Citation
Observation of a Higgs Boson in the H to ZZ to 4L Decay Channel and Using Z to 4L Decays as a Calibration Tool in Studies of the Higgs Boson Properties

Material Information

Title:
Observation of a Higgs Boson in the H to ZZ to 4L Decay Channel and Using Z to 4L Decays as a Calibration Tool in Studies of the Higgs Boson Properties
Creator:
Snowball, Matthew A
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (261 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
AVERY,PAUL RALPH
Committee Co-Chair:
KORYTOV,ANDREY
Committee Members:
MATCHEV,KONSTANTIN TZVETANOV
YELTON,JOHN M
RANKA,SANJAY
Graduation Date:
5/3/2014

Subjects

Subjects / Keywords:
Average linear density ( jstor )
Electrons ( jstor )
Higgs boson ( jstor )
Leptons ( jstor )
Mass ( jstor )
Momentum ( jstor )
Muons ( jstor )
Photons ( jstor )
Signals ( jstor )
Simulations ( jstor )
4l -- cms -- four-lepton -- higgs -- lepton -- lhc -- measurement -- properties -- snowball -- z-4l
Physics -- Dissertations, Academic -- UF
Genre:
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 Higgs boson in the decay channel H to ZZ to 4 leptons is performed using data from proton-proton collisions corresponding to and integrated luminosity of 5.1 inverse femtobarns at a center-of-mass energy of 7 TeV and 19.7 inverse femtobarns at a center-of-mass energy of 8 TeV data. A new boson is observed as a narrow resonance with a local significance of 6.8 standard deviations, a measured mass of 125.6 +/- 0.4(stat.) +/- 0.2 (syst.) GeV, and a total width less than or equal to 3.4 GeV at a 95% confidence level. The production cross section of the new boson times the branching fraction to four leptons is measured to be 0.93 +0.26 -0.23(stat.) +0.13 -0.09(syst.) times that predicted by the standard model. Its spin-parity properties are found to be consistent with the expectations for the Standard Model Higgs boson. In addition, measurements of the Z to 4 lepton mass and width are presented. The mass of Z boson decaying to 4 leptons is found to be 91.16 +/- 0.23 GeV while the width is found to be 2.98 +0.54 -0.50 GeV. Spin-parity properties of the Z boson are shown to be consistent with expectation from the Standard Model. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
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, 2014.
Local:
Adviser: AVERY,PAUL RALPH.
Local:
Co-adviser: KORYTOV,ANDREY.
Statement of Responsibility:
by Matthew A Snowball.

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright Snowball, Matthew A. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
907295091 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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OBSERVATIONOFAHIGGSBOSONINTHEHTOZZTO4LDECAYCHANNELAND USINGZTO4LDECAYSASACALIBRATIONTOOLINSTUDIESOFTHEHIGGS BOSONPROPERTIES By MATTHEWALEXANDERSNOWBALL ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2014

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c 2014MatthewAlexanderSnowball 2

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Tomywife,whohasenduredmissedanniversaries,missedbirthdays,andcountless nightsalonesothatImaymakehistory 3

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ACKNOWLEDGMENTS Firstandforemost,Ithankmyfamilyforalloftheirloveandsupport,andfor keepingmestraightwhentimesweretough.IthankAndreyandPaulfortheirguidance, patience,andforpushingmetobebetter.Mostofall,Ithankthemforgivingmea chancetodowhatIlove.IthankPedjaandAlexeyforallthelongdaysandnights workingtogether.Also,fortheirguidanceandalltheexcitingtimesweshared.Ithank TongguangandAurelijusforalloftheirhelpandpatienceduringsomeverylongdays. IthankJustinforalloftheridestoandfromCERN,forpickingmeupattheairportat "zerodarkthirty",andformakingsureIdidn'tmissoutonsomefunwhileinEurope. IthanktheCMScollaborationandallitsmembersfortheinsightfuldiscussionsand opportunitiespresentedtomyselfduringmytimeasamember. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 9 LISTOFFIGURES ..................................... 12 ABSTRACT ......................................... 22 CHAPTER 1THESTANDARDMODEL .............................. 23 1.1FundamentalParticlesandForces ...................... 23 1.1.1FundamentalParticles ......................... 23 1.1.2FundamentalForces .......................... 25 1.2TheOnceElusiveHiggs ............................ 28 1.2.1TheHiggsMechanism ......................... 30 1.2.2ProductionanddecayoftheHiggsboson .............. 33 1.2.2.1Gluongluonfusion ...................... 33 1.2.2.2Vectorbosonfusion ..................... 34 1.2.2.3Associatedproduction .................... 34 1.2.3DecayoftheHiggs ........................... 36 1.2.3.1LowmassHiggs ....................... 36 1.2.3.2IntermediatemassHiggs .................. 37 1.2.3.3HighmassHiggs ....................... 38 1.2.4HiggsWidth ............................... 39 1.2.5TheoreticalConstraintsonHiggsMass ................ 40 1.3BeyondtheStandardModel .......................... 40 1.3.1ThreeGenerations ........................... 40 1.3.2HierarchyProblem ........................... 41 1.3.3Matter .................................. 42 1.3.4GrandUnicationandBeyond ..................... 42 2EXPERIMENT .................................... 44 2.1TheLargeHadronCollider .......................... 44 2.1.1DesignandOperationalParameters ................. 45 2.1.2PhysicsattheLargeHadronCollider ................. 46 2.2TheCompactMuonSolenoidDetector .................... 48 2.2.1Geometry ................................ 50 2.2.2InnerTracker .............................. 51 2.2.3ElectromagneticCalorimeter ..................... 55 2.2.4HadronicCalorimeter .......................... 58 2.2.5SuperconductingSolenoid ....................... 60 5

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2.2.6MuonSystem .............................. 61 2.2.6.1Drifttubes .......................... 62 2.2.6.2Cathodestripchambers ................... 63 2.2.6.3Resistiveplatechambers .................. 64 2.2.6.4Muonmomentumresolution ................ 65 2.2.7TriggerSystem ............................. 65 2.2.7.1Level1trigger ........................ 67 2.2.7.2Highleveltrigger ....................... 68 2.2.8DataAcquisition ............................ 70 2.3Computing ................................... 70 3PHYSICSOBJECTS ................................. 73 3.1Electrons .................................... 74 3.1.1ReconstructionandIdentication ................... 74 3.1.2ImpactParameterSelection ...................... 78 3.1.3Isolation ................................. 78 3.1.4MomentumAssignment ........................ 81 3.1.5EnergyCalibrations ........................... 85 3.1.6DerivationofScaleandResolutionCorrections ........... 85 3.1.7ScaleandResolutionMeasurementsfrom Z ee ......... 87 3.1.8Electronscalelinearitymeasurementfrom Z ee J / and .. 89 3.1.9EfciencyMeasurement ........................ 91 3.1.10ReconstructionEfciency ....................... 92 3.1.11SelectionEfciency ........................... 96 3.1.12Summary ................................ 98 3.2Muons ...................................... 103 3.2.1ReconstructionandIdentication ................... 103 3.2.2IdenticationandGhostMuonRemoval ............... 104 3.2.3ImpactParameterSelection ...................... 105 3.2.4Isolation ................................. 105 3.2.5EnergyCalibrations ........................... 107 3.2.6DerivationofScaleandResolutionCorrections ........... 107 3.2.7ScaleandResolutionMeasurementsfrom Z J / and ...... 107 3.2.8EfciencyMeasurement ........................ 113 3.2.9Tracking,ReconstructionandIdenticationEfciency ........ 113 3.2.10SelectionEfciency ........................... 115 3.2.11Summary ................................ 118 3.3Photons ..................................... 120 3.3.1ReconstructionandIdentication ................... 120 3.3.2Isolation ................................. 122 3.4Jets ....................................... 123 6

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4SEARCHINGFORHIGGS ............................. 125 4.1 H ZZ 4 AnalysisStrategy ....................... 125 4.2Datasets,Simulation,andTriggers ...................... 125 4.2.1CollisionDataandTriggers ...................... 126 4.2.2Simulation ................................ 127 4.2.2.1Signal: H ZZ 4 .................... 130 4.2.2.2Irreduciblebackground: q q ZZ 4 .......... 132 4.2.2.3Irreduciblebackground: gg ZZ 4 .......... 133 4.2.2.4Reduciblebackground: Z + jets WZ + jets ........ 133 4.2.2.5Reduciblebackground: t t SingleTop ........... 133 4.3EventSelectionandCategorization ...................... 134 4.3.1Trigger .................................. 134 4.3.2PrimaryVertexSelection ........................ 135 4.3.3LooseandTightLeptons ........................ 135 4.3.4BestCandidateSelection ....................... 137 4.3.5FinalStateRadiationRecovery .................... 138 4.3.6SelectionEfciency ........................... 141 4.3.7ControlofSelectionComponentsinData .............. 142 4.4EventCategorization .............................. 143 4.4.1DiscriminationintheDi-jetCategory ................. 146 4.4.2Discriminationinthe0/1JetCategory ................ 150 4.4.2.1Signal pT 4 model ...................... 150 4.4.2.2Irreduciblebackground pT 4 model ............. 152 4.4.2.3Reduciblebackground pT 4 model ............. 152 4.5BackgroundEstimation ............................ 154 4.5.1IrreducibleBackgroundModel ..................... 154 4.5.1.1CrossSectionandUncertainties .............. 155 4.5.1.2ShapeModel ......................... 157 4.5.2ReducibleBackgroundModel ..................... 160 4.5.2.1MethodusingOppositeSignLeptons ........... 161 4.5.2.2MethodusingSameSignLeptons ............. 164 4.5.2.3Combinedresultsanduncertainties ............ 166 4.5.2.4LineShape .......................... 166 4.6SignalModel .................................. 169 4.6.1LowMassSignalModel ........................ 169 4.6.2SignalModelUncertaintiesfor m H < 400GeV ............ 175 4.6.3HighMassSignalModel ........................ 176 4.6.4SignalModelUncertaintiesfor m H # 400GeV ............ 179 4.6.5SignalNormalizationUncertaintyandSystematics ......... 180 4.6.5.1TotalSignalCrossSection ................. 181 4.6.5.2BranchingratioBR ( H 4 ) ................ 181 4.6.5.3SignalAcceptance ...................... 181 4.6.5.4SignalEfciency ....................... 182 4.7Event-by-Event(EbE)Uncertainties D mass .................. 185 7

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4.7.1CalibrationofEbEUncertainties ................... 187 4.7.2Modelingofthe D mass .......................... 188 4.7.3ValidationoftheEbEUncertaintiesinData ............. 192 4.8KinematicDiscriminants ............................ 193 4.9SearchResults ................................. 199 4.9.1Yields .................................. 199 4.9.2EventDistributions ........................... 202 5STATISTICALANALYSIS .............................. 205 5.0.3SummaryofSystematicUncertainties ................ 206 5.0.4ExclusionLimits ............................. 209 5.0.5SignicanceofExcess ......................... 209 5.1PropertiesMeasurement ........................... 212 5.1.1Mass ................................... 212 5.1.2SignalStrength ............................. 216 5.1.3Width .................................. 218 5.1.4SpinParity ................................ 219 5.1.4.1FractionofCP-violatingeventsinthepeak ........ 219 5.1.4.2Alternativespin-paritymodels ............... 221 6USING Z 4 .................................... 230 6.0.5ValidationofHiggsMassandWidth .................. 231 6.0.6ValidationofSpinParity ........................ 236 7CONCLUSIONS ................................... 241 APPENDIX AMUONDATA-MCSCALINGFACTORS ...................... 242 BSIGNALMODELDETAILS ............................. 246 REFERENCES ....................................... 253 BIOGRAPHICALSKETCH ................................ 261 8

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LISTOFTABLES Table page 1-1First,second,andthirdgenerationsofquarksandleptons.Alsolistedarecharge andinteractiontypes. ................................ 24 1-2ForcecarriersandtheircouplingconstantsforthethreeforcesoftheStandard Model. ......................................... 24 1-3CrosssectionsinpbforassortedHiggsmassesandproductionmechanisms attheLHC. ...................................... 36 2-1HitdensityoftheCMStrackerfordifferentradiallyoutwardlengths. ....... 53 2-2SummaryoftheCMStrackingsystem. ...................... 55 3-1BDTcutvaluesfortheBDTbasedelectronID. .................. 77 3-2Electronreconstructionefcienciesandscalefactorsfor8TeVdatawithcombined statisticalandsystematicerrors. .......................... 95 4-1Datasetsandtriggersusedintheanalysis. .................... 128 4-2Triggersin2012dataanalysis. ........................... 129 4-3MonteCarlosimulationdatasetsusedforsignalandbackgroundprocesses. (XX=tuneZ2star) .................................. 130 4-4FSRalgorithmrate,purity,andpercentagegainforHiggsand ZZ ....... 140 4-5Reduciblebackgroundyieldspredictedbybothmethodsandassociatedstatistical uncertainties. .................................... 166 4-6Signalacceptance A fordifferentQCDscales. .................. 182 4-7Correctionfactorsfortheper-leptonmomentumuncertaintiesderivedfrom Z (high pT muonsandall pT electrons)and J / events(low pT muons)in dataandsimulations. ................................ 188 4-8Listofkinematicdiscriminantsusedinthecross-sectionandspin-parityanalyses. ............................................. 197 4-9Thenumberofestimatedbackgroundandsignaleventsandnumberofobserved candidates,afternalinclusiveselection,inthefullmeasurementrange100 < m 4 < 1000GeV. ................................. 200 4-10Thenumberofestimatedbackgroundandsignaleventsandnumberofobserved candidates,afternalinclusiveselection,inthefullmeasurementrange121.5 < m 4 < 130.5GeV. ................................. 201 9

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5-1Systematicuncertaintiesinpercentfor7TeV. ................... 207 5-2Systematicuncertaintiesinpercentfor8TeV. ................... 208 5-3Normalizationuncertaintyinpercentplacedon Z + X estimateforboth7and 8TeV. ......................................... 209 5-4Signalexpectedandobservedsignicance( # )attheminimumofthep-value (125.7 GeV )for7+8TeVcombineddata,for3Dt(nominal),2Dtand1D t. ........................................... 210 5-5Besttvaluesforthemassofthenewbosonandforthe Z boson,bothmeasured inthe4 " = e nalstates,with1D,2Dand3Dt,respectively,asdescribed inthetext. ...................................... 214 5-6Besttvaluesforthemassofthenewbosonmeasuredinthe4 " = e nalstates,with3Dt,showingthecontributionoftheleptonscaleuncertainty inthetotalmassuncertainty. ............................ 214 5-7Correctionfactorsandeventyieldsinthedifferentchannelsofthealternative spin-parityhypotheses. ............................... 225 5-8Correctionfactorsandeventyieldsinthedifferentchannelsofthealternative spin-parityhypotheses. ............................... 226 5-9Listofmodelsusedinanalysisofspin-parityhypothesescorrespondingto thepurestatesofthetypenoted. ......................... 229 6-1Resultsforthemasstofthe Z 4 peakforindividualchannelsandthe cumulative 4 channelwiththeiruncertainties. .................. 232 A-1Muonefciencynumbersfordata,simulationandforthedata/simulationscale factor,for 5 < pT < 7.5 GeV. ............................ 242 A-2Muonefciencynumbersfordata,simulationandforthedata/simulationscale factor,for 7.5 < pT < 10 GeV. ........................... 243 A-3Muonefciencynumbersfordata,simulationandforthedata/simulationscale factor,for 10 < pT < 15 GeV. ............................ 243 A-4MuonEfciencynumbersfordata,simulationandforthedata/simulationscale factor,for 15 < pT < 20 GeV. ............................ 244 A-5MuonEfciencynumbersfordata,simulationandforthedata/simulationscale factor,for 20 < pT < 30 GeV. ............................ 244 A-6MuonEfciencynumbersfordata,simulationandforthedata/simulationscale factor,for 30 < pT < 40 GeV. ............................ 245 10

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A-7MuonEfciencynumbersfordata,simulationandforthedata/simulationscale factor,for 40 < pT < 100 GeV. ........................... 245 11

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LISTOFFIGURES Figure page 1-1AllofthematterparticlesandforcecarriersoftheStandardModel ....... 25 1-2Feynmandiagramofelectronscatteringviaphotonexchange. ......... 26 1-3PrecisionmeasurementsofthethetopquarkandWbosonareusedtopredict thepossiblemassofaHiggsboson.[ 1 ] ...................... 29 1-4Pictureillustratingthenon-zerovacuumexpectationvalueoftheHiggseld. 31 1-5FeynmandiagramsforggH(topleft),VBF(topright),VH(bottomright),and ttH(bottomleft)productionmechanisms. ..................... 34 1-6LHCHiggsCrossSectionsat7TeV(a)and8TeV(b)forthedifferentproduction modes.Theoreticaluncertaintiesareshownbythecoloredbands. ....... 35 1-7Higgsbranchingratioswithuncertaintyforlowmass(left)andupto1TeV (right). ........................................ 37 1-8Higgscrosssectiontimesbranchingratios7TeV(left)and8TeV(right). .... 38 1-9Higgstotalwidthasafunctionofmass. ...................... 39 1-10Higgsmassboundsasafunctionof [ 2 ]. .................... 41 2-1LHCacceleratorcomplex. ............................. 45 2-2AnexplodedviewoftheCMSdetectorandthesubdetectorsthatcomposeit. Inthisrepresentation,boththebarrelandendcapsareclearlydiscernible. .. 52 2-3CoordinatesystemusedbytheCMSexperiment. ................ 53 2-4TrackingsystemasinstalledinCMS. ....................... 54 2-5Resolutionoftransversemomentum(left),transverseimpactparameter(middle), andlongitudinalimpactparameter(right)formuonswith pT = 1,10,and100 GeVrespectively. .................................. 55 2-6ElectromagneticcalorimeterlayoutinCMS. .................... 56 2-7EnergyresolutionoftheECALinidealconditions. ................ 58 2-8LocationsofthedifferentHCALsubsystems(HB,HE,HO,HF). ........ 60 2-9DiagramofthemagneticeldthroughoutCMS. ................. 61 2-10LayoutoftheCMSmuonsystem. ......................... 62 12

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2-11DTelectriceldshapedbythecathodes,anode,andinsulatingstrips(left). DTchamberlayoutforsingleDTstationinCMS(right). ............. 63 2-12CSCchamberasitwouldbeinstalledonanendcapdiskonCMS(left).Multi-wire proportionalchambersuchasthosethatmakeuptheCSCchambersinCMS (right). ........................................ 64 2-13Resistiveplatechamberconstruction. ....................... 65 2-14Muonmomentumresolutionversus pT forbarrelandendcapmuons. ..... 66 2-15OverviewoftheCMStriggersystem ........................ 67 2-16OverviewoftheL1triggersystem ......................... 68 2-17ExampleHLTpathforisolatedelectronbasedtrigger. .............. 70 2-18TieredcomputingmodelusedbyCMS. ...................... 72 3-1Distributionofclustershapevariable # i i forthetrainingsampleW+jetsand thetestsampleZ+jetson2012datainthebarrel(left)andintheendcap(right) ............................................. 76 3-2DistributionofelectronBDToutputfortrainingsampleW+jets,testsample Z+jetson2012data(fakes)andpromptelectrons( Z ee simulation)inthe barrel(left)andendcap(right) ........................... 76 3-3ROCcurvesfortheelectronmultivariateidentication(BoostedDecisionTrees) comparedwiththecut-basedselectionworkingpoints.Electroncandidates with pT > 20GeVareshownforbarrel(left)andendcap(right). ........ 77 3-4Methodforcalculatingparticleowbasedisolation. ............... 79 3-5Averageestimateofeventenergydensityintheevent, $ ,andparticle-isolation componentsasafunctionofthenumberofreconstructedvertices(left).Effect oftheeffectiveareacorrectiononthetotalparticleisolation(right). ...... 80 3-6Effectivewidthof E reco / p true distributionsasafunctionof pT andfourdifferent regionsofthecalorimeter. ............................. 83 3-7AcomparisonofthereconstructedHiggsbosonmassdistributionsafterapplying MonteCarlotodatacorrectionsforthestandardelectronmomentumassignment andtheregressionassignment,forthe4e(left)and2e2 (right)channel. ... 84 3-8Datatosimulationcomparison,for Z ee events.Left:eventswithboth electronswith | % | < 1and R 9 < 0.94.Right:eventswithoneelectronwith | % | < 1 and R 9 < 0.94andtheotherelectronwith1.566 < | % | < 2and R 9 < 0.94. .... 86 13

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3-9 Z ee eventscategorizedaccordingtotheelectronclassicationforthe bestcategoryofevents,withbothnon-showeringelectronsinthebarrel(golden orbig-brem)(left)andtheworstcategory,withbothshoweringelectronsin theendcap(right). .................................. 88 3-10Asafunctionofthenumberofvertices,differencesbetweendataandMCof thepeakposition,dividedbythepeakpositioninMC. .............. 88 3-11Instrumentaldi-electroneffectiveresolutionasmeasuredfrom Z ee events andcomparedtosimulation. ............................ 89 3-12Templatetsforthe Z ee whentheprobehas 34 < pT < 40 GeVinthe centralbarrel, | % | < 1(left),orintheendcap(right)for8TeVdata. ........ 90 3-13Examplesoftsto8TeVdatafor J / ee events,whereelectronprobehas 7 < pT < 10GeVinthebarrel(left)and ,whereelectronprobehas10 < pT < 15GeVinthebarrel(right). ........................ 91 3-14Extradata/MonteCarloshiftsasafunctionofelectron pT for7TeVdata(left) and8TeVdata(right)computedwith J / ! and Z intodi-electronresonances. ............................................. 91 3-15The m !! distributionsandsuperimposedtemplatetsforpassing(left)and failing(right)probesusedfortheelectronidenticationefciencymeasurement inthe10-15GeV pT bin(top)andfor 2.0 $ | % | < 2.5 (bottom). ......... 93 3-16Electronreconstructiondata-to-simulationefciencyratiofor8TeV"January 22"re-recodata,obtainedwithtagandprobetechniquedescribedinthetext, asafunctionofthesupercluster | % | and pT ................... 94 3-17The m ee distributionsandsuperimposedtemplatetsforpassing(left)and failing(right)electronprobesusedfortheelectronidenticationefciencymeasurement inthe7-10GeV pT bininthebarrel(top)andendcap(bottom). ........ 97 3-18The m ee distributionsandsuperimposedfunctionalformtsforpassing(left) andfailing(right)probesusedfortheelectronidenticationefciencymeasurement inthe7-10GeV pT binandforbarrel(top)andendcap(bottom). ....... 98 3-19Electronidenticationefcienciescomputedwiththetag-and-probemethod on7TeVdataasafunctionoftheprobe pT infourdifferent % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and(d) 2 $ | % | < 2.5 ..... 99 3-20Electronidenticationefcienciescomputedwiththetag-and-probemethod on8TeVdataasafunctionoftheprobe pT infourdifferent % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and(d) 2 $ | % | < 2.5 ..... 100 14

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3-21Datatosimulationscalefactorsforelectronselectionefciencycomputedwith thetag-and-probemethodon7TeVdataasafunctionoftheprobe p T infour different % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and (d) 2 $ | % | < 2.5 ................................... 101 3-22Datatosimulationscalefactorsforelectronselectionefciencycomputedwith thetag-and-probemethodon8TeVdataasafunctionoftheprobe p T infour different % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and (d) 2 $ | % | < 2.5 ................................... 102 3-23Efciencyofuncorrectedparticleowisolationandcorrectedparticleowisolation (both # & andEffectiveAreacorrectedisolation)asafunctionofthereconstructed numberofverticesin Z eventsselectedfromdata. ............ 106 3-24Exampletstothedimuonmassshapesinthecentralbarrel, | % | < 0.7 (0.4 for J / ),indata(left)andsimulation(right),formuonsfrom J / ! and Z Average pT ofthetwomuonsis5-7GeVfor J / ,10-20GeVfor and20-45 GeVfor Z ...................................... 109 3-25Exampletstothedimuonmassshapesintheendcap,( 1.6 < | % | < 2.0 for J / 1.5 < | % | < 2.4 for and 1.3 < | % | < 1.9 for Z ),indata(left)and simulation(right),formuonsfrom J / ! and Z ................. 110 3-26Relativedifferencebetweenthedimuonmassscalesindataandsimulation extractedfrom J / ! and Z decays,asfunctionoftheaveragemuon pT (left)and | % | (right)forthe7TeVdata(top)and8TeVdata(bottom). ...... 111 3-27Relativedifferencebetweenthedimuonmassresolutionsindataandsimulation extractedfrom J / ! and Z decays,asfunctionoftheaveragemuon pT (left)and | % | (right)forthe7TeVdata(top)and8TeVdata(bottom). ...... 112 3-28Muontrackingefciencyasafunctionofthemuon % for8TeVre-reconstructed dataandMC,asafunctionof % (left)andthemultiplicityofprimaryvertices (right). ......................................... 114 3-29MuonreconstructionandidenticationefciencyforParticleFlowmuons,measured withthetag-and-probemethodon7TeVdata(top)and8TeVdata(bottom) asfunctionofmuon pT ,inthebarrel(left)andendcaps(right).. ........ 115 3-30Efciencyfortherequirementonthe3Dimpactparametersignicance | SIP 3 D | < 4 asfunctionofthemuonpseudorapidity(top),for7TeVdata(left),and8TeV data(right),formuonswith pT > 20 GeV,andin8TeVdata(top)asfunction ofthenumberofreconstructedvertices(left)andacomparisonbetweenthe prompt-recoandthere-reco(right). ........................ 116 15

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3-31MuonisolationefciencyforParticleFlowmuonspassingtheimpactparameter requirements,measuredwiththetag-and-probemethodon7TeVdata(top) and8TeVdata(bottom)asfunctionofmuon pT ,inthebarrel(left)andendcaps (right). ........................................ 117 3-32Combineddata/MCscalefactorfortracking,identication,signicanceofimpact parameterandisolationfor7TeV(left)and8TeV(right)dataasfunctionof lepton pT and % ................................... 118 3-33Combineddataefciencyfortracking,identication,signicanceofimpact parameterandisolationfor7TeV(left)and8TeV(right)dataasfunctionof lepton pT ...................................... 118 3-34Reconstructionefciencyforphotonsproducedbynalstateradiationin H ZZ 4 events. .................................. 122 4-1LuminositydeliveredandrecordedtoCMSduring2011(left)and2012(right). ............................................. 127 4-2Crosssectiontimesbranchingratiofor H 4 (left).Enhancementincross sectionduetosameavornalstateinterference(right). ............ 131 4-3 pT 'sof4muonsrespectivelyinsimulated H ZZ 4 decays. ....... 135 4-4125GeVHiggssimulatedeventswithatleastoneFSRphoton(left)andall events(right),withandwithouttheFSRalgorithmappliedtoselection. .... 140 4-5SignalselectionefcienciesfromMCfora4 systemasafunctionofHiggs bosonmasshypothesis,forthefull m H rangein8TeVsignalsamples. .... 141 4-6Comparisonof Z 1 invariantmassin(left) e + e and(right) + ,between8 TeVdataandMonteCarloexpectations. ..................... 143 4-7Comparisonofleptonworstisolation(top)andleptonworst SIP 3 D (bottom)for leptonsinasampleof(left) Z 1 e + e and(right) Z 1 + ,between8 TeVdataandMonteCarloexpectations.Leptonsfrom Z 1 areexcluded. .... 144 4-8ComparisonofFisherdiscriminant D jet in Z 1 +2jetsinasampleof(left) Z 1 e + e and(right) Z 1 + ,between8TeVdataandMonteCarloexpectations. ............................................. 145 4-9Signaldi-jetratiofromMCfora4 systemwithinthegeometricalacceptance inthe4 (left),4e(middle)and2e2 (right)channelsasafunctionofHiggs bosonmasshypothesisfor8TeVsignalMCsamplesggH(top)andVBF(bottom). ............................................. 146 16

