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Measurement of the Standard Model Higgs Boson Produced in Association with a W or Z Boson and Decaying to Bottom Quarks

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Title:
Measurement of the Standard Model Higgs Boson Produced in Association with a W or Z Boson and Decaying to Bottom Quarks
Creator:
Curry, David A
Place of Publication:
[Gainesville, Fla.]
Florida
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University of Florida
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english
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1 online resource (97 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
FURIC,IVAN KRESIMIR
Committee Co-Chair:
KONIGSBERG,JACOBO
Committee Members:
ACOSTA,DARIN E
AVERY,PAUL RALPH
MATCHEV,KONSTANTIN TZVETANOV
ENQVIST,PER ANDREAS JON

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Subjects / Keywords:
cms -- higgs -- quarks
Physics -- Dissertations, Academic -- UF
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bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Physics thesis, Ph.D.

Notes

Abstract:
A search for the standard model Higgs boson decaying to bottom quark pairs when produced in association with a W or Z vector boson is presented. Data samples corresponding to an integrated luminosity of 35.9 inverse femtobarns at sqrt(s) = 13 TeV recorded by the CMS experiment at the LHC during Run 2 in 2016 have been analyzed in 5 channels: Z(uu)H, Z(ee)H, Z(vv)H, W(uv)H, W(ev)H. An excess of events is observed in data when compared to the background only hypothesis (absence of a Higgs to bbar signal process). For a Higgs boson of 125 GeV the measured signal significance is 3.3 standard deviations while the expected signal significance is 2.8. The measured signal strength is found to be mu = sigma/sigma(SM) = 1.19 +/- 0.35. ( en )
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In the series University of Florida Digital Collections.
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Includes vita.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2017.
Local:
Adviser: FURIC,IVAN KRESIMIR.
Local:
Co-adviser: KONIGSBERG,JACOBO.
Statement of Responsibility:
by David A Curry.

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LD1780 2017 ( lcc )

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MEASUREMENTOFTHESTANDARDMODELHIGGSBOSONPRODUCEDINASSOCIATIONWITHAWORZBOSONANDDECAYINGTOBOTTOMQUARKSByDAVIDCURRYADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2017

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c2017DavidCurry

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DedicatedtomyMotherforalwayssupportingme

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ACKNOWLEDGMENTSFirstandforemost,thankyoutotheUniveristyofFloridafortheoppurtunitytostudyphysicsandforprovidingathrivingresearchenvironment.Thankyoutomyadvisor,IvanFuric,forcontinuedsupportthroughtheupsanddownsofgraduateresearch.ThankyoutoallmycolleaguesatCERNandatUFforwhosehelpwasnecsessarytogetthisfar:PierluigiBortignon,MicheledeGruttola,JacoKonigsberg,DarinAcosta,GaelPerrin,LucaPerozzi,StephaneCooperstein,ChrisPalmer,andSean-JianWang. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................... 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 10 CHAPTER 1INTRODUCTIONANDOPENINGREMARKS .................... 11 2THEORETICALFOUNDATIONS ........................... 13 2.1HistoricalDevelopment ............................. 13 2.2TheStandardModel ............................... 14 2.3QuantumElectrodynamics ............................ 15 2.4QuantumChromodynamics ........................... 16 2.5WeakInteractions ................................ 19 2.6TheHiggsMechanism .............................. 21 2.7TheHiggsBoson ................................. 24 3THECMSEXPERIMENT ............................... 27 3.1LHC ....................................... 27 3.2CMSDetector .................................. 30 3.3Tracker ...................................... 31 3.4Calorimeters ................................... 32 3.5MuonSystems .................................. 34 3.6Trigger ...................................... 35 4PARTICLEIDENTIFICATION ............................. 38 4.1EnergyLossesbyParticlesinMatter ...................... 38 4.2Electrons ..................................... 39 4.3Muons ...................................... 42 4.4Jets ........................................ 45 4.5LeptonIsolation ................................. 47 4.6b-JetIdentication ................................ 47 4.7Neutrinos ..................................... 48 4.8JetEnergyRegression .............................. 49 5THEVHBBANALYSIS ................................ 52 5.1Backgrounds ................................... 53 5.1.1Drell-Yan ................................. 55 5

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5.1.2tt ..................................... 56 5.1.3Diboson .................................. 57 5.1.4SingleTop ................................ 57 5.2DataandSimulation ............................... 57 5.2.1Data ................................... 57 5.2.2Simulation ................................ 58 5.2.3SimulatedEventReweighting ...................... 59 5.3Triggers ..................................... 60 5.4AnalysisObjectSelections ............................ 64 5.4.1Pile-UpandPrimaryVertexSelection .................. 64 5.4.2Electrons ................................. 68 5.4.3Muons .................................. 69 5.4.4Jets .................................... 70 5.4.5MissingEnergy .............................. 71 5.5MultivariateStrategy .............................. 71 5.6ControlRegions ................................. 72 5.7Systematics ................................... 76 6RESULTS ....................................... 87 6.1SignalandControlRegionsts ......................... 87 6.2SignalStrengthCalculation ........................... 87 6.3Blinding ..................................... 90 6.4ResultsVH .................................... 90 6.5NextSteps .................................... 91 6.6Conclusions .................................... 93 REFERENCES ........................................ 94 BIOGRAPHICALSKETCH ................................. 97 6

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LISTOFTABLES Table page 2-1HiggsBosonBranchingRatios ............................ 25 3-1LHCluminositytermsanddenitions ......................... 29 5-1SignalcrosssectionsandbranchingratiosforMhiggs=125atp s=13. ...... 53 5-2Listof2016datasamplesusedfortheSingleMuondataset. ............. 58 5-3SignalMonteCarlosampleswithMhiggs=125 ................... 59 5-4ListofMonteCarlodibosonsamples ......................... 59 5-5ListofMonteCarloV+jetsleadingordersamples .................. 60 5-6ListofMonteCarloV+jetsleadingordersamples .................. 61 5-7ListofMonteCarloV+jetsnext-to-leadingordersamples ............. 61 5-8TopandQCDMonteCarlosamples .......................... 62 5-9ListofL1andHLTtriggersusedforthe2016dataset ................ 63 5-10VariablesusedintheBDTtraining. .......................... 73 5-11Preselectioncutsforeachchanneltodenethesignalregion. ............ 75 5-12DenitionofcontrolregionsfortheZ(``)Hchannel. ................. 76 5-13ControlRegionScaleFactors ............................. 83 6-1SignalRegionEventYields .............................. 87 6-2ExpectedandObservedEventYields ......................... 91 7

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LISTOFFIGURES Figure page 2-1VisualrepresentationofthefundamentalparticlesoftheStandardModel ...... 14 2-2FeynmandiagramforComptonScattering ...................... 15 2-3FundamentalQCDFeynmandiagram ......................... 17 2-4Gluon-GluonCoupling ................................. 18 2-5Zbosonneutralcurrentdecay. ............................ 19 2-6Wbosondecay ..................................... 19 2-7HiggsPotentialEnergy ................................ 22 2-8HiggsproductionattheLHC ............................. 25 2-9SMHiggsbosonproductioncrosssections ...................... 25 3-1AnoverviewoftheLHC ................................ 28 3-2OnequarterviewoftheCMSdetector ........................ 35 3-3OverviewoftheRun2UpgradedLevel1Trigger ................... 36 4-1Outputoftheelectron-identicationBDT ...................... 42 4-2ElectronReconstructionEciency ........................... 43 4-3Tag-and-probeResultsforMuonEciency ...................... 45 4-4Distributionsofdijetinvariantmass .......................... 51 5-1FeynmandiagramsforVHbbproduction ....................... 53 5-2FeynmandiagramfortheDrell-Yanbackgroundprocess ............... 56 5-3Feynmandiagramforthettbackgroundprocess. ................... 56 5-4FeynmandiagramfortheZZdibosonbackgroundprocess. .............. 57 5-5SingleElectronTriggerEciencies(WP80) ...................... 64 5-6DoubleElectronTriggerEciencies(WP90) ..................... 65 5-7DoubleMuonTriggerEciencies(RunsBCDEFG) .................. 66 5-8DoubleMuonTriggerEciencies(RunH) ...................... 66 5-9METTriggerEciency ................................ 67 8

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5-10BDTOutputforSignalandBackground ....................... 74 5-11EciencyandbackgroundreductionintheSignalRegion .............. 75 5-12Z+udscgcontrolregionplots(lowVpT) ...................... 77 5-13Z+udscgcontrolregionplots(highVpT) ...................... 78 5-14ttcontrolregionplots(lowVpT) .......................... 79 5-15ttcontrolregionplots(highVpT) .......................... 80 5-16Z+bbcontrolregionplots(lowVpT ........................ 81 5-17Z+bbcontrolregionplots(highVpT ........................ 82 5-18SystematicImpactandPulls .............................. 86 6-1Post-tBDTOutput ................................. 88 6-2Post-tControlRegionDistributions ......................... 89 6-3Best-tSignalStrengthParameter .......................... 92 6-4SignaloverBackgroundLogDistribution ....................... 93 9

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyMEASUREMENTOFTHESTANDARDMODELHIGGSBOSONPRODUCEDINASSOCIATIONWITHAWORZBOSONANDDECAYINGTOBOTTOMQUARKSByDavidCurryDecember2017Chair:IvanK.FuricCochair:JacoKonigsbergMajor:PhysicsAsearchforthestandardmodelHiggsbosondecayingtobottomquarkpairswhenproducedinassociationwithaWorZvectorbosonispresented.Datasamplescorrespondingtoanintegratedluminosityof35.9fb)]TJ /F5 7.9701 Tf 6.587 0 Td[(1atp s=13TeVrecordedbytheCMSexperimentattheLHCduringRun2in2016havebeenanalyzedin5channels:Z()H,Z(ee)H,Z()H,W()H,W(e)H.Anexcessofeventsisobservedindatawhencomparedtothebackgroundonlyhypothesis(absenceofaH!bbsignalprocess).ForaHiggsbosonof125GeVthemeasuredsignalsignicanceis3.3standarddeviations,whichcrossesthe3.0standarddeviationevidencethreshold,whiletheexpectedsignalsignicanceis2.8.Themeasuredsignalstrengthisfoundtobe==SM=1.190.35. 10

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CHAPTER1INTRODUCTIONANDOPENINGREMARKSTheStandardModel(SM)haslongpredictedtheexistenceofaHiggsFieldthatisresponsibleforbreakingtheelectroweaksymmetryandgivingmasstotheWandZvectorbosons,aswellastheothermassiveparticlesoftheStandardModel( 1 )( 2 )( 3 ).Detectionofthequantaofthiseld,theHiggsboson,hasbeenagoalofexperimentsfromLEP(theLargeElectron-PositronCollideratCERN),theTevatronatFermilab,andcurrentlytheLHCalongwithCMSatCERN.Inthesummerof2012observationsofaresonanceat125GeVwereannouncedbytheATLASandCMSexperimentsattheLHC.ThemaindecaymodesoftheHiggsbosonthatfueleditsdiscoveryweretheZZandchannels( 4 ).TheexactmannerinwhichtheHiggsbosoncouplestoquarks,andwhetherthiscouplingisinagreementwithcurrentStandardModelpredictions,stillremainsunresolved.ThegoalofthisthesisisacompletedescriptionofthemeasurementoftheunobserveddecayoftheHiggsbosontobottomquarkpairs(bb),andwhetherthisdecayrateisconsistentwithStandardModelpredictions.ThedetectionofthisbottomquarkdecaymodehasbeenaconsiderablechallengeduetothenaldecaystatesoftheHiggsbosonexistingwithinanoverwhelmingseaofeventsthataretopologicallysimilar.AttheLargeHadronColliderthereexistsanabundanceofproton-protoncollisionsthatleadtonalstatesthatcontainsbottomquarkpairs.Toaidinreducingbackgroundcontaminationarisingfrombbnalstates,werequirethattheb-quarkpairbeproducedinconjunctionwithaWorZvectorboson.InSection1westartwithasummaryofthetheoreticalbackgroundoftheStandardModel,thevariousforcesfundamentaltoparticleinteractionsintheLargeHadronCollider,andtheHiggsmechanism.Section2willprovideanoverviewoftheLargeHadronCollider(LHC)andtheCompactMuonSolenoid(CMS).Thevarioussub-detectorsofCMSandtheirrolesinindentifyingHiggsbosonsignatureswillbediscussed. 11

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Reconstructingparticlesfrommeasurementsmadeinthesub-detectorsisthegoalofSection3.Muons,electrons,jets,andneutrinosarediscussed.Techniquestoidentifydierenttypesofquarksthroughamethodcalledb-taggingarepresented.Section4willcovertheanalysisstrategyusedinthemeasurementoftheHiggscouplingtob-quarkpairs.Selectionsofallphysicsobjectsarealsogiveninthissection.Controlregionsaredescribedindetailandplotsshowingthelevelofdatatosimulationagreementareprovided.Lastly,section5describestheresultsofthisthesis:foraHiggsbosonmassof125GeV,wendevidenceforanexcessofsignaleventswithalocalsignicanceof3.3standarddeviations. 12

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CHAPTER2THEORETICALFOUNDATIONS 2.1HistoricalDevelopmentTodaywehaveaconcisemodelofallexperimentallyveriedfundamentalparticlesandtheforcesthatgovernthemHowever,thiswasnotthecaseasthephysicsworldmovedintothe1970's.Itwassuspectedthattherelurkedamorefundamentalsetofparticles(whatwenowknowasquarks)thatmakeuptheprotonandneutron,butdenitiveevidenceforaparticularquarkmodelhadnotyetbeenfound.Atheoreticalmodelofquarkswasproposedin1964byMurrayGel-MannandGeorgeZweigindependently.ExperimentsfromtheStanfordLinearAccelerator(SLAC)inthelate1960'sinwhichelectronswerescatteredohydrogenanddeuteriumbroughtforthstrongevidencethattheprotonwasnotfundamentalandthatitwascomposedofpoint-likeobjectswithcharges+2/3and-1/3( 5 ).TheseexperimentswheremuchliketheRutherfordscatteringexperimentsintheearly20thcenturyinwhichitwasfoundthattheatomwasnotfundamentalandcontainedpositivechargelocalization(ie.,anucleus).By1969theup,down,andstrangequarkshadbeendiscoveredatSLACandthequarkmodelofGel-MannandZweigappearedtodescribenatureaccurately.ThenalnailintheconwhichcementedthequarkmodelasthebestdescriptorofnaturewasthediscoveryoftheJ= in1974bytwoindependentgroups:theBurtonRichterledgroupatSLAC,andtheSamuelTingledgroupatBrookhavenNationalLabratory( 6 ).TheJ= isalsoreferedtoascharmonium,asitisabound-stateofacharmquarkandananti-charmquark,witharestmassof3.097GeV.Ithasamuchlongerlifetimethanexpectedduetothesuppressionofitshadronicdecaymodesandasresulthasaverynarrowdileptonresonance.ThisclearexperimentalsignatureisnowusedintheLHCandothermodernparticledetectorsasacalibrationpoint.UntiltheRichter-Tingdiscoverythetheorizedcharmquarkhadremainedelusive,andtheseaofheavyparticles(pions,kaons,etc.)andquarkspreviouslydiscoveredremainedpartofadisorganizedorderingsystem.ThediscoveryoftheJ= tookpartinwhatisnowknownasthe 13

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NovemberRevolutioninphysics:thedevelopmentoftheStandardModelthatwasspurredonbytheJ= discovery. 2.2TheStandardModel Figure2-1. AvisualrepresentationofthefundamentalparticlesoftheStandardModel. TheStandardModelofparticlephysics(visuallyrepresentedinFigure 2-1 )isaconcisedescriptionofallexperimentallyobservedparticlesandtheirinteractions.TodatetherehavebeennoexperimentalresultsthatcontradictthepredictionsoftheStandardModel.IthasbeenaresoundingsuccessindescribingtestablephenomenaandthelastundiscoveredfundamentalparticlepredictedbytheStandardModel,theHiggsboson,wasdiscoveredin2012( 7 ).Threegenerationsofquarksandleptonsdescribethefermioniccomponents(fermions 14

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have1/2integerspinandobeyFermi-Diracstatistics),whiletheremainingparticlesaregaugebosons(integerspinandobeyingBose-Einsteinstatistics).Thegaugebosonsarethemediatorsoftheelectromagnetic(photon),strong(gluon),andtheweak(W,Z)forces.Theseforcesaredescribedbythetheoryofquantumgaugesymmetryandbelongtothegaugegroup: SU(3)xSU(2)xU(1)(2{1)SU(3)describestheinteractionofgluonsthroughcolorcharge,andcontains8gaugebosonsarisingfromlinearcombinationsofthethreecolorchargesandtheiranti-charges:red,blue,andgreen.SU(2)describesthethreebosonsofweakisospin(W+,W-,Z).U(1)describesthehyperchargeanditsassociatedgaugeboson,thephoton.ThecombinationofSU(2)andU(1)createthetheoryoftheElectroWeakforce( 6 ).Anintroductiontoeachoftheseforceswillnowbegiven. 2.3QuantumElectrodynamicsInteractionsbetweenchargedparticlesoccurduetotheelectromagneticforce,whichisdescribedastheexchangeofaphoton.AfundamentalFeynmandiagramforthisprocessisgiveninFigure 2-2 ,inwhichtwoelectronsinteractbyexchangeofaphoton. e)]TJ /F3 11.9552 Tf -6.356 111.388 Td[(e)]TJ /F3 11.9552 Tf 143.495 -120.065 Td[(e)]TJ /F3 11.9552 Tf -6.356 111.388 Td[(e)]TJ /F1 11.9552 Tf -308.185 -128.302 Td[(Figure2-2. FeynmandiagramfortheQEDinteractionoftwochargedparticlesbyvirtueofphotonexchange(ComptonScattering). WithintheFeynmandiagramsofQED,electricchargemustbeconservedateachvertex( 8 ).InFigure 2-2 anelectronentersandleavesateachvertex,makingthetotalchargebeforeandafterequaltonegativeone(thephotonwithzeroelectricchargedoesnotviolate 15

