnature,whileothershavedistinctupanddownvariations.Nearlyalluncertaintieshavebeensymmetrizedeitherbecauseofpracticalreasons(theire®ectissmallsowecansimplifythemortheyhappentocomeoutsymmetric)orfortheoreticalreasons(thereisaphysical88motivationforthemtobesymmetric).Forthesesymmetricsystematicuncertaintiesbothupanddownvariationsareconsideredandthegreaterofthetwoisused[121].²Luminosity-Theuncertaintyontheintegratedluminosityis§2.1%.ItisobtainedfromVanDerMeerscansareperformedinwhichthebeampositionsinthex¡yplanearevaried[122,123].²PileUp-Pileupisdiscussedbrie°yinChapter3.Hereweneedtoevaluatehowwellweestimatethedegreetowhichpileupinterfereswithourabilitytodistinguisheventsfromeachother.Thisisoneofthefewuncertaintiesthatwasnotsymmetrizedhavingdi®erentuncertaintiesfortheupanddownvariations[124].²Leptone±ciencyscalefactors-LeptonsfromoursimulatedMonteCarlosamplesareneededtoreplicateourdatainidenti¯cationcriteria(ElectronID,MuonIDSystematic,andMuonIDStatistics),isolationcriteria,andtriggersimulation(ElectronTrigger,MuonTrigger).AprescriptionforhowtoassessthisuncertaintyisprovidedbytheEGamma(whichevaluateselectronsandphotons)andMuongroupswhicharederivedfromZ¡>``samples.[109,125]²Electroncalibration-Electronmomentumscale(ElectronScale)andresolution(Elec-tronResolution)arehandledseparatelyfromleptone±ciencyscalefactors.ScalecorrectionsarederivedfordataandsmearingcorrectionsforMonteCarlo.Thesecor-rectionsassessthesystematicuncertaintiesassociatedwiththeprocessingofphotons,andinthiscase,electrons[126].²Muoncalibration-Muonmomentumscaleandresolutionarehandledseparatelyfromleptone±ciencyscalefactors.Muontrackidenti¯cation(MuontrackID),transverse89momentumscale(MuonScale),andresolution(MuonResolution)arecorrectedaswellas[125].²EmissTcalibration-Leptonandjetenergyandmomentumscaleandresolutionuncer-taintiespropagateintocalculationsofEmissT(givingMETScaleandMETResolution).Howweincludesofttracksintothiscalculationcorrespondstoasourceofuncer-tainty[127].²Jetenergyscale(JES)-JESanditsuncertaintyarederivedcombininginformationfromtest-beamdata,collisiondata,andsimulation.TheJESuncertaintyissplitintoseveralorthogonalcomponentsusinginsitutechniquesresultinginindependente®ectiveuncertainties.Thisisdeterminedwith8TeVdataandextrapolatedto13TeVrunningconditions[128].²Jetenergyresolution(JER)-Theprecisionwithwhichajet'senergyismeasuredhasanuncertaintyassociatedwithit.Amis-modelingofthisenergyresolutioncanleadtovaryingacceptancesin¯nalstatekinematics[128,129].²b-jettagging-b-tagingscalefactorsareusedonaper-eventbasistocorrectb-taginge±ciency.Thisisdeterminedwith8TeVdataandextrapolatedto13TeVrunningcon-ditionsusingthreeindependenteigenvectorsforthee±ciencyofb-jets,c-jets,andlightjetsaswellastwoparameterstoaccountfortheextrapolationfrom8to13TeV[130].²Initial-stateradiationand¯nal-stateradiation(ISR/FSR)-ISR/FSRisevaluatedonthet¹tsamplebyvaryingtherenormalizationandfactorizationscalesupanddownbyafactoroftwofromthenominalvalueof1.Thisprocessisdonetot¹tbecauseitisthedominantbackgroundtosingletopanalysesandissmallwhencomparedtoother90uncertaintiesthata®ecttheotherbackgrounds.