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4-10Signaldi-jetratiofromMCfora4 systemwithinthegeometricalacceptance inthe4e(left),4 (middle)and2e2 (right)channelsasafunctionofHiggs bosonmasshypothesisforthe8TeVsignalsamplesWH(top),ZH(middle), and t t H(bottom). .................................. 147 4-11Comparisonofpseudorapiditygapandinvariantmassofthetwotaggedjets inthedi-jetcategoryfordifferentHiggsproductionmechanismsand ZZ background. ............................................. 148 4-12Comparisonofthelinearsherdiscriminantshapesofthedominantproduction mechanismsinthedi-jetcategory(left).Comparisonofthetransversemomentum shapesofdifferentproductionmechanismsinthe0/1jetcategories(right). .. 149 4-132D pT 4 vs m 4 templatesforggH(topleft),VBF(topright),WH(bottomleft) andZH(bottomright)at8TeV. ........................... 151 4-142D pT 4 vs m 4 templatesfor q q ZZ (left)and gg ZZ (right)at8TeV. ... 152 4-15Datato POWHEG comparisonfordatainthe Z productionanalysisat7TeV[ 3 ]. 153 4-16Proledistributionofthevariable pT 4 / m 4 versus m 4 forreduciblebackground at8TeV,ttedwithaconstantline. ......................... 154 4-17Fittothe pT 4 / m 4 distributionafterselectionforreduciblebackgroundata center-of-massenergyof8TeV. .......................... 155 4-18PDF + s uncertaintiesfor pp ZZ 4 (left)atNLOand gg ZZ 4 (right). ........................................ 157 4-19QCDscaleuncertaintiesfor pp ZZ 4 (left)atNLOand gg ZZ 4 (right)processes. .................................. 158 4-20Fitsofsimulationusingthechosenempiricaltfunctionfor q q ZZ (left) and gg ZZ (right). ................................. 159 4-21Fakeratesmeasuredforprobemuonswhichsatisfythelooseselectioncriteria, measuredina Z ( "" )+ sampleinthe7TeVdata(left)andthe8TeVdata (right). ........................................ 162 4-22Fakeratesmeasuredforprobeelectronswhichsatisfythelooseselectioncriteria, measuredina Z ( "" )+ e samplewithin | M inv ( 1 2 ) % M Z | < 10GeV,inthe7 TeVdata(left)andthe8TeVdata(right). ..................... 163 4-23Averagefakeratestobeappliedtothecontrolsample(closedreddots),compared tothefakeratesmeasuredinthefakeratesample(closedblackdots)and intheOSfakeratesample(opensquares).Thefakeratescorrespondingto Barrel(Endcap)electronsforthe7TeV(right)and8TeV(left)dataareshown. ............................................. 165 17

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4-24Predictionforthereduciblebackgroundinallthreechannelstogether(black dots)ttedusinganempiricalshape(bluecurve)withindicatedtotaluncertainty (yellowband)(left).Contributionsfromthe2P2F-like(green)and3P1F-like (red)processesarettedseparately. ....................... 167 4-25Fitsofthe m 4 distributionsforchannelswithelectronfakesforthe(a)2P2F component,(b)3P1Fcomponent,and(c)thesumofthetwofunctions. .... 168 4-26Probabilitydensityfunctions f ( m 4 l | m H ) forasignalwith m H = 126GeV(top) or m H = 200GeV(bottom)atthereconstructionlevelafterfullleptonand eventselectionsareappliedfor4 (left),4e(center)and2e2 (right)events. 170 4-27Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmass m H = 126 GeVatthereconstructionlevelafterfullleptonandeventselectionsareapplied fordifferentproductionmodesintheUntaggedCategory(blackpoints). .... 172 4-28Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmass m H = 126 GeVatthereconstructionlevelafterthefullleptonandeventselectionsare appliedfordifferentproductionmodesintheDi-JetCategory(blackpoints). 174 4-29Fourleptoninvariantmassdistributionwiththenominalleptonmomentum (black)andaftertheextrascaleshiftsareappliedtotheMonteCarlo(blue) withthedoubleCrystalBalltsuperimposed,forthe4e(left)and2e2 (right) nalstatesfor8TeVsimulationwith m H = 126GeV. ............... 176 4-30Fourleptoninvariantmassdistributionatgeneratorlevelbeforeandafterthe CPS+interferencecorrectionsforaHiggsmassof900GeVproducedingluon fusion(left)orinvectorbosonfusion(right). ................... 178 4-31Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmassatthereconstruction levelafterthefullleptonandeventselectionsareappliedfor m H = 600GeV at8TeVfor4 (left),4e(center)and2e2 (right)events. ............ 179 4-32Instrumentaluncertaintiesin7TeVdatarelatedtodata/MCdifferencesinefciencies inreconstruction,identication,isolationand SIP 3 D asafunctionof m H ,for (topleft)4echannel,(topright)4 channel(bottomleft)2e2 channel(electron onlyuncertainties),(bottomright)2e2 channel(muononlyuncertainties). .. 183 4-33Instrumentaluncertaintiesin8TeVdatarelatedtodata/MCdifferencesinefciencies inreconstruction,identication,isolationand SIP 3 D asafunctionof m H ,for (topleft)4echannel,(topright)4 channel(bottomleft)2e2 channel(electron onlyuncertainties),(bottomright)2e2 channel(muononlyuncertainties). .. 184 4-34Comparisonoffour-leptonmasserrorscalculatedfromthetwoapproaches tocomputetherelativeper-eventerror D mass on8TeVHiggsMCsamplewith m H = 125GeVfor4e(topleft),4 (topmiddle),2e2 (topright),4 + ( (bottom left)and2e2 + ( (bottomright). .......................... 186 18

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4-35Four-leptonrelativemasserrordistributions D mass (points)andtsforsignal MonteCarlosampleat8TeVwith m H = 126GeVfor4 (left),4e(middle), and2e2 (right)events. ............................... 190 4-36Four-leptonrelativemasserrordistributions D mass (points)andtsfor qq ZZ (top)and gg ZZ MonteCarlosamplesat8TeVfor4 (left),4e(middle), and2e2 (right)events. ............................... 190 4-37InterpolationoftheparametersfortheLandau+Gaussianusedtodescribe D mass in 434 for4 channelat8TeV.Topleft: ld ,topright: # ld ,bottomleft: gs ,bottomright: # gs ................................ 191 4-38Four-lepton D mass distributionfrom8TeVdata(7TeVissimilar)controlregion forZ+Xbackgroundfor4 (left),4e(middle)and2e2 (right),withtssuperimposed. ............................................. 191 4-39Correlationbetweenthepredictedper-eventmasserrorfromtheleptonuncertainty andthemeasuredmasserror,throughtsto Z + (left)and Z e + e (right)in8TeVdataandsimulation. ........................ 192 4-40IllustrationofaHiggsproductionanddecay ab H Z 1 Z 2 4 with thetwoproductionangles ) and $ 1 shownintheHiggsrestframeandthree decayangles ) 1 ) 2 ,and $ showninthe Z ( ) restframes[ 4 ]. .......... 194 4-41 D bkg fora m H = 126GeVHiggs(topleft), q q ZZ (topright)inthelow massregion,and q q ZZ inthehighmassregion(bottom)withdataevents overlaid. ....................................... 198 4-42Distributionofreconstructedinvariantfourleptonmass.Blueis ZZ MC,green isfromdatadriven Z + X ,andredis m H = 126GeVHiggsMC. ........ 202 4-43Distributionofreconstructedinvariantfourleptonmasssplitbychannelfor7 TeVdataandMC.Blueis ZZ MC,greenisfromdatadriven Z + X ,andredis m H = 126GeVHiggsMC. ............................. 203 4-44Distributionofreconstructedinvariantfourleptonmasssplitbychannelfor8 TeVdataandMC.Blueis ZZ MC,greenisfromdatadriven Z + X ,andredis m H = 126GeVHiggsMC. ............................. 203 4-45Distributionofreconstructedinvariant Z 1 (left)and Z 2 (right)mass,aswellas theircorrelationforeventswith121.5 > m 4 > 130.5GeV(bottom).Blueis ZZ MC,greenisfromdatadriven Z + X ,andredis m H = 126GeVHiggsMC. 204 5-1Observedandexpected95%CLupperlimitontheratiooftheproductioncross sectiontotheSM-likeexpectation.7TeVand8TeVdatasamplesareused. 210 19

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5-2Signicanceofthelocaluctuationswithrespecttothestandardmodelexpectation asafunctionoftheHiggsbosonmassforanintegratedluminosityof5.1fb 1 at7TeVand19.7fb 1 at8TeVinthelowmassrange110-180GeVonthe leftandinthewholemassrange100-1000GeVontheright. .......... 211 5-3Twodimensionallikelihoodscanformass m H versussignalstrength = # /# SM forthe3Danalysis L 3 D ( m 4 D mass K D ) ...................... 212 5-41Dlikelihoodscanasafunctionofmassincludingstatisticalandsystematic uncertaintiesfor1D(left)analysis,2D(middle)and3Danalysis(right). .... 213 5-51Dlikelihoodscanasafunctionofmassforthedifferenttscenariosfor4 (left),4e(middle)and2e2 (right)nalstates. .................. 214 5-61Dlikelihoodscanasafunctionofmassforthedifferenttscenariosforthe combinationofallnalstates,7and8TeVdata. ................. 215 5-7BesttvaluefortheHiggsmassinthedifferentchannels(points)andforthe combinationofthethreechannels(line,withbarrepresentingthe1 # uncertainty) forthedifferenttcongurations:1D( L ( m 4 l ) )ontheleft,2D( L ( m 4 l D mass ) ) onthemiddle,3D( L ( m 4 l K D ), D mass )ontheright. ................ 215 5-8Signalstrengthversus m H neartheobservedexcess(left)andsignalstrength inthedi-jetand0/1jetcategories(right). ..................... 216 5-9Likelihoodcontoursonthesignalstrengthmodiersassociatedwithfermions( F ) andvectorbosons( V )shownat68%and95%CL. ............... 217 5-101DlikelihoodscanasafunctionofHiggsdecaywidthwiththe3Dlikelihood t. ........................................... 218 5-11Scanof % 2ln L in1D(left)asafunctionof f a 3 ,where f a 3 isthefractionofobserved 0 eventsinthedataset.ExpectationwithAsimovdatasetisalsoshownin the1Dprojection. .................................. 220 5-12Distributionof D bkg indataandMCexpectationsforthebackgroundandfora signalresonanceconsistentwithSMHiggsbosonat m H = 125.6GeV(left) andthe D dec bkg distributionfortheproductionindependentscenario(right). ... 223 5-13Distributionsof D J P witharequirement D bkg > 0.5.Distributionsindata(points witherrorbars)andexpectationsforbackgroundandsignalareshown. .... 227 5-14(Top)Distributionof q = % 2ln( L J P / L SM ) fortwosignaltypes( 0 + represented bytheyellowhistogramandalternative 0 hypothesisbythebluehistogram) for m H = 125.6GeV.(Bottom)Asummaryofthetwelvealternativehypotheses tested. ........................................ 228 20

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6-1Four-leptonmassdistributioninthe7TeV(left)and8TeV(right)GENMCfor Z 4 (toprow), Z 4 e (secondrow), Z 2 2 e (thirdrow),and Z 2 e 2 (lastrow)ttedwithaBreit-Wigner. ..................... 233 6-2Four-leptonmassdistributioninthe7TeV(left)and8TeV(right)GENMCfor Z 4 (toprow), Z 4 e (secondrow), Z 2 2 e (thirdrow),and Z 2 e 2 (lastrow)ttedwithaBreit-WignerconvolutedwithaCBwithoating ,and # ....................................... 234 6-31Dlikelihoodscansofthe Z masstswithHiggsconguration,nominalconguration, andrelaxedcongurationfromlefttoright(toprow).Correspondingmass distributionswithoverlaidts(bottomrow). .................... 235 6-4ProbabilityratioswhereprocessAis gg H 4 andprocessBis q q ZZ 4 (top)andprobabilityratioswhereprocessAis gg H 4 and processBis q q Z 4 (bottom)for4e(left),4 (middle),and2e2 (right). 237 6-5Templatesusedinthe Z 4 spin-parityanalysisforggH(top), Z 4 (middletop),qqZZdoublyresonantonly(middlebottom),andZ+Xcontrol regiondata(bottom).Fromlefttoright:4e,4 ,2e2 .............. 239 6-6Distributionofatest-statistic q = % 2ln ( L 0 + / L Z ) oftheZbosonhypothesis testedagainsttheSMHiggsbosonatat M Z hypothesis(left)." f a 3 "typemeasurement likelihoodscan(right). ................................ 240 6-7Kinematicvariablescomparison.Fromlefttoright:Top:MassZ1,MassZ2, MassZ1vsZ2.Bottom:Momentumofhighestmomentumlepton,pTof 4 system,cosineoftheanglebetweenZ2andthenearestlepton. ........ 240 B-1Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdf asafunctionof m H for m H < 400GeVat7TeV. ................. 246 B-2Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdf asafunctionof m H for m H < 400GeVat8TeV. ................. 247 B-3Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdf asafunctionof m H for m H # 400GeVat7TeV. ................. 248 B-4Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdf asafunctionof m H for m H # 400GeVat8TeV. .................. 249 B-5Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmassatthereconstruction levelafterthefullleptonandeventselectionsareapplied. ............ 251 B-6Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmassatthereconstruction levelafterthefullleptonandeventselectionsareapplied. ............ 252 21

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy OBSERVATIONOFAHIGGSBOSONINTHEHTOZZTO4LDECAYCHANNELAND USINGZTO4LDECAYSASACALIBRATIONTOOLINSTUDIESOFTHEHIGGS BOSONPROPERTIES By MatthewAlexanderSnowball May2014 Chair:PaulAvery Cochair:AndreyKorytov Major:Physics AsearchfortheHiggsbosoninthedecaychannelHtoZZto4leptonsisperformed usingdatafromproton-protoncollisionscorrespondingtoandintegratedluminosity of5.1inversefemtobarnsatacenter-of-massenergyof7TeVand19.7inverse femtobarnsatacenter-of-massenergyof8TeVdata.Anewbosonisobservedas anarrowresonancewithalocalsignicanceof6.8standarddeviations,ameasured massof125.6+/-0.4(stat.)+/-0.2(syst.)GeV,andatotalwidthlessthanorequalto 3.4GeVata95%condencelevel.Theproductioncrosssectionofthenewboson timesthebranchingfractiontofourleptonsismeasuredtobe0.93+0.26-0.23(stat.) +0.13-0.09(syst.)timesthatpredictedbythestandardmodel.Itsspin-parityproperties arefoundtobeconsistentwiththeexpectationsfortheStandardModelHiggsboson.In addition,measurementsoftheZto4leptonmassandwidtharepresented.Themass ofZbosondecayingto4leptonsisfoundtobe91.16+/-0.23GeVwhilethewidthis foundtobe2.98+0.54-0.50GeV.Spin-paritypropertiesoftheZbosonareshowntobe consistentwithexpectationfromtheStandardModel. 22

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CHAPTER1 THESTANDARDMODEL Particlephysicsisthestudyofthemostfundamentalconstituentsofmatterand forcesthroughwhichtheyinteract.Therearemanytheoriestodescribewhatwe knowabouttheseparticlesandforces,butthereisonethathaswithstoodmultiple high-precisiontestsovertime[ 5 ].TheStandardModelisacollaborativetheoryof thefundamentalworld.Ithasbeendevelopedovermostofthetwentiethcentury,but wasonlysemi-nalizedinthe1970s.TheStandardModeldescribesthefundamental particles, bosons and fermions ,aswellastheforcesthroughwhichtheycaninteract. Theseforcesareknownas weak,electromagnetic, and strong .Insection 1.1 ,these fundamentalparticlesandforceswillbedescribed.ThenalpieceoftheStandard Model,the Higgsboson ,wasonlyrecentlydiscoveredin2012bytheexperimentsatthe LargeHadronCollideratCERN.Section 4 willdescribethesearchfortheHiggsinthe H ZZ 4 decaychannel,aswellasthemeasurementsofthenewlydiscovered boson'sproperties.WhiletheStandardModelisanincrediblysuccessfultheory,itfails tofullydescribetheknownuniverse.Todaythesearchcontinuesforphysicsthatgo beyondtheStandardModelasdescribedin 1.3 1.1FundamentalParticlesandForces 1.1.1FundamentalParticles Therearetwotypesoffundamentalparticles, fermions and bosons .Fermionscarry half-integerspin( 1 2 3 2 ,etc.)whilebosonscarryintegerspin(0,1,etc.).Matterismade upoffermions,whichcanbefurthersplitintotwotypes: quarks and leptons .Quarks andleptonsaredividedintothree"generations"asshowninTable 1-1 .Eachgeneration ofquarkconsistsofan"up"typewithcharge + 2 3 anda"down"typewithcharge % 1 3 Quarksalsopossessacolorchargered,green,orblue.Thetypesofquarksinorder ofincreasingmassare u d s c b t 23

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QuarksmayinteractviaallthreefundamentalforcesintheStandardModel, weak electromagnetic ,or strong ,butareneverfoundisolatedinnatureduetoreasons explainedinsection 1.1.2 .AsdescribedbyQuantumChromodynamics(QCD),the theoryofthestrongforce,quarkscanjoininpairsas mesons ( q 1 q 2 )ortripletsas baryons ( q 1 q 2 q 3 )tomakecolor-neutral hadrons .Themostwidelyrecognizedhadrons aretheprotonandneutronwhichareformedwith uud and udd quarksrespectively. Table1-1. First,second,andthirdgenerationsofquarksandleptons.Alsolistedare chargeandinteractiontypes. Gen.1Gen.2Gen.3Charge Interactions Quarks u c t + 2 3 strong,electromagnetic,weak d s b % 1 3 Leptons e -1 electromagnetic,weak e # 0 weak Table1-2. Forcecarriersandtheircouplingconstantsforthethreeforcesofthe StandardModel. Force Weak ElectromagneticStrong ForceCarrier W ,Z Photon( # )Gluon(g) Mass(GeV) 80.4,91.2GeV 0 0 CouplingConstant G F & 1.2 10 5 GeV 2 $ = 1 137 $ s & 0.1 InteractionRange 10 16 cm ( 10 13 cm Leptonsmayinteractviaonlythe weak or electromagnetic forcessincetheycarry nocolorcharge.Infact,quarksaretheonlyparticlestocarryacolorchargeotherthan gluons.Eachgenerationofleptonsconsistsofachargedleptonandanassociated neutralneutrinoofthesameavorasthechargedlepton.Thelightestchargedlepton isthe electron withmass0.511MeV,followedbythemuonwithmass105.7MeV,and nallythetauwithmass1.78GeV.Here 1 aneVrepresentstheamountofenergy gained(orlost)byasingleelectronmovingacrossanelectricpotentialdifferenceofone volt.Eachchargedleptoncanhaveeitherapositiveornegativeintegerchargeof 1 1 1eV = 1.6 10 19 J,1MeV = 1 10 6 eV,1GeV = 1 9 eV 24

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whileeachneutrinoisneutralorhas0charge.Inadditiontocharge,allleptonscarrya leptonavorquantumnumber:electron,muonortau,withanti-particleshavingopposite unitsofchargeandleptonavornumber. !" !"#$%&' # #$%&' ("!)$*&' ( ()" ()("!$*&'$ *)+, #"+$%&' #$ -(&%,./ (,#$%&' #$ 0 0)(()' #"!$*&' #$ -!"!$&' % # -,"()$%&' % $ -(.".$%&'$ % / /1/#(&), ,".(($%&' #& # '!), (,.")$%&' #& $ (%! (")))$*&' #& % "$)(), %' % & .1!), % & % 2 /("!$*&' % & +,"#$*&' & ( & '%--3 -"4,3 #$%&./3 5!%&67/"(),8%!./9:)-),; ;;;;; ,%'/3 /1/#(&), ,/!(&4,) '!), ,/!(&4,) (%! ,/!(&4,) 290)-), <90)-), =$&//98/,/&%(4),-9 )>9?%((/&9@A/&'4),-B < # % ( Figure1-1. AllofthematterparticlesandforcecarriersoftheStandardModel Bosonsarethecarriersofthefundamentalforcesasdescribedinsection 1.1.2 .Thebestknownforce-carrieristhemassless,neutral,spin-1photonwhichis responsibleformediatingtheelectromagneticforcebetweenchargedparticles.There arethreeweakforcecarriersduetoreasonsdescribedinsection 1.2 ,bothwithspin 1.Theyarethe W andZbosonswithcharge 1 and 0 respectively.Finally,the massless,neutral,spin-1gluonisthestrongforcecarrier.However,unliketheother forcecarriers,gluonscarrybothacolorandanti-colorcharge,thustheycaninteractwith othergluons.Furtherdiscussiononthisisavailableinsection 1.1.2 1.1.2FundamentalForces Eachofthethreefundamentalforcescanbedescribedbyadedicatedtheory suchasQuantumElectrodynamics(QED),QuantumChromodynamics(QCD),and ElectroweakTheory(EWK)whichisthecombinationofweakandQED.QEDisthe 25

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mathematicaldescriptionofhowchargedparticlesinteract,viaexchangeofphotons. ThesimplestexampleofQEDisshowninFigure 1-2 .It'sfoundersreadlikeawho's whooftwentiethcenturyphysicstheory,withthelikesofFeynman,Schwinger,Dyson, andothersattheforefrontofthetheory.FeynmancalledQED(forwhichhewonthe NobelPrizein1965)the"jewelofphysics"dueitsabilitytopredictquantitiessuchasthe electronmagneticmomenttoextremelyhighprecision.Intheeldtheoryrepresentation oftheStandardModel,theelectromagneticforceisrepresentedbythe U ( 1 ) symmetry group. Figure1-2. Feynmandiagramofelectronscatteringviaphotonexchange. ElectroweakTheoryistheunicationoftheelectromagneticandweakforces. Weakinteractionsarecategorizedbyshortrange,pointlikeinteractions,oftenwith avorchangingdecaysortheexchangeofa W or Z boson.Boththeweakand electromagneticforceinteractionsaregovernedbyprobabilityamplitudesthatinclude termsoftheform g 4 ( q 2 % | m | 2 ) 2 (11) wheremisthemassofthemediatingboson,qisthemomentumtransfer,andg istheforcecouplingconstant.BothQEDandweakinteractionsarevectoralinnature, suggestingthattheycouldbeunied.Duetothepointlikenatureoftheinteractions,the weakbosonsmustbeheavyandinturnledtothepredictionofthemassesofthe W 26

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and Z bosons.Subsequently,the W and Z bosonswerediscoveredatCERNin1983 bytheUA1andUA2collaborations[ 6 7 8 9 ]. Ineldtheoryrepresentation,thegaugegroupoftheStandardModelis SU ( 3 ) C ) SU ( 2 ) L ) U ( 1 ) Y .The U ( 1 ) Y symmetrygroupisrelatedtothecouplingsofQEDtheory, the SU ( 2 ) L symmetrygroupisrelatedtothecouplingsoftheweaktheory,whilethe SU ( 3 ) C symmetrygroupisrelatedtothegaugecouplingsinQCD.Glashow,Salam, andWeinbergusedthisrepresentationtounitetheelectromagneticandweakforcesin electroweaktheorybyrestructuringtheforceswithinthe SU ( 2 ) L U ( 1 ) Y basis[ 10 ]for whichtheywontheNobelPrizein1979.Fromthisbasis,theywereabletoderivethe eldstodescribethe W Z ,and ( ( A )bosonsintermsoftheoriginalbasiselds A i and B asshowninequations 12 13 14 .Thesetermscanthenbeenteredintothe StandardModelLagrangiantoderivetheunicationofQEDandtheweakforce. W = 1 2 A 1 iA 2 # M W = 1 2 gv (12) Z = 1 g 2 + g # 2 gA 3 % g # B # M Z = 1 2 v $ g 2 + g # 2 (13) A $ = 1 g 2 + g # 2 g # A 3 + gB # M A =0 (14) ThestrongforceismediatedbygluonsandgovernedbyQuantumChromodynamics. Asitsnameimplies,thestrongforceismuchstrongerthantheelectromagnetic andweakforces,althoughitonlyactsonaveryshortrange & 10 15 m # whichis approximatelythesizeofthenucleusofanatom.Thismakessense,becausethestrong forceiswhatholdsnucleitogether.QCDpossessesapropertyknownasAsymptotic Freedomwhichmeansthelargerthedistancebetweentwostronglyinteracting 27

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particles,thestrongertheforcefeltbetweenthem.Thispropertykeepstheprotons andneutronsthatmakeupmatter,fromsplittingapart.TherelativeweaknessofQCD atsmalldistancesalsoallowsforQCDtobetreatedperturbativelyinthemathematical formulationsthatcalculateimportantphysicalquantitiessuchascrosssectionsof processes.Thishasanimportantimplicationthatnoquarksmayexistaloneinnature. Whenaquarkgainssufcientenergytobesplitfromitspartner,thenquark-antiquark pairsarecreatedfromthequarkseatopartnerwiththeminaprocesscalled hadronization .Thishasimportantramicationsexperimentallyatahadroncolliderthatwillbe furtherdiscussedinChapter 2 .IntheeldtheoryrepresentationoftheStandardModel, stronginteractionsarerepresentedbythe SU ( 3 ) C symmetrygroup.Here, C represents QCDcolor,whichmustbeconservedinallstronginteractions. 1.2TheOnceElusiveHiggs TheStandardModelisaremarkabletheoreticalachievementthatdescribesa largenumberofprocessesremarkablywell.Butuntil2012,therewasstilloneimportant piecemissingexperimentalevidence.In1964,threeindependentgroupsoftheorists publishedpapersdescribingwhatwouldbecomeknownastheEnglert-Brout-Higgs -Guralnik-Hagen-Kibblemechanism,ortheHiggsmechanismforshort.Inthesepapers [ 11 12 13 ],inordertoexplainthemassesoftheelectroweakbosons,amechanism wasproposedthroughwhichaeldisintroducedtotheStandardModelwhichhas non-zerovacuumexpectationvalue 1-4 .Thisnon-zerovacuumexpectationvalue resultsinthebreakingofelectroweaksymmetry,andconsequentlythecreationofa newscalareldanditsmassivescalarbosonwhichwouldbecomeknownastheHiggs boson.TheonlyfreeparameterintheHiggsmechanismisthemassoftheHiggs boson.Thismeansthatexperimentallydidn'tknowexactlywheretolook(although theStandardModeldoesprovidesomecluesonwheretheHiggscouldnotbe 1-3 ). Earlylimitsonthemassbegantobepublishedinthe1970swiththerstbeing18.3 28

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MeV.Astechnologyadvanced,morepowerfulacceleratorscameonlineandthesearch continued. TheexperimentsatLEP,theLargeElectronPositroncollideratCERNmounted therstdedicatedsearches,culminatingintheirexclusionofaStandardModelHiggs withmassbelow114.4GeV[ 14 ].Duringroughlythesametimeframe,theTevatron, aproton-anti-protonmachinewasalsogatheringdataatFermilabintheUSA.The TevatronwouldrununtilthestartoftheLHC,andonlythenwouldtheyseeevenahint ofaHiggsboson[ 15 ].Inacrueltwistoffate,likenedtoacosmicprank,bothTevatron andLEPwouldfalljustshyofbeingabletoreachthemassneededtoclaimobservation theHiggsboson. [GeV] t m 140150160170180190200 [GeV] W M 80.15 80.2 80.25 80.3 80.35 80.4 80.45 80.5 80.55 =117.5 GeV H M =127.5 GeV H M =600 GeV H M =1000 GeV H M WA top band for m 1 WA W band for M 1 68%, 95%, 99% CL fit contours < 1 TeV H M top & m W excl. M 68%, 95%, 99% CL fit contours [117.5, 127.5] GeV H M t & m W excl. M =117.5 GeV H M =127.5 GeV H M =600 GeV H M =1000 GeV H M G fitter SM May 12 Figure1-3. PrecisionmeasurementsofthethetopquarkandWbosonareusedto predictthepossiblemassofaHiggsboson.[ 1 ] Ultimately,in2000adecisionhadtobemadewhethertocontinuerunningLEP ortoshutdownandbegininstallationoftheLargeHadronCollider(LHC).Sinceno compellingevidencefortheexistenceofaHiggsinthereachablemassrangeofthe LEPmachine,itwasdecidedthatitwastimetomoveontotheLHC.Itwasover9years laterbeforecollisionswouldbeseenintheformerLEPtunnel.In2010thesearchfor theHiggsattheLHCbegan.ItwouldbeonlytwoshortyearslateronJuly4,2012that 29

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adiscoverywouldbeannouncedastheworldwatched.ThediscoveryofaHiggs-like bosonnear125GeVwaspublishedbybothgeneralpurposeexperimentsattheLHC, ATLASandCMS,shortlythereafter[ 16 ],[ 17 ].Aswillbeshowninthisthesis,both experimentscollecteddatathroughtheendof2012allowingforstudiesoftheproperties ofthenewlydiscoveredboson.Withthesemeasurements,ithasbeendeterminedthat thisbosonisverylikelytheStandardModelHiggsbosonaspredictedbyP.Higgset.al. ThediscoveryoftheStandardModelHiggsbosonisthenalpuzzlepiecetoatheory whichhasaccuratelydescribedmostoftheUniverseasweknowittoday,theStandard Model. 1.2.1TheHiggsMechanism UntiltheHiggsmechanismwasproposed,therewasnomathematicalreasonfor theweakbosonstohavemass.The W and Z bosons,however,arenotmassless asweknowfromexperiment.Also,theunicationoftheelectromagneticandweak interactionsintoelectroweaktheoryrequiresanexplanationofwhythe W and Z bosonsshouldbemassive,whilethephotonremainsmassless.Infact,inthe electroweakLagrangian,amasstermforthegaugebosonswouldviolategauge invariancewhichwouldmakethetheorynon-renormalizeable.Thesimplestsolutionto thisproblemistoaddanexternalscalareldcalledtheHiggsField[ 18 ].Thisisdone viaintroductionofadoubletofcomplexscalareldsintotheelectroweakLagrangianas showninequations 15 and 16 = % & + 0 ( ) = 1 + 2 % & 1 + i 2 3 + i 4 ( ) (15) L = ( D )   ( D ) + V   # (16) 30