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conservationofelectriccharge).TheQEDLagrangiandescribestheinteractionbetweenaspin-1/2eldandanelectromagneticeldandisgivenby L= (iuD)]TJ /F3 11.9552 Tf 11.955 0 Td[(m) )]TJ /F4 11.9552 Tf 13.151 8.088 Td[(1 4FvFv.(2{2)ThekineticenergytermintheQEDLagrangianisthelasttermwhere F=@A)]TJ /F6 11.9552 Tf 11.955 0 Td[(@A,(2{3) A=(,A),(2{4)and D=@+ig1 2W+ig01 2YB.(2{5)GaugeinvarianceoftheU(1)symmetrygrouprequiresthiskinetictermtobeinvariantundertransformationsoftheform A(x)!A(x))]TJ /F10 7.9701 Tf 9.299 4.936 Td[((x),(2{6)forany(x)( 8 ).Thistransformationholdsforamasslessgaugeboson,whichthephotonis,butdoesnotholdforcaseswherethegaugebosondoeshavemass.ThispointishighlightedinordermotivatethefundamentalproblemthatissolvedbytheHiggsMechanism:allowingtheWandZvectorbosons,forcecarriesoftheEWKSU(2)group,toacquiremasswithoutviolatingthegaugesymmetryoftheQEDLagrangianandbyextensiontheElectroWeakLagrangianofsection2.5.BeforeweturntofurtherdiscussionsofEWKtheoryandtheHiggsMechanism,anintroductiontoQuantumChromodynamics(QCD)isgiven. 2.4QuantumChromodynamicsQCDdescribestheinteractionsbetweenquarksandgluonsand,analagoustoQEDandcharge,willinvolvetheabsorptionoremissionofagluon.Gluons,likethephoton,are 16

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gq(green)q(blue)q(blue)q(green)Figure2-3. FeynmandiagramfortheQCDinteractionoftwoquarksbyvirtueofgluonexchange. masslessandhavespin1,butalsopossesscombinationsoftwocolorcharges(red,greenorblueandantired,antigreenorantiblue),whichleavethetotalcolrochargeofthegluontobezero.Quarkscanhaveoneofthreecolors:red,green,blue,whiletheanti-quarkshaveanti-red/green/blue.Again,analogoustoQED,wehaveafundamentalQCDFeynamndiagraminFigure 2-3 ,inwhichtwofermionsinteractbyexchangeofamasslessvectorboson( 9 ).UnliketheQEDreaction,theinitialandnalstateparticleshavebeenslightlyalteredduetotheadditionalQCDdegreeoffreedom:color.InQCDanewconservationassociatedwithcolorisintroduced:justlikewithelectricchargeinQED,colormustbeconservedateachvertex.Sincethemediatorofthestrongforcecarriesacolorcharge,itispossibleforquarkstoenterandleaveareactioninadierentstate(color)andcolorconservationwillstillbemet(Figure 2-3 ).Couplingbetweengluonsisalsopossibleandcanleadtogluonemissionbyagluon(Figure 2-4 ).ThisprocesscanoccurbeforeoraftertheprimaryinteractionandiscalledISRorFSR:intialornalstateradiation.Anotherveryimportantphenomenonthatresultsfromgluonself-coupling,aswellasthefactthatgluonscarrycolor\charge",isQCDanti-screening.Inordertomakesenseofanti-screeningonecanrstlookattheQEDanalogy:electronscreening.Invacuumachargedparticlewillexistinaseaofvirtualelectron-positronpairsthatcoupletothechargedparticlethroughvirtualphotoninteractions.Toanobserversomedistanceawayfromtheloneparticle, 17

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thechargethathe/shewouldmeasurewillbelowerthantheparticle'sactualchargevalue.Theparticleschargeappearssmallerthanitactuallyisandwesaythattheparticlestruechargedisscreened,ordiminished.Thisverysamescreeningeectalsohappensforquarks(particleswithcolor\charge").Foraquarkinvacuumtherealsoexistsaseaofquark-antiquarkpairsthatcoupletoitthroughgluoninteractionsandtheeectistodiminshtheobservedcolorcharge,orstrengthofthestrongforce,asobservedfromadistance.However,becauseofthegluoncolorchargeandabilitytoself-coupletherealsoexistsaseaofgluonselfinteractionssurroundingthequark.Theoveralleectofthethegluonself-couplingsistomakethecolorappearstrongerthanitactuallyis.Thisiscalledanti-screening.Sincethegluon-gluoncouplingsarelesssuppressedthanquark-antiquarkcouplingsatlowenergies,anti-screeningwilldominate.Astheenergyofanincomingparticleincreases,sodoesitsabilitytoprobesmallerlengthscales.Whatthismeansisthatforhigherenergiesoneisabletomeasurethetruecharge,eitherelectricorcolor,ofthesourceparticle.Forthecaseofelectromagnetismthismeanstheobservedchargestrengthwillincreasewithenergy,asitwasorignallydiminished,orscreened.Forparticlesthatcarrycolorthismeansthattheobservedcolorstrengthgoesdownwithenergy,sincetheircolorstengthwasoriginallyinated,oranti-screened.Thisresultsinthestrongcouplingconstant(s)decreasingwithincreasingenergy.Forproton-protoncollsionsathighenergieswithinexperimentalparticlecollidersthismeanstheamountofquark-antiquarkpairswithintheprotonincreasesathighenergy( 9 ).Itisexactlythislargefractionofqqpairsthatmakeproton-protoncollidersfeasibleforstudyingqqinitiatedprocess,suchastheassociatedproductionHiggschannelthisthesisisfocusedon. 2.5WeakInteractionsWeakinteractionsarecharacterizedbytheemissionorabsorptionofWandZbosons:themediatorsoftheweakforce.Allquarksandleptonsinteractthroughtwotypesofweakinteraction:charged,mediatedbytheW+/W)]TJ /F1 11.9552 Tf 7.085 -4.338 Td[(,andneutral,mediatedbytheZ.ExamplesofchargedandneutralweakinteractionsareshowninFigures 2-5 2-6 ( 9 ). 18

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gggFigure2-4. Gluon-GluonCoupling Z0e+e)]TJ /F1 11.9552 Tf -178.256 -131.639 Td[(Figure2-5. Zbosonneutralcurrentdecay. TheneutralcurrentprocessdepictedinFigure 2-5 isaZbosondecayingintoaleptonanditsanti-particle.AsimilardiagramexistsforaZbosondecayingintoaquark-anti-quarkpair.ThechargedcurrentreactiondepictedinFigure 2-6 isanegativelychargedWbosondecayingintoanelectronandanti-electronnuetrino.Asimilardiagramexistsforthepostivecurrentreactionwheretheelectronbecomesananti-electronandtheanti-electronnuetrinobecomesanonanti-type.Afundamentalconceptinknowingwhichtypesofweakinteractionsareallowedisthatofleptonnumberconservation.Eachgenerationoflepton(electron,muon,tau,andtheir W)]TJ /F4 11.9552 Tf 160.926 -60.387 Td[(vee)]TJ /F1 11.9552 Tf -308.185 -128.301 Td[(Figure2-6. Wbosondecay.Theexampleheredepictstheminuschargedcurrentweakreaction. 19

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associatedneutrino)hasauniqueleptonnumber:+1isassignedtothenon-antivarietyand-1foranti-type.Themediatorsoftheweakforce,theW/Zbosons,aregivenaleptonnumberofzero.AsshowninFigures 2-5 2-6 theleptonnumberisconservedateachvertex(zerobeforeandafter).BranchingfractionsfortheWbosoncanbederivedbyconsideringallpossiblequarkandleptonicdecays.ForpositiveWbosonsdecayingintoleptonswehavethefollowingpossiblemodes: W+!e++ve,(2{7) W+!++v,(2{8) W+!++v.(2{9)Andthehadronicdecaymodesare: W+!u+d=s=b,(2{10) W+!c+d=s=b.(2{11)Thusthereare9possibledecaymodesfortheW,where2/3ofthetimetheWdecayshadronicallyandtheother1/3toleptons.ExperimentallydeterminedvaluesforWbranchingratiosare67.60%forhadronicmodes,and10.80%forthepossibleleptonicdecays.TheZbosonexperimentallydeterminedbranchingratiosare69.1%tohadrons,20.0%toallneutrinodecays,and3.6%foreachotherleptonic(electron,muon,tua)decaymode( 10 ).Weakinteractionscombinedwiththeelectromagneticinteractionsofsection2.3giveustheSU(2)xU(1)EWKgroupoftheStandardModel.ThekineticenergytermoftheEWKLagrangianisgivenby Lkin=1 4WviWvi)]TJ /F4 11.9552 Tf 13.151 8.088 Td[(1 4BvBv,(2{12) 20

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where Wvi=@Wi)]TJ /F6 11.9552 Tf 11.955 0 Td[(@Wi+gijkWjWk,(2{13) Bv=@B)]TJ /F6 11.9552 Tf 11.956 0 Td[(@B.(2{14)WiarethethreeguagebosonsofSU(2)andBthegaugebosonofU(1)thatwehaveseenpreviously,thephoton.DuetothenecessitiesofgaugetheoryallfourEWKgaugebosonsaremassless,yettheWandZbosonshaveexperimentallyveriednon-zeromasses( 9 ).AnewmechanismisthusrequiredthatgivesrisetothemassiveWandZbosonsthatweobserve,whileleavingthephotonmassless. 2.6TheHiggsMechanismInvarianceoftheEWKLagrangian(eq.2-12)underrotationspreventsamasstermfromsimplybeingaddedtoit.Instead,wehavetoaddanewsystemoreld()whichsatiesthefollowing: Itmustbeacomplex,scalareld-topreserveLorentzinvarianceofthevacuumstate ItmustgiverisetothreemassivebosonsbelongingtotheSU(2)group ItmustkeepthephotonmasslessAcomplex,scalardoubletisdened: =0B@+01CA,(2{15)andanewterminvolvingthisdoubletisnowaddedtotheLagrangian: LHiggs=(D)y(D))]TJ /F3 11.9552 Tf 11.955 0 Td[(V(),(2{16)where V()=2y+(y)2,(2{17)and D=(@)]TJ /F4 11.9552 Tf 11.956 0 Td[(1=2ig)]TJ /F4 11.9552 Tf 11.955 0 Td[(1=2ig0B).(2{18) 21

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Figure2-7. PlotoftheHiggsPotentialEnergywhen>0and2<0. Inordertoensureanon-zerovacuumexpectationvalueforwetake>0and2<0.Thischoiceforandcreatea\mexicanhat"potentialeld,ascanbeseeninFigure 2-7 .Masslessgaugebosons(ie.,thephoton)occupytheminimumstatesofthepotentialenergyeld,whiletheweakvectorbosonsspontaneouslybreakthesymmetrybymovingoutoftheminumumpotentialwell.Pertubationsaboutthisnon-zerominumumvacuumstatecreateexcitationsintheHiggsFieldwhicharetheHiggsBosonssoughtafterinthisthesis.WenowchooseanorientationofintheSU(2)spacethatbreaksthesymmetryofSU(2),andthusgivingmasstotheWandZbosons,whileleavingtheU(1)symmetryunbroken: =1 p 20B@01CA,(2{19)Agaugetransformatinonofthisscaledoubletisalsodened: !U()=1 p 20B@0+H1CA(2{20) 22

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where U()=expi .(2{21).Additionally,thegaugebosonsofSU(2),Wi,arealsoaectedbythistransformation,whilethephotonisleftunchanged: B!B,(2{22)while W 2!U()W 2U)]TJ /F5 7.9701 Tf 6.586 0 Td[(1())]TJ /F3 11.9552 Tf 14.587 8.088 Td[(i g(@U())U)]TJ /F5 7.9701 Tf 6.586 0 Td[(1().(2{23)SubstitutingbackintotheEWKLagrangianyieldsthefollowingforthekineticterm: jDj2=1 p 2(0)1 2gW+1 2g0B21 p 20B@01CA.(2{24)Lastly,thephysicalbosons(i.e.thosethathavemassforthecaseoftheWandZ)thatareobservedaredenedascomplex,linearcombinationsofthemasslessgaugebosons: W+)]TJ /F10 7.9701 Tf -8.525 -7.892 Td[(=W1+)]TJ /F3 11.9552 Tf 9.298 0 Td[(iW2 p 2,(2{25) Z=gW3)]TJ /F3 11.9552 Tf 11.955 0 Td[(ig0B p g2+g02,(2{26) A=g0W3+igB p g2+g02.(2{27)ThekinetictermoftheEWKLagrangiannowyields 23

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jDj2=g22 4W+Wu)]TJ /F4 11.9552 Tf 9.741 -4.936 Td[(+1 2(g2+g02 4ZZ+...(2{28)whereallnon-masstermshavebeendropped.ThepotentialtermoftheEWKyields V()=1 2(22)H2+...(2{29)TheWandZbosonshavenowaquiredamassgivenby MW=g 2v;MZ=p g2+g02 2v;MH=p 2,(2{30)wherevisthevacuumexpectationvalue(VEV)andcanbewrittenas v=2 .(2{31)visextractedformeasurmentsofmuondecayusingtheFermirelation Gf p 2=g2 8M2W=1 22;v2=(246GeV)2.(2{32)TheHiggsmassnowdependsonlyonthechoiceoflambda,whichisnotdetermineduniquelybytheStandardModelandmustbedeterminedexperimentally. 2.7TheHiggsBosonTheHiggselddescribedinprevioussectioncanbedetectedbymeasurmentofitsexcitation,theHiggsboson.OnJuly4th,2012thetwogeneral-purposedetectors(CMSandATLAS)attheLargeHadronCollider(LHC)announcedthediscoveryoftheHiggsboson.TheHiggsbosonwasobservedwithamassof125GeVwithstandarddeviationsbetween5and6each( 4 ).Proton-Proton(pp)collisionsoccuringattheLargeHadronColliderwillbetherelevantmethodofHiggsproduction.Quark-antiquarkpairsandgluonswithintheprotonwillberesponsibleforinitiatingtheHiggsproductionmechanisms.ThesemechanismsforHiggscreationareshowninFigures 2-8 ( 11 ).Themostabundantproductionmechanismsare 24

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Figure2-8. HiggsproductionattheLHC.(a)gluon-gluonfusion,(b)vectorbosonfusion,(c)associatedvectorbosonproduction,(d)associatedtopquarkproduction. Figure2-9. TheSMHiggsbosonproductioncrosssectionsasafunctionofcenterofmassenergyforppcollisions. gluon-gluonandvectorbosonfusion(VBF),followedbyassociatedproductionwithavectorboson(VH),andassociatedproductionwithatopquarkpair(ttH).Thisthesiswillfocusontheassociatedproductionchannelandmotivationsforthischoicewillbediscussedinchapter5.Cross-sectionsfortheseproductionmechanismsareshowninFigure 2-9 .TheStandardModelisabletopredictthebranchingratiosoftheHiggs(sumamrizedinTable 2-1 foramassof125GeV( 11 )).TheHiggsbranchingratiosinfermionicdecaysgetlargerasthefermionmassesincrease.ThebehavioroftheHiggscouplingtofermionsistoincreaseasthesquareofthefermionmass( 7 ).ThisfeatureoftheHiggshavinghighercouplingtomoremassiveparticlesisa 25

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Table2-1. HiggsBosonbranchingratiosforamassof125GeVatp s=13TeV. DecayChannelBranchingRatioRel.Uncertainty H!2.2810)]TJ /F5 7.9701 Tf 6.586 0 Td[(35% H!ZZ2.6410)]TJ /F5 7.9701 Tf 6.586 0 Td[(24.2% H!W+W)]TJ /F4 11.9552 Tf 33.916 -4.339 Td[(2.1510)]TJ /F5 7.9701 Tf 6.586 0 Td[(14.2% H!+)]TJ /F4 11.9552 Tf 48.069 -4.338 Td[(6.3210)]TJ /F5 7.9701 Tf 6.586 0 Td[(25.7% H!bb5.710)]TJ /F5 7.9701 Tf 6.587 0 Td[(13.2% H!+)]TJ /F4 11.9552 Tf 46.821 -4.339 Td[(2.1910)]TJ /F5 7.9701 Tf 6.586 0 Td[(46.0% consequenceofhowthetheoryisbuiltandwearetestingwhetherthisistrueornotbymeasuringtheHiggscouplingtobquarks.ForaHiggsdecayingtoZZ/WW,couplingtohighermassesisnotfollowed.AssummarizedinthelatestParticleDataGroupHiggsBosonReview( 12 )theZbosonaquiresanextrafactoroftwointhedenominatorofitscouplingtotheHiggsboson.ThiscausesthelighterWbosontohaveastrongercouplingtotheHiggsthantheheavierZboson.TheaforementioneddiscoveryoftheHiggsBosonattheLHCwasdoneatanoperatingcenterofmass(p s)energyof7and8TeV.TheLHChasnowenteredanewperiodofincreasedenergy,calledrun2,ofp s=13TeV.Withthisincreaseincenterofmasscollisionenergythereisanassociatedincreaseinthecross-sectionsandtheiruncertaintiesforvariousnalstatesasshownFigure 2-9 ( 7 ).Thisincreaseincross-sectionisaresultofmorequark-antiquarkpairsandgluonshavingahighenoughenergyinordertoinitiatetheirrespectiveproductionmechanisms.Also,astheprotonenergyincreasessodoestheabundanceofquark-antiquarkpairsandgluons,whichwillincreasetherateofHiggsproduction.NowthatthetheoreticalfoundationsfortheHiggsbosonhavebeenintroducedanditsmainproductionmodesdiscussed,wenowturntoadiscussionoftheexperimentalmethodsandapparatiusedtodetecttheHiggsboson. 26