²NLOsubtraction-TheuncertaintiesofhowtheNLOsubtractionmethodisappliedisevaluatedonthet¹tsample.PowhegandaMC@NLOaretwotoolsthatareusedtocalculatehigherordercorrections.Acomparisonofthetwotoolsappliedtot¹tisusedtoestimatethisuncertainty.²Partonshowering(PS)andHadronization-TheuncertaintyonpartonshoweringandhadronizationisevaluatedbycomparingtheclustermodelinHerwigandtheLundstringmodelinPythiaappliedtot¹t.Acomparisonofthetwotechniquesimplementedinthesetoolsisusedtoestimatetheuncertaintyonthisprocess.²PartonDistributionFunction(PDF)-TheuncertaintiesthatcomefromthechoiceofPDFisevaluatedonthet¹tsamplebycomparingPDF4LHC15andCT10.²Normalization-NormalizationuncertaintiesforDibosonandZ+jetsareestimatedfromcontrolregions.Fort¹t[131],singletop[132],andt¹tZ[133],theoryuncertaintiesonscalevariations,PDF,andtop-quarkmassareused.²MCStatistics-Theuncertaintyduetolimitedstatisticsinoursimulatedsamplesisassessedbytakingthesumofthesquareoftheweightsofeacheventineachsample.Whenselectingforanarrowpieceofphasespaceinordertolookforsmallsignalsasisdoneinthisanalysis,itbecomesincreasinglydi±culttobothseparatesignalfrombackgroundandmaintainmeaningfulstatisticsbothforMCanddata.91Systematicst¹tOtherTopZ+jetsDibosontZbackgroundtotalPileUpUP-11%64%94%10%-2.4%5.8%PileUpDOWN2.1%-13%6.8%1.8%0.69%1.3%Normalization§5.5%§10%§20%§20%§-§10%MCStatistics§8.3%§9.2%§47%§3.0%§1.6%§9.9%PDF§4.3%----§2.3%PSandHadronization§0.86%----§0.46%NLOsubtraction§20%----§11%ISR/FSRRadLo27%----14%ISR/FSRRadHi-24%-----11%Table7.1:Systematicuncertaintiesrelatedtobackgroundnormalizationandtheorymodel-ing.OtherTopisthecombinationoft¹tVandsingletop.92Systematicst¹tOtherTopZ+jetsDibosontZbackgroundtotalMuonIDSystematic§0.57%§0.90%§1.1%§0.90%§1.0%§0.77%MuonIDStatistics§0.48%§0.90%§0.57%§0.60%§0.69%§0.570%ElectronID§2.6%§1.8%§1.1%§1.5%§1.7%§2.1%ElectronTrigger§2.1%§5.4%§6.8%§1.8%§0.69%§1.3%ElectronReconstruction§1.2%§0.90%§1.1%§0.90%§0.69%§1.0%ElectronScale§1.7%§3.8%§0%§1.2%§0%§0.99%ElectronResolution§0.86%§2.9%§0%§0.30%§0.34%§0.72%MuonScale§0.48%§2.1%§0.57%§0.60%§0.69%§0.57%MuonResolution§0.48%§7.0%§2.8%§0.90%§0.69%§0.41%MuontrackID§1.3%§1.9%§0.57%§0.60%§0.69%§0.82%METScale§0.67%§0%§0%§0.60%§0.34%§0.46%METResolution§1.3%§0%§0%§0%§0.34%§0.77%JER§4.7%§4.5%§130%§8.4%§1.40%§10%bTagSFb-jets§5.7%§1.2%§1.1%§0.30%§1.2%§3.2%bTagSFc-jets§0.48%§1.3%§6.0%§10%§0%§2.0%bTagSFlightjets§1.7%§2.1%§12%§13%§1.0%§2.4%JES1up1.2%-3.0%150%9.6%0%15%JES1down-4.7%-3.0%130%8.4%1.3%10%JES2up0.76%-2.1%290%4.5%0.34%27%JES2down-2.1%-1.2%0%-3.4%0%-1.7%JES3up4.1%-0.90%190%10%0.69%20.90%JES3down-4.6%2.1%0%-10.0%-0.69%-4.1%Table7.2:Systematicuncertaintiesrelatedtoobjectidenti¯cation,resolution,andscale.OtherTopisthecombinationoft¹tVandsingletop.937.2StatisticalAnalysis