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where D = + % igt a W a + i 2 g # YB (17) TheLagrangianinequation 16 isnowinvariantunder SU ( 2 ) L U ( 1 ) transformations. Thepotentialcannowbewrittenasinequation 18 V   # = % 2   %   # 2 (18) Choosing 2 > 0 and > 0 leadstothefamous"Mexicanhat"potentialasshown inFigure 1-4 whichhasaminimumfor v 2 2 .Theminimumofthepotentialisnotfoundfor asinglevalueof andthechoiceofthegroundstate   0 # isarbitrary.Thismeans thechosencoordinateisnotinvariantunderrotationsinthe   0 # plane.Thisis commonlyreferredtoas SpontaneousSymmetryBreaking .Byxingthegroundstateto beonthe 0 axis,thevacuumexpectationvalueofthe eldisnow Figure1-4. Pictureillustratingthenon-zerovacuumexpectationvalueoftheHiggseld. = 1 + 2 % & 0 v ( ) v 2 = % 2 (19) Andbyrewritingthe eldinagenericgaugeintermsofitsvacuumexpectation value, becomes 31

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* = 1 + 2 e i v % a t a % & 0 H + v ( ) = 1 + 2 % & 0 4 ( ) a =1,2,3. (110) wheretherearenowfourmasslessscalar eldsknownas Goldstoneelds [ 19 20 ].Therearefournewdegreesoffreedom.Threeofthesedegreesareusedupby givingmasstothe W + W ,and Z bosonswhichcannowhavemasstermsincluded intotheirLagrangianswhicharewritten(neglectinghigherorderterms)asshownin equations 111 114 .Thenaldegreeoffreedombecomesthemassive,scalarHiggs bosonwithmass m H = + & 2 v where v = 1 $ 2 G F .Since isunknowninthetheory,the massoftheHiggsistheonlyunknownparameter.Further,thefermionscanbemadeto coupletotheHiggseld,allowingthemtoacquiremassaswellsincetheminimumfor theHiggseldisstillinvariantunderthe U ( 1 ) symmetrygroup. L H = 1 2 + a H + a H + 2 H 2 (111) L HW = 1 4 v 2 g 2 W a W   a + 1 2 vg 2 HW a W   a = m 2 W W a W   a + g HW HW a W   a (112) L HZ = 1 8 v 2 g 2 + g # 2 # Z Z + 1 4 g 2 + g # 2 # HZ Z = 1 2 m 2 Z Z Z + 1 2 g HZ HZ Z (113) where L = L H + L HW + L HZ (114) 32

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1.2.2ProductionanddecayoftheHiggsboson TherearevewaystoproduceaStandardModelHiggsboson.Thedominant way,whichaccountsforabout10timesmore125GeVHiggsthantheotherproduction mechanismsattheLHC,isgluongluonfusionthroughatopquarkloop(ggH).Gluon gluonfusionisfollowedbyvectorbosonfusion(VBF)thenassociatedproduction withavectorboson(WH,ZH)andnallyassociatedproductionwithapairoftop quarks(ttH).Feynmandiagramsfortheseproductionmechanismsareshownin Figure 1-5 .CrosssectionsfortheseprocessesattheLHCareshowninFigure 1-6 Allcrosssectionsareatthenext-to-nextto-leadinglogarithmic(NNLL)orderinQCD andnext-to-leadingorder(NLO)inEWKinthecomplexpolescheme.HereNNLL andNLOrefertotheaccuracyoftheFieldTheorycalculation.Eachprocesscanbe representedbyanendlessnumberofFeynmandiagrams,eachwithanincreasing numberofvertices.TheFeynmandiagramwiththelowestnumberofpossiblevertices isreferredtoasleadingorder(LO)forthatprocess.Asverticesareadded,suchas aradiatedgluonorloop,ordersareincreasedbecomingnext-to-leadingorder(NLO), next-to-next-to-leadingorder(NNLO),andsoon.Forexample,processescalculated atNLOrefertocalculationsusingdiagramsuptooneaddedloopinreferencetoLO. KnowledgeofhowaHiggsisproducedandhowitdecaysgivenacertainmasscan helpexperimentalistsobservetheHiggssignalaboveStandardModelbackgrounds,or processeswhicharisefromtheStandardModelwhichhavethesamenalstateasthe givenHiggsdecaychannel. 1.2.2.1Gluongluonfusion ThemajorityofHiggsbosonsproducedattheLHCarebygluongluonfusiondue tothehighluminosityofgluonsat7and8TeV.Infact,thedecidingfactorinincreasing thecenterofmassenergyfrom7to8TeVin2012wasbecauseofthegaininluminosity benettingtheHiggssearches,morethan25%increaseinproductionforaHiggsmass 33

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Figure1-5. FeynmandiagramsforggH(topleft),VBF(topright),VH(bottomright),and ttH(bottomleft)productionmechanisms. of125GeV.At125.6GeV,theggHcrosssectionforaStandardModelHiggsatcenter ofmassenergyof8TeVisapproximately19 pb withabout15%uncertainty. 1.2.2.2Vectorbosonfusion VectorbosonfusionisthesecondleadingHiggsproductionmechanismatthe LHC.Formostofthemassrange,itisaboutoneorderofmagnitudesmallerthanggH, comingcomparableonlyaroundaHiggsmassof1TeV.Inthisproductionmechanism, aHiggsiscreatedbythefusionoftwo W or Z bosonsthathavebeenradiatedfroma pairofquarks.Thisleavesaveryclearexperimentalsignaturewithtwohighenergyjets intheforwardregionofthedetector.Usingthissignature,experimentalistscanenhance thesignaltobackgroundratioofthisproductionmechanism,despiteitsrelativelylow crosssection.At125.6GeV,theVBFcrosssectionforaStandardModelHiggsat centerofmassenergyof8TeVisabout1.6 pb withabout3%uncertainty. 1.2.2.3Associatedproduction AssociatedproductionisdenedbyaHiggsproducedinassociationwitheither a W boson,a Z boson,ora t t pair.Thecrosssectionfortheassociatedproduction isseveralordersofmagnitudesmallerthanggHformostofthemassrange,and isconsiderednegligibleaboveaHiggsmassof400GeV.The W Z ,and t t pair 34

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Figure1-6. LHCHiggsCrossSectionsat7TeV(a)and8TeV(b)forthedifferent productionmodes.Theoreticaluncertaintiesareshownbythecolored bands. provideawaytoseparatethistypeofmechanismfrombackground,allowingittobe useddespiteitsverylowcrosssection.Forsometypesofsearches,suchasaHiggs decayingtoa b b pair(see 1.2.3 ),thisisthemainproductionmechanismasthe W and Z bosonprovideasignaturethatallowsamethodforndingeventswithHiggsdecaying tobquarksinoverwhelmingQCDbackground.At125.6GeV,theWH,ZH,andttHcross 35

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sectionsforaStandardModelHiggsatcenterofmassenergyof8TeVareabout0.7, 0.4,and0.1 pb withabout2,3,and10%uncertaintyrespectively. Table1-3. CrosssectionsinpbforassortedHiggsmassesandproductionmechanisms attheLHC. ggH VBF WH ZH ttH m H (GeV)7TeV8TeV7TeV8TeV7TeV8TeV7TeV8TeV7TeV8TeV 10023.629.71.62.01.21.50.660.810.160.24 12515.119.31.21.60.60.70.340.420.090.13 180 6.99.80.81.00.150.200.100.120.030.04 300 2.63.60.340.440.020.030.010.020.0050.008 10000.020.030.010.021.2.3DecayoftheHiggs BecausetheHiggsisarelativelyheavyelectroweakparticle,itwantstodecays quickly.WhatitdecaystodependsstronglyonitsmassasshowninFigure 1-7 .The Higgstypicallywilldecaytotheheaviestparticlesavailable.Inthelowmassregion,its decaysaredominatedbyfermions,namelybquarks,astheyaretheheaviestfermion inthatmassrange.AstheHiggsbecomesheavier,(above m H = 150GeV),itsdecays becomedominatedby W and Z pairs,andabovethemassoftwotops,decaysto t t areallowed.Theexperimentaldiscoverythenstronglydependsontheabilityofthe experimentaliststodevelopsearchmethodsforthedominatedecaymodesindifferent massregionsthatallowaHiggssignaltobeseenwhilerejectingasmuchbackground aspossibleinthegivensearchchannel.Abreakdownofthemassrangesusedinthe Higgssearchareexplainedbelow. 1.2.3.1LowmassHiggs Inthelowmassregion,Higgsdecaysto b b pairsalmost80%ofthetime.However, theQCDbackgroundinthischannelismanyordersofmagnitudelargerthanHiggs.B quarksarealsodifculttoreconstructinadetector.Whentheydecayinthedetector, theyfragmentinto jets ofmanyhadrons.Thesejetsaredifculttoperfectlyreconstruct. Becauseofthis,itisnecessarytoexploitotherchannelsinthisregionthatwillallowfor abetterchanceatdiscovery. 36

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[GeV] H M 80100120140160180200 Higgs BR + Total Uncert [%] -4 10 -3 10 -2 10 -1 10 1 LHC HIGGS XS WG 2013 b b !! c c gg "" Z WW ZZ [GeV] H M 90 200 300 400 500 1000 Higgs BR + Total Uncert [%] -4 10 -3 10 -2 10 -1 10 1 LHC HIGGS XS WG 2013 b b !! c c t t gg "" Z WW ZZ Figure1-7. Higgsbranchingratioswithuncertaintyforlowmass(left)andupto1TeV (right). OneofthesechannelsistheHiggsdecayingtotwophotons( H (( ).Although H (( hasabranchingratioroughlythreeordersofmagnitudebelow H b b ,it isoneofthemostsensitivechannelsduetotheexcellentmassresolutionfromtwo wellreconstructed,highenergyphotons.Itisalsooneofthecleanestchannelswith backgroundscomingonlyfromelectronconversionsinthedetectormaterialaswell aselectroweak q q (( production. H (( alsoallowsforincludingexperimental methodsthatexploitVBFproduction,makingitoneofthebesthopestondalowmass Higgsintheregionbelow120GeV. 1.2.3.2IntermediatemassHiggs AstheHiggsmassclimbsabove120GeV,thedecaysto WW and ZZ become available.Becausethedecaystotwo Z 'swouldrequireatleastoneZtobefarfrom m Z 0 ,or offshell ,inthisregion,thedecaysto WW arepreferred,especiallybetween 150and170GeVwhenthetwo W 'sareon-shell.However,experimentallythe WW channelsareimpossibletofullyreconstructduetothepresenceoftwoneutrinos ( H WW "-"),whichescapedetection,orthepresenceoftwojetsanda neutrino( H WW "jj ).Thiscausesawidemassdistributiononcereconstructed which,alongwiththerelativelyhighbackground,makesdiscoveryinthischannelvery challenging. 37

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ThepreferredchannelfordiscoveryintheintermediatemasssearchistheHiggs decayingtotwo Z bosonswhichtheneachdecaytotwochargedleptons( H ZZ 4 )foratotaloffourchargedleptonsinthenalstate.Thischannelisknownasthe "GoldenChannel"becauseitisthecleanestchannelduetothepresenceoffourhigh momentum,wellreconstructedleptons,andrelativelylowbackgroundwhicharisesonly from q q ZZ and gg ZZ productionandexperimentalbackgroundswhichare minimal.Sodespiteitslowbranchingratiointhisregion,the H ZZ 4 providesa channelwithahighsignaltobackgroundratioandtheabilitytoreconstructHiggsmass veryprecisely.Additionally,ifaHiggswasdiscoveredinthismassrange, H ZZ 4 providesanexcellentplatformformeasurementofthespin-paritypropertiesofthe Higgs. [GeV] H M 100150200250 BR [pb] -4 10 -3 10 -2 10 -1 10 1 10 LHC HIGGS XS WG 2011 SM = 7TeV s l = e, # $ $ e $ = $ q = udscb b b $ l % WH b b l + l % ZH # + # % VBF H # + # % H & & q q $ l % WW $ l $ + l % WW q q l + l % ZZ $ $ l + l % ZZ l + l l + l % ZZ [GeV] H M 100150200250 BR [pb] -4 10 -3 10 -2 10 -1 10 1 10 LHC HIGGS XS WG 2012 = 8TeV s l = e, # $ $ e $ = $ q = udscb b b $ l % WH b b l + l % ZH b ttb % ttH # + # % VBF H # + # & & q q $ l % WW $ l $ + l % WW q q l + l % ZZ $ $ l + l % ZZ l + l l + l % ZZ Figure1-8. Higgscrosssectiontimesbranchingratios7TeV(left)and8TeV(right). 1.2.3.3HighmassHiggs Above180GeV,themostviablechannelfordiscoveryisstillthe H ZZ channels. AsHiggsbecomesheavier,thewidthincreasesasdiscussedinsection 1.2.4 ,making detectorresolutionlessimportant.Therefore,channelssuchas H ZZ ""-, 38

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H ZZ "".. ,and H ZZ "" q q canbeusedtoincreasethechancesfor discoveryorexclusionofaStandardModelHiggs. 1.2.4HiggsWidth ThetotalwidthoftheHiggs( % H ),whichisasumoveralldecaychannels,varies greatlywithmassasshowninFigure 1-9 .Below m H = 190GeV,ameasurementofthe intrinsicwidthoftheHiggsresonanceisnotpossiblesincethewidthislessthan1GeV whichisthelimitofexperimentalresolutionoftheLHCexperiments.Above m H = 190 GeV,the % H isdominatedbythepartialwidthof H WW ( % WW )and H ZZ ( % ZZ ) andincreasesrapidlytobecomeabout100GeVfora m H = 500GeV. [GeV] H M 100 200 300 1000 [GeV] H -2 10 -1 10 1 10 2 10 3 10 LHC HIGGS XS WG 2010 500 Figure1-9. Higgstotalwidthasafunctionofmass. Bysummingoverthevectorbosonpartialwidths,thetotalwidthinthehighmass regioncanbeapproximatedas % H & % ( H VV ) = 3 32 / m 3 H v 2 (115) 39

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Thisleadsto % H & m H at m H & 1.4TeV.When % H islargerthan1TeV,theoretical problemsarisethatsuggestthattheHiggscannolongerbeconsideredaparticle.In particular,unitarityisviolatedbytheStandardModelpredictions.Thissuggestsalimitof 1TeVforthemassoftheHiggs.ThereforetheHiggsmustbeobservedbeforetheTeV scaleorelsenewphysicsmustbefound. 1.2.5TheoreticalConstraintsonHiggsMass Accordingtoequation 116 ,theHiggsmassisonlyvalidiftheradiativecorrections tothemassremainnite.Theapproximateexpressionforthesizeoftheradiative correctionsisshowninequation 117 .Thereforetondatheoreticalupperbound,itis requiredthat ,thequarticcouplingoftheHiggspotential,remainpositive,atleastupto themaximumenergythattheStandardModelremainsvalid, .Tondthelowerbound, itismerelyrequiredthat staypositiveupto .Figure 1-10 showstheseboundsversus .Sincethetruevalueof isunknown,experimentalistsmustsearchoveralargemass range,uptoatleast700GeV.However,if isoftheorderofthePlanckscale(10 19 GeV),thenthemassoftheHiggsisconstrainedtobebetween130and190GeV.Higgs isjustthesimplestmechanismtoexplainEWKsymmetrybreaking.ShouldtheHiggs notbediscoveredbelow700GeV,thenamorecomplicatedmechanismisneeded. 1.3BeyondtheStandardModel TheStandardModelisatestamenttomoderntheoryandexperimentthathas accuratelypredictedtheexistenceofdozensofparticles,howtheseparticlesinteract, aswellasothereffects.Butitis,atbest,anincompletetheoryoftheuniverse.Someof theseshortcomingsarediscussedbelow. 1.3.1ThreeGenerations Theexistenceof3generationsofquarksandleptonshasbeentestedrepeatedly overthepasthalf-century,withthelatesttestcomingfromtheHiggssearchesatthe LHC.Ifafourthgenerationexisted,themassofthefourthgenerationparticleswouldbe muchheavierthanthoseinthethirdgeneration.Thiswouldresultinanenhancement 40

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Figure1-10. Higgsmassboundsasafunctionof [ 2 ]. totheStandardModelHiggscrosssectionbynearlyanorderofmagnitudeforreasons discussedinsection 1.2.3 .ResultsinthesearchforaHiggsinthecaseofafourth generationhaveexcludedthefourthgenerationwith95%CLfortheentireStandard ModelHiggsmassrange[ 21 ].DirectsearchesattheLHChavealsoprovenfruitless [ 22 ],[ 23 ].AndsoitremainsthatintheStandardModel,thereisnophysicalreasonfor onlythreegenerationstoexist.Additionally,theStandardModelcannotexplainwhy thesethreegenerationsofquarksandleptonshavethemassestheydo. 1.3.2HierarchyProblem ThePlanckscale( M P & 10 19 GeV)isthepointwhereeldtheorybreaksdowndue totheexistenceofquantumgravity.ThediscrepancybetweenthemassofthePlanck scaleandthemassoftheHiggsisknownasthe"HierarchyProblem".Ifonewasto writeanexpressionfromtheStandardModelLagrangianforthemassoftheHiggs,it wouldlooklike m 2 H = m 0 2 H + # m 2 H (116) 41

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where m 0 H isthemassparameterpresentintheStandardModelLagrangian,and # m 2 H isthequantumradiativecorrectionstothemasswhichareexpectedtobelarge. Thesecorrectionscanbeapproximatedas # m 2 H & 2 16 / 2 2 (117) where isthedimensionlessYukawacouplingconstant,and istheenergyat whichtheStandardModelisnolongervalid,orabout1TeV.Thereforeitisexpectedthat massoftheHiggsbeatleastafewhundredGeV. ThisproblemcanbesolvedbyatheoryknownasSupersymmetry(SUSY).In SUSY,allbosonsandfermionshavesuperpartnersthataremuchheavierthantheir StandardModelpartner.ThesesuperpartnersmustbemuchheavierthanStandard Modelparticles,otherwisetheywouldhavebeenobservedalready.Directandindirect searchesforSUSYareongoingattheLHCinaracetoplacethelatestlimitsonthe massofgluinos[ 24 ],[ 25 ].Sofar,therehasbeennoexperimentalevidenceforthe existenceofSUSY. 1.3.3Matter Oneofthegreatestmysteriesintheuniverseiswhytheuniverseiscomposedof mostlymatterandnotanti-matter.Itisthoughtthatthetwoexistedinequalquantities aftertheBig-Bang,however,todayweseeonlymatter.Suchalargeimbalancecannot beexplainedbytheStandardModel. Fromcosmology,weknowthatthereexistslargequantitiesofdarkmatter,with someestimatesshowingupto23%oftheknownuniverse.TheStandardModelagain hasnoanswerfortheexistenceofdarkmatterorwhythereissomuchofit. 1.3.4GrandUnicationandBeyond Justastheelectromagneticandweakforcesuniteatacertainenergy,itistheorized thatathighenoughenergies,alltheforces,includinggravitywouldunite.Thissuggests 42

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thattheStandardModelisitselfonlyapieceofalargeruniedtheoryandtheforceswe seetodayarejustdifferentmanifestationsofthesameforce.Thisisgenerallyreferred toasGrandUnicationTheory(GUT).ItisclearthattheStandardModelcannotfully explaintheknownuniverse,andthereforethesearchforphysicsbeyondthosepredicted bytheStandardModelcontinueinthehopethat,shouldtheybefound,theywillprovide someclueastowhethertherecanbeatheoryofeverything. 43

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CHAPTER2 EXPERIMENT 2.1TheLargeHadronCollider TheLargeHadronCollider(LHC)isaproton-protoncolliderandcurrentlythe world'smostpowerfulparticleacceleratoroperatedbytheEuropeanOrganizationfor NuclearResearch(CERN).Itresidesina27km(17mi)circumferencetunnelbetween 50-175munderthesurfaceontheborderofSwitzerlandandFrancenearthecityof Geneva.ThetunnelistheformerhomeoftheLargeElectronPositroncollider(LEP) whichoperatedfrom1989till2000.ThedecisiontodecommissionLEPandbegin installationoftheLHCwasprimarilybasedonthesearchfortheStandardModelHiggs andbeyondStandardModelphysicssuchasSUSY.AsLEPwasaleptoncollider,it wasnotabletoreachashighcenterofmassenergiesasahadroncollidersuchasthe LHC.Therefore,inordertoadvancetheHiggssearchtohigherenergiessinceitwasnot observedatLEPorTevatron,itwasnecessarytodismantleLEPinfavoroftheLHCin 2000. InstallationoftheLHCwascompletedin2008,withrstbeamsseenonSeptember 10,2008.Ninedayslater,anelectricalfaultinabout100superconductingmagnet connectionscausedaquench,orimmediatelossofsuperconduction.Thiscausedan explosivelossofsixtonsofliquidheliumwhichcauseddamagetoover50magnets andtheirmounts.Theimplicationsofthisincidentwerewidespread,causingdelays ofoneyearaswellasthedecisiontoruntheLHCatlowerenergiesthanexpected.It wasn'tuntilNovember19,2009thatbeamswouldbecirculatedagainintheLHC,this timewithoutincident.In2010,collisionsbeganat900GeVandeventuallyincreasedto 7TeVcenterofmassenergy.Collisionscontinuedat7TeVthrough2011andinorder toimprovetheprospectsfortheHiggssearch,thedecisionwasmadetoincreasethe centerofmassenergyto8TeVin2012.Atbeginningof2013,theLHCwasshutdown foraperiodofapproximatelytwoyearsforlongshutdown1(LS1)inordertoupgrade 44

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partsonboththeLHCmachineaswellasallthedetectors.Beamsandphysicsare expectedtoresumein2015,atcenter-of-massenergyofapproximately13TeV. Figure2-1. LHCacceleratorcomplex. 2.1.1DesignandOperationalParameters TheLHCwasdesignedtoreach 14TeV centerofmassenergy( + s )andluminosities of 10 34 cm 2 s 1 [ 26 ],[ 27 ].Themaximum + s isconstrainedbythestrengthofthe magnetsthatguidethechargedparticlesaroundtheringandcircumferenceofthe ring.Thereareapproximately1600NbTisuperconductingmagnetsaroundtheLHC. 1232ofthesearedipolemagnetswhichguidethehadronsaroundthering,while396 arequadrapolemagnetsusedto"squeeze"thebunchesofprotonsclosertogetherto increasethechancesofacollision.Allofthesemagnetsarekeptatatemperatureof about 1.9 K ( % 271.25 % C )byatotalof120tonsofliquidhelium.Inthisstate,themagnets aresuperconducting,meaningtheyhavenoelectricalresistance.Thisallowsthemto provideaeldof8.3T. 45

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Inordertogetthebeamsofprotonstotheirnominalenergy,theLHChasmany smalleracceleratorringsasshowninFigure 2-1 .Protonsstartoutashydrogenatoms whicharethenstrippedoftheirelectronsintheLINAClinearacceleratorwheretheyare thenacceleratedto50MeV,sendingthemtotheProtonSynchrotronBoosterwhere theyareacceleratedto1.4GeV.Onceat1.4GeV,theprotonsaresenttotheProton Synchrotronwheretheyareacceleratedfurtherto26GeVandthenontotheSuper ProtonSynchrotronwheretheyreach450GeVandcannallybeinjectedtotheLHC mainring.Thiscanallbeaccomplishedinabout20minutes.Onceinthemainring, llsofbatchesofprotonscanbehelduptoabout24hours.Therearetwoseparate vacuumbeamtubesthroughouttheLHCsothatprotonstravelingineachdirectionhave theirowntubewhilesharingallthesamemagnets.Designspecicationscallfor2,808 bunchesofprotonsperbeam,withabout 10 11 protonseach.Accelerationoftheprotons isdonethroughRadioFrequencymodulationwithanoperatingfrequencyof40MHzin themainring.Thiswouldallowforbunchestobespaced25nsapart.However,during therstrunperiod,50nsbunchspacingwasusedsothenumberofallowedbunches perbeamwasreducedbyafactorof2. Therearefourmaindetectorsaroundthering.ATLASandCMSarethetwogeneral purposedetectorsdesignedtosearchforStandardModelphysics,Higgs,SUSY,and otherbeyondStandardModelphenomenon.ALICEisalargetimeprojectionchamber designedtosearchfornewphenomenoninheavyioncollisions,suchasquark-gluon plasma,andonlycollectsdataforabout1montheveryoperationalyear.LHCbisa specialpurposedetectorforinvestigatingBphysics,CPviolation,andwhythereismore matterthananti-matterintheuniverse. 2.1.2PhysicsattheLargeHadronCollider SincetheLHCisaproton-protoncollider,itisimportanttorememberthatprotons aremadeupofquarksandgluons.Thesepartonsarethe u and d quarkswhichgive theprotonitspositivecharge,andthegluonswhichholdittogether.Theseparticlesas 46

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wellastheseaofquark-antiquarkpairscanallparticipateinthecollision.Collisionsof interesttonewphysicsarehardscatteringcollisionsinwhichthereisalargemomentum transferbetweenindividualpartons.Becausetheprotonsarenotfundamentalparticles, thepartonsactuallycarryonlyafractionoftheenergyoftheproton.Thereforecollisions ofthesepartonswillalwaysbeatancenterofmassenergywhichislessthanthe energyofthetwobeams.Anyofthesetypesofcollisionscangiverisetoaparticleof interestsuchasaHiggsboson. Inordertoclaimadiscoveryofanynewparticle,itisnecessarytohavesufcient statisticalaccuracyinthecalculationofdatacollected.Itisthereforeofparamount importancetoknowtheoverallinteractionratethatanacceleratorcanprovide.The probabilityofproducingacertainphysicalinteractionisknownasthecrosssection ( # ),ortheeffectiveareaatargetparticlepresentstoanincidentparticle.Thequantity describinghowfrequentlytwoparticleshavethechancetointeractisknownasthe instantaneousluminosity, L ( t ) .Thenumberofexpectedeventsforagivenprocessis then N exp = # t 2 t 1 L ( t ) dt (21) Here, # usuallyincreaseswith + s ,makingiteasytoseethatthehighertheenergy ofthecollideraswellasthebettertheluminosityitcanprovide,thehighernumberof eventswillbeproduced.Instantaneousluminositycanbecalculateddependingonthe beamparametersas L = fn b N 1 N 2 A e (22) 47

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where N isthenumberofprotonsineachbunch( N 1 = N 2 attheLHC), f isthe frequencyofrevolutions, n b isthenumberofbunchesperbeam,and A e istheeffective areaofthebeam. A e canbefurtherdescribedas A e =4 /0 n & ( r (23) where 0 n isthetransversebeamemittance(designvalueof3.75 m),and ( $ r is thebetafunction,whichmeasuresbeamfocusatthecollisionpointcorrectedbythe relativisticfactor ( r .Finally,theinstantaneousluminosityattheLHCcanbewrittenasa functionofknownquantitiesas L = fn b N 2 ( r 4 /0 n & (24) TheLHCwasdesignedtosurpassallothercollidersontheplanetinorderto makegiantleapstowardsnewphysics.Thedesigncenterofmassenergyof14TeVis seventimeshigherthanthenexthighestenergycollider,theTevatron( + s = 2TeV), andnoothercolliderhasreachedluminositiesashighas 10 34 cm 2 s 1 .Thisbrings anewsetofchallengestophysicsattheLHCforboththoseoperatingthemachine andtheexperimentalistsattemptingtondnewphysics.Inordertodealwiththis dynamic,experimentshadtobedesignedthatcouldnotonlycopewiththischallenging environment,butexcelinthesearchfornewphenomenon. 2.2TheCompactMuonSolenoidDetector TheCompactMuonSolenoid(CMS)detectormeasuresa"compact"25mlongand 15mindiameter,weighingatotalof12,500tons.Asageneralpurposedetector,the CMSexperimentneedstobeexible,yetpreciseenoughtocovertopicsvaryingfrom precisionmeasurementsatenergiesofafew100GeVtosearchesfornewparticlesand 48