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CHAPTER3THECMSEXPERIMENTTheCompactMuonSolenoid(CMS)isamultipurposegeneraldetectorcapableofdetectingallwellknownparticles.CMSexistswithintheLargeHadronCollider(LHC)inGeneva,Switzerland.TheEuropeanOrganizationforNuclearResearch(CERN)employsthousandsofscientistsfromaroundtheworldandoperatestheLHC.WithintheLHCtwobeamsofprotonsareacceleratedinadjacent,circulatingringsinoppositedirections.Collisionsbetweenthesebeamshappenatfourdierentpointsalongthering:ATLASandCMS(general-purposedetectors),ALICE(QCDmeasurementsindense,heavyionenvironments),andLHCb(dedicatedtob-quarkphysics).ThischapterwillgivebriefdescriptionsoftheLHCandCMSdetectorandmotivationsfortheirdesign. 3.1LHCTheLHCisaproton-protoncolliderwitharadiusof27kmandacurrentoperatingcenterofmassenergyofp s=13TeV.Toachievethisenergyprotonsareacceleratedthroughachainoflinearandcircularaccelerators,ofwhichtheLHCisthelaststageofacceleration( 13 ).ThischainoflinearandcircularacceleratorsisreferredtoastheCERNacceleratorcomplexandiscomprisedofolderacceleratorsfromthepreviousgenerationofhighenergyexperimentsatCERN.ThechainbeginswithLINAC2,alinearaccelerator,whichservesasthesourceofprotonsandinitalstageofacceleration.InLINAC2bottlesofhydrogengasfeedtheinitialchamberswhichionizethehydrogenatomsyieldingclustersofprotons.Radio-Frequency(RF)cavitiesthencreateelectriceldswhichthenacceleratetheprotonclusterstoaninitialenergyof50MeV.ThenextstageofboostistheProtonSynchrotronBooster(PSB)whichsplitstheincomingprotonclusterintofourdiernetcircularpaths,whichnowboosttheprotonsto1.4GeV.These1.4GeVprotonsthenmakeittoanothersynchrotron,theProtonSynchrotron(PS),andthenlastlybeforetheLHCcomestheSuperProtonSynchrotron(SPS)whereanenergyof450GeVisachieved. 27

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Figure3-1. AnoverviewoftheLHC OncetheclusterofprotonsreachtheLHCtheyaresplitintotwobeampipes(oneclustermovingclockwiseandtheothercounter-clockwise)thattraversethefullcircumferenceoftheLHC(27km).RFcavitiesarestationedatfourpointsalongtheLHCbeampipesthatservetwomainfunctions:one,tofurtherincreasetheprotonenergyfrom450GeVto6.5TeV,andtwo,tomaintaintheclustersofprotonsintightpackets,orbunches.Havingtightprotonbunchesiscrucialforobtaininghighluminositycollisionsandformodellingpile-up.Eachcollidingprotonbunchisseparatedintimeby25nanoseconds.Whenbunchescollidetherearemultipleproton-protoninteractionsthatoccurinadditiontorareevents,suchastheHiggsdecaythisanalysisaimstostudy.Theseadditionalcollisionsarereferredtoaspile-up.Pile-upcanbein-time,whenthecollisionscomefromthesamebunch,orout-of-time,whencollisionscomefromtheprecedingorfollowingbunch.Theabilitytomodelpile-updependsontheLHC'sabilitytomaintaintightlyclusteredbunches,andisachievedthroughtheuseofoscillatingelectriceldsintheRFcavities.ThefrequencyoftheRFcavityistunedtothecircularfrequencyofthecirculatingprotonbunches.Asaresult,whenabuncharrivesatanRFcavitytheforwardprotonswhoarriveslightlyearlyfeelaslowingdowneectfromtheRFcavityelectriceldwhichishasnotbeenfullyipped. 28

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Theprotonswhicharelaggingbehindattherearofthebunchwillarriveaftertheelectriceldhasbeenippedandpointsinthesamedirectionoftheprotonsmovementandwillthusexperienceanacceleration.Theprotonsinthemiddleofthebunchfeelnoaccelerationbecausetheelectriceldisperpendiculartoitstrajectory.Theendresultisaself-correctingtighteningofeachprotonbunch.Additionally,eachbunchiskeptinacircularorbitbya3.8Teslasuperconductingmagnet.Finally,collisionswilltakeplacebetweenbunchesofprotonsintwomainpointsoftheLHCring:ATLASandCMS,twogeneralpurposedetectorsthatarecurrentlysearchingfornewphysics.Onemeasureofacollidersperformanceisitsluminosity:therateofparticlescolliding,andisoftenthoughtofastheoperatingtimeofanexperiment,ortheamountofdatacollected.TheLHCwasdesignedwithhavinghighluminosityinmindandcurrentlyhasaninstantaneousluminosityof1034cm)]TJ /F5 7.9701 Tf 6.587 0 Td[(2s)]TJ /F5 7.9701 Tf 6.586 0 Td[(1( 14 ).TheformalexpressionofinstantaneousluminosityattheLHCisgivenby: L=kbfN2p (3{1) VariableDenition Lorentzfactor kbnumberofbunches ffrequencyofrevolution N2pnumberofprotonsperbunch eectivecollisionarea Table3-1. LHCluminositytermsanddenitions AtthisluminositytheCMSdetectorwouldbesavingmanyterabytesofdatapersecond,whichisveryimpracticaltorecordandstore.Insteaddedicatedtriggersareemployedthatservetoonlyrecordthoseeventswhicharedeemedinterestingtophysicsanalyses(seesection3.6forfurtherdiscussionoftheCMStrigger). 29

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3.2CMSDetectorTheCMSdetectorislocatedinCessy,France,100metersbelowthesurface.Atypicalhighenergyppcollisionwillproduceawidevarietyofparticles,eachwithdierentproperties.Identyngtheseparticles,ortheirdecays,andmeasuringtheirenergiesandmomentaisadesigngoalofCMS.Atalengthof21.6metersandadiameterof15meters,CMSiscomposedofmanysubdetectorsthateachspecializeindetectingandmeasuringasubsetoftheparticlesproducedincollisions.Theinnerdetectormeausuresthepathsofchargedparticlesandisonlyafewradiationlengthsthickinordertonotimpedemovementtothenextlayerofdetectors.Surroundingtheinnerdetectorarethecalorimeters:theelectromagneticcalorimetermeasurestheenergyofchargedparticlesandphotons,andthehadroncalorimetermeasurestheenergyofparticlesthatinteractbythestrongforce.TheouterlayersofCMSarecomposedofdedicatedmuondetectorsinboththebarrelandendcapregions.FromtheintialstagesofCMSdesignthedetectionofisolatedleptons(electronsandmuons)andisolatedphotonshavebeenacentraldesigngoal.DetectionoftheseisolatedparticlesarekeycomponentsinHiggsandBeyondStandardModel(BSM)searches( 15 ),asevidencedbythetwokeyanalysesthatcontributedtotheHiggsbosondiscovery:ZZdecayswhichresultin4isolatedleptons,andthediphotondecaymode.ForcaseofBSMsearches,highenergymuondetectioniskeyforheavyZbosondecaysto+)]TJ /F1 11.9552 Tf 10.986 -4.339 Td[(.ThekeycomponentofCMSthatallowsforprecisemomentummeasurementsisitsextremelystrongmagnetthatenablescurvedtrajectoriesofparticlestraversingthedetector.Insections3.2and3.3theCMSdetectionofmuonsandelectronsisdiscussedfurther.TheCMScoordinantesystemisdenedwiththez-axispointingalongthebeamline,x-axistowardsthecenteroftheLHC,andy-axisupwards.Twonewvariables,pseudo-rapidity()andrapidity(y),areusefulincollidersandaregivenbythefollowingequations: =)]TJ /F3 11.9552 Tf 9.298 0 Td[(lntan 2.(3{2) 30

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y=1 2lnE+pzc E)]TJ /F3 11.9552 Tf 11.955 0 Td[(pzc.(3{3)Whereisthepolaranglewithrespecttothez-axis(alongthebeamline),Eisthetotalenergyoftheparticleandpztheparticlesmomentumalongthez-axis.Underlargeboostswherethecollidingprotonsanditsconstituentscanbeconsideredrelativistic,isaverygoodapproximationoftherapidity(y).Thisapproximationisveryvaluablebecauseitisoftendiculttogetanaccuratemeasurementofaparticlestotalenergyandbeamlinemomentum.WhenthisapproximationcanbemadethedierenceinbetweentwoparticlesisLorentzinvariantunderaboostinthezdirection.Again,forhadroncollidersthisbecomesveryimportantasthecompositenatureofcollidingprotonsmeansthatpartoninteractionscarrydierentboostsalongthez-axis.Thevariablerangesfromzero,whenaparticleistravellingalongthebeamline,andtoinnitywhenaparticleisparalleltothebeamline.Aparticlethathasanabsolutepseudo-rapiditygreaterthan2.4willbereferedtoasforwardandelsewherereferedtoasbeingcentral.Theselimitsrelatetothegeometryandspatialextentofthesub-detectors,aswillbedescribedinthefollowingsections. 3.3TrackerTherstdetectorencounteredbyparticlesproducedincollisionswillbethetracker.Composedalmostentirelyofsiliconpixels,thetracker'saimispathreconstructionofhighenergyparticles,aswellasdetectionofshortlivedparticleswhichmayonlylivelongenoughtointeractinthetracker.Achallengeofthetrackeristhehighuxofpartcilesduetoitsproximitytothebeamline:roughly10millionparticlespersquarecentimeterpersecond( 16 ).Thesiliconlayersinthetrackeractasreverse-biasedp-njunctionswhichproduceelectricalsignalswhenachargedparticlepassesthroughthem.Sincethegoalofthetrackerispathreconstructionandnotenergymeasurement,thetrackerwillnotimpedetheparticleandonlyrecorditspath.Onenotablefeatureofthetrackerisitsabilitytoaccuratelymeasuremomentumindierentregionsofthedetector.Infact,thefollowingdiscussionwillalsoholdfor 31

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momentummeasurementsanywhereintheCMSdetector.Thetrackerwillattempttoprovideamomentummeasurementbasedonaparticlesmeasuredtrajectory:chargedparticlesfollowacurvedpathinthepresenceofamagneticeldandthiscurvatureishigherforlowermomentumparticles.Akeygeometricalquantitythatrelatesaparticlescurvatureandthetracker'sabilitytoassignmomentumisthesagitta(s):thedistanceonacirculararcfromthecenterofthearctoitsbase.Therelationshipbetweenmomentumresolution,s,andthemagneticeld(B)isgivenby p p/p sB.(3{4)Ascanbeseenfromthisequationformomentumresolution,anincreaseinthemagneticeldand/orthesaggittaresultsinasmalleruncertaintyonmomentummeasurements.Electricalsignalsdetectedinthedierentlayersofthetrackerareusedtoreconstructachargedparticlespathintoanobjectcalledatrack.Tracksarecrucialindeterminingthemomentumandtrajectoryofchargedparticles,inadditiontowheretheprimaryinteractionverticesarelocated.Aprimaryvertexisthemostlikelycoordinateofwheretheinitialcollisiontookplace.Reconstructionofaprimaryvertexisdonebyrequiringaminumumnumberofhigh-qualitytracksandhavingthelargestsquaredtransversemomentumsumassociatedtoit.Primaryverticescanbemeasuredwitharesolutionofbetterthan50m( 17 ).Suchhighspatialresolutionbecomesinstrumentalinidentifyinglonglivedparticles,suchasthebquarksinthisanalysis,thatdecaywithinthetrackerandwillbedescribedfurtherinSection3.6. 3.4CalorimetersAftertheinnertrackerthenextsub-detectorsforaparticletointeractwitharetheelectromagneticcalorimeter(ECAL)andthenthehadroniccalorimeter(HCAL).Theirdesignissuchthataparticle,andallofitsdecayproducts,arecompletelyabsorbedwithinthemediumofthecalorimeters,allowingforanenergymeasurementoftheparticle.Bothcalorimetersaresituatedbeforethemagneticsolenoidinordertoensurethataportionofaparticlesenergy 32

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wouldnotbelostininteractionswiththesolenoidmaterialandthrowothecalorimeterenergymeasurement.TheECALisscintillatingcalorimetermadeof15,000leadtungstatecrystalsintheendcaps,whilethebarrelcontains61,200.Unlikecalorimetersthathaveaseparateabsorberandcollector,theCMSECALishomogenous.Leadtungstatewaschoosenasthehomogenousmaterialbecauseitcanproducelightinfast,well-denedburststhatallowforprecisemeasurements.Incidentchargedparticlesproduceelectromagneticshowersastheparticletraversesthecrystal.Leadtungstatecanproduceroughly30photonsperMeVofanincomingparticle.Thesephotonsignalsareampliedanddetectedbysiliconavalanchephotodiodesinthebarrelandvacuumphototdiodesintheendcaps( 16 ).Asideeectofhavingmanyindividualphotodiodesistheabilitytoprovidespatialresolutioninadditiontoanenergymeasurement.Theaverageenergylostbyelectronscanbedividedintotwomainregimeswhicharesignicant:energiesmorethan10MeVwherebrehmstrahlungdominates,andbelow10MeVwhereenergylossesthroughionizationbecomesdominant.Asaconsequenceofthisenergydependence,highenergyelectronsandphotonswillproducesecondaryphotonsbybrehmstrahlung,orsecondaryelectronsbypairproduction.Thesesecondaryparticlesthencontinuethiselectromagneticcascadeuntilthereisinsucientenergytocontinue.Thisprocessofelectromagneticcascadingcreatesaspreadofenergyinthecalorimetersreferedtoasacluster.Associatedclusterscanbegroupedtogethertoformsuper-clusters.Themeasurementofenergywithanelectromagneticcalorimeterisbasedontheprinciplethattheenergyreleasedinthedetectormaterialbythechargedparticlesoftheshower,mainlythroughionizationandexcitation,isproportionaltotheenergyoftheincidentparticle.ECALresolutionwillimproveasaparticle'senergyincreasesasshowninthefollowingformula: (E E)2=(S p E)2+(N E)2+C2(3{5) 33

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WhereSisthestochasticterm,Nisthenoisetermduetoelectronicnoiseinthedetector,andCisaconstanttermwhichdoesnotdependonenergy.Thislattertermiscausedbyinstrumentaleectsthatcanoriginatefromimperfectionsinthedetectormaterial,theelectronicreadoutsystem,andfromphysicalwearandradiationdamage.TheHCALiscomposedofalternatinglayersofadenseabsorber,madeofbrass,andtilesofplasticscintillators.Brasswaschoosenastheabsorberduetoitsshortinteractionlengthandbecauseitisrelativelyeasytoproduce.Whenaparticletraversestheaborbingbrasslayerstronginteractionsoccurwiththenucleuiofthebrasscausingacascadeofparticlesatlowerenergies.Withineachlayeroftilesopticalberscalledwavelength-shiftingbersofdiameterslessthan1mmabsorbthelightproducedintheabsorber.TheresolutionfortheHCALfollowsthesameformastheECAL(Formula3-5). 3.5MuonSystemsTheoutermostsub-detectorsarethemuonsystems:drifttubes(DT)inthebarrelregion,cathodestripchambers(CSC)intheendcap,andresistiveplatechambers(RPC)inbothbarrelandendcap( 16 ).TheDTandCSCsystemshaveecientspatialresolution,whiletheRPCsystemexcelsattimingmeasurements.Sincemuonsonlyinteractelectroweakly,theirinteractionsintheHCALareneglibleandtheirlargermassalsomakesenergylossesduetobremsstrahlungandionizationintheECALminimal.Assuchthemuonsystemscanbeplacedoutsidethemagnetwithoutfearofaectingmuonenergymeasurements.DTsarecomposedof4cmwidegaslledtubeswithasinglewireinthecenter.Whenachargedparticlepassesthroughthetubeitwillionizethegasandcauseelectronstoowontothewire,creatingacurrent.Thissignalalongwiththeknowndriftvelocityoftheionizedelectronsallowsforatwo-dimensionalspatialmeasurement.CSCsarearraysofgaslledchambersenclosingapositivelychargedanodewireandanegativelychargedcathodecopperstripthatpassesperpendiculartotheanode.Ionizedelectronsmovetowardtheanode,whilepositiveionsareattractedtothecathode.Inthiswaytwoperpendicularcoordinatesareassignedtopassingparticles. 34

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RPCsconsistofalternatinglayersofapositively-chargedanodeplateandanegatively-chargedcathodeplate.AgasvolumesitsbetweentheanodeandcathodeandmuchliketheCSCandDTsystems,useionizationtodetectparticles. Figure3-2. OnequarterviewoftheCMSdetector.DT,CSC,andRPCsystemsareshown. WithinboththeCSCandDTsystemsthereexistmultiplestationsthatamuonwilldepositenergyinto.Hitsfromsuccessivestationscanthenbecombinedtoformapaththemuonhadtakenandthusassignamomentumtothemuon.EectiverangeinetaoftheCSCsis0.9-2.4,whiletheRPCscurrentlystopat=1.6.InformationiscurrentlysharedbetweentheDT,RPC,andCSCsystemsinorderformuonstobedetectedthatpassthroughboththebarrelandendcap. 3.6TriggerUnlikethesub-detectorsdiscussedinthepreviouschapters,whichhaveadenitephysicallocationwithinthedetector,theCMStriggersystemhasnosingle,physicallocation.OneofthechallengesofanyCMSanalysisistorecordandselectrelevantphysicscollisionsoutoftheoverwhelmingnumberofcollisionsthatoccurwithinCMS.FortheLHCdesignedinstantaneous 35

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luminosityof1.51034cm)]TJ /F4 11.9552 Tf 7.084 -4.338 Td[(2sec)]TJ /F4 11.9552 Tf 7.085 -4.338 Td[(1,thereare23collisionsforeverybeamcrossing,whichoccurswithafrequencyof25nanoseconds.Thisresultsinaninputrateof109eventsthatoccureverysecond.ThegoaloftheCMStriggeristoreducethisinputrate(109Hz)byafactoratleast106tocreateaninputrateof1kHz,whichisthelimitingrateoftheCMSstoragefarm.Thetriggerissplitintotwoonlinelevels:Level1(L1),reducingtheinputrateto100kHz;Level2,theHighLevelTrigger(HLT),recievestheoutputoftheL1triggerandfurtherrecudestheinputrateto1kHz.TheL1triggerwasupgradedforruntwo(shownin 3-3 )andisdividedintothreemaincategroies:L1muontrigger,L1calorimetertrigger,andL1globaltrigger( 18 ). Figure3-3. OverviewoftheRun2UpgradedLevel1Trigger ThemaintechnologyupgradetotheL1TistheuseofAdvancedMezanineCards(AMC)whichtsintothemicroTCAtelecommunicationsstandard.TheboardsoftheL1systemcommunicateviaopticalseriallinkswithabandwidthof10gigabytespersecond.TheL1Muontriggerisfurtherdividedintothreesubcategoirescorrespondingtothemuonsub-detectorsdiscussedinsection3-5:DriftTubeTriggerinthebarrel,CathodeStripChamberTriggerintheendcap,andResistivePlateChamberTriggerintheoverlapregion.Whetherornotthedecisiontotriggerwassentbyoneofthemuonsub-systems,alltriggerobjectsfoundaresentupstream.TriggerTimingandControlsystem(TTC),which 36