Maximumlikelihoodratiotestsareamongthemostusedmethodsinstatisticsbecauseoftheirstrengthinhypothesistestingandgenerality.Apopularvariantofthismethodisthepro¯lelikelihoodratiotestwhichconsidersnuisanceparameterswhicharenotofprimaryinterest(µ)tobefunctionsoftheparameterwhichisofinterest(¯).Theparameterofinterest,¯,inthiscaseisde¯nedastheratioofthemeasuredcrosssectiontothestandardmodelcrosssection.Thenuisanceparameters,µ,aremeasuresofsystematicuncertaintieswhicharemodeledbyGaussianstatistics.Bypro¯lingwesimplifytheproblemof¯nding¯andµwhichoptimizesthelikelihoodfunctioninEquation7.1toconstrainµ=f(¯)sothatwecanoptimizeEquation7.2whichisoftenapreferableprocedurewhenonlyonenuisanceparameterisimportant.L(¯;µjdata)(7.1)L(¯;f(¯)jdata)(7.2)Becausewehaveonlyoneparameterwhichneedstobeoptimizedforapro¯lelikelihood¯tisperformed.Thisprocedureisfurthersimpli¯edbyonlyconsideringadistributionofasinglebin.Thissimpli¯cationmakesthepro¯lingofthenuisanceparameterseasy,aseachissimplyaGaussian,notdependentontheparameterofinterestatall.Thesenuisanceparametersaretreatedascorrelatedbetweensourcesofsignalandbackgroundintheoptimizationprocedure.Thesignalcross-sectionisthenextractedfromthelikelihoodfunction.Theextractedcross-sectionmeasurementis¾tZ=448§672(stat)§448(syst)fb.94Thisis1.9timestheexpectedStandardModelcross-sectionof236fbwhichisduetothedataexcessovertheexpectedbackgroundshowninTable6.2.Becauseofthelargeuncertaintiesthisisstillinagreementwiththestandardmodelexpectation.Thiscorrespondstoanupperboundatthe95%con¯dencelimitonthetZcross-sectionof¾tZ=1345fb.Alowerboundcannotbesetduetolargesystematicuncertainties.ThemostnotablesystematicuncertaintiesinthisanalysisaretheexperimentaluncertaintiesJESandJER,MCstatisticsforsamplesthathaveamis-reconstructedlepton,andnormalizationuncertainties.7.3Outlook InordertoestimatethepotentialsensitivitytotZwithincreaseddatacollection,aseriesofsimpli¯edstatisticalanalysesisperformed.Systematicuncertaintiesareremovedinordertoseethee®ectsofincreasedstatisticsinanidealizedway.Theexpectedyieldsobtainedbythisanalysisarescaledupbyafactorof10toestimatetheexpectedprecisionofthecross-sectionmeasurementwiththefull2016dataset,whichcorrespondstoanintegratedluminosityofapproximately30fb¡1.Theexpectedyieldsarethenalsoscaledupbyafactorof100inordertoestimatetheexpectedprecisionofthecross-sectionmeasurementwiththefullRun2andRun3dataset,whichcorrespondstoanintegratedluminosityofapproximately300fb¡1.Whenthisisperformedwiththeeventyieldsofthisanalysiswecangetanexpecteduncertaintyonthecross-sectionof150%.Withthefull2016datasettheexpecteduncertaintydropsto50%.Withthefullsetofrun2datatheexpecteduncertaintyfallsto20%.Thisanalysisiscurrentlystatisticslimited,butwiththefullrun2datasetwewillbecomesystematicslimited.ThemostimmediategainscanbemadefromincreasingMCstatistics,withlonger-termgainstobemadefrombetterunderstandingJESandJER.To95improvethesensitivityofthisanalysis,morecomplexmultivariateanalysismethodscouldbeemployed,thepro¯lelikelihoodcouldbeperformedonastrongdiscriminatingdistribution,and/orcontrolregionscouldbe¯tandincludedinthestatisticalanalysis.BeyondthatwewillneedtowaitfortheLHCtodelivermoredatainordertoputfurtherconstraintsonthetZcross-section.96Chapter8 Conclusion 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