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phenomenonuptotheTeVscale[ 28 ].InordertoensurethatCMSwasabletofully executeitsproposedscienticprogram,severalrequirementshadtobemet. First,CMSneededtobeabletoefcientlydetectandaccuratelymeasureleptons producedwithlowmomentumasinthecaseofheavy-avorhadrondecays,aswell asleptonsproducedwithveryhighmomentumthatcouldcomefromthedecayofa theoreticalheavyparticlesuchasahighmassHiggsorSUSYparticleofseveralTeV. ThisimpliesthatCMSneededhighperformancechargedleptonidenticationaswellas excellentmomentumresolutionofabout1%forawiderangeofmomenta.Thiswould alsoallowtheexperimenttoensurethatanarrowresonance,suchasalowmassHiggs, wouldbeeasilyobservableabovearelativelyatirreduciblebackgroundcontinuumas inthecaseof H ZZ 4 Next,CMSneededtobeabletodiscriminatebetweenparticlessuchastheHiggs decayingtophotonsandsecondaryhadronicprocessescreatingphotons.Similarly,the experimenthadtobeabletohaveverygoodidenticationofjetscomingfromheavy quarksandtaus.Third,theexperimentneededtobeabletoreliablymeasurethetotal transverseenergyofallparticlesproducedinacollision.ThiswouldallowCMSto determineiftherewasanimbalanceintheeventwhichwouldimplythattherewere neutralparticles,suchasneutrinos,whichescapeddetection. Finally,CMShadtodealwith 10 9 interactionspersecondbeingprovidedby theLHCbeams.Thisrequiremententailscreatingsystemstoreducethenumberof collisionstoanacceptablerateandthenreconstructingandrecordingonlytheevents thatweredeemedinteresting. Tosuccessfullymeetalloftherequirementsandcopewiththechallengesof operatingattheLHC,CMSwasdesignedasaseriesofconcentricallylayeredbarrel ofsubdetectorswithasuperconductingsolenoidtoprovideamagneticeldandend capsoneithersideofthebarrel.Insidethesolenoid,directlysurroundingthebeamline sitsasiliconbasedtrackingdetector.Outsideofthetrackeristhescintillatingcrystal 49

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basedelectromagneticcalorimeter(ECAL)andthebrassbasedhadroniccalorimeter (HCAL).Outsideofthesolenoid,thereisamuonsystemwhichutilizesthreetypesof subdetectorswhichareintertwinedwiththeironmagneticeldreturnyolk.Allofthe subdetectorsofCMSareconnectedthroughthedataacquisitionsystem(DAQ)andthe triggersystem. 2.2.1Geometry TheCMSexperimentusesaright-handedcoordinatesystemwiththeoriginatthe collisionpointonthebeamlineatthecenteroftheexperiment.TheZaxispointsalong thebeamline,whiletheYaxispointsverticallyupwardandtheXaxispointshorizontally outwardfromtheexperimentcentertowardsthecenteroftheLHCring.Further,the angle ) isdenedasthepolaranglewithrespecttotheZaxisandtheangle isdened astheazimuthalanglewithrespecttotheX-Zplane.Thetransversemomentumofany particleorthogonaltotheZaxisisdenedaspT = p sin ) andsimilarlyfortransverse energy,E T = E sin ) BecausetheLHCiscollidingprotons,whichthemselvesare"balls"ofquarksand gluonswhicheachcarryadifferentproportionofthetotalmomentumoftheproton,the resultingeventsinCMSwillhavetheircenterofmassboostedrelativetothelabframe alongthebeamaxis.Anewcoordinatesystemwhichisapproximatelyinvariantunder boostsinthisdirectioncanbedened,called pseudorapidity anddenedas % = % ln tan ) 2 .. (25) Pesudorapdidityisthemasslessapproximationofrapiditywhichisdenedas y =ln E + P z E % P z (26) 50

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& ln 1+ cos ) 1 % cos ) (27) =ln cot 2 ) # (28) Anotheradvantageofusingpseudorapidityisthatthedistributionofparticles producedincollisionsisapproximatelyuniformin % .ThebarrelportionofCMSis denedfor | % | < 1.5whiletheendcapsdenetheregion1.5 < | % | < 3.0withtheforward hadroniccalorimetersextendingallthewayoutto | % | = 5.0.Formallythetracking systemandelectromagneticcalorimetercovertheregion | % | < 2.5whilethemuon systemscoveroutto | % | < 2.4.ThisallowsCMStocoveralargeregionofphasespace givingitagoodchancetocaptureandmeasuremulti-leptoneventswhicharenecessary tousethe H ZZ 4 channel. 2.2.2InnerTracker TheinnertrackeristheinnermostcomponentofCMS,surroundingtheinteraction pointandbeampipe,itsdetectingareaisfrom4.4cmto1.1mradiallyoutwardfrom thebeampipewithanoveralllengthof5.8mprovidingcoveragein | % | upto2.5.The purposeoftheinnertrackeristoprovidespatialmeasurementsofchargedparticles aswellasaccuratelymeasurethecurvatureofchargedparticlesinthemagneticeld inordertocalculatetheirmomentum.Thetrackingsystem,asshowninFigure 2-4 hadtobeabletoprovidenegranularityneartheinteractionpointinordertodealwith the1billioninteractionspersecondbeingproducedbytheLHC.Italsohadtobevery resistanttoradiationwhichwouldsaturatetheareaneartheinteractionpoint.Inorderto copewiththeseconditions,theCMStrackerisbasedonsilicondetectortechnology. Toprovidethenestgranularity,the3innermostlayersofthetracker,rangingfrom 4to15cmradiallyoutwardfromtheinteractionpoint,aremadeofsiliconpixels,witha 51

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Figure2-2. AnexplodedviewoftheCMSdetectorandthesubdetectorsthatcompose it.Inthisrepresentation,boththebarrelandendcapsareclearly discernible. totalof65millionpixels,eachwiththeirownelectronicchannel.Thespatialresolutionof the100 150 m 2 pixelsisaround10 minthe r % planeandabout20 minthe r % Z plane.ThesepixelsallowsCMStodetectnotonlytheprimaryvertexineachevent,but alsosecondaryverticeswhichcanarisefromalonglivedheavyavorparticlesdrifting awayfromtheinteractionpointandthendecaying,andinteractionswhichoccurfrom differentbunchcrossingsknownas pile-up .Thenext10layersofthetracker,ranging from25to110cmradiallyoutwardfromtheinteractionpoint,consistofpixelstrip detectorswhichalsoprovideexcellentgranularitysincethedensityofparticlesdecrease astheytraveloutward.Thedensityofparticlehitsundernominaloperatingconditions (25ns)areshowninTable 2.2.2 .Thesiliconstriplayersarefurtherdividedintotherst fourlayersknownasthetrackerinnerbarrel(TIB)withstripsmeasuring10cm 180 m andthesixouterlayersknownasthetrackerouterbarrel(TOB)withstripsmeasuring 52

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Figure2-3. CoordinatesystemusedbytheCMSexperiment. 25cm 180 m.Thetrackeriscompletedwiththetrackerinnerdisks(TID)andenclosed withthetrackerendcaps(TEC)providingcoverageintheregion124cm < | Z | < 280cm and22cm < r < 113.5cm. Table2-1. HitdensityoftheCMStrackerfordifferentradiallyoutwardlengths. HitDensity( mm 2 )radius(cm) 1MHz 4 60kHz 22 3kHz 115 Whilesiliconhasmanyadvantagesinuseasatrackingdetector,ithassome disadvantagesthatmustbeovercome:siliconrequireshighpowerelectronicswhich mustsitonthedetector,makingalarge,efcientcoolingsystemnecessary.There alsomustbesomeconsiderationfortheamountofmaterialusedassiliconisavery densematerial.Particlesfromcollisionswillinteractwiththedensematerialcausing phenomenonsuchasmultiplescattering,bremsstrahlungradiation,photonconversions, andnuclearreactionswhichcouldcauseseriouscomplicationswhenreconstructing theeventandattemptingmeaningfulphysics.ThesilicontrackingdetectorinCMS hasthereforebeenoptimizedsoastohaveenoughmaterialtomakehighprecision 53

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measurementsofchargedparticleswithaslittlecosttoefciencyandprecisionas possible.Table 2-2 summarizestheconstructionsoftheCMSinnertracker. Figure2-4. TrackingsystemasinstalledinCMS. Achargedparticle'spaththroughthetrackerwillbecurvedduetothemagnetic eldprovidedbythesuperconductingsolenoid.Itsmomentumcanthenbemeasured accordingto P = qBR (29) where q isthechargeoftheparticle, B isthemagneticeld(3.8TinCMS),and R istheradiusofcurvatureasmeasuredbythetracker.Particleswithhighermomentum 54

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havetrackswithlesscurvaturewhichresultsinaworsemomentumresolution.The trackeritselfismadeofnonhomogeneouspixelsandstrips,thereforeresolutionwill alsovarywith % .Figure 2-5 showstheresolutionofmuonswith pT = 1,10,and100 GeVrespectivelyasafunctionof % fortransversemomentum( pT ),transverseimpact parameter( d 0 ),andlongitudinalimpactparameter( z 0 ).Forchargedparticleswith pT & 40GeV(common pT fromZdecays),theresolutionisexpectedtobeabout1%inthe barrelandupto3%athigh % Figure2-5. Resolutionoftransversemomentum(left),transverseimpactparameter (middle),andlongitudinalimpactparameter(right)formuonswith pT = 1,10,and100GeVrespectively. Table2-2. SummaryoftheCMStrackingsystem. Section Region DetectorType Area PIXEL r < 10cm pixels 100 m 150 m TIB + TID20cm < r < 55cmmicrostrips10cm 150 m TOB + TEC55cm < r < 110cmstripsupto25cm 180 m 2.2.3ElectromagneticCalorimeter TheECALispositionedoutsideoftheinnertrackerandismadeupofover75,000 homogeneousleadtungstate(PbWO 4 )crystals,with61,200crystalsinthebarrelregion (EB)covering | % | < 1.479and7,324crystalsineachofthetwoendcaps(EE)covering 1.479 < | % | < 3.0.Thereisasmallcrackbetweenthetworegionsat1.4442 < | % | < 1.56.Figure 2-6 showsadiagramofthelayoutoftheECAL. 55

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Figure2-6. ElectromagneticcalorimeterlayoutinCMS. ThedesignoftheECALwasmotivatedbythestringentrequirementsofhigh precisionandgranularityalongwithexcellentenergyresolutionneededtocompetein thesearchfortheHiggsbosonwhenitdecaystotwophotons( H (( )aswellasto copewiththeextremeoperatingconditionsoftheLHC.Forthisreason,itwasdecided tousethedensePbWO 4 crystals(8.28 g / cm 3 )whichallowthemtohaveaveryshort radiationlengthof0.89cm[ 29 ].Eachcrystalis25.8radiationlengthsintheEBand24.7 radiationlengthsintheEEandaretypically22 22mmonthefrontfaceand26 26mm ontherearface.PbWO 4 waschosennotonlyforitsdenseness,butalsoforitslight response,radiationhardnessandcompactness.AttachedtothebackfaceofeachEB crystalisanavalanchephotodiode(APD)tocollectthelightthatresultsfromacharged particlepassingthroughthecrystalcausinganelectromagneticshower.TheAPDshave 56

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anactiveareaof25mm 2 .Similarly,crystalsintheEEusevacuumphototriodes(VPT) whichhaveanactiveareaof280mm 2 .Asabonus,thesecrystalsalsoprovideavery quickresponsewithascintillationdecaytimeshortenoughtoallow80%ofthelightto beemittedwithinthe25nsbunches. ByplacingtheECALinsideofthesuperconductingsolenoid,theECALisableto captureparticlesbeforetheyhavetraversedalargeamountofmaterial.Alead-silicon strippreshowerdetectorwasinstalledinfrontoftheEEsectionstohelptheECAL distinguishphotonsfromparticlessuchasneutralpions.Thepreshowerdetector isatwolayeredsamplingcalorimeter,withtherstlayermadeofleadtocreatean electromagneticshowerandthesecondlayermadeofsiliconstripdetectorstomeasure thedepositedenergy.Thisalsoimprovesthepositionmeasurementofphotonsand electrons. Thelightoutputofthecrystalsdependsheavilyontemperature,thereforeitwas necessarytoincludeacoolingsystemintheECAL.Thecoolingsystemmaintainsa temperatureof18 % C 0.05 % C andisalsomonitoredcloselyduringcollisions.Although theECALcrystalsareresistanttoradiation,theyarenotimpervious.Eachoperational runreducestheiropticaltransmissionafewpercentwhichiscausedbythediscoloration ofclearcrystals.Becausethiseffectdependsontheamountofradiationthecrystals areexposedto,theeffectsarenotuniformintheECAL,withcrystalsclosertothebeam pipe(higher | % | )receivinghigherradiation,thereforehavingmorevisibleeffects.In ordertomonitorthisinrealtime,alasermonitoringsystemwasinstalledwiththeECAL. Duringregularintervals,laserpulsesareinjectedintothecrystalsthroughberoptic cableallowingthecrystaltransparencytobemeasured.Theeffecthasbeenmeasured tobebetween1-2%intheEBforlowluminosityruns,to10-20%intheEEforhigh luminosityruns.Thiseffectisreversible.Bykeepingthecrystalsat18 % C whentheLHC isnotprovidingcollisions,thethermalagitationoftheatomsinthecrystalscausesthe atomstocomebackintotheiroriginalstructure. 57

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TheenergyresolutionoftheECALhasbeendeterminedtobe # ( E ) E 2 = 2.8% + E 2 + 0.12 E 2 + ( 0.30% ) 2 (210) wheretherstterminduetothestochasticandstatisticalnatureofelectromagnetic showering,thesecondtermisduetonoisecomingfromelectronics,digitization,and pile-up,andthethirdtermarisesfromthegeometricnon-uniformityandcalibration uncertaintyoftheECAL[ 30 ].Theresolutionasafunctionof E ,asshowninFigure 2-7 hasbeendeterminedfromatestbeamand3X3clusterofcrystals.Theresolutionis verygoodatbetterthan1%fordepositsover30GeV. Figure2-7. EnergyresolutionoftheECALinidealconditions. 2.2.4HadronicCalorimeter Thehadroniccalorimeter(HCAL)islocatedbetweentheECALandthesuperconducting solenoid(1.77m < r < 2.95m)withonlytheouterHCALplacedoutsidethemagnet, andisdesignedtoabsorbneutralandchargedhadrons[ 31 ].Indoingso,theHCAL 58

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measurestheirenergieswhichbecomethebasisforreconstructingjetsanddetermining themissingtransverseenergy(MET)inaneventwhicharisesfromparticlesescaping detection,suchasneutrinos.TheHCALconsistsoffoursections:theHCALbarrel(HB), endcap(HE),forward(HF),andouter(HO)coveringallthewayupto | % | < 5.2making CMSnearlyperfectlyhermetic. TheHB,HO,andHEaresamplingcalorimetersmadeofplasticscintillatorswith brassandstainlesssteelabsorbers.Theenergyreadoutisdoneviawavelengthshifting beropticcables.Theabsorberscausehadronicandelectromagneticshowerswhich arethensampledatseveraldifferentdepthsbythescintillatingplasticdetectors.The lightisthenfedtodedicatedopticaldecoderunits(ODU)whichbreakdownthesignal intosectionscoveringanareaof0.087 0.087in % % .Finallythelightisdirectedto thehybridphotodiodes(HPD)forreadout.Theforwardregionischaracterizedbyhigh amountsofradiationfromsofteventsmakingitanecessitytousematerialsthatcan sustainthehighradiationaswellasrespondtotheshowersquickly.TheHFistherefore aCerenkovlightdetectormadeofquartzberswithanembeddedsteelabsorber. Photomultiplierstubes(PMT)areconnectedtothebersthroughlightguidesandare usedtoconvertlightintoelectricalsignals.ThesignalfromtheHFisonlyabout10ns wide,whichcaneasilycompetewiththe25nsbunchspacing.Figure 2-8 showsthe locationsofdifferentsub-systemsoftheHCAL. TheenergyresolutionoftheHCALisdenedas # ( E ) E 2 = 90% + E 2 + ( 4.5% ) 2 forHB,HE (211) # ( E ) E 2 = 172% + E 2 + ( 9.0% ) 2 forHF (212) 59

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Figure2-8. LocationsofthedifferentHCALsubsystems(HB,HE,HO,HF). wherethersttermisduetothestatisticalnatureofhadronicshowering,andthe secondtermisduetothegeometricnon-uniformityandcalibrationuncertaintiesofthe HCAL. 2.2.5SuperconductingSolenoid TheCMSsuperconductingsolenoidisarguablythemostimportantfeatureofthe detectorwhichbearsitsname.Thesolenoid,whichisthelargesteverbuilt,ismade of4layersofNbTicoils,makingit12.5mlongand6mindiameterandweighing220 tons[ 32 ].Itisemersedinaliquidheliumbath,coolingtoatemperatureof4K,allowing theNbTitobecomesuperconducting.Thisallowsthecoilstopass20kAofcurrent creatinga3.8Teldinsidethesolenoid,storinganenormous2.5GJofenergy.Outside ofthesolenoid,asteelreturnyoke,consistingof5layersinthebarrelandthreedisks intheendcaps,guidesthe2Treturneldbackaroundtheoutsideofthesolenoidwhile providingsupportstructureforthedetector. 60

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Figure2-9. DiagramofthemagneticeldthroughoutCMS. Thesolenoidprovidesthelargebendingpowerneededtobeabletomakeefcient andprecisemomentummeasurementsandchargeassignmentsinthetracker. Additionally,thereturneldprovidesbendingpowerinthemuonsystemsoasto providetheabilitytomakeasecondmomentummeasurement.Figure 2-9 showsa representationofthemagneticeldthroughoutthedetector. 2.2.6MuonSystem InCMS,muonsareeasilyidentiedsincetheyaretheonlychargedparticles whichwillpassthroughthematerialsintheECAL,HCAL,andmagnetwithoutbeing absorbed.Muonsalsoplayanimportantroleinmanyphysicssearches.Maybenomore sothaninthesearchfortheHiggsbosoninthedecaychannel H ZZ 4 ,where therearefourmuonsinthenalstate.Thischannelhasprovidedthemotivationforthe constructionoftheCMSmuonsystemwhichconsistsofthreetypesofsubdetectors: drifttubes(DT),resistiveplatechambers(RPC),andcathodestripchambers(CSC) [ 33 ]. Theoveralllayoutofthesesubdetectorshasbeenchosentoprovidewideangular coveragewithnoacceptancegapsandalsoaccordingtotheoccupancyrateofthe differentregionsinthedetector.DuetothegeometryofCMS,themuonsubdetectors 61

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areattachedtothesteelreturnyokesin4cylindricallayersinthebarrel,and4layersof disksintheendcapsprovidingatotalof25,000m 2 ofdetectorarea.Figure 2-10 shows thelayoutofthemuonsystem,andeachsubsystemiffurtherdescribedbelow. Figure2-10. LayoutoftheCMSmuonsystem. 2.2.6.1Drifttubes Theoccupancyrateinthebarrel( | % | < 1.2)isexpectedtoberelativelylow( < 10Hz/cm 2 ),especiallywhencomparedwiththeendcapswhichallowsfortheuseof drifttubes.TheDTsareconstructedofcellseach42mmX13mm.Eachcellconsists oftwoaluminum"I"beams,usedascathodes,enclosingan50 mstainlesssteelwire locatedatthecenterofthecellwhichservesasananode.Anelectriceldisthen createdbetweentheanodeandcathodes,andshapedasshowninFigure 2-11 left,by theinstallationofpositivelybiasedinsulatedstripsgluedtotheplanesadjacenttothe wire.Asmuonspassthroughthecell,theyionize,orbreakoutelectronsfrom,thegas mixtureinsidethevolume.Thetimeittakesfortheseelectronstodrifttotheanodeis usedtomeasurethedistancebetweenthemuontrackandthewire. Thegasmixtureineachcellis85%argon(Ar)and15%carbondioxide(CO 2 ) guaranteeinggoodquenchingpropertiesadriftvelocityof5.4cm/ s.Thisdriftvelocity 62

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correspondstoamaximumdrifttimeof390nsorabout15bunchcrossings.This gasmixturealsohasthebenetofbeingnon-ammablesoitcansafelybeusedin undergroundenvironments.Spatialresolutionofeachcellis180 mwithanefciency of99.8%.Theangularresolutionoftheentirechamberisapproximately1.8mrad.The DTsareplacedincircularwheelsalongthebeamaxis,eachwith12azimuthalsectors. Therearefourstations,goingradiallyoutward(MB1-4)whichareeachmadeof12 chambers,saveforMB4whichcontains14asshowninFigure 2-10 .Figure 2-11 right showsalayoutofasingleDTchamber. Figure2-11. DTelectriceldshapedbythecathodes,anode,andinsulatingstrips(left). DTchamberlayoutforsingleDTstationinCMS(right). 2.2.6.2Cathodestripchambers Asdiscussedearlier,theforwardregionofthedetectorischaracterizedbyahigh occupancyrateofuptomorethan100Hz/cm 2 aswellasanintenseandnon-uniform magneticeld.Forthisreason,cathodestripchambers(CSCs)havebeenchosenfor themuonsysteminthisregioncovering0.9 < | % | < 2.4.TheCSCsaretrapezoidal shapedmulti-wireproportionalchambersconsistingoftwocathodeplanes,oneofwhich hasbeensegmentedintostripsintheradialdirection,andanarrayofanodewires stretchedinbetweentheseplanesandrunningorthogonaltothestrips.Asamuon passesthroughachamber,itgeneratesanavalancheofelectronsonthewiresthat inducesachargeonthecathodestrips.Byhavingnarrowstripsandthenmeasuringthe 63

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chargesoneachstripaswellasonthewires,itispossibletoreachaspatialresolution of50 m. Figure2-12. CSCchamberasitwouldbeinstalledonanendcapdiskonCMS(left). Multi-wireproportionalchambersuchasthosethatmakeuptheCSC chambersinCMS(right). EachCSCcontains6layersoftheseproportionalchambersabletomake measurementsintwodimensions.Bothendcapsconsistof4disksofCSCs(ME1-4). ME1has3ringsofchambersstackedintheradialdirectionforatotalof36chambers, whileallothershave2ringsforatotalof18chambers.ME4constructionwasnot completefortherstrunperiodandisbeingnishedduringLS1.Figure 2-12 leftshows arepresentationoftheinteriorofoneoftheCSCs,whileFigure 2-12 showsawhole CSCchamber. 2.2.6.3Resistiveplatechambers Resistiveplatechambers(RPCs)areplacedinboththebarrelandendcapmuon systemcovering | % | < 2.1.Whiletheirspatialresolutionisfairlylimited,theirtiming resolutionisexcellentatabout3ns,makingthemexcellentdetectorsforthemuontrigger systemwhichismainlyusedtoidentifybunchcrossings.TheRPCsareconstructed withfourplatesofbakelite,aplasticknownforitshigh-resistivity,formingtwo2mmgaps 64

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whicharelledwithamixtureof95%C 2 H 2 F 4 gasand5%C 4 H 10 gas.Outsideofthe gaps,theyarecoatedwithgraphite.Insulatedaluminumstripsthenreadoutthesignals. ThereisanelectriceldformedacrossthegapswhichallowstheRPCstomaintain timingresolutionatahighoccupancyrate.Inthebarrel,therearesixlayersofRPCs whileintheendcapstherearefourdisksoftrapezoidalshapedRPCsattachedtothe CSCs.Figure 2-13 showsadiagramoftheRPCconstruction. Figure2-13. Resistiveplatechamberconstruction. 2.2.6.4Muonmomentumresolution Usingonlythemuonsystem,amomentumresolutionof10%(20%)isachievedfor pT = 40GeVmuonsinthebarrel(endcaps).However,informationfromthetrackercan becombinedwiththemuonsystemtodrasticallyimprovethepermuonresolution.The resolutionofaglobalmuonoronethatusesinformationfromboththetrackerandmuon system,isabout1%(2%)formuonswith pT < 100GeVinthebarrel(endcaps).For high pT muonsabove100GeV,resolutionclimbstoabout8%forthebarreland10% fortheendcaps.Figure 2-14 showstheresolutionofthemuonsusingjustthemuon system,justthetrackingsystem,andacombinationofthetwo. 2.2.7TriggerSystem TheLHCisdesignedtoprovidecollisionsatarateof40MHzwithabunchspacing of25ns.Thisbunchspacingallowstimefortheexperimentstoreadoutandrecorddata fromeachcollision.Ifeverycollisionweretoberecorded,itwouldlleveryharddisc 65

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Figure2-14. Muonmomentumresolutionversus pT forbarrelandendcapmuons. intheworldinamatterofdays.Themajorityoftheseeventsareun-interestingfornew physicsaswell,astheyareprocesseslikeminimumbiasQCDandsoftcollisions.For thisreason,itwasnecessarytoderivealtersystemtoonlyselecteventswhichare usefulandinteresting.Thissystemiscommonlycalledthetriggersystem.Thetrigger systemmustberobustandprecisebecauseitistherststageofphysicsanalysis fromwhichallfurtheranalysiswillderive.Figure 2-15 showsthedesignoftheCMS triggerandDataAcquisitionsystem(DAQ).Thetriggerisatwostagesystem,withthe rststagecalledtheLevel1triggerwhichmakesdecisions"online"orwithcustomized hardwareonthedetectorinrealtime.Decisionsonwhethertokeeporrejecttheevent aremadeinabout3.2 s,reducingtheoverallrateof40MHztoamoremanageable 100kHz. Thesecondstageofthetriggersystemisafarmofthousandsofcpu'scalledthe HighLevelTrigger(HLT).UnliketheL1,whichwasdesignedtobeextremelyefcient andveryfast,theHLTcantakemoretime,about50ms-1s,todecidewhetheranevent isinterestingforacertainphysicsanalysisandthereforemustbemoreexible.While theL1usessignalsfromdifferentsubdetectors,theHLTistherststepinanalysisto usehigherlevelphysicsobjectssuchaselectronsandmuons.HLTcodeiswrittenby 66

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membersofthedifferentphysicsanalysesgroupstoselecteventsthathaveasignature thatcouldrepresentasignaleventintheiranalysis.TheHLTisabletobringtheL1rate of100kHzdowntoabout300-500Hz.Thisistheratewrittenpermanentlytodiscand arethenfullyreconstructedforuseinphysicssearches. Figure2-15. OverviewoftheCMStriggersystem 2.2.7.1Level1trigger TheL1triggersystemissplitintotwoparallelworkowsasshowninFigure 2-16 Bothworkowsbeginatthesubdetectorlevel,thenmovetoregionalandglobal levels.ThetwoworkowsthenmergetoformanoverallglobaltriggertomaketheL1 accept-rejectdecision. Localtriggerscreatetriggerprimitivegroups(TPGs)whicharemadeupofcoarse informationcomingfromthesubdetectors.Thisinformationisthenpassedtoaregional triggerlevel.Forthecalorimeter,thisiscalledtheregionalcalorimetertrigger(RCT). TheRCTbuildsL1candidatessuchaselectrons,photons,jets,andtausbycombining informationfromboththeECALandHCALTPGs.Forthemuonsystem,theDTtrack nderandCSCtrackndercombineinformationwiththeRPCtriggertoformL1trigger trackcandidates.Thefourmostrelevantcandidatesofeachcategoryarethensentto theglobalcalorimetertrigger(GCT)ortheglobalmuontrigger(GMT).TheGCTand GMTthensortthesecandidatesandsendthemtotheglobaltrigger. OncetheglobaltriggerhasreceivedtheGCTandGMTdata,itcomparesthe candidatestotheL1triggermenu.Thetriggermenuisalimitedlistofcandidate 67

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selectionsforeventsthatshouldbekept.Asenergyandluminosityincrease,some triggersinthemenumayneedtohavetheirselectioncriteriatightened,orbepre-scaled (selectingonlythe n th event)inordertoavoidalargeincreaseinrate.Ifacandidate collectionsatisesatleastoneofthetriggersintheL1menu,theeventiskeptandthe eventispassedtotheHLTforfurtherscrutiny.Anexampleofapossibletriggeror bit intheL1menuwouldbe'L1 SingleEG8Iso',whichwouldrequireatleastoneisolated electronorphoton(electronorphotonwithlittlehadronicactivitysurroundingit)witha transverseenergygreaterthan8GeV. Figure2-16. OverviewoftheL1triggersystem 2.2.7.2Highleveltrigger TheHLTisdesignedtotaketheobjectspassedfromtheL1triggerforfurther reconstructionandselection.Thisisdoneinstagestominimizecpuusage.There are3stagesgenerallyreferredtoaslevel2,2.5,and3.Level2startswiththeobjects passedfromtheL1triggerandbuildsnergranularityobjectsusinginformationfromthe calorimeterandmuonsystem.Foranobjectsuchasanelectron,thisisthestagewhere clustersofenergyfromtheECALandpreshowerarecombinedwithL1candidates. Totrytorecoverenergylosttobremsstrahlungradiationwhichwillspreadtheenergy 68