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isresponsibleforsynchronoustimingbetweenallthetriggersubcomponents.Asmentionedpreviously,theL1triggerhasbeenupgradedinordertohandlethehigherluminosityandresultingpile-upthatisexpectedfromtheincreasedcollisionenergy.AllsubsystemshavedeployedimprovedreconstructionalgorithmsfortheobjectsneededinLevel1triggefdecisions.TheL1CalorimeterTriggerisresponsiblefortriggerdecisionsbasedonmeasurementsofprimitivesintheHCALandECALsub-detectors.TriggertowerenergysumsinboththeHCALandECALareaccompaniedbyabitrepresentingthetransverseextentoftheelectromagneticenergydepositintheECALcase,andabitrepresentingthepresenceofminimumionizingenergyfortheHCALcase.AnintermediateRegionalCalorimeterTrigger(RCT)recievestherststageoftriggerinformationfromtheECALandHCALandisresponsibleforformingthefollowingprimitives:electrons,photons,taus,andjets.Additionally,theRCTisresponsibleforidentifyingisolatedornon-isolatedelectronsandmuons.ThemaintasksoftheL1GlobalTrigger(GT)istosynthesizeinformationfromtheL1MuonsandCalorimeterTriggersandtopassaLevel-1triggerdecisionupstream.Additionally,theL1GlobalTriggerstoresthecoordinatesin(,)spaceforalltriggerobjects.ThenaloutputoftheL1GTisadecisiontoaccept,calledL1A,orrejecteachbunchcrossing. 37

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CHAPTER4PARTICLEIDENTIFICATIONTheCMSsub-detectorsrecordenergyandrawhitinformationfromparticlespassingthroughthedetector.ThemaintechniquewithinCMSforparticlereconstructionistheparticleow(PF)algorithm( 19 ),whoseaimisidentifyingandreconstructingalltheparticlesfromtheinitialcollisionbycombininginformationfromthedierentsub-detectors.AsimplieddescriptionofthePFalgorithmcanbedescribedasfollows.TracksfromthetrackerareextrapolatedthroughtheECALandHCAL,andiftheypasswithinspeciedboundariesofthecalorimetersuper-clusters,achargedparticleisassociatedtothem.Electronsareassignedfromsuper-clustersintheECALtocurvedtrajectoriesinthetracker,andsimilarprocessesoccurintheHCALtocreatechargedhadroncandidates.Onceallthetrackshavebeendealtwith,theremainingclustersintheECALareassociatedtophotonsandtheneutralhadronstoclustersintheHCAL.Muonswillbereconstructedfromchargedtrackertracksthathavenoassociatedenergydepositsinthecalorimeters,andwithenergydepositsintheCSCsorDTs.Reconstructionofelectrons,muons,jets,andneutrinos(intheformofmissingenergy)fromtheinformationrecordedinthesub-detectorswillbesummarizedinthissection. 4.1EnergyLossesbyParticlesinMatterIdenticationofdierentparticleswilldependonthedierentwaystheyinteractwithmatterandlooseenergy.Themainprocessesforenergylossareionizationandradiation.Ionizationistheprocessbywhichchargedparticlesinteractwithelectronsboundtoatoms,resultinginanenergytransfer.Otherthanelectronsandpositronsenergylossduetoionizationwilldominateoverradiationlossforallbutthehighestattainableenergies.Theexpressionforenergylossduetoionizationbyaparticleasittravelsthroughamediumisgivenby: )]TJ /F3 11.9552 Tf 13.151 8.087 Td[(dE dx=Dq2ne 2ln2mec222 I)]TJ /F6 11.9552 Tf 11.955 0 Td[(2)]TJ /F6 11.9552 Tf 13.15 8.087 Td[(() 2,(4{1)wherexisthedistancetravelledthroughthemedium,Disaconstant(5.110)]TJ /F5 7.9701 Tf 6.586 .001 Td[(25MeVcm2),meistheelectronmass,=v c,=(1)]TJ /F6 11.9552 Tf 12.557 0 Td[(2))]TJ /F5 7.9701 Tf 6.586 0 Td[(1=2,neisthemediumelectrondensity,Iis 38

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themeanionizationpotentialoftheatomsaveragedoverallelectrons,andisadielectricscreeningcorrectionforrelativisticparticles.Chargedparticleswillalsoloseenergyduetothebremsstrahlung(translatedfromGermanasbrakingradiation)mechanism.Theelectriceldofanucleuswillaccelerateanddeceleratepassingparticles,causingthemtoradiatephotons.Forelectronsandpositronsthiswillbethedominantmechanismofenergyloss.Therateofenergylossduetobremsstrahlungisgivenby: )]TJ /F3 11.9552 Tf 13.151 8.088 Td[(dE dx=E LR,(4{2)whereLRistheradiationlengthandisgivenby: 1 LR=4~ mc2Z(Z+1)3naln183 Z1=3.(4{3)ThemostimportantcharacteristicofFormulas4-1and4-3arethe1=m2dependence,wheremisthemassofanychargedparticle.Sinceionizationlossesareonlyweaklydependentonthechargedparticlemass,bremsstrahlungwilldominateforthecaseoflowmassparticlessuchastheelectron.Formuons,whosemassisroughly200timesthatoftheelectron,anyenergylossduetoradiationissuppressedbythe1=m2dependence.Ionizationlosseswilldominateformuonsandduetothefactthatthattheydonotinteractbythestrongforcewillpenetratethethedetectormorethantheotherchargedparticles. 4.2ElectronsElectronreconstructionisdonethroughacombinationoftrackerandECALmeasurements.Asanelectronpassesthroughtheinnersilicontrackeritwillradiatephotonsasitstrajectoryiscurvedduetothemagneticeld.TheamountofbrehmstrahlungfromtheelectronwilldependonitspTandwillspreadoutin(alsoproportionaltopT).ThissprayofenergyfromtheelectronwillberecordedbytheECALasclustersalongapath.Combiningtheseclusterscreatesasuper-cluster,whoseenergyweightedmeanisthenpropagatedbackintothetracker.Matchingacurvedtrajectoryfromthetrackertoasuper-clusterintheECALwillalsodierentiateelectronsfromphotons,wherethelatterwillnotleavebehindacurvedtrajectory 39

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inthetracker.BycombiningtrackerandECALmeasurementsweutilizethelowmomentumeciencyofthetrackerwiththehighmomentumqualityoftheECAL,creatinganelectronwhoseenergyresolutionisoptimizedacrossawiderangeofenergies( 20 ).Itisnecessarytoemployadvancedreconstructiontechniquesthatclassifysuperclusterpatternsintodistinctcategoriesbasedontrackreconstruction.ThecurrentelectrontrackreconstructionalgorithmusedinCMSisaGaussianSumFilter(GSF).Duetobrehmsstrahlunglossesfromelectronspropagatinginahighlynon-Gaussianway,aKalmanFilterwhichreliesonGaussianprobabiltydensityfunctionsmaynotbeideal.TheGSFalgorithmmodelsbrehmsstrahlungenergylossesbytreatingeachobservablesensitivetobrehmsstrahlungasaGuassianandbuildinga\mixture"orsumofGuassians.TheGSFalgorithmaidsinsuperclusteridenticationandthecreationoftheaftormentionedelectroncategories.Thesesuperclusterpatterncategoriesareusedtodierentiatebetween\well-measured"and\poorlymeasured"electronsand,ingeneral,implydierentenergy-momementummeasurementsanddierentelectronidenticationperformance.Thefourelectroncategoriesare: GoldenElectrons.Thisclassrepresentsthoseelectroncandidateswhichareassociatedwithlowbrehmsstrahlung,withareconstructedtrackwellmatchingthesuperclusterandawellbehavedsuperclusterpattern. { asuperclusterformedbyasinglecluster(i.e.withoutobservedbremsstrahlungsub-cluster) { ameasuredbremsstrahlungfractionbelow0.2 { amatchingbetweenthesuperclusterpositionandthetrackextrapolationfromlastpointwithin0.15rad { anEsc=pinvalueinexcessof0.9,whereEscisthemeasuredsuperclusterenergyandpinisthemomentummeasuredattheprimaryvertex. BigBremElectrons.ThisclasssharesmostofthecharacteristicswiththeGoldenelectronclass-wellbehavedsuperclusterpattern(i.e.thebremsstrahlungphotonsaremergedinsidethesinglecluster),noevidenceofenergylossthroughphotonconversion-anddiersonlyinthatBigBremelectronsradiatealltheirbrehmsstrahlunginasinglestepwhencrossingthetrackersiliconelayers.Thisisclassisdenedby { asuperclusterformedbyasingleseedcluster 40

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{ ameasuredbremsstrahlungfractionabove0.5 { anEsc=pinvaluebetween0.9and1.1Thelasttwoelectroncategoriesarethosewithgoodenergy-momentummatchingandmeasurement,butfailtobeclassiedasGoldenofBigBrem,aredenedbythefollowingclass. NarrowElectrons.Thisclasshasalargebremsstrahlungfraction,butnotaslargeastheBigBremclass,andawellbehavedsuperclusterpattern.Itscharachteristicsare { asuperclusterformedbyasingleseedcluster { anEsc=pinvaluebetween0.9and1.1 { ameasuredbremsstrahlungfractionand/oramatchingoutsidetherangeofGoldenandBigBremelectrons.Thelastclassconstitutestheremainingelectronsthatarethoughtofasthe\bad"electons: ShoweringElectons. { asuperclusterpatternidentiedwithseveralbremsstrahlungsub-clusters. { energy-momentum(Esc=pin)matchingwhichfailsoneofthethreedenitionsusedinthepreviousclasses.Electonsusedinthisanalysisarefurthercategorizedbytheoutput(MVAID)ofaMultivariatediscriminator,inthiscaseaBoostedDecisionTree(BDT)algorithm( 21 ).Asetofdiscriminatingvariables,selectedtohavethehighestcorrelationsbetweenelectronandnon-electronlikeevents,usedintheCMSelectronMVAIDBDTare SuperClusterenergy/trackmomentumatvertex betweenSuperClusterpositionandtrackdirectionatvertexextrapolatedtoECALassumingnoradiation betweenSuperClusterpositionandtrackdirectionatvertexextrapolatedtoECALassumingnoradiation RatioofenergyinHCALbehindSuperClustertoSuperClusterenergy Energyin3x3crystals/energyin5x5crystals EnergyofclosestBasicClustertotrackimpactpointatECAL/outermosttrackmomentum 41

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EnergyofclosestBasicClustertotrackimpactpointatECAL/innermosttrackmomentum betweentrackimpactpointatECALandclosestBasicCluster 1 E(SuperCluster))]TJ /F5 7.9701 Tf 40.708 4.707 Td[(1 p(trackatvertex) Bremfraction=(trackmomentumatvertex-trackmomentumatECAL)/(trackmomentumatvertex) RMSwidthoftheshowerin RMSwidthoftheshowerin Figure4-1. Outputoftheelectron-identicationBDTforelectronsfromZe+edata(dots)andsimulated(solidhistograms)events,andfrombackground-enrichedeventsindata(triangles),intheECALa)barrel,andb)endcaps( 20 ). PerformanceoftheelectronMVAIDdiscriminatorwastestedonZandJ=decaysintoe+e)]TJ /F1 11.9552 Tf 10.986 -4.339 Td[(pairsinDataandsimulatedDrell-Yanevents( 22 ).TheoutputoftheMVAIDBDTispresentedinFigure 4-1 ,andelectrontrackreconstructioneciencypresentedinFigure 4-2 4.3MuonsDuetotheirlargemassandinabilitytointeractthroughthestrongforce,muonswilltraversetheinnersub-detectorswithminimalenergylossandreachtheoutermuonsub-detectorsinrelativeisolation.WithinCMS,muontracksarerstconstructedindependentlyintheinnertracker(trackertrack)andintheoutermuonsystems(standalonemuontrack)( 23 ). 42

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Figure4-2. EciencyasafunctionofelectronpTfordielectroneventsindata(dots)andDYsimulation(triangles)( 20 ). Standalonemuontracksareconstructedsoleyfrominformationfromtheoutermuonsystems:CSC,DT,andRPC.The\base"primitivesmeasuredarehitsinthemuonchambers,whicharethenusedtobuildsegmentsor\trackstubs".Duringoinereconstructionthesesegmentsareusedtogenerate\seeds"consistingofpositionanddirectionvectorsandanestimateofthemuontransversemomentum.Theseinitialestimatesareusedasseedsforthetracktsinthemuonsystem,whichareperformedusingsegmentsandhitsfromDTs,CSCsandRPCsandarebasedontheKalmanltertechnique.Theresultingobjectisastandalonemuon.TrackermuontracksarerequiredtohavepT>0.5GeVandareconstructedsoleyfromenergydepositsintheinnertracker.OncemuontrackshavebeenassignedtherearetwoapproachesthatCMSusestobuildmuonobjectsfrommuontracks: GlobalMuonReconstruction.Startingwithastandalonemuontrack,acorrespondingtrackermuontrackisfoundbycomparingparametersofthetwotracks.Theresultingobjectisaglobalmuontrack,whichisttedbyaKalman-ltertechnique.Atlargetransversemomenta,pT>200GeV,theglobalmuontrackimprovesontheenergyresolutionofthetrackermuononlytduetoinecienciesintrackertrackreconstructionathighmomenta. TrackerMuonreconstruction.Inthiscasetracksarerstidentiedinthetrackerwhichsatisfythefollowingmomentumcriteria:pT>0.5GeVandtotalmomentumpT>2.5 43

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GeV.Nextthesecandidatemuontracksareextrapolatedtosegmentsintheoutermuonssub-systemsbytakingintoaccountthemagneticeld,theaverageexpectedenergylosses,andmultipleCoulombscatteringinthedetectormaterial.Theextrapolatedtrackandthesegmentareconsideredmatchediftheirlocaldistanceislessthan3cmorifthevalueofthepull(dierenceinlocalpositionsoftheextrapolatedtrackandthesegment,dividedbytheircombineduncertainty)islessthan4.Atlowmomenta(pT<5GeV)trackermuonreconstructionismoreecientthanglobalmuonreconstructionduetoonlyonemuonsegmentbeingrequiredontheoutermuonsub-systems,whereasasthetypicalglobalmuonreconstructionrequiresmorethanonemuonsegmentindierentstationsofthemuonsub-systems.Standalonemuons,comprisedofonlystandalonemuontracks,aretypicallynotusedinphysicsanalysesduetotheirworsemomentumresolutionandhighercontaminationratesfromcosmicrays.Afteramuonobjecthasbeenreconstructedthereexistsdierentalgorithmsformuonselectiondependingontheneedsofindividualanalyses:identicationeciencyversuspurity.Thethreemostcommonmuonselectioncategoriesare: SoftMuonselection.ThiscategoryrequiresthemuontobeaTrackerMuon,withtheadditionalrequirementthatamuonsegmentismatchedinbothxandycoordinateswiththeextrapolatedtrackertrack,suchthatthepullforlocalxandyislessthan3. TightMuonselection.Thiscategoryrequiresthemuontobeaglobalmuonwiththe2=d.o.foftheglobalmuontracktlessthan10andatleastonemuonchamberhitincludedintheglobalmuontrackt.Thetrackermuontrackisrequiredtobematchedtoatleasttwomuonsegmentsfromthemuonsub-systems,inadditiontousingmorethan10innertrackerhits(includingatleast1pixelhit),andhaveatransverseimpactparameterjdxyj<2mmwithrespecttotheprimaryvertex.Inightmuondecays(muonsnotoriginatingfromprimaryinteractions)aregreatlyreducedwiththisselection. Particle-FlowMuonselection.Muonsfromthiscategoryareanextensionoftrackerandglobalmuons.InformationfromthevariousCMSsub-detectorsareusedinadjustingselectoncriteria,suchastheenergydepositioninthecalorimeters.Thegoalofthiscategoryistooptimizetheselectionofmuonswithinjetswithhigheciency,whilepreventingthemisidenticationofchargedhadronsasmuons.MomentumassignmentecienciesforthethreemuoncategoriesareshowinFigure 4-3 usingJ=!+)]TJ /F1 11.9552 Tf 10.986 -4.338 Td[(eventsforpT<20GeVandZ!+)]TJ /F1 11.9552 Tf 10.986 -4.338 Td[(eventsforpT>20GeV( 24 ). 44

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Figure4-3. Tag-and-proberesultsforthemuoneciencyasafunctionofmuonpTindatacomparedtosimulation.Muons(left),Particle-FlowMuons(middle),andTightMuons(right)inthebarrelandoverlapregions(top),andintheendcaps(bottom). 4.4JetsIndividualquarkshaveneverbeenobservedaloneinnature.Onlythoseobjectsthatarecolorneutralhavebeenobserved.Whenquarksarecreatedtheymustcombinewithotherquarkstocreatecolorneutralobjects.Thisprocessiscalledhadronizationandleadstotheformationofobjectscalledjets.InthehighenergycollisionsoftheLHCquarkswillhavelargemomentaandthustheparticlescreatedduringhadronizationwillbecollimatedinacone-likestructure(jet)fromthequarkthatinducedthehadronization( 25 ).ThebasicconstituentsofjetsaretrackertracksandclustersintheECALandHCAL.Approximately90%ofthemeasuredjetenergywillcomefromchargedhadronsandphotonsmeasuredinthetrackerandECAL,whiletheremaining10%willcomefromneutralhadronenergydepositsintheHCAL.Manyalgorithmstoidentifyandclassifyjetshavebeendeveloped.Themostwidelyusedalogrithmisthe\anti-kt"algorithm,whichusestherelativetransversemomentaoftheparticleowobjects( 26 ).ForeverytwoPFobjectspiandpj,twoquantitiesarecalculatedforthem: 45

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dij=R2ij R2min(p)]TJ /F5 7.9701 Tf 6.586 0 Td[(2T,i,p)]TJ /F5 7.9701 Tf 6.586 0 Td[(2T,j),(4{4)and di=p)]TJ /F5 7.9701 Tf 6.587 0 Td[(2T,1.(4{5)Risthedistanceinthe/plane,andRisthedesiredsizeofthejetcone.Ifdijislessthanditheanti-ktalgorithmwillcombineobjectsiandjintoajet.ThisisrepeateduntilnomorePFobjectsremain.TheeectofthealgorithmistocombinehigherpTjetconstitiuentsrstandthenlowerpTobjectswithawiderangle.Theresultisacone-likestructureintherapidity-azimuthal(y,)plane.CMSalsoemploysasuiteofcorrectionstothemeasuredjetenergies-JetEnergyCorrections(JEC)-whichseektoosetimperfectionsinthejetenergymeasurementsandjetreconstructiontechniques.Energiesofthereconstructedjetsarerelatedtothejetenergiesatparticlelevelandthreefactorizedcorrectionsareappliedtotheraw(uncorrected)jetenergymeasurement.TherstfactorizedJECcorrectionaccountsforthepresenceofenergyoriginatingfrompile-upjetsthatareerroneouslyaddedtoajetsenergymeasurement.Asubtractiontothejetenergyismadefromaquantityderivedfrom,theaverageenergydensityperevent,andthejetarea( 27 ).ThesecondJECcorrectionaccountsforthepTandresponseofjetsduetonon-linearitiesinthecalorimeters.Thethirdcorrectionistotheaverageresponseperjet,orthejetenergyscale(JES).Anadditionalhurdleinjetreconstructionisseperatingjetsthatarisefromtheprimaryinteractionvertexandthosethatarisefrompile-up(PU)collisions.PUcollisionscanclusterandformenergydepositsintheECALandHCAL;thesereconstructedobjectsarereferedtoasPUjets.OnaveragePUjetstendtobesoft(lowpT),butmultiplePUjetscanoverlapandformahighpTjetthatcouldbeusedbytheVHbbanalysis.Additionally,astherateofPUjetsincreasestherateofhighpTPUjetsincreasesquadratically( 27 ).Approximately50%of 46

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all30GeVjetsarePUjets.CMSemploysalikelihooddiscriminatorusedtoidentifyandrejectPUjets.Thediscriminatinginputsusedinthelikelihooddiscriminatorinclude12variablesrelatedtojetshapeandvertexrelatedquantities.AhighPU-jetrejectioneciencyisachievedofupto90to95%forcentraljetswithjj<2.5,whileretaining99%ofthenon-PUjetsfromhighpTinteractions. 4.5LeptonIsolationOneofthechallengesofleptonidenticationintheVHbbchannelisdistinguishingleptonswhoseoriginisthetheW/Zbosonversusleptonsthatwerecreatedinthedecayofajet.Thetechniquedevelopedtohelpinthisprocessiscalledleptonisolation( 28 ).Leptonisolationseekstomeasurethetotalenergyinaregionaroundtheleptonandassignavaluetotheleptonthatisrepresentativeofitsprobabilitytobeborninajetdecay.Thehighertheenergyoftracksaroundalepton,thehighertheprobabilityforittohavebeencreatedduringthedecayofajet.Eachsub-detectoremploysuniquetechniquestomeasureleptonisolation.Thetracker,forexample,usesthefollowingequationtoisolateleptontracks: Isolation=PtracksipiT pleptonT.(4{6)Thesummationisoveralltracksdetectedinaconein)]TJ /F6 11.9552 Tf 13.046 0 Td[(space:acceptance


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todistinguishjetsarisingfromb-quarksfromtheotherquarkavors( 25 ).Asecondaryvertexisthepointatwhichtheb-hadrondecays.Thispointwillbedisplacedwithrespecttotheprimaryvertex(pointofinitialb-quarkhadronization).Secondaryvertexcandidatesmustsatisfythefollowingcriteria: secondaryverticesmustsharelessthan65%oftheirassociatedtrackswiththeprimaryvertex. invariantmassassociatedwiththesecondaryvertexmustbelessthan6.5GeV. theightdirectionofeachcandidatehastobewithinaconeofR<0.5aroundthejetdirection.TheCMVAv2algorithmprovidesacontinuousdiscriminatoroutput,rangingfrom-1to1,combininginanoptimalwaytheinformationabouttrackimpactparametersandidentiedsecondaryverticeswithinjetsandinformationofanysoftleptonpresentinthejet.Aboosteddecisisontree(BDT)algorithmisthediscriminatingtoolofchoiceforb-jetidenticationwithinCMS,whichprovidesanoutputscoreintherangeof-1to1.CalibrationoftheCMVAv2discriminatorisachievedbyusingatag-and-probemethod( 29 )togenerateasetofweightsusedtocorrectthesimulatedCMVAv2distributionwithrespecttothedistributionobservedindata.ThisprocedureinvolvescreatingabinnedCMVAv2distributionofthe\probe"jetindataandadditionallyabinneddistributionfromsimulation.Eachbininthetwodistributionsarecomparedandthesimulatedbinadjustedtomatchtheobservedbincontents.ThisprocedureiscarriedoutforvariousbinsinpT,,andforlightandheavyhadronavourjets,wheretheendresultisajet-by-jetweightusedtoreweightalljets. 4.7NeutrinosNeutrinosoccurinthedecayofWbosonsandjets.JetenergyassignmentandassociatedproductionHiggsdecaysrelyontheabilitytorecordthepresenceofaneutrino.Becauseoftheirstability,neutralcharge,weakly-interactingnature,andlowmass,neutrinoswillpassthroughCMSwithoutregisteringinanyofthesub-detectors.Instead,thepresenceofmissingenergyinthetransverseplanewillserveasanindicatorofaneutrino.Particlesinthe 48

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LHCcollidehead-on(alongthez-axis)andhavezerotransverse(x-yplane)momentum.Conservationofenergythereforerequiresthenalstatetoalsohavezerotransversemomentum.Acollisionischaracterizedbyaninitialtotalenergyandmomentum(Ei,~pi)oftheinitialstateparticles.Inthenalstatewehavenparticleswithtotalenergyandmomentumgivenby: E=nXiEi,~p=nXi~pi.(4{8)WhenE
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vtx3dL{3-dightlengthofthejetsecondaryvertex vtx3deL{erroronthe3-dightlengthofthejetsecondaryvertex vtxPt{transversemomentumofthejetsecondaryvertex vtxNtrk{numberoftracksassociatedwiththejetsecondaryvertex neEmEf{fractionofjetconstituentsdetectedintheECALthathaveneutralcharge neHEF{fractionofjetconstituentsdetectedintheHCALthathaveneutralcharge nPVs{numberofprimaryvertices SoftLeptPtRel{relativetransversemomentumofsoftleptoncandidateinthejet SoftLeptPt{transversemomentumofsoftleptoncandidateinthejet SoftLeptdR{distancein)]TJ /F6 11.9552 Tf 11.767 0 Td[(spaceofsoftleptoncandidatewithrespecttothejetaxisBycorrectingthejetenergy,theinvariantmassoftheHiggsbosoncandidatejetsarealsocorrected(seeFigure 4-4 ).Boththeresolutionandthescalebiasesimproveaftertheregression.Thetusedinalldijetmassplotsisacombinationofacrystalballfunction(forsignalmodelling)andaBernsteinpolynomial(forbackgroundmodelling). 50

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Figure4-4. DistributionsofdijetinvariantmassinsignalZ(``)H(topleft),Z()H(topright),andW(`)H(bottom)eventsbeforeandaftertheregressionisapplied. 51

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CHAPTER5THEVHBBANALYSISNowthattheframeworkfordetectionandreconstructionofphysicsobjectshasbeendescribedingeneraldetailinthepreviouschapters,wenowturntothespecicsofmythesistopic:theVHbbanalysis.Asmentionedintheintroduction,thegoaloftheVHbbanalysisisthemeasurementoftheStandardModelHiggsbosoncouplingtobottomquarkpairs.Duetotheoverwhelmingrateofnalstatesthatcontainb-quarkpairsrelativetob-quarkpairsthatarisefromHiggsdecays,theadditionalrequirementofthepresenceofavectorboson(WorZ)isimposedonthenalstateselection,referedtointhisthesisastheVHbbchannelortheHiggsstrahlung(Higgsradiation)process.Table 5-1 summarizesthecrosssectionsandbranchingfractionsforthemainHiggsproductionmechanisms.ThecrosssectionsarecomputedatNNLOforaHiggsmassof125GeV( 30 ; 31 ; 32 ).AlthoughtheWHandZHHiggsstrahlungchannelshaveamuchlowercrosssectionthanthegluonfusionorvectorbosonfusionchannels,thelackofanadditionalhandle,suchasanassociatedvectorboson,makesthemmuchmoredicultwhenattemptingtoisolatesignalevents.Threenalstates,orchannels,aredenedintheVHbbanalysis:Z(``)H(thefocusofmycontributionstotheanalysis),W(`)H,andZ()H.Allhavethecommontraitofapairofbottomquarksrecoilingagainsttheassociatedvectorbosonandareuniquelydenedbythedecaymodeandtypeofassociatedvectorboson: Z(``)H:AboostedZbosondecaysintoaZbosonandaHiggsboson,wheretheHiggsdecaysintobottomquarkpairsandtheZdecaysintoelectronormuonpairs. Z()H:AboostedZbosondecaysintoaZbosonandaHiggsboson,wheretheHiggsdecaysintobottomquarkpairsandtheZdecaysintoneutrinopairs. W(`)H:AboostedWbosondecaysintoaWbosonandaHiggsboson,wheretheHiggsdecaysintobottomquarkpairsandtheWdecaysintoanelectronormuonandaneutrino.ThegeneralizedassociatedHiggsproductionprocessesareshowninFigure 5-1 ,wheretheincidentparticlesareeitherquarkorgluonpairs.InRun1,withalowercenterofmassenergyof7and8TeV,thegluoninitiatedVHbbchannelwasnotconsideredduetoitshigh 52

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Table5-1. SignalcrosssectionsandbranchingratiosforMhiggs=125atp s=13. process (pb) QCDScale PDF ggH 44.14 +7.6-8.1% 3.1%VBFH 3.782 +0.4-0.3% 2.1%WH 1.373(0.840+0.533) +0.5-0.7% 1.9%ZH 0.8839 +3.8-3.1% 1.6% decay BR Uncertainty H!bb 58.24% +0.72-0.74% activationenergyassociatedwithatopquarkloop.However,withthecurrentRun2centerofmassenergyof13TeVtherearesucientamountsofgluonpairswithhighenoughenergytoproducetopquarkloopsthatcontributeinasignicantwaytothenalVHbbsignalregion.Approximatelytwo-thirdsoftheeventsinthesignalregionarefromquarkinitiatedprocessesandone-thirdfromgluoninitiatedprocesses. Figure5-1. Feynmandiagramsforthequark(left)andgluon(right)inducedHiggsStrahlungprocess. WhatfollowsinthischapterisathoroughdescriptionofeachcriticalcomponentintheVHbbanalysis,buildingonthegeneralizedCMSreconstructiontechniquesgiveninthepreviouschapter. 5.1BackgroundsFinalstatesthatpossessthesameexperimentalsignatureasoursignalprocess-twobottomquarkswithaninvariantmassnear125GeVrecoilingfromavectorboson-arereferedtoasbackgrounds.Identfyingthesebackgroundprocessesandtheircharachteristicsthatdistinguishthemfromsignalprocessesisamaintaskofthisanalysis,andfurthermoreall 53

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analysesatCMSengagedinmeasurementsorsearchesoffundamentalparticles.VHbbsignaleventsarecharacterizedby: twob-jetswithanexpectedinvariantmassverycloseto125GeVbasedoncurrentexperimentaldata. b-jetpairpTspectrumthatisharderandfallslessgraduallythanmainbackgroundsources. isolatedleptonsnotarisingfromtheassociatedvectorbosonarenotexpected. b-jetpairisexpectedtorecoilback-to-backtothevectorbosoninthetransverseplane(ie.,azimuthalopeningangleof).Additonallythefollowingvariableshavepotentialusefullness,dependingonthesignalchannel,insignalversusbackgroundseparationandwhoseabreviationswillbeusedinthetablesandguresthroughoutthisthesis: M(jj):dijetinvariantmass;itpeaksatMhiggsforsignalandMZfordibosonevents,fallssharplyforV+jets,andpeaksbroadlyovertheregion100{160forttevents. pT(jj):transversemomentumoftheHiggscandidate. pTj:transversemomentumoftheHiggscandidatedaughters. pT(V):vectorbosontransversemomentum,whichishighlycorrelatedwithpT(jj)forsignalandmostbackgrounds. CMVA:continuousoutputoftheCMVAdiscriminant,optimizedseparatelyforthejetwiththehighervalue(CMVA1),andtheonewiththelowervalue(CMVA2). Mt:thetopmassreconstructedineventswithaleptonicdecayingWandoneoftheb-jets. (V,H):azimuthalopeninganglebetweenthemomentaofthevectorbosonandtheHiggscandidate. (J1,J2):distanceinpseudorapiditybetweenthetwojetscomprisingtheHiggscandidate. R(j,j):distancein{spacebetweenthetwojetscomprisingtheHiggscandidate. Naj:numberofadditionaljetsintheeventapartfromtheHiggscandidate.Onlycentraljetswithjj<2.5areconsidered,butthepTthresholdandnumberofadditionaljets 54

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toallowareparameterstobeoptimizedseparatelyforeachchannel.Inpractice,theoptimalthresholdwasfoundtobepT>20inallchannelswhereajetvetoisapplied. Nal:numberofadditionalisolatedleptons,apartfromthoseassociatedwiththeWorZdecay.OnlyleptonssatisfyingpT>20andjj<2.5areconsideredinthecount. pfMET:missingtransverseenergycalculatedwithparticle-owobjects. (pfMET,J):azimuthalopeninganglebetweenthepfMETvectordirectionandthetransversemomentumoftheclosestcentraljetinazimuth.OnlyjetssatisfyingpT>30andjj<2.5areconsidered.ThisvariablehelpsinreducingresidualQCDbackgroundintheZ()Hchannel,wherethesourceofthemissingtransverseenergyistypicallyfromuctuationsinthemeasuredenergyofasinglejet. '(pfMET,lept.):azimuthalopeninganglebetweenthepfMETvectordirectionandtheleadingleptondirection.ThisvariablehelpsinreducingeventsoffullyleptonicdecayofttinZ()Hanalysis. minR(H,aj):minimumdistancebetweenanadditionaljetandtheHiggscandidate.ThisvariablehelpsinreducingttbarbackgroundintheZ()HandW(`)Hchannels. Nsoft5:numberofadditionalsofttrack-jetswithpT>5.Giventhesesignalcharacteristicsandvariabledenitionswenowturntoadiscussionofeachbackgroundsourceandtheirdistinguishingcharacteristics. 5.1.1Drell-YanTheDrell-Yanprocess,alsoreferedtoasV+jets,isthedominantbackgroundcontaminantforallthreeVHbbchannelsandisshowninFigure 5-2 .HereoneormorejetsfromthedecayofaradiatedgluonisaccompaniedbyaWorZvectorbosoninthenalstate.ThemainchallengeoftheV+jetsbackgroundistheidenticalnalstateobjectlist:twob-jetsandtwoisolatedleptons.However,thedijetpaircanbedistinguishedfromasignaldijetpairbyitssofterpTspectrumandinvariantmassspectrumthatpeakslowerthanforsignal.Additionally,thedominantcontributiontotheDrell-YanprocesscomesfromV+light(udscg)jets-jetsformedfromthehadronizationofup,down,strange,charmquarks,orgluons-andcanbeseperatedoutbyuseofb-taggingonbothHiggsdaughterjets.InthemostsensitiveregionsofthesignalphasespaceitistheV+bbcontributionsthatdominate. 55

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gZqqbb`+`)]TJ /F1 11.9552 Tf -234.107 -121.997 Td[(Figure5-2. FeynmandiagramfortheDrell-Yanbackgroundprocess. 5.1.2ttTopquarkpairproductionpresentsasignicantbackgroundchallengeatthehigherRun2centerofmassenergy,wherethettproductioncrosssectionhasincreasedbyafactorofthreecomparedtotheRun1.ThettdecaychainisshowninFigure 5-3 whereonecanseeanalstatewhichcontainstwoWbosondecaysandatleasttwob-jets.Theexperimentalsignatureoftwoisolatedleptonsandtwob-jetsisreproducedhere,butcanbemitigatedbythefollowingtttopologicalconditions:thepresenceofadditionaljets(jetmultiplicity)wellbeyondnalstatejetmultiplicities,whichoccursmainlyduetoafullyhadronicdecayofoneoftheWbosons;theazimuthalopeningangleisnotpeakedassharplynearandismorebroadlydistributed;andlastly,inthecase,atopmassreconstructionisutilizedinordertorejectjetswithmasssimilairtothetopmass. ttW+W)]TJ /F4 11.9552 Tf 88.005 -49.284 Td[(l/q`+/q0bq0/lq/`+bFigure5-3. Feynmandiagramforthettbackgroundprocess. 56