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overseveralcrystalsintheECAL,clustersofenergyintheECALareformedcalled superclusters Level2.5istherstleveltouseinformationfromtheinnertracker.Forelectrons, thismeansthatsuperclustersintheECALarematchedwithtracksintheinnertracker. Similarly,tracksinthemuonsystemarematchedwithtracksfromtheinnertrackerat thisstagetoformglobalmuons.Ifasuperclusterismatchedtoatrackwithenoughhits inthepixellayerandTECforforwardtracks,thenitformsa seed .Ifaseedisfoundfor anelectron,oramuonsystemtrackismatchedtoatrackintheinnertracker,thenthe fulltrackreconstructionhappensinlevel3.Atanypointinthesethreestages,theevent canberejected.Becauseofthelargeamountofcputimeneededtofullyreconstructall tracks,thisallowsfortheHLTtomakeadecisioninlessthan1swhilereducingtherate toamanageable500Hz. TheHLTmenuconsistsoforder200different paths ,eachonestartingwithfrom atleastoneL1bit.Figure 2-17 showsadiagramofoneexampleoftheseHLTpaths. OrganizingthelargeamountofdataowingfromtheHLTisveryimportantgiven theamountofphysicistswhowillbeaccessingthedataatsitesallaroundtheworld. ThereforeoncethedatahaspassedanHLTtrigger,itissortedintooneofmany datasetsaccordingtotheobjectspresentintheeventandtheselectionpassed.For example,aneventwithtwomuonswith pT 'sgreaterthan17and8GeVrespectively wouldbesenttothe"DoubleMu"dataset. Ideally,thesignalefciencyforagiventriggershouldbearound100%,however thisisnotalwayspossible.JustastheL1bitsmayneedtobetightenedorpre-scaled, HLTpathsalsomayneedtheirselectionstightenedorpre-scaledwhichcoulddecrease signalefciency.Thereisingeneral,adelicatebalancingactofallowingtheloosest possibleselectionforagivensignal,whiletryingtokeeptheratetoareasonablelevel. Forallthesereasonstherehasbeenandcontinuestobe,signicanttimeandeffort devotedtounderstandingandvalidatingtheHLTtriggerpaths. 69

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Figure2-17. ExampleHLTpathforisolatedelectronbasedtrigger. 2.2.8DataAcquisition TheCMSdataacquisitionsystem(DAQ)structureisshowninFigure 2-15 along withtheCMStriggersystem.TheDAQsendsdatafromnearly650readoutmodules tothe"lterunits"thatprocessthedata[ 34 ].TheDAQrunsonlineonaround3000 cup'sforbufferingandprocessingoftheevents.Frontenddrivers(FEDs)readout thedetectorsensorsthroughanetworkwithabandwidthof100Gb/s.TheFEDssit inaroom70mfromthedetectorcalledthe countingroom .Cablesrunningfromthe underneaththedetectorinchannelsintheconcreteoor,providetheFEDsinthe countingroomwitheventsatthesamerateastheL1trigger,about100kHz.Thishigh rateisunusualintheworldofcolliderphysics,asmanydetectorswillonlypartially reconstructtheeventbeforesendingtotheDAQ.Becauseoftheentanglementofthe triggerwiththeDAQ,thecompletesystemisknownasTriDASinCMS,ortriggerand dataacquisitionsystem. 2.3Computing Oncedatahasbeencollected,itmustbeprocessedandmadeavailableto physicistsaroundtheworld.Thisisaccomplishedviaawiderangeofcomputing 70

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centersatCERN,anduniversitiesandlaboratoriesinover15countries.Tomakethis processrobustandefcient,atieredmodelofcomputingwasestablished. Figure 2-18 showsthetieredcomputingmodelusedbyCMS.Theowofdata beginsatCERNwiththeTier-0.Here,thedatacomingfromCMSisprocessedinto datasetsclassiedbythetypesofphysicsobjectsinside.Therearethreebasictypes ofthesedatasets.RAWcontainshighlydetailedinformationaboutinteractionsinsub detectors.RECOcontainsafulldescriptionoftheeventwithallbasicphysicsobjects aswellasaddedcollectionssuchasrecordsofhitsinthetrackerandmuonsystem. AODcontainsalloftheinfothattheRECOdatasetscontain,exceptdetailedinformation aboutsubdetectors.Thishelpstosavespacewhenthedatasetsaredistributedtothe othertiercentersaroundtheworld.OncedatahasbeenprocessedattheTier-0itis usuallyintheRAWorRECOformat.InordertofurtherprocessthedatasetintoRECO orAOD,itisdistributedtotheTier-1'stooneofeightdifferentcountriesviahighspeed cablesrunundergroundandevenunderoceans.CountrieswithTier-1'sareGermany, Spain,France,Italy,Russia,Taiwan,theUnitedKingdom,andtheUnitesStates. IntheUS,ourTier-1islocatedatFermilaboutsideofChicago,IL.TheFNAL Tier-1hasseveralthousandcpu'savailablewith15Pbofdiscstorageand22Pboftape storage,andhaspledged40%oftheCMSTier-1computingworldwide.Oncedatahas reachedaTier-1,itisreadytobedistributedtoTier-2'sandTier-3'snationwide.The UScurrentlyhassevenTier-2'sandmorethanadozenTier-3's.Mostoftheanalysis jobsarerunatTier-2'sandTier-3's(whicharejustsmallTier-2's).UniversityofFlorida operatesoneofthemostheavilyusedTier-2'sintheworld,withover22,000cpu's and2Pb'sofdiscstorage.Tier-2'saretheworkhorsesofthecomputingmodel,with hundredsofthousandsofcomputinghoursusedeverymonthattheUFTier-2alone. Withoutthesecomputingcentersandtheabilitytoprocessandusedatasetsthatare hundredsofTBinsize,physicsresearchofthismagnitudewouldnotbepossible. 71

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Figure2-18. TieredcomputingmodelusedbyCMS. 72

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CHAPTER3 PHYSICSOBJECTS ThereconstructionoftheSMHiggsbosoninthedecaychain H ZZ 4 imposesverystringentleptonreconstruction,identication,andisolationrequirementsin ordertobesensitivetoalowmassHiggs,forwhichatleastoneoftheleptonshasa pT withintherange5-15GeV.Inthiskinematicregiontheneedisforanoptimalefciency, whileretainingalowrateofmisidentiedleptonsfromQCD-inducedsourcesofjets. Theidenticationofisolatedleptonsemergingfromtheeventprimaryvertexallowsfora drasticreductionofQCD-inducedsourcesofmisidentied,or fake leptons.Atthesame time,toallowforprecisemeasurementsoftheHiggsbosonmassandotherproperties, theanalysisneedspreciseenergy-momentummeasurementsforallleptons. Withfourleptonsinthenalstate,itismandatorytohaveahighleptonreconstruction efciency.ForHiggsbosonmassesnear126GeV,oneleptonpaircomesfromavirtual Z bosonwherethesoftestleptoninthatpairusuallyhas pT < 10GeV.Tomaintain higheventselectionefciencyatlowmasses,maintaininghighleptonreconstruction efciencyandproperenergy-momentumcalibrationatlow pT allwhileensuring sufcientdiscriminationagainsthadronicjetsisessential,butchallengingnonethe less.Inthisregionafullcombinationofinformationprovidedbythetrackerand electromagneticcalorimetryforelectronsorbythetrackerandmuonspectrometer formuons,aswellasusingadvancedsoftwaremethodsofreconstructingtheevent, suchas particleow (PF)[ 35 ]becomesparamount.Forthesereasons,theanalysis willmakeuseofhighstatisticssourcesofpromptleptonstocalibratetheefciency, mis-identicationrate( fakerate ),andenergyscaleandresolution.The Z "" standard candleiswidelyused,togetherwithotherlowmassresonances,whichareneededto calibratelow pT leptons,namelythe "" (1S,2S,3S)andthe J / & "" Thisanalysisalsomakesuseofphotonsbyrecollectionofnalstateradiation (FSR).Photonswillsometimesbeemittedbyoneofthefourleptonsinthenal 73

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statewhichcanleadtoanincorrectfour-leptonreconstructedHiggsmassdueto energytakenbytheemittedphoton.Therefore,analgorithmhasbeendevelopedto re-collectphotonsthatarelikelyfromFSR.Theanalysisalsomakesuseofjetswhen characterizingeventsaftertheyhavebeenselected.Eventscanbecharacterizedas non-VBFlikeorVBF-likewherethereisafourleptonnalstateandtwohigh pT forward jetswithhighinvariantmass.Wedenejetswithinagivenacceptanceandapply selectionsthatreducetheeffectofthecalorimeternoiseandeffectofpile-up. Inthischapter,thebasicsofleptonreconstruction,identicationandisolationare presented.Jetandphotonreconstructionisalsocovered,aswellascalibrationsdone ondatacontrolsamplesrelevantforthisanalysis.Muchofthissectionisdetailedin reference[ 36 ]ofwhichtheauthorwasalsoacontributingauthor. 3.1Electrons 3.1.1ReconstructionandIdentication Theelectronreconstruction[ 37 ]combinesECALandtrackerinformation.Electron candidatesarereconstructedfromclustersofenergydepositsintheECAL,which arethenmatchedtohitsinthesilicontracker.Inordertoimprovethereconstruction efciencyfortheverylow pT electrons,these ECAL-seeded electronsarecomplemented with tracker-seeded electrons,whicharemergedinauniquephysicscollection.The CMSelectronreconstructionalgorithmisdescribedin[ 38 ],[ 39 ],[ 40 ]andsection 2.2.3 TheenergydepositedintheECALismeasuredinarraysofclusters(superclusters) whichcollectbremsstrahlungphotonsemittedinthetrackervolume.Superclustersare usedtosearchforhitsintheinnermosttrackerlayerswhichareusedtoseedelectron tracks.Thisprocedureiscomplementedbyatracker-drivenapproachtoimprovethe reconstructionefciencyatlow pT .Trajectoriesinthetrackervolumearereconstructed usingadedicatedmodelingoftheelectronenergylossandttedwitha Gaussian SumFilter (GSF).Acleaningisperformedtoresolveambiguouscaseswhereseveral tracksarereconstructedduetotheconversionofradiatedphotonsinthetracker 74

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material.Electroncandidatesarepreselectedusingloosecutsontrack-clustermatching observablestopreservethehighestpossibleefciencywhileremovingpartoftheQCD background. Forthe H ZZ 4 analysis,theelectroncandidatesarerequiredtohave transversemomentum pT largerthan7GeVandareconstructed | % | < 2.5.The reconstructionefciencyforisolatedelectronisexpectedtobeabove & 90% overthe fullECALacceptance,apartfromsomenarrow"crack"regions. TheidenticationofelectronsreliesonaBoostedDecisionTree(BDT)multivariate technique[ 41 ]thatcombinesobservablessensitivetotheamountofbremsstrahlung alongtheelectrontrajectory,thegeometricalandmomentummatchingbetweenthe electrontrajectoryandassociatedclusters,aswellasshowershapeobservables.The multivariateidenticationwastrainedusingaHiggsbosonMonteCarlosampleforthe signalanda W +1 -fakeelectrondatasampleforbackground.ThisallowstheBDTto betraineddirectlyonadatacontrolsampleforafake-enrichedsamplewhichispoorly describedbysimulation.Figure 3-1 showsthecomparisonofthedistributionforthe W +1 -fakeelectronusedinthetrainingandthe Z +1 -fakeelectronwhichisthereal backgroundoftheanalysis. ThedistributionsoftheoutputoftheBDTforthefakesinthetrainingandtest samples,W+jetsandZ+jetsdata,andforrealpromptelectrons(from Z ee simulation)isshowninFigure 3-2 .Thedistributionsshowverygoodagreement betweenthetrainingandapplicationsampleintheanalysis,whicharebothindependent andbuiltondata.Verygooddiscriminationpowerbetweenpromptandfakeelectronsis observed. Foridenticationonly,theimprovementoftherejectionpoweragainstfakes,tested onthedatacontrolsamplesdescribedabove,isvisibleinawiderangeofefciencies foraBDTIDwithrespecttoacutbasedapproach.Foratypicallooseworkingpoint, thegaininefciencyatthesamebackgroundrejectionpointisabout10%perleptonfor 75

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Figure3-1. Distributionofclustershapevariable # i i forthetrainingsampleW+jetsand thetestsampleZ+jetson2012datainthebarrel(left)andintheendcap (right) Figure3-2. DistributionofelectronBDToutputfortrainingsampleW+jets,testsample Z+jetson2012data(fakes)andpromptelectrons( Z ee simulation)inthe barrel(left)andendcap(right) pT > 20GeVanditbecomesevenlargerforlower pT .Signalvsbackgroundefciency or ROC curvesareshowninFigure 3-3 .SignalisfromDrell-YanMonteCarlosimulation samples.Backgroundisfromjetsfakingelectronsinadatasampledominatedby Z+jets. Anoptimizationoftheworkingpointusedintheanalysishasbeenperformed byscanningthecutvaluesforeachcategoryusedinthetrainingoftheBDT(three % 76

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Figure3-3. ROCcurvesfortheelectronmultivariateidentication(BoostedDecision Trees)comparedwiththecut-basedselectionworkingpoints.Electron candidateswith pT > 20GeVareshownforbarrel(left)andendcap(right). regionsandtwo pT bins),performingtheanalysisforeachscenarioandoptimizing theexpectedsignicanceoftheone-,two-,andthree-dimensionalts(asusedinthe statisticalanalysis).Sincepartofthecontributiontotheexpectedsignicancecomes fromthemuonchannels( 4 and 2 e 2 ),inthecasewhenthesignicanceofthetwo scenariosisthesame,theoptimalpointforthe 4 e channelonlyischosen,whichisthe mostsensitivechanneltoelectronidenticationforobviousreasons. ThecutvaluesontheBDToutputresultingfromtheoptimizationprocedureare summarizedinTable 3-1 Table3-1. BDTcutvaluesfortheBDTbasedelectronID. pT range(GeV) % range BDTCutValue(BDT > ) | % | < 0.8 0.47 5 < pT < 10 0.8 < | % | < 1.479 0.004 | % | > 1.479 0.295 | % | < 0.8 -0.34 pT > 10 0.8 < | % | < 1.479 -0.65 | % | > 1.479 0.60 77

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3.1.2ImpactParameterSelection Toensurethattheleptonsareconsistentwitharisingfromacommonprimary vertex,theyarerequiredtohaveanassociatedtrackwithasmallimpactparameter withrespecttotheeventprimaryvertex.Thesignicanceoftheimpactparameterto theeventvertexisused, | SIP 3D = IP ) IP | ,where IP istheleptonimpactparameterin threedimensionsatthepointofclosestapproachwithrespecttotheprimaryinteraction vertex,and # IP istheassociateduncertainty.Hereafter,a"primarylepton"isalepton satisfying | SIP 3D | < 4 3.1.3Isolation Inthisanalysis,particlebasedisolationisapplied,whichhasbeenfoundtobethe bestperformingtypeofisolationintermsofseparationfromfakes.Isolationisdened byperformingthescalarsumofthetransversemomentumoftheparticleow[ 35 ] candidatesreconstructedina # R coneof0.4centeredaroundtheelectron,denedas RelPFiso= / chargedhadron p T + / neutralhadron p T + / photon p T p lepton T (31) Theparticle-basedisolationofa GSF electronrequiressomevetoesonthe candidatesinthecone.Theelectron/gammaphysicsobjectgroup's(POG)recommendations arefollowed: barrelandendcap: 1. vetoallthereconstructedparticleowelectrons(inthemostofthecases,this requirementremovesthepf-electroncorrespondenttotheGSFelectron,with allitsbremclusters) 2. vetoallthechargedhadronsthatsharethesameGSFtrackortheclosest CTFtrackwiththeelectron 3. vetoalltheparticleowphotonsthatsharethesameSuperClusterwith theelectroncandidate.Thisrequirementismeanttoremoveelectronswith missinghitsinthepixelsgreaterthan0thatareacceptedbytheselection,but particleowreconstructsasphotons endcap: 78

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1. vetoallthechargedhadronsinacone # R =0.015aroundtheelectron 2. vetoallthephotonsinacone # R =0.08aroundtheelectron Withthesevetoesthefootprintoftheelectroninbothbarrelandendcapisreduced tolessthan1%(see[ 41 ]). Figure3-4. Methodforcalculatingparticleowbasedisolation. Isolationvariablesareamongthemostpile-upsensitivevariablesinthisanalysis. Pile-upcausesthemeanenergydepositedinthedetectortoincrease,leadingtothe riseofthemeanisolationvalues.Thus,theefciencyofacutonisolationvariables stronglydependsonpile-upconditions.Inordertohaveapile-uprobustanalysis,the isolationvariablehastobecorrected. Thedegradationofisolationperformanceduetopile-upcanbepartlymitigated byassociatingthechargedparticleowcandidatestotheprimaryvertices.However, theneutralcomponent(neutralhadronandphotons),forwhichthisassociationcannot betriviallydone,needspecialtreatment.Amongseveralcorrectionmethods,theone using FastJet [ 42 ],[ 43 ]energydensity( $ )intheeventhasbeenchosentoestimatethe meanpile-upcontributionwithintheisolationconeofalepton.A $ variableisdenedfor 79

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eachjetinagiveneventandthemedianofthe $ distributionforeacheventistaken.The correctiontotheneutralcomponentoftheisolationvariableisthenappliedaccordingto theformula corr 0 neutral pT = max ( uncorr 0 neutral pT % $ A e ,0GeV) (32) wherethe effectivearea ( A e )ofagivencomponentisdenedastheratiobetween theslopeoftheaverageisolation iso and $ asafunctionofnumberofvertices. Theelectron A e arecomputedonselected Z ee eventsindatainseveral % bins tocopewiththetruncationoftheisolationconeintheendcap.Theaverageisolation sumsforuncorrectedandcorrectedparticleowisolationareshowninFigure 3-5 Electronsareselectedwith pT > 20GeVandinadatasampledominatedby Z ee events.Electronsinthebarrelwith | % | < 1areshown.Afterthecorrectionsfortheneutral componenttheaverageisolationbecomesalmostindependentofthenumberofvertices intheevent. Figure3-5. Averageestimateofeventenergydensityintheevent, $ ,and particle-isolationcomponentsasafunctionofthenumberofreconstructed vertices(left).Effectoftheeffectiveareacorrectiononthetotalparticle isolation(right). 80

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Thecutoncorrectedparticleowisolation,relativetotheelectron pT was optimizedwiththeoptimalvaluefoundtobeRelPFiso < 0.4. 3.1.4MomentumAssignment TheelectronmomentumisestimatedfromthecombinedmeasurementofECAL clusterenergyandthetrackmomentum.Sincetheenergyresolutionimproveswith themomentumfortheECAL,whileitdecreaseswithmomentumforthetracker,the combinationdependsontheenergyitself,butalsoontheclusterandthetrackquality. Amultivariateregressionapproachisusedfordeterminingthemomentumofthe electronincludinginformationfromanumberofqualityvariablesofbothclusterand track,tosignicantlyimprovetheresolutionofthemeasurement.Themainimprovement isintheECALresolution,sinceforthebulkofthemomentum( eT > 15 GeV)the measurementisdominatedbyECAL,butforverylow pT electronsthesimultaneous useofECALandtrackervariablesfurtherimprovesthemomentumandthereforethe massresolutionofthe4 invariantmass.Differentsetsofinputvariablesareusedinthe regressiondependingonwhethertheelectronisdetectedinthebarrelortheendcapof theECAL.Detailsofthemethodandperformancecanbefoundinreferences[ 44 ],[ 45 ]. ThemeasuredrawECALenergyoftheelectronsuper-clusterisrstcorrectedfor differenteffectssuchas: thenon-containmentoftheelectronshowerinthereconstructedclusters theenergyleakageinthegapsbetweencrystals,modulesandsuper-modulesas wellasinthetransitionregionbetweenthebarrelandtheendcaps theenergyleakageinthehadroniccalorimeter theenergylostbecauseofupstreammaterial additionalenergydepositscomingfrompile-upinteractions,overlappingthe electronshower Theirimpactonthemeasuredelectronenergyisassessedfromvariousinformation: theenergyofthesuper-cluster 81

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thepositionofthesuper-cluster,formaterialbudgeteffects therelativepositionswithrespecttomoduleandsuper-modulegaps,forenergy leakagebetweenmodules shapevariablesandlocalcrystalcoordinates,forenergyleakageoutsidethe clustersandbetweencrystals therelativepositionsandenergies,aswellasbasicshapevariables,ofthethree sub-leadingclustersformingthesuper-cluster informationfromtheenergydepositsinthepreshower thenumberofreconstructedprimaryverticesandameasureoftheenergydensity ofthepile-upintheevent Intotal,60variablesareusedforbarreland62forendcap. Eachregressionistrainedseparatelyforbarrelandendcapelectrons.Inorder totestagainstover-training,thesesampleswereexplicitlydividedintwo.Onlyone halfoftheeventsareusedfortraining,whiletheremaininghalfareusedtotestthe performanceoftheregression.Thetargetoftheregressionischosentobetheratio ofthegeneratedenergytotherawenergyofthesuperclusterforbarrelelectrons,and theratioofthegeneratedenergytothesumofthesuperclusterrawenergyandthe preshowerenergyforendcapelectrons. Theperformanceisevaluatedasafunctionofelectron pT andforfourdifferent % regions,wheretheregressionenergymeasurementusedinthisanalysis,iscompared totheoneusedpreviouslyinthisanalysis[ 44 ]andthesuperclustercorrectedenergy. ThisisshowninFigure 3-6 .Averygoodimprovementinresolutionwithrespectthe standardcorrectionsisobservedoverawiderangeof pT spectrumandpseudorapidity. TheregressioncorrectedECALenergyislinearlycombinedwiththetrack momentumusinganotherBDTforestinordertobenetfrombothmeasurementsin thenalmomentumestimation.Thisforestevaluatesonecombinationofweightbased oninputvariablesfrombothmeasurements ThecorrectedECALenergyanditsrelativeerror 82

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Figure3-6. Effectivewidthof E reco / p true distributionsasafunctionof pT andfour differentregionsofthecalorimeter. Thetrackmomentumanditsrelativeerror TheratiooftheECALenergyandthetrackmomentum,andtheerroronthisratio Theratioofthetworelativeerrors Theelectroncategory TwoagsforECALdrivenandtrackerdrivenelectrons Aagforelectronsinthebarrelorendcaps. Forfurtherdetails,see[ 45 ]. InFigure 3-7 ,thecomparisonofthereconstructedHiggsbosonmassforthefour electronsandtwoelectronstwomuonsnalstateareshown.Atissuperimposed 83

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andtheparameterestimatingthecoreresolutionisshownas # dCB .TheeffectiveRMS ofthedistribution,includingthetailsinthemassrangeshownisalsoreported.An improvementintheresolutionofmorethan10%isobserved,inagreementwithwhatis observedwith Z eventsindata. Figure3-7. AcomparisonofthereconstructedHiggsbosonmassdistributionsafter applyingMonteCarlotodatacorrectionsforthestandardelectron momentumassignmentandtheregressionassignment,forthe4e(left)and 2e2 (right)channel. 84

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3.1.5EnergyCalibrations Thequalityofthemomentummeasurementforelectronscansubstantiallyvary dependingontheelectroncharacteristics. Theresolutionismainlydominatedbytheuctuationsofthemeasuredenergy duetobremsstrahlunginthetrackermaterial.Thisresultsina 4 massresolutionthat variesbroadly,byasmuchasafactorof2-3.Mixingtogethereventswithwelland poorlymeasured 4 massesdilutestheHiggssearchsensitivity.Therefore,theanalysis usesthepropagationoftheleptonuncertaintytoestimatethe 4 massforproper accountingofthesignalmassresolutionsforindividualevents.Inordertohaveagood determinationofthisuncertainty,butabovealltohaveadescriptionoftheresolutionof thesignalmodelwhichcorrespondstothedata,onemustmeasuretheuncertaintyon highstatisticscontrolsamples,dependingontheelectronkinematicsandquality,which isdonewitha Z ee sample. Theabsolutescalehasalsotobecalibratedondata,becausethemeasurementof theHiggsmassdependscruciallyontheuncertaintythatwecanassigntotheleptons inthefullphasespaceoftheanalysisfora125GeVHiggs,whichcoversleptonsfrom7 to100GeV.Allofthesemomentacanbecoveredwith Z ee andlowmassresonance samples. 3.1.6DerivationofScaleandResolutionCorrections Inthissection,thederivationofthecorrectionsthathavetobeappliedonsimulation toachieveagoodmatchingoftheenergyresolutionobservedindataareshown.This isdonethroughtheapplicationofextrasmearingandthederivationofcorrectionsto thescalethatareappliedtodatatoremovethedetectorbiases.Bothcorrectionsare derivedon Z ee controlsample. Theprocedureisdescribedin[ 46 ]( H (( analysis),anditisrepeatedhereforthe particularenergyregressionusedinthisanalysis.Theprocedureconsistsoftwosteps: 85

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Absolutescalecorrectionsfordata. Thesuperclusterenergyscaleistuned andcorrected,varyingthescaleinthedatatomatchtheMonteCarloin Z ee events.Thedata-MCdifferenceistimedependent;moreoverthetime dependenceisnotthesameindifferentpseudorapidityregionswhileitisvery similarforshoweringandnonshoweringelectrons.Thisisdoneintwo R 9 bins, sincethisvariablecategorizestwodifferentkindsofclusters.Thenalenergy scalecorrectionisthenderivedastheproductofthetwocorrectionsinn(run range)x4(pseudorapidityregion)x2( R 9 )categories. MCenergysmearing. AmethodwhichappliesdirectsmearingtotheMC energieshasbeendeveloped[ 46 ]toestimatemoreefcientlytheeffective resolutionoftheelectromagneticcalorimeter.Theelectronsuperclusterenergyis modiedbyapplyingaGaussianmultiplicativefactorcenteredin 1+# P andwith a # # resolution,where # P istheenergyscalecorrectionand # # istheadditional constanttermintheenergyresolution. Twoexamplesoftheeffectoftheapplicationsofthescaleandsmearingcorrections on Z ee eventsareshownintwocategoriesinFig. 3-8 .Redlledhistogram representstheun-smearedsimulation.Blackhistogramrepresentsthesimulation afterthesmearinghasbeenapplied,andpointsrepresents8TeVdatawiththescale correctionsapplied. Figure3-8. Datatosimulationcomparison,for Z ee events.Left:eventswithboth electronswith | % | < 1and R 9 < 0.94.Right:eventswithoneelectronwith | % | < 1and R 9 < 0.94andtheotherelectronwith1.566 < | % | < 2and R 9 < 0.94. 86

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Aftertheseoverallcorrections,datatosimulationdifferencesstillexistsbecause oftheslightkinematicandphasespacedifferencesbetweenthecalibrationsample ( Z ee )andtheapplicationsample(electronsfromlowmassHiggsdecay).Inthe followingsections,theexperimentalsystematicsrelatedtothiscalibrationaredescribed. 3.1.7ScaleandResolutionMeasurementsfrom Z ee Forelectrons, Z ee invariantmasscanbebuiltindifferentcategoriesin % and separatingwellandpoorlymeasuredelectronsusingtheelectronclassication.This classicationdescribestheamountofenergyradiatedbybremsstrahlungandthequality ofreconstruction,therebyseparatingdifferentmomentumresolutions.Eventsarelooked atinlowandhighpile-upregions.ThedistributionsarettedwithaBreit-Wigner(xed parameters)convolutedwithaCrystalBall(freeparameters).Figure 3-9 showsthe resultsobtainedthiswayusing2012dataandcomparingtoMCexpectations.Reddots are2012datawithatsuperimposed(redline).Bluesquareissimulationwithat superimposed(blueline). Systematicuncertaintiesonelectronenergyscalecanbeextractedfromthese results.TheuncertaintyisestimatedasthemaximumdeviationbetweendataandMCof thetted Z ee peakpositionindifferentcategoriesof % andelectronclasses.Overall, dataandMCagreeswithin0.4%.SplittingbyECALregion,wereach0.1%forelectrons inthebarrel,andupto0.4%forelectronsintheECALendcaps. Thedependencyoftheelectronmomentumscalewithrespecttopile-uphas alsobeenchecked.Thereconstructed Z ee peakisbuiltfordifferentslicesof numberofvertices,inbothdataandMC,andarettedasdescribedabove.Thereare nosignicantvariationsofthe Z peakwiththenumberofvertices,anddataiswell describedbytheMC,ascanbeappreciatedinFigure 3-10 Fortheresolution,asimilarstrategyhasbeenadopted,comparingthetted # CB betweendataandMC.Thelargestrelativedifferenceamountsto10%.Thesystematic uncertaintyistakenasthedifferencebetweenthepredictedandmeasuredresolution. 87

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Figure3-9. Z ee eventscategorizedaccordingtotheelectronclassicationforthe bestcategoryofevents,withbothnon-showeringelectronsinthebarrel (goldenorbig-brem)(left)andtheworstcategory,withbothshowering electronsintheendcap(right). Figure3-10. Asafunctionofthenumberofvertices,differencesbetweendataandMC ofthepeakposition,dividedbythepeakpositioninMC. ThisisshowninFigure 3-11 .Eventsarecategorizedaccordingtotheelectronclassand pseudorapidityregionofeachleg( G :goldenelectroncategory, S :showeringelectron, B :electroninthe | % | rangeoftheECALbarrel, E :electroninthe | % | rangeoftheECAL endcaps).Resultsarepresentedfordatacollectedat + s =8 TeV 88