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5.1.3DibosonVectorbosonpairproductionisalsoarelevantbackgroundduethedijetmassresonanceoverlappingwiththesignaldijetresonance.AlthouththeinvariantW/Zmasspeaksmuchlowerat80/91GeVrespectively,signicantoverlapoftheresonancesstilloccursduetojetreconstructioninecienciesthatleadtoabroaddijetmassspectrum.Thedominantbackgroundcontributionarisesfromdibosonnalstateswhereonebosondecaysleptonicallyandtheotherintoab-jetpair.Gooddijetmassresolutioniskeytodistinguishingthisprocessfromsignal.Threevectorbosondecaymodearepossible:ZZ(showninFigure 5-4 ),WW,andWZ. ZZqqbb`+`)]TJ /F1 11.9552 Tf -239.167 -121.997 Td[(Figure5-4. FeynmandiagramfortheZZdibosonbackgroundprocess. 5.1.4SingleTopThesingletopbackgroundarisesfromthreechannels:tW,t-channel,ands-channel.Singletopeventsaremorediculttorejectrelativetosignal,butthecrosssectionissuchthatittypicallyrepresentsonly10-20%ofthetotalbackgroundinW(`)HandevenlessinZ(``)HandZ()H.ForZ(``)Hrejectionofsingletopeventsismadeeasyduetothetypicalabsenceoftwoisolatedleptons,adijetmassthatdoesnotpeakneartheHiggsmass,andanazimuthalopeninganglethatisnotpeakedassharplynear. 5.2DataandSimulation 5.2.1DataThedatausedinthisthesiswascollectedin2016fromtheCMSdetectorwithtotalintegratedluminosityof35.9fb)]TJ /F5 7.9701 Tf 6.586 0 Td[(1.Theproton-protoncollisionswererecordedwitha25nanosecondbunchspacing.IntheZ(``)Hchanneldoublemuonandelectrondatasetswere 57

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used,whileW(`)HusedthesinglemuonandelectrondatasetsandZ()HusedtheMETdataset.Table 5-2 summarizestheluminositybreakdownperdatasetcollectedduring2016andisrepresentiveofluminositybreakdownfortheotherdatasetsintheVHbbanalysis. Table5-2. Listof2016datasamplesusedfortheSingleMuondataset. DatasetRL() SingleMuon Run2016B-03Feb2017-v15.9SingleMuon Run2016B-03Feb2017-v25.9SingleMuon Run2016C-03Feb2017-v12.7SingleMuon Run2016D-03Feb2017-v14.3SingleMuon Run2016E-03Feb2017-v14.1SingleMuon Run2016F-03Feb2017-v13.2SingleMuon Run2016G-03Feb2017-v13.8SingleMuon Run2016H-03Feb2017-v111.8 TotalLumi35.9 5.2.2SimulationMonteCarlogeneratedsamples(simulation)thatreproduceexpectedCMSdataareavitalcomponentoftheVHbbanalysis.ThesesimulatedsamplesareusedtomodelexpectedStandardModelprocessesandallowcontrolregionstobeconstructedthatvalidatedetectoroperationandtheoreticalmodeling.TheMonteCarlosamplesusedweretakenfromtheCMSRunIISummer16productionsre-miniAODv2withtheAsymptotic25nsconditions.Tablescontainingthenumberofevents,crosssections,andintegratedluminosityaregivenforHiggsbosonsignalevents(Table 5-3 ),di-vectorbosonproduction(Table 5-4 ),vectorbosonplusjets(Table 5-5 ),andwithQCDmulti-jet(Table 5-8 ).Simulatedeventcreationisachievedthroughuseofoneormoreofthefollowingeventgenerators:8( 33 ; 34 ),( 35 ),( 36 ),5( 37 )withMLMmerging( 38 ),oraMC@NLO( 39 )withFxFxmergingscheme( 40 ).Partonshowerandhadronisationareperformedwith8( 34 )usingtheCUETP8M1tune( 41 ).TheNNPDF3.0partondistributionfunctions(PDF)( 42 )areusedforallsamples.Additionally,triggerandobjectreconstructionemulatorsfromeachCMSsub-systemareusedinthenalphysicsobjectsandtriggerbitswithinthesimulatedsamples. 58

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TheproductioncrosssectionsforW+jetsandZ+jetsarerescaledtonext-to-next-to-leading-order(NNLO)crosssectionscalculatedusingthe3.1program( 43 ; 44 ; 45 ).ThettandsingletopquarksamplesarealsorescaledtotheircrosssectionsbasedonNNLOcalculations( 46 ; 47 ). Table5-3. SignalMonteCarlosampleswithMhiggs=125 SampleGeneratormH(=c2)(pb)eventsRL() /WplusH HToBB WToLNu M125 13TeV powheg pythia8POWHEG+PYTHIA81250.840*0.108535*0.582413174678039.05 /WminusH HToBB WToLNu M125 13TeV powheg pythia8POWHEG+PYTHIA81250.533*0.108535*0.5824129053812410.58 /ZH HToBB ZToLL M125 13TeV powheg pythia8POWHEG+PYTHIA8125(0.8839-0.1227)*0.10974*0.58244926620102213.80 /ZH HToBB ZToNuNu M125 13TeV powheg pythia8/aMC@NLO+PYTHIA8125(0.8839-0.1227)*0.20103*0.5824120583113661.96 /ggZH HToBB ZToLL M125 13TeV powheg pythia8POWHEG+PYTHIA81250.1227*0.10974*0.58242998600192975.96 /ggZH HToBB ZToNuNu M125 13TeV powheg pythia8POWHEG+PYTHIA81250.1227*0.20103*0.58242396838168136.79 Table5-4. ListofMonteCarlodibosonsamples SampleGenerator(pb)eventsRL() /WW TuneCUETP8M1 13TeV-pythia8PYTHIA8118.79936408.37 /WZ TuneCUETP8M1 13TeV-pythia8PYTHIA847.13100000021.22 /ZZ TuneCUETP8M1 13TeV-pythia8PYTHIA816.52398560059.65 5.2.3SimulatedEventReweightingDespitemuchworkandadvances,theeventgeneratorsanddetectorsimulationsdescribedintheprevioussectionstillcreatesimulatedeventdistributionsthatcontaindiscrepencieswithobserveddata.TheVHbbanalysisemploysasuiteofdatadriveneventreweightingproceduresinordertomitigatedierencesbetweensimulationanddata.Thedierentreconstructionchallengesmitigatedbyreweightingtechniquesare PileUp b-tagging Leptontriggerandidentication NLOtoNNLOcorrections 59

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Table5-5. ListofMonteCarloV+jetsleadingordersamples SampleGenerator(pb)eventsRL() /DY1JetsToLL M-10to50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA87253980000054.5 /DY2JetsToLL M-10to50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA8394.51940000050.2 /DY3JetsToLL M-10to50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA896.47496000052.2 /DYJetsToLL M-50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA84960*1.23491000009.9 /DYJetsToLL M-50 HT-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA8147.40*1.231061000072 /DYJetsToLL M-50 HT-200to400 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA840.99*1.239652000235.4 /DYJetsToLL M-50 HT-400to600 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA85.678*1.23100100001759 /DYJetsToLL M-50 HT-600to800 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA81.367*1.2382900006111 /DYJetsToLL M-50 HT-800to1200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA80.6304*1.2326700004280 /DYJetsToLL M-50 HT-1200to2500 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA80.1514*1.235960003940 /DYJetsToLL M-50 HT-2500toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA80.003565*1.23399000109000 /DYBJetsToLL M-50 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA871.77*1.23147000020.9 /DYBJetsToLL M-50 Zpt-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA83.027*1.2340800001320 /DYBJetsToLL M-50 Zpt-200toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA80.297*1.2321100006670 /ZJetsToNuNu HT-100To200 13TeV-madgraphMADGRAPH5+PYTHIA8280.35*1.23524019915.20 /ZJetsToNuNu HT-200To400 13TeV-madgraphMADGRAPH5+PYTHIA842.75*1.23503292795.7 EWKsignaltheorycorrections ttpTmodeling 5.3TriggersEachchannelintheVHbbanalysisusesauniquetriggersetinordertocollecteventsthatareconsistentwiththesignalhypothesis.TheZ(``)Htriggerswillbedescribedrst,followedbytheZ()Htriggersummary.TheW(e)HandW()Hchannelsutilizesingleleptontriggers,whiletheZ(ee)HandZ()Hchannelsemploydi-leptontriggerswhicharemoreecientfortheexpecteddi-leptonnalstatesignature.Table 5.3 summarizesthetriggersusedinthisanalysis.Inordertovalidateandcorrectanydiscrepanciesbetweensimulated 60

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Table5-6. ListofMonteCarloV+jetsleadingordersamples SampleGenerator(pb)eventsRL() /ZJetsToNuNu HT-400To600 13TeV-madgraphMADGRAPH5+PYTHIA810.73*1.2395443572.32 /ZJetsToNuNu HT-600ToInf 13TeV-madgraphMADGRAPH5+PYTHIA84.116*1.2396454931905.21 /WJetsToLNu TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA861526.7*1.21867000001.72 /WJetsToLNu HT-100To200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA81345*1.217930000058.9 /WJetsToLNu HT-200To400 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA8359.7*1.213965000110.1 /WJetsToLNu HT-400To600 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA848.91*1.217760000159.2 /WJetsToLNu HT-600To800 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA812.05*1.21186800001543 /WJetsToLNu HT-800To1200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA85.501*1.2162000001130 /WJetsToLNu HT-1200To2500 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA81.329*1.2168750005174 /WJetsToLNu HT-2500ToInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA80.03216*1.21263400082200 /WBJetsToLNu Wpt-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA86.004*1.213979072662.7 /WBJetsToLNu Wpt-200toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA80.8524*1.2128929813393.3 /WJetsToLNu BGenFilter Wpt-100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA826.1*1.216690000256.3 /WJetsToLNu BGenFilter Wpt-200toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia8MADGRAPH5+PYTHIA83.545*1.21116500003286.3 Table5-7. ListofMonteCarloV+jetsnext-to-leadingordersamples SampleGenerator(pb)eventsRL() /DYJetsToLL Pt-50To100 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia85+8369.32.19E+078.23E+00 /DYJetsToLL Pt-100To250 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia85+881.24990007.87 /DYJetsToLL Pt-250To400 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia85+82.99160900073.6 /DYJetsToLL Pt-400To650 TuneCUETP8M1 13TeV-amcatnloFXFX-pythia85+80.3881626000628 /DYJetsToLL Pt-650ToInf TuneCUETP8M1 13TeV-amcatnloFXFX-pythia85+80.03.7416290007360 /DYToLL 0J 13TeV-amcatnloFXFX-pythia85+84760496000006.98 /DYToLL 1J 13TeV-amcatnloFXFX-pythia85+8 /DYToLL 2J 13TeV-amcatnloFXFX-pythia85+83414230000010.5 61

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Table5-8. TopandQCDMonteCarlosamples SampleGenerator(pb)eventsRL() /TT TuneCUETP8M1 13TeV-powheg-pythia8+8831.76187626200+97994442343 /ST tW top 5f inclusiveDecays 13TeV-powheg-pythia8 TuneCUETP8M1+835.6100000028.09 /ST tW antitop 5f inclusiveDecays 13TeV-powheg-pythia8 TuneCUETP8M1+835.699940028.07 /ST t-channel top 4f leptonDecays 13TeV-powheg-pythia8+8136*0.32599940022.6 /ST t-channel antitop 4f leptonDecays 13TeV-powheg-pythia8+881*0.325169540064.4 /ST s-channel 4f leptonDecays 13TeV-amcatnlo-pythia8+810.3299840096.74 /QCD HT100to200 TuneCUETP8M1 13TeV-madgraphMLM-pythia85+827990000820958000.003 /QCD HT200to300 TuneCUETP8M1 13TeV-madgraphMLM-pythia85+81712000187843790.011 /QCD HT300to500 TuneCUETP8M1 13TeV-madgraphMLM-pythia85+8347700542676500.16 /QCD HT500to700 TuneCUETP8M1 13TeV-madgraphMLM-pythia85+82.94e4195428470.66 /QCD HT700to1000 TuneCUETP8M1 13TeV-madgraphMLM-pythia85+86831451006756.60 /QCD HT1000to1500 TuneCUETP8M1 13TeV-madgraphMLM-pythia85+812071519364512.59 /QCD HT1500to2000 TuneCUETP8M1 13TeV-madgraphMLM-pythia85+8119.9393907732.85 /QCD HT2000toInf TuneCUETP8M1 13TeV-madgraphMLM-pythia85+825.42196177477.2 andobservedtriggerbehavior,triggeremulationisrequiredforalleventsusedintheVHbbanalysis.Correctionscalefactorsarederivedusingthetag-and-probemethod,whichutilizesdi-leptoneventsfromZbosons.Thetriggerecienciesaremeasuredaftertheapplicationofoineleptonidenticationandisolationselections.ForZ(``)H,whichutilzesadi-leptontrigger,eachlegofthetriggermusthavetheeciencycalculatedseparatelyduetodierentselectionsfortheleptonsassociatedwitheachleg.Forbothsingleanddi-leptontriggers,thecomputeddate/MCcorrectionscalefactorsareveryclosetoone.ThecorrectionscalefactorandtheiruncertaintiesforelectrontriggersareshowninFigures 5-5 and 5-6 asafunctionofelectronpTand. 62

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Table5-9. ListofL1andHLTtriggersusedforthe2016dataset,andthechannelstowhichtheyapply. ChannelL1SeedsHLTPaths W(e)HL1 SingleMu20HLT IsoMu24ORHLT IsoTkMu24 Z()HL1 SingleMu20HLT Mu17 TrkIsoVVL Mu8 TrkIsoVVL v*ORHLT Mu17 TrkIsoVVL TkMu8 TrkIsoVVL v*ORHLT Mu17 TrkIsoVVL Mu8 TrkIsoVVL DZ v*ORHLT Mu17 TrkIsoVVL TkMu8 TrkIsoVVL DZ v* W(e)HL1 SingleIsoEG22erORHLT Ele27 WPTight GsfL1 SingleEG25 Z(ee)HL1 SingleEG30ORHLT Ele23 Ele12 CaloIdL TrackIdL IsoVL DZL1 SingleIsoEG22erORL1 SingleIsoEG24ORL1 DoubleEG 15 10 Z()HL1 ETM50||L1 ETM60||L1 ETM70||L1 ETM80HLT PFMET110 PFMHT110 IDTightORHLT PFMET120 PFMHT120 IDTightORHLT PFMET170 NoiseCleanedORHLT PFMET170 HBHECleanedORHLT PFMET170 HBHE BeamHaloCleaned Additonally,reconstructioninecienciesformuonsinthetracker,whichvaryintimethroughoutthe2016collectiontimeperiod,areaccountedfor.ThedoublemuontriggerecienciesfordataandMCarestudiedseparatelyforrunsB,C,D,E,F,GandforrunH.ThecorrespondingscalefactorsareshowninFigures 5-7 5-8 .FortheZ()Hchannel,whichdoesnottriggeronleptonsbutratheronmissingenergy,adierenttriggerapproachisneeded.ThemaintriggerforZ()HisHLT PFMET110 PFMHT110 IDTight,whichisseededatL1byanORofL1 ETMtriggers.Theoveralltriggereciencyhasbeenmeasuredusingthedatacollectedbythesingle-muonandsingle-electrontriggersandrequiringthepresenceoftwojetsinthetrackeracceptanceintheevent.InordertoavoidbiasfromtheL1MET(calo-MET),theleptonisrequirednottobebacktobackwiththereconstructedMET.Themeasuredeciencyisthenappliedonthesimulation.Figure 5-9 showsthetriggereciencyforvarioustriggersandtheORasfunctionoftheoinemin(MET,MHT) 63

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distributionsobtainedindatainthesingle-electron(right)datasets.Thetopplotshavebeenobtainedonthefulldataset. Figure5-5. DistributionsofHLT Ele27 WPTight GsfeciencyasfunctionofpTandfor2016data.TheecienciesaremeasuredafterapplyingWP80inthegeneralpurposeelectronMVAIDsplusisolationselection.Theturn-oncanbeseenasrisingeciencyinpTabove27GeV. 5.4AnalysisObjectSelectionsInthissectionspecicselectionsforallphysicsobjectsusedintheVHbbanalysis-electrons,muons,jets,b-jets,andmissingenergy-willbediscussed.Additionally,atreatmentofpile-upandprimaryvertexselectionwillalsobegiven. 5.4.1Pile-UpandPrimaryVertexSelectionAsdescribedinSection3.1pile-up(PU)referstoadditonalcollisionsperbunchcrossing.PUcanbeeitherin-timeorout-of-time.In-timePUreferstocollisionsoccuringinthesamebunchcrossingasthesignalvertex.Out-of-timePUreferstocollisionsthatoccurinneighboringbunchcrossings,whicharespaced25nsapart. 64

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[][Leg1] [][Leg2] Figure5-6. DistributionsofHLT Ele23 Ele12 CaloIdL TrackIdL IsoVL DZeciencyasfunctionofp Tandfor2016data.TheecienciesaremeasuredafterapplyingWP90inthegeneralpurposeelectronMVAIDsplusisolationselection. 65

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Figure5-7. DistributionsforeachlegoftheHLT Mu17 TrkIsoVVL Mu8 TrkIsoVVL v*ORHLT Mu17 TrkIsoVVL TkMu8 TrkIsoVVL v*triggerasfunctionofpTandforRunB,C,D,E,F,G.Theleftgurecorrespondstothe8GeVlegscalefactor.Therightgurecorrespondtothe17GeVlegscalefactor,requieringthesecondmuontopassthe8GeVleg. Figure5-8. DistributionsforeachlegoftheHLT Mu17 TrkIsoVVL Mu8 TrkIsoVVL v*ORHLT Mu17 TrkIsoVVL TkMu8 TrkIsoVVL v*triggerasfunctionofpTandforRunH.Theleftgurecorrespondstothe8GeVlegscalefactor.Therightgurecorrespondtothe17GeVlegscalefactor,requieringthesecondmuontopassthe8GeVleg. Asignalvertexisaspecialcaseofaprimaryvertex,orpositionswhereproton-protoncollisionsoccur.AllprimaryverticesarereconstructedfromtracksusingtheDeterministicAnnealingclusteringalgorithm( 17 ).Therequirementsforallprimaryvertexcandidatesareazpositionwithin24cmofthedetectorcenter,aradialpositionwithin2cmofthebeamspotaxis,andavertextexceedingfourdegreesoffreedom.ThesignalvertexisselectedamongstalltheprimaryvertexcandidatesbychoosingthevertexwiththelargestPp2T,wherePp2TisthesquaredsumofthepTofallelementaryparticlesassociatedwithagivenvertex. 66