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Figure3-11. Instrumentaldi-electroneffectiveresolutionasmeasuredfrom Z ee eventsandcomparedtosimulation. 3.1.8Electronscalelinearitymeasurementfrom Z ee J / and Thestudiesdescribedabovecheckthescalemainlyforelectronswithrelatively highmomenta.Furtherpossiblenon-linearityinthemomentumestimationmaybe accountedfordifferentiallywithrespecttheMonteCarlowhenpropagatingtheelectron calibrationestimatedatthe Z scaletothescaletypicaloftheelectronsofanHiggswith mass m H & 125GeV. Thesedata-MCdiscrepanciesmaybeduetotheimperfectionofmaterialinthe forwardregionoftheECAL,aswellasanimperfectdescriptionofdetectorgeometry. Toestimatethis,weperformtsofthe Z ee invariantmassdistributionfor different pT and | % | oftheprobeelectrons.IneachtthesignalPDFisdescribedwitha templatebuiltonDrellYanMonteCarlo,andsmoothedinthecaseoflowstatistics.Then thetemplatetisperformedallowingonesinglescaleparametertooattomatchdata andMonteCarlo.Theprocedureisvalidatedallowinganextrasmearinginthet.With thesetemplatets,extrasmearingisaccomplishedthatiscompatiblewiththeofcial onesreportedabove. 89

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Figure 3-12 showsanexampleofthesetsof Z ee for8TeVdataforthe15-20 GeV pT bin. Figure3-12. Templatetsforthe Z ee whentheprobehas 34 < pT < 40 GeVinthe centralbarrel, | % | < 1(left),orintheendcap(right)for8TeVdata. Sincethepurityandstatisticsisnotgoodfor pT < 15GeV,thescalecanbe measuredwithacleansampleofboosted J / and (1S)thatcanbeselectedindata withdi-electrontriggersandtheelectronselectionusedinthisanalysis.Thetopologyof this(nonisolated)sampleissuchthattheycannotbeusedforefciencymeasurements, butstillthescaleisreliableandtheycancompletethegapinthe pT range7-15GeV. The (2S,3S)cannotberesolved,sotheycannotbeusedtoestimatetheelectron scale.ThettothemainpeakisperformedwithaCrystalBallfunction.Examplesof thesetsforthelowest pT binsareshowninFigure 3-13 Extrashiftsasafunctionof pT and | % | aresummarizedinFigure 3-14 for7and 8TeVdata.Theextrashiftisnegligiblearoundthepointwherethecalibrationwasdone, whilethereisanextrashiftwhengoingtolower pT .Themaximumdriftis & 0.1%inthe barreland & 0.3%intheendcapforboth7and8TeVdata.Conservatively,thevalue obtainedin8TeVfortheendcapdataisalsousedfor7TeVdata(thedifferencebeing onlyintheendcap). 90

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Figure3-13. Examplesoftsto8TeVdatafor J / ee events,whereelectronprobe has7 < pT < 10GeVinthebarrel(left)and ,whereelectronprobehas 10 < pT < 15GeVinthebarrel(right). Figure3-14. Extradata/MonteCarloshiftsasafunctionofelectron pT for7TeVdata (left)and8TeVdata(right)computedwith J / ! and Z intodi-electron resonances. 3.1.9EfciencyMeasurement Theefcienciesforreconstruction,identication,andtriggerforelectronsand muonsismeasuredwithdatabasedonaselectionofeventsofinclusivesingle Z production.Thetag-and-probetechnique[ 47 ],[ 48 ]combinestherequirementsofamass constraintfromapairofbasicobjects(e.g.tracksformuons,orclustersofcalorimetry 91

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cellsforelectrons)withatightleptonselectionappliedononeleg(the tag ),sotoensure sufcientpurity.Theotherleg(the probe )isusedtomeasuretheefciencyofagiven reconstructionalgorithmoridenticationcriterium.Theefciencyisdenedastheratio ofthenumberofpassingprobestothetotalnumberofprobesbeforethecut. Inthissection,themeasurementofthereconstructionandselection(including identication,isolationandimpactparametercuts)efciencyforelectronsisdescribed. 3.1.10ReconstructionEfciency Theelectronreconstructionefciencyhasbeenmeasuredinthedataset"January 22"re-recoanditsscalefactormeasuredwithrespectthe"Summer12"simulationfor the8TeVdatawithtemplatetstothedi-electroninvariantmassdistributionina Z ee sample. Theselectionrequiresonereconstructedelectronidentiedwithatightcut-based identicationwith pT > 25GeVmatchedtotheelectrontriggerlegofthededicated tag-and-probetrigger.Theprobeisareconstructedsupercluster,whichmaymatch ( pass )ornotmatch( fail )thesuperclusterofareconstructedelectrondifferentfrom thetag.Inordertoreducethebackgroundinthefailsampleupto pT =30GeV,a trackerisolation / pT trk / pT e < 0.15isrequired.Inaddition,theeventmusthave PF % MET < 20GeVtoreducebackgroundssuchas W + jets .Thebiasintroduced bytheserequirementsontheefciencyisestimatedonsimulationtobemuchlessthan 1%.Thisbiasiscoveredbythesystematicuncertainty.Twoexamplesofpassandfail tsfortwo % binsofthekinematicbin10 < pT < 15GeVareshowninFigure 3-15 .Black pointsrepresentdata,whilethebluelineisthesignalmodelfromsimulation. Thedata-MCscalefactorsarefoundtobeconsistentwithoneinallthe pT bins consideredintheanalysis(seeTable 3-2 andFigure 3-16 ).Thesystematicuncertainty rangesfrom5%(7%)inthebarrel(endcap)forthe10-15GeVbin,to1%forbothbarrel andendcapfor pT > 20GeV.Thisscalefactor,withitsuncertainty,isappliedtothe 92

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Figure3-15. The m !! distributionsandsuperimposedtemplatetsforpassing(left)and failing(right)probesusedfortheelectronidenticationefciency measurementinthe10-15GeV pT bin(top)andfor 2.0 $ | % | < 2.5 (bottom). analysistogetherwiththeidenticationandisolationscalefactors,describedlaterinthis section. 93

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Figure3-16. Electronreconstructiondata-to-simulationefciencyratiofor8TeV "January22"re-recodata,obtainedwithtagandprobetechnique describedinthetext,asafunctionofthesupercluster | % | and pT 94

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Table3-2. Electronreconstructionefcienciesandscalefactorsfor8TeVdatawith combinedstatisticalandsystematicerrors. p T % Dataeff. errorMCeff. errorScalefactor error 10-150-1.44420.868 0.0480.898 0.0020.967 0.054 15-200-1.44420.936 0.0480.939 0.0010.997 0.051 20-300-0.8 0.952 0.0100.969 0.0000.982 0.010 30-400-0.8 0.967 0.0100.978 0.0000.988 0.010 > 400-0.8 0.972 0.0100.982 0.0000.990 0.010 10-150-1.44420.868 0.0480.898 0.0020.967 0.054 15-200-1.44420.936 0.0480.939 0.0010.997 0.051 20-300.8-1.44420.962 0.0100.969 0.0000.993 0.010 30-400.8-1.44420.972 0.0100.979 0.0000.993 0.010 > 400.8-1.44420.976 0.0100.983 0.0000.992 0.010 10-151.4442-1.5660.804 0.1350.714 0.0081.126 0.190 15-201.4442-1.5660.733 0.0690.767 0.0050.955 0.090 20-301.4442-1.5660.895 0.0140.881 0.0021.015 0.016 30-401.4442-1.5660.936 0.0100.950 0.0010.985 0.011 > 401.4442-1.5660.957 0.0100.971 0.0010.985 0.010 10-151.566-2.50.937 0.0560.854 0.0021.097 0.066 15-201.566-2.50.907 0.0460.897 0.0011.012 0.052 20-301.566-2.00.937 0.0100.948 0.0010.988 0.010 30-401.566-2.00.953 0.0100.960 0.0000.992 0.010 > 401.566-2.00.961 0.0100.969 0.0000.991 0.010 10-151.566-2.50.937 0.0560.854 0.0021.097 0.066 15-201.566-2.50.907 0.0460.897 0.0011.012 0.052 20-302.0-2.50.894 0.0100.892 0.0011.002 0.011 30-402.0-2.50.913 0.0090.909 0.0011.004 0.010 > 402.0-2.50.931 0.0090.928 0.0001.004 0.010 95

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3.1.11SelectionEfciency Indata,electrontagsofthetagandprobepairaredenedasanelectronfullling thefollowingcriteria: pT > 20 GeV and | % | < 2.5 passingtheVBTFSimpleCuts,WorkingPoint60%(WP60)whichinvolvescuts onpureidenticationvariables( | # % in | | # in | H / E and # i i ),trackandcalorimeter isolationaswellasconversionremoval[ 49 ]. beingmatchedgeometricallytothelegofthedoubleobjecttriggerusedforthe studythathasrequirementontheelectronIDattriggerlevel. Thesetagsarecombinedwithaprobewhichisselectedasareconstructed electronwithintheacceptanceandtheirinvariantmassisthencomputed.Thebasic techniquereliesontheextractionofthesignalyieldforpairsinwhichtheprobepassed ornotpassedtheselectioncriteriatoevaluatethesingleelectronefciency.Twotting techniqueshavebeenadoptedtoextractthesignalandbackgroundyields: FitswithMC-driventemplates .Thismethodusestheshapeofpassingand failingprobesforthesignalwhichisthesmoothedbinnedhistogramderivedfrom thefullsimulationof Z ee eventswiththesameselectionappliedondata,with thescalewhichisallowedtooatandthewidthtoscalebyaddingextrasmearing totthedata.Thismethodhastheadvantagethattheshapeofthesignalismore constrainedtotheMonteCarloandthetsinthemostdifcultpartofthephase spaceconvergemorestably.AnexampleofthetemplatetisshowninFigure 3-17 .Blackpointsrepresentdata,whiletheredlineisthebackgroundmodeland thebluelineissignal+background. Fitswithanalyticalfunction .Thismethodusestswherethesignalshapeis fullyparametric(ABreitWignerconvolutedwithaCrystalballisusedtomodelthe resolutionfunctionincludingthetails)andmostoftheparametersareleftoating indata.Thistechniqueismoreversatile,becausethefunctionalformwithoating parametersadaptsmoretothedata,butitcanconvergetosomebadshapefor thecaseswherethesignal/backgroundratioislow.Anexampleoftemplatetis showninFigure 3-18 .Againhere,blackpointsrepresentdata,whiletheredlineis thebackgroundmodelandthebluelineissignal+background. Sincethetwomethodsareappliedonanoverlappingcontrolsample,buttheyhave differenttsystematics,thatformostofthecasesisthedominatinguncertainty.Thetwo 96

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Figure3-17. The m ee distributionsandsuperimposedtemplatetsforpassing(left)and failing(right)electronprobesusedfortheelectronidenticationefciency measurementinthe7-10GeV pT bininthebarrel(top)andendcap (bottom). arecombined,takingtheaverageoftheefciencyineachkinematicbin,andtakingthe maximumdeviationinthettedvaluesastheuncertainty. Themeasuredidenticationefciencies,shownseparatelyforthetwomethodsasa functionoftheelectronprobe pT (with pT > 7 GeV )areshowninFigure 3-19 for7TeV dataandinFigure 3-20 for8TeVdata.Theefciencymeasuredonsimulationisalso showninthesameplot. Thetotaluncertaintyiscomputedasthefollowing: Statisticaluncertainty :sincethetwomethodsarebasedonthesamedataset, statisticaluncertaintyistakenfromtheoneofthetwo Systematicuncertainty :itistakenasthedifferencebetweenthettedvaluefrom thetemplateandthefunctionalformt 97

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Figure3-18. The m ee distributionsandsuperimposedfunctionalformtsforpassing (left)andfailing(right)probesusedfortheelectronidenticationefciency measurementinthe7-10GeV pT binandforbarrel(top)andendcap (bottom). Totaluncertainty :itistakenasthesuminquadratureofthetwoabove Theuncertaintiesareshowningure 3-21 andinFigure 3-22 for7TeVand8TeV, respectively. 3.1.12Summary Belowisasummaryofallrequirementsonelectronobjectsintheanalysis. Longitudinalimpactparameterlessthan0.5mmwithrespecttotheprimaryvertex 98

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A B C D Figure3-19. Electronidenticationefcienciescomputedwiththetag-and-probemethod on7TeVdataasafunctionoftheprobe pT infourdifferent % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and(d) 2 $ | % | < 2.5 Horizontalimpactparameterlessthan1cmwithrespecttotheprimaryvertex | SIP 3D | lessthan4.0 Maximumof1missinghitinthetrackerallowed pT greaterthan7GeV BDTelectronIDpassescutsasshowninTable 3-1 RelPFIso < 0.4 99

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A B C D Figure3-20. Electronidenticationefcienciescomputedwiththetag-and-probemethod on8TeVdataasafunctionoftheprobe pT infourdifferent % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and(d) 2 $ | % | < 2.5 100

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A B C D Figure3-21. Datatosimulationscalefactorsforelectronselectionefciencycomputed withthetag-and-probemethodon7TeVdataasafunctionoftheprobe p T infourdifferent % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and(d) 2 $ | % | < 2.5 101

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A B C D Figure3-22. Datatosimulationscalefactorsforelectronselectionefciencycomputed withthetag-and-probemethodon8TeVdataasafunctionoftheprobe p T infourdifferent % bins:(a) | % | < 0.78 ,(b) 0.78 $ | % | $ 1.442 ,(c) 1.566 $ | % | < 2 and(d) 2 $ | % | < 2.5 102

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3.2Muons 3.2.1ReconstructionandIdentication InthestandardCMSreconstructionforppcollisions,muontracksarerst reconstructedindependentlyintheinnertracker( trackertrack )andinthemuonsystem ( standalone-muontrack ).Basedontheseobjects,tworeconstructionapproachesare used[ 47 ]: GlobalMuon(outside-in). and TrackerMuon(inside-out). GlobalMuonreconstruction(outside-in). Foreachstandalone-muontrack, amatchingtrackertrackisfoundbycomparingparametersofthetwotracks propagatedontoacommonsurface,anda global-muontrack isttedcombining hitsfromthetrackertrackandstandalone-muontrack,usingtheKalman-lter technique[ 50 ].Atlargetransversemomenta, pT 200 GeV ,theglobal-muont canimprovethemomentumresolutioncomparedtothetracker-onlyt[ 51 ],[ 52 ]. TrackerMuonreconstruction(inside-out). Inthisapproach,alltrackertrackswith pT > 0.5GeVandtotalmomentum p > 2.5GeVareconsideredaspossible muoncandidatesandareextrapolatedtothemuonsystemtakingintoaccountthe magneticeld,theaverageexpectedenergylosses,andmultiplescatteringinthe detectormaterial.Ifatleastonemuonsegment(i.e.,ashorttrackstubmadeof DTorCSChits)matchestheextrapolatedtrack,thecorrespondingtrackertrack qualiesasaTrackerMuon.Track-to-segmentmatchingisperformedinalocal (chamber)coordinatesystem,wherelocal x isthebest-measuredcoordinate(in the r plane)andlocal y isthecoordinateorthogonaltoit.Theextrapolatedtrack andthesegmentareconsideredtobematchedifthedistancebetweenthemin local x islessthan3cm,orifthevalueofthepullforlocal x islessthan4,where thepullisdenedasthedifferencebetweenthepositionofthematchedsegment andthepositionoftheextrapolatedtrack,dividedbytheircombineduncertainties. TrackerMuonreconstructionismoreefcientthantheGlobalMuonreconstruction atlowmomenta, p 5 GeV ,becauseitrequiresonlyasinglemuonsegmentinthe muonsystem,whereasGlobalMuonreconstructionisdesignedtohavehighefciency formuonspenetratingthroughmorethanonemuonstationandtypicallyrequires segmentsinatleasttwomuonstations. Thankstothehightracker-trackefciency[ 53 ]andaveryhighefciencyof reconstructingsegmentsinthemuonsystem,about99%ofmuonsproducedinpp collisionsandhavingsufcientlyhighmomentumarereconstructedeitherasaGlobal 103

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MuonoraTrackerMuon,andveryoftenasboth.CandidatesfoundbothbytheGlobal MuonandtheTrackerMuonalgorithmsthatsharethesametrackertrackaremerged intoasinglecandidate.Muonsreconstructedonlyasstandalone-muontrackshave worsemomentumresolutionandlessfavorablecollisionmuontocosmic-raymuonratio thantheGlobalandTrackerMuonsandaretypicallynotusedinphysicsanalyses. 3.2.2IdenticationandGhostMuonRemoval Thecombinationofdifferentalgorithmsprovidesarobustandefcientmuon reconstruction.Agivenphysicsanalysiscanachievethedesiredbalancebetween identicationefciencyandpuritybyapplyingaselectionbasedonvariousmuon identicationvariables.Forthisanalysiswechoosethe ParticleFlowMuonselection ThePFMuonsareselectedamongthereconstructedmuontrackcandidatesby applyingminimalrequirementsonthetrackcomponentsinthemuonsystemandtaking intoaccountamatchingwithsmallenergydepositsinthecalorimeters.Moredetailsof theParticle-FlowMuonselectionaredescribedin[ 54 ]. Startingfromthe52XreleasesofCMSSW,achangeinthetrackreconstruction hasbeenimplementedtobetterreconstructtracksfromnuclearinteractions.This reconstructionfavorsshortertracksingeneralandleadstothecreationof"badmuons" (orghostmuons).Twotypeswereidentied: SplitTracks :thetrackertrackofamuonisbrokenintwo,andbothtracksare identiedasmuons.Thesignatureisasfollows:thetrackssharemuonsegments, haveasmall # R,andhavethesamecharge. MismatchTracks :thetrackofanotherparticleintheeventisfoundtobe compatiblewiththesamemuonhits.Thesignatureis"sharedsegments". Theseghostmuonshavealmostnoinuenceinthesignalregionthankstothe applicationofParticleFlowMuonIdenticationcriteria(seenextsection).However, inthebackgroundcontrolregionwherethesecriteriaarerelaxed,ghostmuonsare allowedtoenter,andthuscouldperturbtheestimationofreduciblebackground.Simple selectioncriteriaareappliedtoalleventsintheanalysistoremovetheseghostmuons: 104

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Requirea # R > 0.02 betweenthemuons.Itrejectssplittracks(andsomelow massresonances). Requirethenon-Global,TrackerMuontobearbitrated.Itremovesalargefraction ofthemismatchtracks. Afterthesecuts,theresidualcontaminationofghostmuonsinthebackground controlregionisestimatedtobefrom4to9%ofthetotalevents.Suchalevelof contaminationisacceptablesincetheoverallbackgroundislowin -channelsanda largeuncertaintyisassignedtothebackgroundyields.Forthisanalysis,anadditional requirementisadded,designedtokilltheremaining"mismatchedtracks"events: Amuonistaggedasghostifithasmorethan 50% ofsharedsegments. PreferenceisalwaysgiventothemuonspassingthePFMuonIdentication criteria. Forsame-signmuonswith # R < 0.03 ,wepickthebestaccordingto # ( pT ) / pT Forothercases,wepickthemuonwiththelargestnumberofsegments.Final ambiguities,ifany,areresolvedbychosingthemuonwithhighest pT AGlobalMuonorTrackerMuonwithwithtwoarbitratedmatchesisnevercleaned. Ithasbeencheckedthattheimpactofalltheseghostmuonscleaningrequirements haveanimpacton H ZZ 4 oftheorderof0.03%,thusnegligible. 3.2.3ImpactParameterSelection Thesameselectionisappliedonthemuonsignicanceofimpactparameterasfor theelectrons,asdescribedinsection 3.1.2 | SIP 3D = IP ) IP | < 4 3.2.4Isolation Isolationformuonsisalsotheparticleowisolation,asdescribedfortheelectrons. Allreconstructedparticleowcandidatesidentiedaselectronsormuonsarevetoedin thecalculationoftheisolationdeposit.Inthisway,thecontributionfromthemuonitself isremovedaswellasanycontributionfromotherleptonsdecayingfromtheHiggs. 105

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Thepileupcorrectionstrategyisdifferentthanfortheelectroncase.Inthecase ofmuons,asocalled # & correctionisusedinsteadoftheeffectiveareaapproachfor electrons.Ithastheadvantagethat A e doesnotneedtobecomputed.Thecorrected isolationisthendenedasfollows: RelPFiso = / chhad pT +max( / neuthad eT + / photon eT % # & ,0) pT lepton (33) where / chhad pT isthesumofthetransversemomentumofthechargedhadrons originatingfromtheprimaryvertex,while / neutrhad eT and / photon eT arethetransverse energyoftheneutralhadronsandthetransverseenergyofthephotonsrespectively. # & istheestimationoftheenergydepositofneutralparticles(hadronsandphotons)from pile-upvertices: # & = 1 2 / chhad PU pT whichiscomputedfromthetracksnotassociated withtheprimaryvertexofthecollision,thusgivinganevent-by-eventestimateofthe pile-upcontribution.Thefactor1/2correspondstoanaiveratioofneutraltocharged particles,measuredinjetsinreference[ 55 ].Figure 3-23 showstheaveragecorrected particleowisolationformuonsindata. Figure3-23. Efciencyofuncorrectedparticleowisolationandcorrectedparticleow isolation(both # & andEffectiveAreacorrectedisolation)asafunctionof thereconstructednumberofverticesin Z eventsselectedfromdata. 106

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Sincetheperformanceofthe # & correctiontotheisolationisalmostidenticalto theeffectiveareacorrection,thesameworkingpointfortheisolationhasbeenchosen, RelPFiso < 0.4. 3.2.5EnergyCalibrations Asithasbeendescribedfortheelectroncaseinsection 3.1.5 ,correctionsfor muonsscaleandresolutionarealsoderived.Inthiscase,theso-called MuScleFit correctionsareused,whicharefoundtoalsoagreewithanalternativemethodof derivationofthecorrectionscalled Rochester corrections. 3.2.6DerivationofScaleandResolutionCorrections Theprecisemeasurementofleptonmomentumisoneofthemaingoalsforthis analysiswhichaimsatreconstructingthemassoftheHiggsbosoncandidateswiththe bestpossibleaccuracy. Forthisreason,thereconstructedmomentaofthemuonswerecorrectedbothin dataandsimulationinordertoremoveremaininglocalbiasesinthemeasured pT Thesebiasesaremainlyduetothenon-perfectknowledgeofthethedetector,as wellasnon-uniformmagneticeldsandthepresenceofmaterialinfrontofsensors. CorrectionswerederivedwiththeMuScleFit[ 56 ],[ 47 ]toolkitonsamplesofrealand simulated Z eventsbothat7and8TeV. MuScleFitisbasedonanunbinnedmaximumlikelihoodt.Ateacheventa probabilityofobservingadimuonwithareconstructedinvariantmassisassigned takingintoaccountthenaturalwidthoftheresonance,thepresenceofpossiblebiases inreconstructingthe pT ofthemuonsandtheniteresolutionofthedetector.Thelast twotermsenterinthelikelihoodthoughaparametrizationanditispreciselythegoalof themaximizationtodeterminethebesttvaluesoftheparameters. 3.2.7ScaleandResolutionMeasurementsfrom Z J / and Themomentumscaleandresolutionafterthecalibrationarevalidatedindatausing dimuonsfrom J / ! and Z decays,tocoverthefullmomentumrangerelevantforthe 107

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H 4 search.PFmuonswith pT > 5 GeV areconsidered,andfor Z decays,thePF isolationand SIP 3D criteriausedintheHiggsanalysisarealsoapplied. Theeventsareseparatedincategoriesaccordingtotheaverage pT and | % | ofthe twomuons,andthedimuonmassdistributionsineachcategoryarettedtoextractthe massscaleandresolution.Asthesignallineshapeforthe H 4 searchisextracted fromsimulatedevents,onlytherelativedifferencebetweendataandsimulationinthe momentumscaleandresolutionisrelevantfortheMuScleFitresult,andthereforethe resultsarepresentedintermsofthetwoquantities # M M = M data % M sim. M sim. # # # = # ( M ) data % # ( M ) sim. # ( M ) sim. (34) In J / decays,theresonantsignalismodeledwithaCrystalBallandthebackground withathirdorderBernsteinpolynomial.Themassscaleandresolutionareestimated fromthemeanandsigmaoftheCrystalBall.For Z decays,theparameterizationused isanumericalconvolutionofaBreit-WignerandaCrystalBall,andthebackground isneglected.For decaysindata,thedimuondistributionismodeledasthesum ofthreeCrystalBallscorrespondingtothe1S,2Sand3Sstates,constrainingthe massseparationbetweenthethreepeakstotheirnominalvaluesfromPDG[ 57 ]and assumingaconstant # ( M ) / M forthethree.Thebackgroundismodeledasafourth orderBernsteinpolynomial.Forsimulated events,onlythe1Sstateisused,andis modeledwithasingleCrystalBall.Exampletstothedimuonmassdistributionin8TeV dataandsimulationareshowninFigures 3-24 and 3-25 TheresultsforthemomentumscaleandresolutionareshowninFigures 3-26 and 3-26 ,respectively.Markersfordifferent pT and | % | binsareslightlydisplaced horizontallyforlegibilitypurposes.Theuncertaintiesshownarestatisticalonly.In7 TeV,afterthecalibration,therelativemomentumscaleisstabletowithin 0.1% ,andthe resolutiontowithinabout 10% .Thecalibrationfor8TeVdataisslightlylessaccurateat lowmomentumthanthe7TeVone. 108

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Figure3-24. Exampletstothedimuonmassshapesinthecentralbarrel, | % | < 0.7 (0.4 for J / ),indata(left)andsimulation(right),formuonsfrom J / ! and Z Average pT ofthetwomuonsis5-7GeVfor J / ,10-20GeVfor and 20-45GeVfor Z 109

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Figure3-25. Exampletstothedimuonmassshapesintheendcap,( 1.6 < | % | < 2.0 for J / 1.5 < | % | < 2.4 for and 1.3 < | % | < 1.9 for Z ),indata(left)and simulation(right),formuonsfrom J / ! and Z 110

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Figure3-26. Relativedifferencebetweenthedimuonmassscalesindataandsimulation extractedfrom J / ! and Z decays,asfunctionoftheaveragemuon pT (left)and | % | (right)forthe7TeVdata(top)and8TeVdata(bottom). 111

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Figure3-27. Relativedifferencebetweenthedimuonmassresolutionsindataand simulationextractedfrom J / ! and Z decays,asfunctionoftheaverage muon pT (left)and | % | (right)forthe7TeVdata(top)and8TeVdata (bottom). 112

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3.2.8EfciencyMeasurement Theoverallofineselectionefciencyformuonsisfactorizedastheproductof: 0 trk theefciencytoreconstructatrackintheinnerdetector( 0 trk ), 0 id | tk theefciencyoftheParticleFlowmuonreconstructionandidenticationformuons thathavebeensuccessfullyreconstructedintheinnertracker( 0 id | tk ), 0 sip 3 d | id theefciencyoftheimpactparameterrequirement,formuonspassingthe identication( 0 sip 3 d | id ), 0 iso | sip 3 d theefciencyoftheisolationrequirement,formuonspassingallpreviousselection criteria( 0 iso | sip 3 d ). 3.2.9Tracking,ReconstructionandIdenticationEfciency Thetrackingefciencyinthesilicontrackerwasmeasuredusinga"tight"muon (withoutdzcut)asatag,satisfyingtheisolationrequirement RelPFIso < 0.2 (computed fromchargedparticlesonly),andmatchedtoanHLTobjectcorrespondingtoasingle muontrigger.Theprobeisrequiredtobeanystandalonemuonwithvalidhitsinthe muonsystem.Theefciencyiscomputedmatchingtheprobetoatrackwith # R < 0.3 (directionsdenedatthepointofclosestapproachtothebeamline).Inaddition,the # z betweenthetagandthematchedtrackshouldbesmallerthan1cmtosuppress pile-up.Acorrectionisappliedtothemeasuredefciencytoaccountforthepossibility ofspuriousmatchesbetweenthestandalonemuonandanothertrackfromacharged hadron,asdescribedin[ 58 ].Thesizeofthiscorrectionisabout5%ofthemeasured inefciency,andthusbelow0.1%inabsoluteefciency. Forthe2010and2011runningperiods,theefciencyfromdataisfoundtobevery closeto100%andinagreementwiththepredictionsfromsimulationtobetterthan0.2% [ 59 ].Aslightlossinefciencyisinsteadobservedinthe2012runningperiod,wherethe tolerancesusedinthetrackingalgorithmhavebeenreducedtocopewiththeincreasein pile-up.Thecomparisonsbetween2012(re-reco'ed)dataandMCareshowninFigure 3-28 .ThedatapresentsaninefciencywithrespecttotheMC,growingas % increases, reaching2%for | % | =2.4 113

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Figure3-28. Muontrackingefciencyasafunctionofthemuon % for8TeV re-reconstructeddataandMC,asafunctionof % (left)andthemultiplicityof primaryvertices(right). Formuonsthataresuccessfullyreconstructedasatrackintheinnertracker,the performanceofthereconstructioninthemuonsystemandtheidenticationcriteriafor PFmuonshasbeenmeasuredin7and8TeVdatausingthetag-and-probemethod usingdimuonsfrom Z (for pT > 15 GeV)and J / decays(for pT < 15 GeV).A detaileddescriptionofthemethod,andresultson2010data,canbefoundelsewhere [ 47 ].Theefcienciesmeasuredfromdata,andthecorrespondingvaluesobtained applyingthesameprocedureonsimulated Z and J / eventsareshowninFigure 3-29 .Thesimulatedeventsusedforcomparisonsinthetwodatatakingperiodshave beenreconstructedwiththesamesoftwarealgorithmsasthedata,andareweighted asfunctionofthenumberofreconstructedprimaryverticestomatchthemultiplicity observedindata. Forthe7TeVdata,inthebarrelregion( | % | < 1.2 )theresultsofthemeasurement ondataareinverygoodagreementwiththepredictionsfromsimulationsforall pT valuesabove5GeVrelevantfortheanalysis,andtheplateauvalueoftheefciency isreproducedinMCwithin 0.3% orbetter.Intheendcaps,theplateauvalueofthe 114

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efciencyisabout 0.8% lowerindatathaninthesimulation,duetosomeissuesin theCSCreadoutsystemduringthesecondpartof7TeVdatataking.Anevenbetter agreementisobservedin8TeVdata,wheretheCSCreadoutproblemwasxed. Figure3-29. MuonreconstructionandidenticationefciencyforParticleFlowmuons, measuredwiththetag-and-probemethodon7TeVdata(top)and8TeV data(bottom)asfunctionofmuon pT ,inthebarrel(left)andendcaps (right).. 3.2.10SelectionEfciency Signicanceofthe3DImpactParameterEfciency Thesametag-and-probemethodhasbeenusedalsotomeasuretheefciencyof therequirementonthesignicanceofthe3Dimpactparameter,formuonspassingthe ParticleFlowidenticationrequirements.Inthiscontext,onlymuonsfrom Z decayscan beused,asthe J / decayscontainasignicantcontaminationofnon-prompt J / 's fromBhadrondecays. 115

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Theefciencyofthe | SIP 3 D | < 4 criteriaisfoundtobeabove99.5%inthebarrel, andabout99%intheforwardpartofthedetector(seeFigure 3-30 ).Inthelatter region,theefciencyindataabout0.1%lowerthaninsimulation.Worse | SIP 3 D | < 4 efciencyduetopixelmisalignmentinthepromptlyreconstructeddataisrecoveredin there-reconstructeddataascanbeseeninFigure 3-30 (rightbottom).Moreover,the efciencydoesnotshowasignicantdependanceonpile-upasitisatasafunctionof thenumberofverticesasshowninFigure 3-30 (leftbottom). Figure3-30. Efciencyfortherequirementonthe3Dimpactparametersignicance | SIP 3 D | < 4 asfunctionofthemuonpseudorapidity(top),for7TeVdata (left),and8TeVdata(right),formuonswith pT > 20 GeV,andin8TeV data(top)asfunctionofthenumberofreconstructedvertices(left)anda comparisonbetweentheprompt-recoandthere-reco(right). IsolationEfciency Theisolationefciency,thelastcomponentoftheofineselectionefciency,has beenmeasuredondatausingthetag-and-probemethodformuonspassingtheParticle 116

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Flowidenticationandthe | SIP 3 D | < 4 criteria.Similartotheefciencymeasurementof impactparameterrequirements,onlymuonsfrom Z decayscanbeused,sincemuons from J / 'sarenotexpectedtobeisolated,especiallyfornon-prompt J / mesons. Themeasurementisstatisticallylimitedinthe5-10GeV pT region,butotherwisean excellentagreementisobservedbetweendataandexpectationsfromsimulationas showninFigure 3-31 Figure3-31. MuonisolationefciencyforParticleFlowmuonspassingtheimpact parameterrequirements,measuredwiththetag-and-probemethodon7 TeVdata(top)and8TeVdata(bottom)asfunctionofmuon pT ,inthe barrel(left)andendcaps(right). ScaleFactors Combiningtheformerfourefciencies(tracking,muonidentication,signicanceof theimpactparameterandmuonisolation),thedata/MCscalefactorsusedtoscalethe MonteCarloeventyieldsareobtainedforne( pT % )-binningandareshownasfunction oflepton pT and % inFigure 3-32 .Theoveralldataefciency(combiningagaintracking, 117

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identication,signicanceoftheimpactparameterandmuonisolation)asfunctionof lepton pT inFigure 3-33 .Tables A-1 A-2 A-3 detailthedataandsimulationefciency alongwiththedata/MCscalefactorfor2012asshowninFigure 3-32 Figure3-32. Combineddata/MCscalefactorfortracking,identication,signicanceof impactparameterandisolationfor7TeV(left)and8TeV(right)dataas functionoflepton pT and % Figure3-33. Combineddataefciencyfortracking,identication,signicanceofimpact parameterandisolationfor7TeV(left)and8TeV(right)dataasfunctionof lepton pT 3.2.11Summary Belowisasummaryofallrequirementsonmuonobjectsintheanalysis. Longitudinalimpactparameterlessthan0.5mmwithrespecttotheprimaryvertex Horizontalimpactparameterlessthan1cmwithrespecttotheprimaryvertex | SIP 3D | lessthan4.0 118

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pT greaterthan5GeV PFMuonand(GlobalorTrackerMuon)ID RelPFIso < 0.4 119

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3.3Photons 3.3.1ReconstructionandIdentication A Z decayintoaleptonpaircanbeaccompaniedbynalstateradiation(FSR), Z " + ( .Ifthephotontransversemomentum, pT $ ,exceeds2GeV,about 8%(15%)ofthedecaysintomuons(electrons)areaffected.Electronmeasured energiesautomaticallyincludetheenergyofalargefractionoftheemittedphotons intheassociatedelectromagneticsuper-cluster,astheyaredesignedtore-collect bremsstrahlungradiatedphotons,andFSRphotonsarecollinearwiththeemitting leptons.Ontheotherhand,muonmeasuredmomentadonotincludetheemitted photons.Finalstateradiationisthereforeexpectedtodegradethe Z massresolution whenmeasuredwiththesolemuonpairs,andinturndegradetheHiggsbosonmass resolutionwhenmeasuredwiththefourleptonsmomenta,especiallyinthe4 andin the2e2 nalstatesand,toalesserextent,inthe4enalstate.Itisalsoexpectedto reducetheefciencyoftheleptonisolationcutwhentheemittedphotonisinthelepton isolationcone. BothanexcellentHiggsbosonmassresolutionandalargeselectionefciencyare essentialingredientsinviewofthesmallproductioncrosssectioninthe 4 channels, inparticulartodiscriminatetheHiggsbosonsignalfromthebackgroundcontinuum. Therefore,thepurposeofthisanalysisistorecovertheFSRphotonswithlarge efciencyandpurity,toremovetheenergyoftherecoveredphotonsfromthelepton isolationcones,andtomeasurethemassoftheHiggsbosoncandidatefromthe momentaoftheleptonsandtherecoveredphotons. Finalstateradiationtendstofavorlowenergyphotonemissioncollineartothe lepton.Anefcientrecoverythusrequiresphotonidenticationandreconstructioninthe vicinityofotherparticles,downtophotontransversemomentaoftheorderoftheHiggs masscoreresolution, i.e., ,downtoacoupleGeV.Lessenergeticphotonsareexpected 120

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todegradethemassresolutioninaninsignicantmanner,andareincreasinglydifcult toreconstructandseparatefromthebackground. Identifyinglowenergyphotonsoverlappingwithotherparticlesisincludedinthe particle-owconceptdevelopedinCMS[ 35 ]. TherearetwotypesofFSRphotonsdenedintheanalysis.Photonsoftype1 areidentiedandreconstructedwiththeparticleowreconstruction,withaspecic clusteringalgorithm,efcientdowntoanenergyof230MeVintheECALbarreland600 MeVintheECALend-caps.Thedeterminationofthephotonenergiesanddirectionsis monitoredinthedatawith / 0 (( decays,andisshowntobeaccurate,reliable,andin agreementwiththepredictionsfromsimulation[ 55 ]. Theparticle-owreconstructionincludesanidenticationofshoweringmuons, tunedforenergeticmuons.Intherarecasesinwhichsuchashoweringmuonis identied,theenergiesoftheparticleowclusterslinkedtothemuondonotgiverise toseparateparticles.Forthetransversemomentaofinterestinthelow-massHiggs bosonsearch,however,theshoweringprobabilityisvanishinglysmall,whichleadsto thelossofanotentirelynegligiblefractionofcollinearFSRphotons.ParticleowECAL clusterslinkedtoidentiedshoweringmuonsarethereforeidentiedasphotonsoftype 2inthisanalysis.Specically,theenergyofthesephotonsissettotheECALenergyof thePFMuon,anditsdirectionischosentobethatofthePFMuon. Inrareoccurrences,theparticleowreconstructionmayidentifyaphotonalthough itisalreadyincludedintheelectronsuper-cluster,duetoimperfectcrosscleaning.It isthereforerequiredthatphotonsbefurtherawayfromthedirectionofanyelectronby 0.05inpseudo-rapidityand2.0radinazimuth. Thelasttwopointsareclearareaofimprovementintheparticle-owreconstruction algorithmlogic,improvementsthatarebeyondthescopeofthisnote. Inthefourmuonnalstate,thetotalefciencyofthephotonreconstructionfor pT $ > 2 GeVand | % $ | < 2.4 ,determinedbymatchingreconstructedphotonsto 121

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Figure3-34. Reconstructionefciencyforphotonsproducedbynalstateradiationin H ZZ 4 events. generatedphotonsfromFSRwithamatchingcutof # R < 0.1 ,isshowninFigure 3-34 a asafunctionof pT $ .Inthefour-muonnalstate,about20%oftheFSRphotonsareof type2. 3.3.2Isolation Thephotonisolationisdeterminedfromthechargedhadrons,photons,andneutral hadronsidentiedbytheparticleowreconstructioninaconeofsize # R =0.3 around thephotondirection.Inthiscone,allchargedhadronscompatiblewithoriginatingfrom thesignalprimaryvertexandwitha pT largerthan200MeV,andallphotonsand neutralhadronswitha pT largerthan500MeVareincludedintheisolationdeposits. Theabsolutephotonisolationisthendenedasthesumofthetransversemomentaof alltheseisolationdeposits.Todiscriminateagainstphotonsthatareproducedinpileup interactions,anadditionalisolationdepositisdenedthatcorrespondstothecharged particlesumfromtheverticesotherthantheprimaryvertex. Finally,thepileup-correctedrelativeisolationisobtainedbydividingtheabsolute isolationbythephotontransversemomentum, pT $ 122

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RelPFIso = / chhad pT + / neuthad eT + / photon eT + / PU eT pT $ (35) 3.4Jets VectorbosonfusionandassociatedproductionmechanismsoftheHiggsbosonare probedbystudyingthekinematicsofthedi-jetnalstateproducedinassociationwitha Higgsboson. Jetsinthisanalysisarereconstructedbycombiningtheenergymeasuredin thecalorimetersandtracksfromchargedparticlesonbasisofthestandardCMS particleowalgorithm[ 35 ]andusingtheAntik T [ 60 ]clusteringalgorithmwithdistance parameter R =0.5 Jetsareonlyconsiderediftheyhave | % | < 4.7 .Duringthejetclustering, constituentsthatoriginatefrompile-uparealsoclusteredwithconstituentsfromthehard scattering.Tocorrectthepile-upcontributiontothejetenergyscale,thecontribution frompile-upisestimatedbytheL1Fastjetmethodwhichreliesonthedenitionofajet area[ 61 ]fromwhichamediandensity( $ ,inGeV/Area)pereventcanbedened.The correction,subtractedfromthejet pT ,equals $ Area .L1FastJethastheadvantage ofbeingabletoremovetheout-of-timepile-upcomponent,buthasthedisadvantageof subtractingtheunderlyingeventcontributionaswell.ThestandardL2andL3jetenergy scalefactors[ 62 ]areappliedontopofthisL1correction.Theselectedjetsarerequired tohave pT > 30 GeVafteralltheabovecorrectionsareapplied. Jetspurelycomingfrompile-upeventsareidentiedbyamultivariateanalysis (MVA)techniquebasedontheBoostedDecisionTree(BDT)method.Adiscriminant isbuilt[ 63 ]basedonthenumberofverticesintheevent,thekinematic( pT % ), compatibilityofthejettothehardinteractionvertexbasedonchargedconstituentsfor jetswithin | % | < 2.75 ,theneutralandchargedconstituentsmultiplicities,andseveraljet shapeproperties(jetradiusweightedbytherelative pT contributionoftheconstituents andthe pT fractioninringsaroundthejetaxis).Amongthethreeworkingpoints 123

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dened,theloosestoneisusedinthe H ZZ 4 analysisasjetidentication(jetID) criteria.Tocross-checkthismethod,Z+jetseventswereselectedindataandcompared withDrell-YanMonte-Carlo,andgoodagreementwasfound[ 64 ]. 124

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CHAPTER4 SEARCHINGFORHIGGS 4.1 H ZZ 4 AnalysisStrategy The H ZZ 4 analysisstrategyreliesheavilyuponexcellentreconstruction, identicationandisolationofchargedleptons.Thesignatureoftwo Z bosonseach decayingtoapairofchargeleptons( + or e + e )aresearchedforinthemassrange 100GeV < m 4 < 1000GeV.Oneorboth Z bosonscanbeoff-shell.Background sourcesaredominatedbyanirreduciblefour-leptoncontinuumfromdirect ZZ or Z ( productionvia q q annihilationand gg fusion.Reduciblebackgroundcontributionsarise from Zbb and t t wherenalstatescontaintwoisolatedleptonsandtwo b jetsproducing chargedleptons,aswellasinstrumentalbackgroundsfrom Z + jetsand WZ + jetswhere jetsaremisidentiedasleptons. H ZZ 4 providesanarrowresonancerisingabovearelativelyatbackground atlow m 4 .Duetotheexcellentreconstructionandmeasurementofchargedleptons intheCMSdetectorandthenatureoftheHiggsdecay,thischannelprovidesthemost accuratemeasurementonthemassoftheHiggs.Further,themethodusedtomeasure themassoftheHiggscanbeveriedindependentlyinthischannelusingthesingly resonant q q Z 4 peakat m Z = 91.18GeVasshowninsection 6.0.5 .The H ZZ 4 topologyalsomakethisthebestchannelforspin-paritymeasurements, sincethemainbackgroundisdirectproductionoftwospinoneobjects,asopposed tothesignalwhichis,presumably,ascalarobjectdecayingtotwospinoneobjects. Conveniently,themethodusedtomeasurethespin-parityoftheHiggscanalsobe repeatedusing Z 4 andisshowninsection 6.0.6 4.2Datasets,Simulation,andTriggers In2010theCMScollectedtherstcollisionsforphysicsanalysis.Theseruns werelowluminosityandservedmainlytoreconrmknownStandardModelprocesses allowingforbettercalibrationofthedetector.In2011,CMScollectedatotalof5.051fb 1 125

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ofdataat + s = 7TeV.ThisallowedCMStoprovidelimitsontheHiggsmassthat surpassedallotherexperimentallimitsfrombothLEPandTevatron[ 65 ]whileproviding excitinghintsthattheHiggsmay,infact,exist.Byspringof2012,theLHChadprovided CMSwithanother5.3fb 1 ofdata,nowat + s = 8TeV.Combiningthisdatawith 2011data,therewasfoundtobesufcientevidencetodeclarediscoveryofanew bosonaround125GeVattheIHCEPconferenceinMelbourne,Australia[ 17 ].Afterthe discovery,theLHCcontinuedprovidingcollisionstoCMSuntiltheendof2012.This thesispresentsresultsfromCMSwiththecompletecertieddatasetof5.051fb 1 of dataat + s = 7TeVand19.712fb 1 ofdataat + s = 8TeV. 4.2.1CollisionDataandTriggers ThedatasamplesusedinthisanalysiswererecordedbyCMSduringthe2011 and2012 pp collisionruns.Toensuretheintegrityofthephysicsresults,CMSimposes arigoroussetofrequirementsonthedatathatspecifythatthedatabeofhighquality andthatallsubdetectorsbeproperlyfunctioningduringtheselectedruns.Thisisdone centrallyandisindependentofanyoftheanalysisstrategies.Figure 4-1 showsthe luminositydeliveredandrecordedbyCMSduring2011and2012.Ofthedatarecorded, 5.051fb 1 of7TeVdataand19.712fb 1 of8TeVdatawerecertiedforuseintheHiggs search.Thenominalintegrated pp luminosityhasanuncertaintyof2.2%[ 66 ]for7TeV (2011)dataand2.6%[ 67 ]for8TeV(2012)data. Theanalysisreliesontheprimarydatasets(PDs)whichareproducedcentrallyand organizedbasedontheHLTcontentasdiscussedinsection 2.2.7.2 .Thecontentof thePDsevolveintandomwiththeHLTmenuasitchangestocopewiththeincreasing instantaneousluminosity.Forboth2011and2012data,theanalysisreliesonthe so-called"DoubleMu","DoubleElectron",and"MuEG"PDs[ 68 ].ThetwoformerPDs areformedbyan OR betweenvarioustriggerswithsymmetricorasymmetric pT requirementsfortwoelectronsormuons,withorwithoutadditionalidenticationand isolationrequirements.Theyalsoincludetriggersrequiringthreesameavorleptons 126

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Figure4-1. LuminositydeliveredandrecordedtoCMSduring2011(left)and2012 (right). abovealow pT thresholdwhichhelprecoveranyinefciencyinthedoublelepton triggers. The"MuEG"datasetsrequirecross-triggersbetweenmuonsandelectronswith similar pT thresholdstothoseforthethedoubleleptonPDs.Thehighest pT thresholds requiredare pT 1 > 17GeVand pT 2 > 8GeV.Table 4-1 showsthedatasetsand triggersusedintheanalysis.Laterintheanalysisselection, pT requirementsfor thetwoleadingleptonswillbemadehigherthanthistoensurecompatibilitywiththe triggerofine.Table 4-2 showsadetailedlistingofthetriggersusedin2012.Inthe analysis,selected4 eventscomefromthe"DoubleMu"PD,and4eeventscomethe "DoubleElectron"PDwhile2e2 areallowedtocomefromeitheraswellasthe"MuEG" PD,whichgainsafew%ofefciencyinthe2e2 channel.Assomeofthesedatasets willhaveduplicateevents,careistakentomakesurenoeventsaredoublecounted. 4.2.2Simulation Inordertooptimizetheanalysisbeforeanydataiscollected,itisnecessaryto simulatesignalandbackgroundprocessesfully,includingsimulatingtheirinteraction andsignatureinthedetector.Thisisacomplicatedandinvolvedprocessoccurringin severalsteps.Generally,therststepistouseawell-knownpublicphysicsprocess generatorsuchas POWHEG [ 69 ], MADGRAPH [ 70 ],or PYTHIA [ 71 ]tosimulatethephysical 127

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Table4-1. Datasetsandtriggersusedintheanalysis. Datasets 2011 2012 /DoubleElectron/Run2011A-16Jan2012-v1/DoubleElectron/Run2012A-22Jan2013-v1 /DoubleMu/Run2011A-16Jan2012-v1 /DoubleMu/Run2012A-22Jan2013-v1 /MuEG/Run2011A-13Dec2012-v1 /MuEG/Run2012A-22Jan2013-v1 /DoubleElectron/Run2011B-16Jan2012-v1/DoubleElectron/Run2012B-22Jan2013-v1 /DoubleMu/Run2011B-16Jan2012-v1/DoubleMuParked/Run2012B-22Jan2013-v1 /MuEG/Run2011B-13Dec2012-v1 /MuEG/Run2012B-22Jan2013-v1 /DoubleElectron/Run2012C-22Jan2013-v1 /DoubleMuParked/Run2012C-22Jan2013-v1 /MuEG/Run2012C-22Jan2013-v1 /DoubleElectron/Run2012D-22Jan2013-v1 /DoubleMuParked/Run2012D-22Jan2013-v1 /MuEG/Run2012D-22Jan2013-v1 Muontriggers HLT_DoubleMu7 HLT_Mu17_Mu8 ORHLT_Mu13_Mu8 ORHLT_Mu17_Mu8 Electrontriggers HLT_Ele17_CaloTrk_Ele8_CaloTrk HLT_Ele17_CaloTrk_Ele8_CaloTrk ORHLT_Ele17_CaloTrk_Ele8_CaloTrkHLT_Ele15_Ele8_Ele5_CaloIdL_TrkIdVL ORHLT_TripleEle10_CaloIdL_TrkIdVL Crosstriggers HLT_Mu17_TkMu8 ORHLT_Mu8_Ele17_CaloTrk ORHLT_Mu17_Ele8_CaloTrk Integratedluminosity 5.051fb 1 19.712fb 1 processrequested.Theresultingles,usuallyinacommonformatsuchasLes HouchesEvent(LHE)[ 72 ]format,arethenprocessedthroughadetectorsimulation andthenreconstructedasiftheywererealdata.Theresultingsimulateddatasetscan thenbeusedtoperformthefullanalysisbeforeattemptingtodothesameondata. Suchaprocessallowsphysiciststooptimizetheeventselectionforthebestsignalto backgroundratiowhileavoidinganybiasthatmayoccurifonewastolookatcollision datarst. 128

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Table4-2. Triggersin2012dataanalysis. Channel Purpose HLTpath L1seed prescale 4e main HLT_Ele17_CaloTrk_Ele8_CaloTrk L1_DoubleEG_13_7 1 ORHLT_Ele15_Ele8_Ele5_CaloIdL_TrkIdVL L1_TripleEG_12_7_5 1 4 main HLT_Mu17_Mu8 L1_Mu10_MuOpen 1 ORHLT_Mu17_TkMu8 L1_Mu10_MuOpen 1 2e2 main HLT_Ele17_CaloTrk_Ele8_CaloTrk L1_DoubleEG_13_7 1 ORHLT_Mu17_Mu8 L1_Mu10_MuOpen 1 ORHLT_Mu17_TkMu8 L1_Mu10_MuOpen 1 ORHLT_Mu8_Ele17_CaloTrk L1_MuOpen_EG12 1 ORHLT_Mu17_Ele8_CaloTrk L1_Mu12_EG6 1 4 backup HLT_TripleMu5 L1_TripleMu0 1 4eand2e2 ZT&P HLT_Ele17_CaloTrkVT_Ele8_Mass50 L1_DoubleEG_13_7 5 4eand2e2 ZT&PlowpT HLT_Ele20_CaloTrkVT_SC4_Mass50_v1 L1_SingleIsoEG18er 10 4 and2e2 ZT&P HLT_IsoMu24_eta2p1 L1_SingleMu16er 4 and2e2 J/psiT&P HLT_Mu7_Track7_Jpsi HLT_Mu5_Track3p5_Jpsi HLT_Mu5_Track2_Jpsi Inthecaseofthe H ZZ 4 analysis,StandardModelHiggsbosonsignal samples,aswellassamplesforalargevarietyofelectroweakandQCDbackground processeshavebeensimulatedusingtheprocessnotedabove.Thesesampleshave beenusedfortheoptimizationoftheeventselectionstrategy,andarefurtherusedin thisanalysisforthecomparisonswithmeasurementsandevaluationofacceptance correctionsandsystematics.Theyarealsousedintheirreduciblebackground estimationandtodeterminethecompositionofthebackgroundsexpectedinthe data-drivenreduciblebackground controlregion Hereandhenceforward, Z standsfor Z Z ,and ( (wherepossible).Fortheevent generation, isunderstoodtobeanychargedlepton,e, or .Theanalysiswillfocus onreconstructednalstateswithelectronsormuons.Table 4-3 summarizestheMonte Carlosimulationdatasetsusedinthisanalysis. Wemakeuseof PYTHIA ,amulti-purposeLOMonteCarlogenerator,forseveral processes.Incaseswhereahigherordergeneratorsuchas POWHEG isused, PYTHIA isusedonlyforthehadronizationandshowering.Fortheunderlyingevent,the"tune Z2"isusedfor7TeVsamples,and"tuneZ2star"isusedfor8TeVsamples.Bothtunes relyon pT -orderedshowers.Thepartondensityfunction(PDF)usedinthemostof the7TeVsamplesisCTEQ6M[ 73 ]andCT10[ 74 ]forall8TeVand2012produced 7TeVsamples.TheNLOcross-sectionforbackgroundprocessesisaccountedforby 129

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Table4-3. MonteCarlosimulationdatasetsusedforsignalandbackgroundprocesses. (XX=tuneZ2star) Process MCCommentsandsamplename generator Higgsboson H ZZ 4 gg H POWHEG m H =110 1000GeV VV H POWHEG m H =110 1000GeV ZZcontinuum q q ZZ 4 e (4 ,4 ) POWHEG ZZTo4e(4 ,4 ) q q ZZ 2 e 2 POWHEG ZZTo2e2mu q q ZZ 2 e (2 )2 POWHEG ZZTo2e(2 )2 gg ZZ 2 2 gg2ZZ GluGluToZZTo2L2L gg ZZ 4 gg2ZZ GluGluToZZTo4L Otherdi-bosons WW 2 2 Madgraph WWJetsTo2L2Nu WZ 3 "Madgraph WZJetsTo3LNu t t andsingle t t t " + b b POWHEG TTTo2L2Nu2B t ( s -channel) POWHEG T TuneXX s-channel t ( s -channel) POWHEG Tbar TuneXX s-channel t ( t -channel) POWHEG T TuneXX t-channel t ( t -channel) POWHEG Tbar TuneXX t-channel t ( tW -channel) POWHEG T TuneXX tW-channel-DR t ( tW -channel) POWHEG Tbar TuneXX tW-channel-DR Z/W+jets( q = d u s c b ) W+jets MadGraph WJetsToLNu Z+jets,m !! > 50 MadGraph DYJetsToLL*M-50 Z+jets, 10 < m !! < 50 MadGraph DYJetsToLL*M-10To50 properre-weightingwhereneeded.TheHiggsbosonsignalprocessesarealsotaken atNLOexceptinthecaseoftheHiggsproductionviagluon-gluonfusionforwhichthe mostrecentNNLO+NNLLcross-sectioncalculationsaretakeninaccount[ 75 ],[ 76 ],[ 77 ]. Detailsofsamplesusedandanyre-weightingusedaredescribedinthesectionsbelow. 4.2.2.1Signal: H ZZ 4 SignalsamplesareproducedforeachoftheveHiggsproductionmechanisms. Thegluon-gluonfusionandVBFsamplesareproducedwith POWHEG atNLO.The CTEQ6M(CT10)PDFsetisusedfortheFall11(Summer12)sampleswithHiggswidths settothosecalculatedbytheLHCHiggsCrossSectionWorkingGroup'sYellowReport 130

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[ 77 ]. pT distributionsin POWHEG samplesaretunedtomatchthelatestcalculationsfrom HRes [ 78 ].ZH,WH,and t t HsamplesareproducedatLOwith PYTHIA .Inallsamples, theHiggsbosonisforcedtodecaytotwoZbosons.EachZbosonisthenforcedto decaytotwochargedleptons( e ). POWHEG gg fusioneventsarere-weightedaccordingtothe gg cross-sectionutilizing NNLLcalculationsinQCDandNLOinEWKpresentedinreference[ 77 ],while POWHEG VBFand PYTHIA WH,ZH,and t t Heventsarere-weightedaccordingtocross-sections utilizingNNLOcalculationsinQCD,NLOinEWK,andusingthecomplexpolescheme. ThecrosssectionsarescaledbythebranchingratioBR( H 4 ).Figure 4-2 (left) showsthetotalcrosssectiontimesBR( H 4 )versusHiggsmassfor + s = 7TeV.In sameavornalstates,interferenceoccursduetotheinterchangeabilityoftheleptons. ThishasanobservableeffectonthecrosssectionasshowninFigure 4-2 (right). Figure4-2. Crosssectiontimesbranchingratiofor H 4 (left).Enhancementincross sectionduetosameavornalstateinterference(right). FortheFall11production,atotalof28MonteCarlosampleswereproducedin therange[115,600]GeV,withastepof10GeVupto230GeV,andthenstepsof 25GeVupto600GeV.InSummer12production,additionalsampleswereproduced rangingfrom650GeVto1000GeV,withastepsizeof50GeV,aswellasadditional 131

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lowmasssampleswithnergranularity.Thechoiceofmasspointsisdrivenbythe natureofthisanalysis,i.e.searchforanarrowpeakoverthecontinuumbackground. IthasbeenshownthatthetestmassesintheStandardModelHiggssearchshould notbemuchfartherapartthantheobservablewidthoftheHiggspeak[ 75 ].Asimple modelwithaGaussian-shapedsignalandatbackgroundshowsthatifwechooseto stepin1 # increments,thelossofsensitivityforaHiggsbosonwithamassrightinthe middlebetweenthechosentestmassesislessthan5%.With2 # increments,thelossof sensitivitycanbeashighas20%[ 75 ].Theincrementsinthemassstepsaretherefore chosentobecloseto1 # .Finegranularitysampleswereproducedinthemassrange aroundtheobservedpeaktoallowformoretrustworthypropertymeasurements.These samplesprovideefcienciesforeventselection,andareusedforttingofthemassline shapetobeusedinthestatisticalanalysis. Forpropertymeasurementssuchasspin-parity,severalhypotheticalmodelsofthe Higgsbosonweresimulatedusing JHUGEN [ 79 ].ThesesamplesincludemodelsforHiggs asapseudo-scalar 0 ,ahigherdimensionalspin 0 + h operator,a q q inducedvector spin 1 resonance,severalgravitonmodels,aswellasseveralproductionindependent models.Thesesamplesareuseddirectlyinthespin-parityanalysisforcomparisonof kinematicsaswellascalculationofefciencies,andbranchingratioandacceptance correctionfactorswhennecessary. 4.2.2.2Irreduciblebackground: q q ZZ 4 Irreducible q q ZZ 4 backgroundsamplesareproducedatNLOwith POWHEG interfacedto PYTHIA forhadronization,showering,andunderlyingevent.These samplesareproducedseparatelyfor4e,4 ,4 ,2e2 ,2e2 ,and2 2 .Theexpected q q ZZ 4 yieldisderivedfromthesesamplesinadditiontothemasslineshape usedinthestatisticalanalysis. 132