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Figure5-9. Distributionsoftriggereciencyasfunctionofmin(MET,MHT)forthedatainthesingle-electronfor2016fulldataset. Overthecourseof2016theaveragePUrangedfrom40to15,dependingonthetimeduringeachll(thelongerallgoes,thelowerthePUbecomesduetoprotondepletion).ThepresenceofPUhasanegativeeectonjetresolutionandHiggsreconstruction.TwodierentapproachestomitigatethenegativeeectsofPUexistwithintheVHbbanalysis: PFnoPU:alsoknownasChargedHadronSubtraction(CHS),PFPUisanalgorithmembeddedinthePFjetprocessingchainthatattemptstolterallchargedhadronsthatdonotappeartooriginatefromtheprimaryinteraction.ThisapproachisveryeectivebutonlyworksinthepseudorapidityregioncoveredbytheTracker.Algorithmsfortaggingbjetsarenotimpacted,sincetheyapplytheirowntrackpre-lteringthatisalsodesignedtobePU-resistant. Fastjet:anexternalsoftwarepackagefromwhichCMSsoftwaretakesvirtuallyallitsjetreconstructionservices( 48 ).InparticularitprovidesthemeanstocalculatethemomentumdensityperunitareaduetoPUforeachevent,whichcanbeusedtosubtractthecontaminationofjetsandleptonisolationconesbasedontheirrespectiveareas.Thesemethodsarethereforereferredtoas"FastjetSubtraction."BoththePFnoPUandFastjetSubtractionmethodsareusedintheVHbbanalysis. 67

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5.4.2ElectronsElectronpre-selectionrequiresallelectroncandidatestohavepT>7,jj<2.4,dxy<0.05,dz<0.2,andalooseisolationcutof0.4.Thenextstageofelectronselectionisdonethroughtheoutputofamultivariatediscriminatorthatistrainedonsimulatedelectronsthatpassasetofcutsmeanttorepresentelectronsthatwouldpassthemostcommonelectrontriggers.Thefollowingvariablesarecurrentlyusedtodiscriminatebetweenrealandfakeelectrons: SuperClusterenergy/trackmomentumatvertex DeltaEtabetweenSuperClusterpositionandtrackdirectionatvertexextrapolatedtoECALassumingnoradiation DeltaPhibetweenSuperClusterpositionandtrackdirectionatvertexextrapolatedtoECALassumingnoradiation RatioofenergyinHCALbehindSuperClustertoSuperClusterenergy Energyin3x3crystals/energyin5x5crystals EnergyofclosestBasicClustertotrackimpactpointatECAL/outermosttrackmomentum EnergyofclosestBasicClustertotrackimpactpointatECAL/innermosttrackmomentum DeltaPhibetweentrackimpactpointatECALandclosestBasicCluster 1/E(SuperCluster)-1/p(trackatvertex) Bremfraction=(trackmomentumatvertex-trackmomentumatECAL)/(trackmomentumatvertex) SigmaEtaEtaclustershapecovariance SigmaPhiPhiclustershapecovarianceAllelectronsusedinthisanalysisthereforerequireasetofoinecutsbasedonECALquantitiesthatreproducetheconditionsusedintheelectronMVAtraining.Thosecutsare:pt>15&((abs(superCluster().eta)<1.4442&full5x5 sigmaIetaIeta<0.012& 68

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hcalOverEcal<0.09&(ecalPFClusterIso/pt)<0.4&(hcalPFClusterIso/pt)<0.25&(dr03TkSumPt/pt)<0.18&abs(deltaEtaSuperClusterTrackAtVtx)<0.0095&abs(deltaPhiSuperClusterTrackAtVtx)<0.065)||(abs(superCluster().eta)>1.5660&full5x5 sigmaIetaIeta<0.033&hcalOverEcal<0.09&(ecalPFClusterIso/pt)<0.45&(hcalPFClusterIso/pt)<0.28&(dr03TkSumPt/pt)<0.18)).TheresultingelectronMVAoutput,referedtoastheelectronMVAID,containsvariousworkingpoints(WP)basedonselectioneciency.Twoworkingpointsareused:90%eciency(WP90)and80%eciency(WP80).Z(ee)HusesthelooseWP90threshold,whileW(e)HusestheWP80thresholdinordertosuppresselectronmisidenticationresultingfromnalstatesthatcontainahighernumberoffakeelectrons.ThepTthresholdsforZ(ee)HandW(e)Hare30and20GeVrespectivelyontheleadingelectron.IntheZ(ee)HchannelthetrailingelectronisrequiredtohavepT>15GeV.TheleptonisolationiscalculatedusingadeltaRconeof0.3.ForW(`)Hanisolationsmallerthan0.06isrequired;forZ(``)Hanisolationlessthan0.15isrequired. 5.4.3MuonsAllmuonsintheVHbbanalysisareglobalmuons(combinedtrackerandmuonsystemobjects)withthefollowingbasicpre-selections:pT>5,jj<2.4,dxy<0.5,dz<1.0,andanisolationcutof0.4.TwoworkingpointsaredenedbytheCMSmuonworkinggroup:looseandtightdenedbelow. Loosemuon: { Particle-FlowMuon:isPFMuon() { isGlobalorTrackerMuon:isGlobalMuon()||isTrackerMuon() 69

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Tightmuon: { thecandidateisreconstructedasaGlobalMuon:isGlobalMuon() { Particle-FlowMuon:isPFMuon() { 2=ndofoftheglobal-muontrackt:globalTrack()->normalizedChi2()<10. { atleastonemuon-chamberhitincludedintheglobal-muontrackt:globalTrack()->hitPattern().numberOfValidMuonHits()>0 { muonsegmentsinatleasttwomuonstations;thisimpliesthatthemuonisalsoanarbitratedtrackermuon:numberOfMatchedStations()>1 { trackertracktransverseimpactparameterw.r.t.theprimaryvertex:fabs(muonBestTrack()->dxy(vertex->position()))<0.2 { longitudinaldistanceofthetrackertrackwrt.theprimaryvertex:fabs(muonBestTrack()->dz(vertex->position()))<0.5 { numberofpixelhits:innerTrack()->hitPattern().numberOfValidPixelHits()>0 { cutonnumberoftrackerlayerswithhits:innerTrack()->hitPattern().trackerLayersWithMeasurement()>5W()Husesthetightmuonrequirements,whileZ(``)Husestheloosemuonrequirements.ThepTlowerthresholdfortheleadingmuoninbothW(`)HandZ(``)His20GeV,whilethetrailingmuonhaslowerthresholdof10GeV.Anisolationconeof0.4isusedwithcut-opointsof0.06forW()Hand0.25forZ()H. 5.4.4JetsAlljetsarereconstructedfromparticleowcandidatesandusetheanti-kTalgorithmwithanRvalueof0.4( 19 ; 49 ),asdescribedinSection4.4.InordertorejectfakejetsresultingfromdetectornoiseandjetsthatarecontaminatedwithPU,loosejetcriteriaisappliedtoalljets.Loosejetcriteriasatisfythefollowing: NeutralHadronFraction<0.99 NeutralEMFraction<0.99 70

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NumberofConstituents>1Andfor<2.4inadditionapply ChargedHadronFraction>0 ChargedMultiplicity>0 ChargedEMFraction<0.99AnyjetthatoverlapswithanisolatedleptonwithinadeltaRconeof0.4isrejected.TheminimumpTrequirementsforalljetsintheW(`)HandZ()Hchannelsis25GeVand20GeVinZ(``)Hduetocleanernalstate.Lastlyalljetswithjj<2.4arerejected.Identifyingb-jetsisdonethroughtheuseoftheCMVAalgorithmofSection4.6.EachjetisassignedaCMVAvaluethatcanaidindecidingwhethertodiscardorselectthejet.Workingpointsaredenedforloose(CMVA>0.5884),medium(CMVA>0.4432),andtight(CMVA>0.9432),whichcorrespondtolightjetmistagratesof10%,1%,and0.1%respectively.Thedierentbackgroundandsignalregionsrequiredierentbtagworkingpointsdependingonb-jetpurityandstatisticcontraintsandwillbedetailedmoreinSection5.5.1. 5.4.5MissingEnergyIdenticationofmissingenergy(neutrinos)iscriticalintheW(`)HandZ()Hchannels,aswellasaidingtheZ(``)Hchannelinobtainingapurettcontrolregion.Themissingtransverseenergy(~EmissT)inaneventisdenedasthenegativevectorialsumofthetransversemomentaofallparticle-owobjectsintheevent.Arecommendedsetofltersdesignedtoremoveinstrumentalnoiseandproblematiceventsareused.Additionalimprovementsto~EmissTisachievedbytakingintoaccountthedierencebetweentheraw(uncorrected)jetpT,whichdoesnotcontainmissingenergycontributions,andthecorrectedjetpTforjetswithpT>15,andjj<4.7.IntheZ()Hchannelaminumumthresholdonthemagnitudeof~EmissTof125GeVisapplied. 5.5MultivariateStrategyInordertofullyutilizethediscriminatingpowerofthemostrelevantvariablesinsignalandbackgroundevents,amultivariateoutputisusedasthenaldiscriminantinabinned 71

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shapeanalysis.TheBoostedDecisionTree(BDT)algorithm,implementedinTMVA( 50 ),ischooseninordertoutlizetheBDTsabilitytolteroutvariableswithlowtargetcorrelation,highsensitivitytooutliers,andhighrobustnessagainstovertrainingwhencomparedtoothersupervisedlearningmethods.ABDTisacollectionofshallowlearners:decisiontreeswithonlyafewlayersofdepth.Asingledecisiontreelearnsthemostdiscriminatingvariableswhenattemptingtoclassifysignalversusbackgroundevents.Eachtreecreatesasetofweightsthatisfedtothenexttreeandusedtocorrectthenextiterationofsignalversusbackgroundclassication.ThenalproductfromthislearningprocedureisasetofweightsthattakeasinputthesetofvariablesusedtotraintheBDT.EveryeventindataandsimulationisfedintotheBDToutputweightsandascoreisassignedintherangeof-1to1,where1ismoresignallikeand-1morebackgroundlike.SeparateBDTshavebeentrainedwithsimulatedeventsineachchannel,whereeveneventsareselectedfortrainingandoddeventsfortestingtheBDTperformance.ThefulllistoftrainingvariablesforeachchannelaregiveninTable 5-10 .OptimizationoftheBDTparameters-treedepth,learningrate,numberoftrees-wasperformedusingagridsearchovertheBDTparametersandusedtheROCcurveintegralasagureofmerit.TheBDToutputforthetrainandtestsetsineachchannelcanbeseeninFigures 5-10 .Ineachchannelitisnecessarytoconstructasignalregionwhichistopologicallyfavorableforsignalversusbackgroundseparation,butalsoonewhichisnotstatisticallylimitedinordertoprovidetheBDTwithsucienttrainingevents.Table 5-11 liststhesignalregionpreselectionsforeachchannel.TheeciencyforthesignalregionpreselectioncutsfortheZ(``)HanalysisisshowninFigure 5-11 5.6ControlRegionsControlregionsareconstructedforeachsignicantbackgroundineachchannelinordertoadjustMonteCarloestimateswhencomparedtodata.TheresultingMonteCarlocorrections 72

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Table5-10. VariablesusedintheBDTtraining. VariableChannelsutilizing M(jj):dijetinvariantmassAll pT(jj):dijettransversemomentumAll pT(V):vectorbosontransversemomentumAll CMVAmax:valueofCMVAfortheHiggsdaughterZ(``)H,Z()HwithlargestCMVAvalue CMVAmin:valueofCMVAfortheHiggsdaughterAllwithsecondlargestCMVAvalue CMVAadd:valueofCMVAfortheadditionaljetZ()HwithlargestCMVAvalue (V,H):azimuthalanglebetweenVanddijetAll pT(j):transversemomentumZ(``)H,Z()HofeachHiggsdaughter pT(add.):transversemomentumZ()Hofleadingadditionaljet (J1,J2):dierenceinZ(``)H,Z()HbetweenHiggsdaughters R(j,j):distancein{Z(``)HbetweenHiggsdaughters pT(add.):transversemomentumZ()Hofleadingadditionaljet (J1,J2):dierenceinZ(``)H,Z()HbetweenHiggsdaughters R(j,j):distancein{Z(``)HbetweenHiggsdaughters Naj:numberofadditionaljetsW(`)H,Z(``)HN.B.denitionslightlydierentperchannel pT(jj)=pT(V):pTbalancebetweenHiggsZ(``)Hcandidateandvectorboson MZ:ZbosonmassZ(``)H SA5:numberofsoftactivityjetsAllwithpT>5GeV Mt:reconstructedtopmassW(`)H '(pfMET,lept.):azimuthalW(`)Hanglebetween~EmissTandlepton ~EmissT:missingtransverseenergyW(`)H,Z(``)H mT(W):WtransversemassW(`)H '(pfMET,jet.):azimuthalZ()HanglebetweenandtheclosestjetwithpT>30 73

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Figure5-10. TheplotsaboveshowtheBDToutputforsignalandbackgroundsimulationineachofthethreeanalysischannels.Fromlefttoright,toptobottom:W(`)HZ(``)H(lowandhighboost),Z()H. arereferedtoasscalefactorsandactaseventweightsappliedtotherelevantsimulatedprocesses.Thebackgroundscalefactorsaretheresultofasimultaneousbinnedmaximumlikelihoodtwiththesignalregionsandthusthecontrolregionsareensuredtobeorthogonaltothesignalregion.Theobtainedscalefactorsaccountforcrosssectiondiscrepanciesandanydierencesintheselectionofphysicsobjects.ThissectiondescribesthecontrolregionsforZ+udscg(Z+LF),tt,andZ+bb(Z+HF)productionasreconstructedintheZ(``)Hchannel.Table 5-12 summarizestheselection 74

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Table5-11. Preselectioncutsforeachchanneltodenethesignalregion. VariableW(`)HZ(``)HZ()H pT(V)>100[50)]TJ /F4 11.9552 Tf 11.955 0 Td[(150],>150>170m``{[75)]TJ /F4 11.9552 Tf 11.955 0 Td[(105]{p`T(>25,>30)>20{pT(j1)>25>20>60pT(j2)>25>20>35pT(jj)>100{>120M(jj)[90)]TJ /F4 11.9552 Tf 11.956 0 Td[(150][90)]TJ /F4 11.9552 Tf 11.955 0 Td[(150][60)]TJ /F4 11.9552 Tf 11.955 0 Td[(160]CMVATCMVALCMVATCMVALCMVALCMVALNaj<2{{Nal=0{=0{{>170Anti-QCD{{Yes(V,H)>2.5>2.5>2.0{{<0.5<2.0{{TightenedLeptonIso.(0.06,0.06){{ Figure5-11. EciencyandbackgroundreductionaftereachcutusedinthesignalregiondenitionfortheZ(``)Hchannel,forsignalandZ+jets,thedominantbackground.TheplothasbeenobtainedrequiringatleasttwojetsandoneleptonwithpT>20. 75

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criteriausedtodeneeachcontrolregionthatentersthescalefactort.TworegionsofvaryingsensitivityareidentiedforthevectorbosonpTthatallowforamorepowerfulBDTtrainingineachregion.ForZ+bbthedijetmassisvetoedaroundthesignalmasspeakof125GeVandatightcutonthebtagdiscriminat(CMVA)isusedinordertolteroutZ+udscgevents.InboththeZ+udscgandZ+bbregionsavectorbosonmassvetoaroundtheZmassisappliedonordertoreducettcontamination.InthettregionanoppositeZmassvetoisapplied,aswellastightCMVArestrictionsinordertoreduceZ+udscgcontamination.Z(``)HcontrolregionplotsareshowninFigures 5-12 5-13 5-14 5-15 5-16 5-17 Table5-12. DenitionofcontrolregionsfortheZ(``)Hchannel. VariableZ+LFttZ+HF pT(V)[50,150],>150[50,150],>150[50,150],>150CMVAV2maxCMVAV2Tight>CMVAV2TightCMVAV2minCMVAV2Loose>CMVAV2LooseMET{{<60(V,H){{>2.5m``75{105veto0{10,75{12085{97M(jj){{veto90{150 Thescalefactorsforbackgorundnormalizationareultimatelyaccountedforandttedduringthesignalextraction,howeverthesescalefactorsareneededearlierforusewithintheBDTtrainingandformodelvalidationwhenplottingthemostimportantvariables.FortheZ(``)HchanneltheZ+jetsandttscalefactorsrepresentthedijetanddileptonsidebandsofthesignalregionrespectively.Muonandelectronregionsarettedtogether.ThettedvariableisCMVAmin(thesub-leadingjetCMVAvalue).Systematicuncertaintiesonthettedscalefactorsaredeterminedbyevaluatingtheeectonthetemplateshapesfromvarioussourcesofsystematics,whichwillbediscussedinthenextsection.Table 5-13 summarizesthetresultsinallthreetopologiesfor13TeVdatafortheSR+CRst. 5.7SystematicsThefullsuiteofuncertaintiesthataecttheVHbbanalysis,fromtheoreticalmodelingtoexperimentalobjectreconstruction,arereferedtoassystematicsandaccountedforinthenal 76

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Figure5-12. DistributionsofvariablesindataandsimulatedsamplesintheZ+udscgcontrolregionforZ()H(left)andZ(ee)H(right)inthelowVpTbin.Fromtoptobottom:dijetinvariantmass,dijetpT,pT(Z),andBDToutputTheplotsarenormalizedusingtheSFstofacilitateshapecomparison. 77

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Figure5-13. DistributionsofvariablesindataandsimulatedsamplesintheZ+udscgcontrolregionforZ()H(left)andZ(ee)H(right)inthehighVpTbin.Fromtoptobottom:dijetinvariantmass,dijetpT,pT(Z),andBDToutputTheplotsarenormalizedusingtheSFstofacilitateshapecomparison. 78

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Figure5-14. DistributionsofvariablesindataandsimulatedsamplesinthettcontrolregionforZ()H(left)andforZ(ee)H(right)inthelowVpTbin.Fromtoptobottom:dijetinvariantmass,dijetpT,pT(Z),andBDToutputTheplotsarenormalizedusingtheSFstofacilitateshapecomparison. 79

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Figure5-15. DistributionsofvariablesindataandsimulatedsamplesinthettcontrolregionforZ()H(left)andforZ(ee)H(right)inthehighVpTbin.Fromtoptobottom:dijetinvariantmass,dijetpT,pT(Z),andBDToutputTheplotsarenormalizedusingtheSFstofacilitateshapecomparison. 80

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Figure5-16. DistributionsofvariablesindataandsimulatedsamplesintheZ+bbcontrolregionforZ()H(left)andforZ(ee)H(right)inthelowVpTbin.Fromtoptobottom:dijetinvariantmass,dijetpT,pT(Z),andBDToutputTheplotsarenormalizedusingtheSFstofacilitateshapecomparison. 81

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Figure5-17. DistributionsofvariablesindataandsimulatedsamplesintheZ+bbcontrolregionforZ()H(left)andforZ(ee)H(right)inthehighVpTbin.Fromtoptobottom:dijetinvariantmass,dijetpT,pT(Z),andBDToutputTheplotsarenormalizedusingtheSFstofacilitateshapecomparison. 82

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Table5-13. 13TeVData/MCscalefactorsforeachcontrolregionineachdecaymodefortheSR+CRst.Theerrorsincludethestatisticaluncertaintyfromthet,andasystematicuncertaintyaccountingforpossibledata/MCshapedierencesinthediscriminatingvariables.ElectronandmuonssamplesinZ(``)HandW(`)Haretsimultaneouslytodetermineaveragescalefactors.Thevaluesrefertothesimultaneuoscontrolregionsplussignalregiontusedforthesignalextraction,andwecheckedthatwegetcompatiblettedvalueforatinthecontrolregionsonly. ProcessW(`)HZ(``)H(lowZpT)Z(``)H(highZpT)Z()H W0b1.140.07{{1.140.07W1b1.660.14{{1.660.14W2b1.490.12{{1.490.12Z0b{1.020.061.020.061.020.07Z1b{0.980.060.990.101.280.17Z2b{1.080.071.290.091.600.100.910.030.990.031.020.050.780.05{{{1.500.25 signalextractionviaabinnedmaximumlikehoodt.Twotypesofsystematicsareimplentedinthet:lognormal(lnn)andshapeuncertainty.ThesourcesofuncertaintyconsideredintheVHbbanalysisare: Luminosity:anuncertaintyof2.5%isassessedfor2016luminosity. LeptonEciency:muonandelectrontrigger,reconstruction,andidenticationecienciesaredeterminedindatausingthestandardtag-and-probetechniquewithZbosons.Thesystematicuncertaintyisevaluatedfromthestatisticaluncertaintiesinthebin-by-binecienciesandscalefactorsasappliedtosignalMonteCarlosamples.Thetotaluncertaintyis1.6%permuon,and1.5%perelectron,whichwetakeasaconstant2%perchargedlepton.Noshapeuncertaintiesareconsidered. UnclusteredMET:wefollowthesuggestedprocedurefromtheJetMETPOGandnda3%systematicuncertaintyonthecalibrationofunclusteredMET(ie,missingenergyassociatedwithparticlesnotclusteredintojets).Noshapeuncertaintiesareconsidered. MET+jetsTrigger:theparametersdescribingthetriggereciencycurvehavebeenvariedwithintheirstatisticaluncertainties.Anuncertaintyof3%isestimated,andnoshapeuncertaintiesareconsidered. JetEnergyScale:thejetenergyscaleforeachjetisvariedwithinonestandarddeviationbasedonpTand,andtheeciencyoftheanalysisselectionisrecomputedtoassessthesystematicvariationonthenormalizationofthesignalandallbackgroundcomponents.Anuncertaintyof2%isfoundforsignal,whilebackgroundcanvaryupto3%.Fortheshapevariation,theBDToutputisrecomputedaftershiftingthescaleup 83

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anddown,andtheobservedvariationintheBDTisusedtosetshapevariation.EachsourceofuncertaintyassessedbytheJETMETgroupisvariedindividually. JetEnergyResolution:wesmeartheenergyresolutionforeachjetusingtheJetMETprescriptionasourdefault,andthenassignasystematicuncertaintybasedonfurthersmearing(upanddown).Anuncertaintyof3%isestimatedforthenormalization.Fortheshapeuncertainty,theBDTisrecomputedafterthesmearingandthemodiedoutputisusedtodenetheshapevariation. b-jetTagging:ocialb-taggingscalefactorsareappliedconsistentlytojetsinsignalandbackgroundevents.Anaveragesystematicuncertaintyof6%perb-jet,12%perc-jet,and15%perfaketag(lightquarksandgluons)areusedtoaccountforthenormalizationuncertainty.Fortheshape,wevarythereshapingoftheCMVAoutputbasedontheocialuncertaintiesprovidedbytheBTVPOG.ThisgivestwonewshapesfortheCMVAoutput(\up"and\down")thatwetheninputtotheBDT.TheresultingmodiedBDToutputisthenusedastheshapevariationduetob-tagginguncertainties.DecorrelationinpTandisimpelmented.systematicassessments). Crosssection:thetotalsignalcrosssectionhasbeencalculatedtonext-to-next-to-leadingorderaccuracy,andthetotaluncertaintyis4%( 51 ),includingtheeectofscaleandPDFvariations. TheoreticalpTSpectrum:thisanalysisisperformedintheboostedregime,andthus,potentialdierencesinthepTspectrumoftheVandHbetweendataandMonteCarlogeneratorscouldintroducesystematiceectsinthesignalacceptanceandeciencyestimates.Recently,twocalculationshavebecomeavailablethatestimatetheNLOelectroweak( 52 ; 53 ; 54 )andNNLOQCD( 55 )correctionstoVHproductionintheboostedregime.BoththeEWKandNNLOQCDcorrectionshavebeenappliedtothesignalMCsamples.TheestimatedeectfromNNLOelectroweakcorrectionsare2%forZHand2%forWH( 52 ; 53 ; 54 ).FortheremainingQCDcorrectionanuncertaintyof5%forbothZHandWHisestimated. (V,H):systematicuncertaintyonthejetangularresolutionisassumedtobenegligible,andthisisconrmedbythegoodagreementobservedinthecontrolregions. Nal:theeciencyoftheleptonvetoisfoundtobe100%inthesimulation,andnoadditionaluncertaintyisassigned. BackgroundEstimate:amixofdata-drivenmethods,simulation,andtheoryuncertaintiescontributetothetotaluncertaintyonthebackgroundestimates.Correlated(luminosity,b-tagging,JEC/JER,andTnPeciencies)anduncorrelateduncertainties(statistical,controlregion,andcrosssection)arecombinedseparately.Anuncertaintyof30%isassumedforsingletop(approximatelytheuncertaintyonthemeasuredcrosssection)anddiboson(assumedtohavethesameuncertaintyasthesignal).Theotherbackgroundsaretakendirectlyfromdata,withtheassociateduncertaintiesfromthecontrolregions. 84

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MonteCarloStatistics:thenitesizeofthesignalandbackgroundMCsamplesareincludedinthenormalizationuncertainties.Inaddition,theshapeoftheBDTisallowedtovarywithinthebin-by-binstatisticaluncertaintiesfromtheMCsamples(inacoherentway),whilealsoconstrainingthetotalintegralwithinitsuncertainty. V+jetsMonteCarlomodel:weconsiderthedierenceintheshapesoutput(BDTandMjj)ofadierentMonteCarloV+jetswithrespecttothenominalMadgraphMC.InparticularHerwigpphighptV+jetssampleswerecomparedwiththeMadgraphones.ThedierenceinBDTshapeobservedbetweenthesetwogeneratorsisthensymmetrizedandusedtodenetheshapevariation. PDFuncertainties:theimperfectknowledgeoftheprotonquarkcontentisencodedinasetofNNPDFMCreplicas.Foreachprocess,theRMSofallthevariationsischeckedineachbinoftheBDTdistributionandthelargestvariationisusedasnormalizationnuisanceinthedatacards. QCDscalevariations:TheQCDnormalizationandfactorizationscalevariations1=2and2areconsideredseparatelyforeachprocessandtakenasuncorrelatedsourcesofsystematicuncertainties(shape+normalization).AsummaryplotshowingtheimpactandpullsonthesignalstrengthofthemostimportantsystematicuncertaintiesisshowninFigure 5-18 85

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Figure5-18. Impactandpullsonthesignalstrengthofthesystematicsourceswiththehighestimpactonthesignalstrength. 86

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CHAPTER6RESULTSThenalamountofpredictedVHbbsignalevents,andwhetherthiscorrespondstoanexcessindatawhenconsideringthebackgroundonlyhypothesis,isdeterminedwithasimultaneousbinned-likelihoodtofthebackgroundcontrolregions(CR)andthesignalregions(SR).ThettedvariablesareminCMVAforthecontrolregionsandBDToutputforthesignalregions.Z()HandW(`)Huseonecategory,whileZ(``)Husestwocategories:lowandhighvectorbosonpT.Inthissectionallresultsandtmethodolgywillbegiven. 6.1SignalandControlRegionstsThedistributionsoftheBDToutput(SR)andminCMVA(CR)usedforthenalcombinedtofallchannelsareshownfortheZ(``)HchannelinFigures 6-1 { 6-2 .Thepost-tplotsconsidertheadjustmentsofallnuisanceparametersinthenalmaximumlikelihoodttoextractthesignal.Weconsiderbothshapeandratechangesinthepost-tplots.Table 6-1 reportstheexpectedsignalandbackgoundsinthesignalregionbins. Table6-1. Thetotalnumberofeventsineachchannel,forthe20%most-sensitiveregionoftheBDToutputdistribution,fortheexpectedbackgrounds,forthe125SMHiggsbosonVHsignal,andfordata.Thesignal-to-backgroundratio(S/B)isalsoshown. Z()HW(`)HZ(``)H ProcessLowpT(V)HighpT(V) Vbb216.8102.5617.5113.9Vb31.819.9141.117.2V+udscg10.29.858.44.134.798.0157.73.2Single-top-quark11.844.62.00.2VV(udscg)0.41.56.40.6VZ()7.76.922.93.8 Totalbackgrounds267.0283.31005.9142.9VH34.726.033.522.1Data3343201030179 S/B0.130.110.0330.156 6.2SignalStrengthCalculationTheprimarytechniqueforextractingthesignicanceoftheobservedandexpectedsignalyieldsiscomputedusingthestandardLHCprolelikelihoodasymptoticapproximation( 56 ), 87

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Figure6-1. Post-tdistributionsofBDToutputforcombinedtfortheZ(``)Hchannelafterallselectioncriteriahavebeenapplied. whichweusewiththeprolelikelihoodteststatistic~q: ~q=)]TJ /F4 11.9552 Tf 9.298 0 Td[(2lnL(dataj,^) L(dataj^,^),0^,(6{1).wherewehaverestrictedtotakeonlypositivevalues.Thelikelihoodisgivenbytheproductoftheindividuallikelihoodsforeachchannel L(dataj,)=Poisson(Nijsi()+bi())p(~j).(6{2)Here\data"iseithertheactualexperimentalobservationorpseudo-datausedtoconstructsamplingdistributions.ThesymbolsNi,siandbirepresenttheobserved,expected 88

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Figure6-2. Post-tdistributionsofthecontrolregionsfortheZ(``)Hchannelafterallselectioncriteriahavebeenapplied. 89

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signal,andexpectedbackgroundratesinbini.Theparameteristhesignalstrengthmodier,==SM,andrepresentsthefullsuiteofnuisanceparameters,with~representingthebestestimateofthenuisancepriortothedataanalysis.Poisson(Nijsi()+bi())standsforthePoissonprobabilitiestoobserveNieventsgiventheexpectedeventratesi()+bi(),withtheunderstandingthatsomeanalysesareunbinnedandusetheextendedlikelihoodformalism.Theprobabilitiesp(~j)encodeinformationonthesystematicerrors.Themaximumlikelihoodestimatesorbest-t-valuesofandaredenoted^and^,while^denotestheconditionalmaximumlikelihoodestimateofallnuisanceparameterswithxed.Inthisanalysistherangeofisrestrictedtothephysicallymeaningfulregime,i.e.itisnotallowedtobenegative.Theshapeandnormalizationofalldistributionsareallowedtovarywithinthesystematicandstatisticaluncertainties.Theseuncertaintiesaretreatedasindependentnuisanceparametersinthetandareallowedtooatfreelyandareadjustedbythet. 6.3BlindingInordertopreventnetuningofresultsexctractedfromdataobservations,weemployasafeguardcalledblinding.Furthermore,allanalysesatCMSarerequiredtostayblindeduntilapprovedtounblind.StayingblindmeanswedonotlookatdatainthesensitiveregionoftheBDTanddijetmassspectrumsuntilalloptimizationsandanalysisparametershavebeenchosen.Alloptimizationsaredonewithreferencetoanexpectedlevelofdata,whichisderivedfromatoyAsimovdataset.Onceapprovedforunblinding,weperformthethefullMLEtondataforthersttimeandlookattheactualttedsignalstrength.Whateverresultsarefound,regardlessifitmatchesourexpectationsornot,aretheresultspresentedinthisthesis. 6.4ResultsVHForaHiggsBosonmassof125GeV,theexcessofobservedeventscorrespondstoalocalsignicanceof3.3standarddeviationswhencomparedtothebackground-onlyhypothesis.Thebesttvalueforthesignalstrength(productioncrosssectionfora125GeVHiggsboson,relativetotheSMcrosssection)H,SM==SM,is1.19+0.21)]TJ /F5 7.9701 Tf 6.587 0 Td[(0.20(stat.)+0.34)]TJ /F5 7.9701 Tf 6.586 0 Td[(0.32(syst.).With 90

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H,SM=1.0theexpectedsignicanceis2.8standarddeviations.Withinerror,theobservedsignalstrengthisconsistentwithaStandardModelHiggsBosonof125GeV.Table 6-2 containstheexpectedandobservedsensitivitiesforthethreeVHbbchannels,aswellasthecombinedresult.Figure 6-3 displaysthebest-tvaluesofthesignalstrength()forthethreechannelsindependently,inadditiontotheWHandZHproductionmodesindependently.TheWHandZHproductionmodesareeachconsistentwiththeStandardModelpredictionswithinuncertainties.Figure 6-4 combinestheBDToutputvaluesofallchannelsandbinstheeventsinsimilarexpectedsignal-to-backgroundratios.Themostsensitivebins(largeS/Bvalues)containanexcessofeventswhentakingtheratioofdatatosimulatedbackground,indicatingthatsignaleventsarepresentinordertocorrectthedata/MCratio. Table6-2. TheexpectedandobservedsignicancesforVHproductionwithH!bbareshownforeachchanneltindividuallyaswellasforthecombinationofallthreechannels. mHiggs=125SignicanceSignicanceexpectedobserved 1.50.01.53.21.83.1 Allchannels2.83.3 6.5NextStepsAlthoughtheevidencethresholdforHiggsdecaystobottomquarkshasbeenreached,thenextgoalisinsight:discovery(5standarddeviations).Duringthecurrentyearof2017,another70fb)]TJ /F5 7.9701 Tf 6.586 0 Td[(1ofdatahasbeencollected.Thisnewquantitiyofdatapresentsuniquechallenges:sucientlevelsofmontelcarlosimulationareneededtoscalewithdataandsystematicerrorsduetobackgrounduncertaintieswillincrease.Nolongerwilllowlevelsofdataplaguethisanalysis,butratheritwillbeuncertaintiesfrommismodellingandexperimentaluncertaintiesthatwillhavetobethefocusofthenextgenerationofVHbbanalyses. 91

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Figure6-3. Thebest-tvalueoftheproductioncrosssectionfora125GeVHiggsbosonrelativetotheSMcrosssectionisshowninblackwithgreenerrorband.AbovethedashedlinearetheWHandZHsignalstrengthswheneachproductionmodehasanindependentsignalstrengthparametersinthet.Wheneachchannelistwithitsownsignalstrengthparameter,theresultsareshownbelowthedashedline. Inadditiontofocusingonsimulationandsystematics,progresscanbemadebyexploitingthelargerdataset.Currently,theBDTsignalregionshavebeenlimitedtotwoatmost.Thisismainlyduetoinsucientstatisticswhencreatingmorecategories.Initialtestsindicatethatthreetofoursingalregionsseperatedinbinsofvectorbosonmomentumwouldprovideaboostinsensitivitycomparedtothecurrentvalueoftwo.Thetrainingmodelcanalsobeupgradedbyexploringneuralnetworkstoperformthesupervisedtrainingcomponent.NeuralnetworkscanalsobeusedinanunsupervisedfashioninordertobuildnewfeaturesfromourexistingonesthatcouldthenbefedintothecurrentBDTmodel. 92

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Figure6-4. CombinationofallchannelsintoasingleeventBDTdistribution.Eventsaresortedinbinsofsimilarexpectedsignal-to-backgroundratio,asgivenbythevalueoftheoutputofthevalueoftheircorrespondingBDTdiscriminant(trainedwithaHiggsbosonmasshypothesisof125).Thebottominsertsshowtheratioofthedatatothebackground-onlyprediction. 6.6ConclusionsThisthesishasdescribedindetailthemeasurementofthestandardmodelHiggsBosonproductioninassociationwithvectorbosonsanddecayingintob-quarkpairs.Adatasamplewithanintegratedluminosityof35.9fb)]TJ /F5 7.9701 Tf 6.587 0 Td[(1correspondingtothefull2016runningperiodandrecordedbytheCMSexperiment,hasbeenanalyzedinvemodes:Z()H,Z(ee)H,Z()H,W()H,andW(e)H.ThettedsignalstrengthforaHiggsBosonmassof125GeVis==SM=1.19+0.35,withanobserved(expected)signicanceof3.3(2.8)standarddeviations.Thethresholdforevidence(3standarddeviations)hasbeenreachedforaStandardModelHiggsbosoncouplingtobottomquarks. 93

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BIOGRAPHICALSKETCHDavidCurrywasborninPasadena,California,intheyearofourLord1981.In2007DavidstartedstudyingphysicsattheUniversityofOregon.AdecadelaterhesuccessfullydefendedhisPhDinphysicsattheUniversityofFlorida. 97