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4.2.2.3Irreduciblebackground: gg ZZ 4 Abovethe2 m Z threshold,thecontributionof gg fusionproduced ZZ isnot negligible.The gg ZZ diagramisofNNLOorderwithrespecttotherstorder Z bosonproductionandcannotbefullycalculated.Thereforeadedicatedgenerator, gg2ZZ ,isusedtoestimatethecalculation[ 80 ]. gg2ZZ produces gg ZZ eventsatLOand istheninterfacedto PYTHIA forhadronization,showering,andunderlyingevent.The expected gg ZZ 4 yieldisderivedfromthesesamplesinadditiontothemassline shapeusedinthestatisticalanalysis. 4.2.2.4Reduciblebackground: Z + jets WZ + jets Z + jets sampleshavebeensimulatedusing MADGRAPH ,eachwithabout40Mevents, theequivalentintegratedluminosityofnearly100fb 1 .Jetsinthesamplesincludelight avors( q = u d s )andheavyavors( q = c b ).Samplesincludebinningin m Z (10 GeV < m Z < 50GeV, m Z > 50GeV).Separately,thereexistshighstatisticssamplesfor m Z > 50GeVhavebinninginjets(1,2,3,or4jets).Sampleswithonlyheavyavorjets ( Zb b Zc c )arealsoavailableandcanbeusedifheavyavoreventsarevetoedinthe inclusivesamples.ThetotalNNLOinclusivecrosssectionusedis3048(3503.7)pbat 7TeV(8TeV).Thesesamplesareusedareusedinconjuctionwith WZ + jets samples todeterminetherelativecompositionofthereduciblebackgroundcontrolregions.They playnoroleinthestatisticalanalysis. 4.2.2.5Reduciblebackground: t t SingleTop A POWHEG generated pp t t 2 2 2 b sampleisusedinconjuctionwiththe otherreduciblebackgroundsamplestodeterminethecompositionofthereducible backgroundcontrolregions.Thesamplecontainsabout10MeventsandanNLOcross sectionof17.32(23.64)pbisusedforthe7TeV(8TeV)generatedsample.Several POWHEG generatedsingletopsamplescorrespondingto3diagrams(tW,t,s-channel) andboth t and t areusedinconjuctionwiththe t t sampleforcompleteness. 133

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4.3EventSelectionandCategorization Asdescribedinsection 4.1 ,theadvantageofthisanalysisisfourwellreconstructed chargedleptonsinthenalstatewithexcellentmassresolutionandlowbackground levels.Unfortunately,the H ZZ 4 channelsuffersfromalowcrosssectioninthe lowmassrangedenedas # nal ( H ZZ 4 ) = # ( pp H ) BR ( H ZZ ) BR ( Z 2 ) 2 (41) Thislowoverallproductionratemeansthattheanalysismusthaveawell-dened, provenstrategy,andaneventselectionthatpreservesthehighestpossiblelepton reconstruction,identication,andisolationefciencieswhilestillbeingabletorejecta largeamountofirreducibleandreduciblebackground.Thishighselectionefciency mustextendwellbelowthe2 m Z thresholdinthecaseofalowmassHiggs.Figure 4-3 showsthetypicallepton pT 'sfora126GeVHiggsdecayingto4muons.Low pT leptonssufferfromworsereconstructionandidenticationefciencyandpurity,therefore specialcaremustbetakenintheeventselectiontoalsorejectthepossibleinstrumental backgroundsarisingfromthis.Inthissection,theeventselectionstrategy,FSRrecovery algorithm,andselectionefciencywillbedescribed. 4.3.1Trigger EventsindataaretakenfromDoubleMu,DoubleEle,andMuEGdatasetswhichare sortedbytriggercontent.Selectedeventsarerequiredtopassadoublemuontrigger,a doubleelectrontrigger,acrosstrigger(e or e),oratriplemuonorelectrontriggerin bothdataandMC.TheMCtriggerrequirementisappliedtomakesurethephasespace inMCisascloseaspossibletodata.Triggerefciencywithrespecttotheanalysisis nearly100%.Detailsonalltriggersusedcanbefoundinsection 4.2.1 andTables 4-2 and 4-1 134

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[GeV] l T p 020406080100 a.u. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Before analysis selection After analysis selection 4 ZZ* H = GeV H m126 = 8 TeV s CMS Simulation, 4 T p 3 T p 2 T p 1 T p Figure4-3. pT 'sof4muonsrespectivelyinsimulated H ZZ 4 decays. 4.3.2PrimaryVertexSelection Eventsmusthaveatleastonegoodprimaryvertex(PV)denedashaving AhighnumberofdegreesoffreedomN DOF > 4 Collisionsrestrictedalongthe z -axisz PV # 24cm Asmallradius$ PV # 2cm CategorizedasnotfakebyCMSsoftware 4.3.3LooseandTightLeptons Therearetwotypesofleptonsusedintheanalysis, loose and tight .Theyare denedbelow. Looseleptons : 1. Muons withingeometricalacceptance | % | < 2.4,beingeitheraglobalor trackermuon,with pT > 5GeV.Theyshouldpassrequirementsof d xy < 0.5 cmonthetransverseimpactparameterand d z < 1cmonthelongitudinal impactparameterwithrespecttoaPV.Non-globaltrackermuonsmustbe arbitratedandcleanedforghost-muons(see 3.2.2 .Inaddition,theremustbe # R > 0.02betweenanyotherleptons. 135

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2. Electrons withingeometricalacceptance | % | < 2.5,passingrequirements of d xy < 0.5cmonthetransverseimpactparameterand d z < 1cmonthe longitudinalimpactparameterwithrespecttoaPV. Tightleptons : 1. Muons meetingtheParticleFlowcriteria,with SIP 3D < 4,andRelPFIso < 0.4 inadditionto thelooserequirements. 2. Electrons meetingtheelectronBDTIDrequirements(seesection 3.1.1 ),with SIP 3D < 4,andRelPFIso < 0.4 inadditionto thelooserequirements. Beforebuildingtightleptons,ane/ crosscleaningprocedureisapplied.Loose electronsarediscardediftheysatisfy # R ( e ) < 0.05,wherethemuonsconsidered areloosemuonspassingParticleFloworglobalmuoncriteria.Isolationcrosscleaning betweentheleptonsisassuredbyusingtheparticleowisolation,whichvetoesallthe particleowcandidatesreconstructedwithintheisolationconeof # R = 0.4.Inthe caseofelectrons,therearerarecaseswheretheparticleowelectrondoesnotmatch withtheselectedelectron,inwhichcasethereareextravetoesappliedintheisolation procedureasdescribedinsection 3.1.3 136

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4.3.4BestCandidateSelection Aftercollectionsoflooseandtightleptonshavebeenformed,bestcandidate selectioncanproceedasfollows. Z 1 selection Apairofsameavor,oppositechargetightleptons( e + e or + )(ortightleptons plusFSRphoton)withreconstructedmass m + ( m + + $ )closesttothenominal Z bosonmass( m Z 0 = 91.1876GeV)isretainedanddenoted m Z 1 .Themass shouldsatisfy40 < m Z 1 < 120GeV. Threeormoreleptons Thereshouldbeanadditiontightleptonintheeventofanyavororcharge. Fourormoreleptonsandsecondmatchingpair Thereshouldbeatleastoneadditionalpairofsameavor,oppositecharge leptonsintheevent.Ifthereismorethanonecombinationthatsatisesthis requirement,thenitisformedfromthehighest pT leptonsremaining.FSR photonsarealsosearchedforaccordingtothealgorithminsection 4.3.5 Z 2 and 4 candidate Thesecondpairofsameavor,oppositechargeleptonsshouldsatisfy4 < m Z 2 < 120GeV.Shouldtheeventsatisfythisrequirement,thereisnowa 4 candidate. pT 1 2 Toconformwiththetriggerrequirements,thetransversemomentumofthehighest andsecond-highest pT leptonsintheeventmustsatisfy pT 1 > 20GeVand pT 2 > 10GeV. QCDsuppression Toreduceeventsthathaveleptonsdecayingfromheavyquarks,itisrequiredthat inthecaseof2e2 events,alloppositecharge,sameavorpairssatisfy m + > 4 GeV,andinthecaseof4eand4 events4/6sameavor,oppositechargepairs satisfy m + > 4GeV. Z 4 phasespace Analysisdenedasrequiring m min Z 1 = 40GeV, m min Z 2 = 4GeV,and m 4 > 70GeV. Theuseofthe Z 4 phasespacewillbediscussedfurtherinsection 6 H ZZ 4 phasespace Analysisdenedasrequiring m min Z 1 = 40GeV, m min Z 2 = 12GeV,and m 4 > 100GeV. ThisprovidesthebestsensitivityforlowmassHiggs. Therstthreestepsreducetheirreducibleandreduciblebackgroundasmuchas possiblewhilekeepingasmuchsignalaspossibleforalowmassHiggs.Thefourthstep 137

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( pT 1 2 )makescertainthattheofinerequirementsforthetwoleading pT leptonsare tighterthanthoseonlinefromtheHLT.Thefthstepreducestheprobabilityofselecting eventscomingfrom t t whichleavereconstructedleptonswith m !! < 4GeV.Finally, therearetwophasespaceselectionsusedintheanalysis.The Z 4 phasespace allowsforalarge Z peaknear91.2GeVwithmanyfourleptonevents.Sincethesearise fromaresonancewithaknownmassandspin-parityproperties,itprovidesauseful standardcandleforthe H ZZ 4 analysis.The Z 4 analysisisdiscussed furtherinsection 6 .The H ZZ 4 phasespaceisusedinthenominalanalysisand isdiscussedfurtherinthesectionsbelow. 4.3.5FinalStateRadiationRecovery Inthesectionabove,theprocedureforbuilding Z candidatesisdescribed.The tightleptonsusedmustpassallselectioncriteria,includingisolation.IfanFSRphoton candidateisselectedintheevent,theisolationmayhavetobemodied.Below, themethodforbuilding Z candidatesinthepresenceofFSRphotonsisdescribed. Currently,theanalysisonlyconsidersFSRphotonswith pT > 2GeVandwellwithinthe trackeracceptance, | % | < 2.4. 1. Photonsareconsideredonlyiftheminimum # R distancewithrespecttoanyofthe leptonsfroma Z candidateislessthan0.5. 2. Ifthedistanceofthephotontotheclosestleptonisbetween0.07and0.5,the probabilitythatthephotonisfrompile-uporfromtheunderlyingeventbecomes larger,duetothelargeannulusarea.Toreducethisprobabilityandincreasepurity, the pT cutonthesephotonsistightenedto4GeVandthephotonisrequiredtobe isolatedaccordingtoequation 35 ,withRelPFIso < 1.0. 3. Forboth Z candidates,onlyphotonsthatmakeamasswiththetightleptonpair closertothenominal Z mass( m Z 0 ),butwithmaximum m !!$ < 100GeV,are selected. 4. Aftersteps1-3havebeenapplied,thebestFSRphotonisselectedasfollows: (a) Ifthereisatleastonephotonwith pT > 4GeV,theonewiththehighest transversemomentumisassociatedtothetightleptonpairtoforma Z boson candidate. 138

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(b) Ifthereisnophotonwith pT > 4GeV,theclosestphotontoanyofthetight leptonsisassociatedtothe Z bosoncandidate. Therefore,aneventcanhavezero,one,ortwoselectedFSRphotons.Ifaphotonis selected,itissubtractedfromthecorrespondingleptonsisolationcones(ifithappensto bewithinoneorbothoftheirisolationcones).TheperformanceoftheFSRalgorithmis quantiedusingbothsimulationanddata.Thegainisfoundtobetwofold. I LeptonsthatemitanFSRphotonwillloseenergy,andthusthe m !! forminga Z candidatewillbesmallerthanwhatitshouldbe,thusshouldthiseventcomefrom thepeakofaHiggsbosonresonance,theeventwillbereconstructedwithmass somewhereinthetail.RecollectingtheFSRphoton(s)bringstheseeventsbackto thepeak,wheretheybelong,improvingsignalresolution. II IsolationefciencyisimprovedsincerecollectedFSRphotonsarenowsubtracted fromtheisolationcone.Thiswillincreaseselectionefciency. TheFSRalgorithmhasbeentestedonsimulatedHiggssignalsampleat125GeV andre-weightedtomaththepile-updistributionindata.Thetotalefciencyiscompared byrunningthefullselectioncriteriawithandwithouttheFSRalgorithmapplied.A comparisonofthefourleptonmassdistributionbeforeandafterFSRrecoveryforevents withanidentiedFSRphotonandoveralleventsisshowninFigure 4-4 (left).The FSRalgorithmincreasesperformancebymovingFSReventsfromthetailbacktothe Higgspeakbulkdistribution.Inaddition,duetotheisolationrequirementsandthenew denitionofthemassesoftheZbosonsmoreeventsareintroducedinthenalselection afterFSRrecovery.InthecaseofHiggssignal,thetailsarereducedandthearithmetic RMSimprovesfrom7.1%to6.9%.Forthe ZZ backgroundcontinuum,performanceis similar.Therate,efciency,andpurityfortheHiggssignaland ZZ backgroundisshown inTable 4-4 TheeffectoftheFSRalgorithmonelectronsismuchsmallerthanotherchannels, duetotheabsorptionofnearbyFSRphotonsbytheECALsuperclusters.Thefour muonnalstateisthemostaffectedbytheFSRcollection.A2%increaseinoverall selectionefciencyisexpected,andismainlyattributedtothesubtractionofrecovered 139

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photonsfromtheisolationconeoftheleptonsandtheincreasedefciencyofthe m Z cutsafterincludingtheFSRphoton.TheeffectoftheFSRalgorithmhasalso beentestedonthereduciblebackground.Inthiscase,fake / 0 'sinsidejetscanbe mis-identiedasFSRphotonswhichcanaffectboththeyieldandshapeofthereducible background.Theseeffectswerestudiedinacontrolregionconsistingofatagged Z candidateandtwolooseleptonsthathavethesamecharge.TheeffectoftheFSR algorithmwasfoundtobe8.6%. Figure4-4. 125GeVHiggssimulatedeventswithatleastoneFSRphoton(left)andall events(right),withandwithouttheFSRalgorithmappliedtoselection. Table4-4. FSRalgorithmrate,purity,andpercentagegainforHiggsand ZZ FinalStateRate(%)Purity(%)Gain(%) H ZZ 4 6.0 80 2.0 4 9.1 82 3.0 2e2 5.0 78 0.6 4e 1.4 72 1.8 q q ZZ 4 6.7 81 2.1 4 10.1 83 3.0 2e2 6.5 77 0.6 4e 1.8 72 1.8 140

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4.3.6SelectionEfciency TheselectionefcienciescalculatedfromsimulationareshowninFigure 4-5 .The efciencyshowniscalculatedwithrespecttoeventsgeneratedwithinthegeometrical acceptance( | % | < 2.5forelectrons, | % | < 2.4formuons).Itrisesfromabout28%/58% /40%at m H = 125GeVtoabout60%/85%/72%at m H = 400GeVforthe4e/4 /2e2 channels.Associatedproductionisonlyconsideredupto300GeV,astheproduction contributionisexpectedtodroprapidlyafter m H = 200GeV. Theefcienciesarettedwiththefunctionshowninequation 42 .Thiswaythe statisticalanalysiscanbeperformedforanygiven m H byasimplemorphingofthe parameterization.Thisisveryusefulsinceitwouldbeimpossibletoproducethousands ofMCsamplesforeverypossiblemasspoint.Similarparameterizationsversus m H is doneforotherinputstothestatisticalanalysissuchasthedi-jetcategoryfractionand thesignallineshape(tobedescribedinsection 4.6.1 ). 0 = a + b Erf m H % c d .. f + g m H + j m 2 H # + k Gauss ( m H | # ) (42) Figure4-5. SignalselectionefcienciesfromMCfora4 systemasafunctionofHiggs bosonmasshypothesis,forthefull m H rangein8TeVsignalsamples. 141

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4.3.7ControlofSelectionComponentsinData Beforetheanalysiscanproceed,itisimportanttoverifythatsimulationdescribes dataforthevariablesthatwillbecutonintheanalysis.Shouldavariablenotbewell describedinMC,theanalysiswouldneedtobere-optimized,orMCwouldneedtobe corrected. Validationisrstperformedusingthehighstatistics Z samplesusingthe Z 1 selectionfromtheanalysis.Figure 4-6 showstheinvariantmassoftwoleptonsas builtfromthe Z 1 selectionintheanalysis.GoodagreementbetweendataandMCis observed.ThebottomrowofFigure 4-6 shows Z e + e eventsseparatedfortwo barrelelectronsandtwoendcapelectronsduetothelargedifferenceincorrections tothescaleandresolutionbetweenthetwo.Slightlybetterdata/MCagreementis seenforthebarrel-barrelpairs,whileintheendcap-endcapevents,theMCappears slightlyover-smeared.Differencesinthegolden(high R 9 )andmoreshowering(low R 9 ) electronsfractionsbetweendataandMCmayleadtothislevelofdisagreement. Figure 4-7 showsthedata/MCcomparisonfortheleptonwithworstisolation pT sumandworst SIP 3D fromfour-leptoneventswith Z 1 selected,wheretheleptonsfrom Z 1 areexcluded.GoodagreementbetweendataandMCisobserved.Finally,Figure 4-8 showsthedatatoMCcomparisonforthevariableusedtodiscriminateVBF/VH likeeventsfromggHlikeeventsinthedi-jetcategory, D jet .ThisisknownastheFisher discriminantandisalinearcombinationofthedi-jetmassandtheiropeninganglein % asdescribedinsection 4.4.1 .Verygoodagreementisobserved. 142

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A B C D Figure4-6. Comparisonof Z 1 invariantmassin(left) e + e and(right) + ,between8 TeVdataandMonteCarloexpectations. 4.4EventCategorization Aftereventshavebeenselected,theycannowbecategorizedfurtherintoone oftwocategories, 0/1jets or di-jet .AForaStandardModelHiggs,thedominant productionmechanismisgluon-gluonfusion( & 88%),followedbyVBF( & 7%),and nallyassociatedproduction.Separatingthe gg fusioneventsfromtheVBF/VHevents becomesrelevantforaHiggscouplingmeasurement,becauseinthecaseof gg fusion 143

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A B C D Figure4-7. Comparisonofleptonworstisolation(top)andleptonworst SIP 3 D (bottom) forleptonsinasampleof(left) Z 1 e + e and(right) Z 1 + ,between8 TeVdataandMonteCarloexpectations.Leptonsfrom Z 1 areexcluded. thereisacouplingofHiggsdirectlytofermionsthroughavirtualquarkloop,whileinthe caseofVBF/VHthereisonlycouplingtovectorbosons. Experimentally,theVBFmechanismcanbeprobedbyexploitingthedistinct topologyofVBFeventswhichhavetwohigh pT forwardjets.Thisdictatestheevent categorizationwhichisdonebynumberofqualifyingjets(asdescribedinsection 3.4 ). Careistakentoremoveoverlapbetweenjetsandthefourselectedleptonsandany 144

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A B Figure4-8. ComparisonofFisherdiscriminant D jet in Z 1 +2jetsinasampleof(left) Z 1 e + e and(right) Z 1 + ,between8TeVdataandMonteCarlo expectations. FSRphotonsbyvetoinganyjetsthatoverlapwiththeleptoncandidatesandFSR photonswith # R < 0.5. Fora m H = 125GeV,about50%oftheVBFproducedeventshavetwojetsin thenalstate,whilefor gg fusion,only8%containtwojets.InWHandZHproduced events,25%and40%respectivelyhavetwojetsinthenalstatefromthevectorboson decayinghadronically.Todeterminetheselectionefciencyforthedi-jetcategory,the fractionofdi-jeteventsinthe4 phasespaceisestimatedinMCforadiscretesetof m H points.Thesepointsarethenttedversus m H withapolynomialfunctiontogeta smoothdependenceversusHiggsmass.Figure 4-9 showstheratioofdi-jetselected eventsovertotaleventsasafunctionofHiggsmassforggHandVBFevents.Figure 4-10 showsthesameratioforWH,ZH,and t t Hevents.Notsurprisingly,almostall t t Heventsendupinthedi-jetcategory.ForVBFproduction,thisfractionisslightly dependenton m H ,rangingfrom60%forlowmasses,downto50%forhighermasses. ggHproductioneventsonlycontributeabout10%ofeventstothedi-jetcategory,upto about30%ataHiggsmassof1TeV. 145

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Figure4-9. Signaldi-jetratiofromMCfora4 systemwithinthegeometricalacceptance inthe4 (left),4e(middle)and2e2 (right)channelsasafunctionofHiggs bosonmasshypothesisfor8TeVsignalMCsamplesggH(top)andVBF (bottom). 4.4.1DiscriminationintheDi-jetCategory AsFigures 4-9 and 4-10 demonstrate,thereismorethanjustVBFeventsinthe di-jetcategory.TofurtherdiscriminatebetweenVBFlikeeventsandggHandVHevents, thekinematicsofthedi-jetsystemcanbeused.InVBFproducedevents,thetwojets aretypicallyproducedbacktobackgivingthemalargeinvariantmass, m jj ,andforming alargepseudorapiditygap.ForggHhowever,thejetstendtobeneareachother,and their m jj issmallerandfollowsafallingspectrum.InthecaseofVHevents,the m jj peaksnearthe W and Z nominalmasses,andthe V jj systemisboosted.Therefore, themaindiscriminationvariablesarethe m jj andthegapbetweenthetwojets, # % jj Figure 4-11 showscomparisonsofthe # % jj and m jj distributionsfordifferent productionmechanismsand ZZ background.Signicantlydifferentshapescanbe 146

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Figure4-10. Signaldi-jetratiofromMCfora4 systemwithinthegeometrical acceptanceinthe4e(left),4 (middle)and2e2 (right)channelsasa functionofHiggsbosonmasshypothesisforthe8TeVsignalsamplesWH (top),ZH(middle),and t t H(bottom). seenfordifferentproductionmechanisms.Tooptimizetheseparationpowerusing thetwovariables,theyhavebeenmergedintoalinearcombinationusingatechnique knownaslinearFisherdiscriminant(herebydenoted D jet ).TheFisherdiscriminantis denedas 147

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A B Figure4-11. Comparisonofpseudorapiditygapandinvariantmassofthetwotagged jetsinthedi-jetcategoryfordifferentHiggsproductionmechanismsand ZZ background. D jet = # % jj + & m jj (43) Thecoefcients and & arederivedthroughanoptimizationperformedintwo trainingsamplesforsignalandbackgroundrespectively.Inthiscase,becausethe separationbetweenggHandVBFisdesired,VBFMCeventswereusedasthesignal andggHeventsusedasthebackground.Takingatwodimensionalplane x =(# % jj m jj ) thetwosetsofeventswillhavemeansof VBF ggH andcovariances VBF ggH respectively.Assumingalineartransformation, w x ,theFigureofmeritforoptimizing theseparationbetweenthesignalandbackgroundis S = ( w VBF % w ggH ) 2 w T VBF w + w T ggH w (44) S isthedistancebetweenthecoresofthetwodistributionsdividedbythesumof theirspreads.Maximizing S givesminimalspreadwithmaximumseparation.Thelinear combinationthatsatisesthisis 148

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w = ggH + VBF ) 1 # ( VBF % ggH ) (45) Here,thevector w denesalineperpendiculartothediscriminantline.Thevector ofFishercoefcients ( & ) isgivenby % & ' & ( ) = w T % & cos / / 2 % sin / / 2 sin / / 2cos / / 2 ( ) w (46) Byusingsimulatedevents,thelinearcombinationthatminimizestheseparation betweenVBFandggHisfoundtobe D jet =0.18# % jj +1.92 10 4 m jj (47) Thedistributionof D jet fordifferentproductionmechanismsand ZZ backgroundis showninFigure 4-12 (left).Theseshapesareusedinthestatisticalanalysistoincrease discriminationinthedi-jetcategory. A B Figure4-12. Comparisonofthelinearsherdiscriminantshapesofthedominant productionmechanismsinthedi-jetcategory(left).Comparisonofthe transversemomentumshapesofdifferentproductionmechanismsinthe 0/1jetcategories(right). 149

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4.4.2Discriminationinthe0/1JetCategory Inthe0/1jetcategory,therearelessthantwojetspassingrequirementsreconstructed alongwiththefourleptonsystem.TherearestillVBFeventslikelytobeinthiscategory asabout50%ofVBFeventshaveatleastonejetreconstructedintheevent.Therefore, additionaldiscriminationisneededinthiscategoryaswell.Here,sincetherearenottwo jets,the pT ofthefourleptonsystemcanbeexploitedtoincreasediscriminationpower betweenVBFlikeandggHevents.Figure 4-12 (right)showsthedistributionofthe pT spectrumfordifferentHiggsproductionmechanismsand ZZ background.Similartothe way D jet isusedinthestatisticalanalysisforthedi-jetcategory,fourlepton pT isusedin the0/1jetcategory. 4.4.2.1Signal pT 4 model Modelingofthetransversemomentumspectrumforthevetypesofsignal(ggH, VBF,WH,ZH, t t H)isobtainedusing2Dtemplatesof m 4 and pT 4 determinedfrom MC.Thelatest POWHEG MonteCarlocontainsthemostup-to-dateNLOpredictionsthat includetheheavyquarkmasseffects,andforggH,theHiggs pT spectrumistunedto reproducetheNNLO+NNLLresultsfrom HRes [ 78 ].Twodimensionaltemplatesof pT 4 versus m 4 arebuiltforeachsignalproductionmechanismaswellasbothreducibleand irreduciblebackgroundstobeusedinthestatisticalanalysisforthe0/1jetcategory. Defaultsignaltemplates(except t t H,whichhasbasicallynoeventsforthe0/1 jetcategory)areshowningure 4-13 .Intherangeabove200GeVnoMCsamples areavailableforWHandZH,astheircontributiontothetotalHiggscross-sectionis negligible,sotemplatesaresimplyconstantover m 4 UncertaintiesforggHinclude: Uncertaintyonthere-summationscale HRes isre-runusingthreedifferent valuesofthere-summationscale,andresultsarecomparedbetweenthedefault value( Q = m H / 2 )andtwoalternativeones( Q = m H and Q = m H / 4 )whichare usedforre-weightingthetemplates.Otherscalesinthecalculation(factorization, renormalization)arevariedfractionallybythesameamount,followingtherecipein [ 78 ]. 150

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Figure4-13. 2D pT 4 vs m 4 templatesforggH(topleft),VBF(topright),WH(bottom left)andZH(bottomright)at8TeV. Uncertaintyontheinnitetop-massapproximation .With POWHEG alternative signalsamplesaregenerated(atgeneratorlevelonly)wherethetopandbottom massesarevariedbytheircurrentuncertainties.Theobserveddifferenceinthe spectrumisusedasasystematicuncertainty. PDFuncertaintieshavealsobeencalculatedbutarefoundtobenegligiblewith respecttothetwosourcesabove. VBFsignalathigh pT 4 doesnotsufferfromre-summationeffectsatNLO,dueto thelowamountofQCGradiation,thereforestandardtheoreticaluncertaintiesareused inthesecalculations. PDFvariations .Considerthespectrumdifferenceatgeneratorlevelbetweenthe setsofPDFs:CT10(default),NNPDF2.1andMSTW2008. Renormalizationandfactorizationscalevariations .Considerthespectrum differenceatgeneratorlevelbetweenthesetsofrenormalizationandfactorization scalesuggestedin[ 81 ]. ForVH/ t t H,NLO-to-LOre-weightingisappliedassystematicuncertainty. 151

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4.4.2.2Irreduciblebackground pT 4 model Justasinthecaseofsignal,irreduciblebackground pT 4 ismodeledbytwo dimensionaltemplatesof pT 4 versus m 4 fromMC.Forthedominant q q ZZ ,the POWHEG simulationsamplesincludeNLOeffects,singleresonantcontribution,and Z / ( interference,aswellaseffectsfromsameavornalstates. DefaultbackgroundtemplatesareshowninFigure 4-14 Forirreduciblebackgroundthefollowingsystematicuncertaintiesareincluded: TheoreticalshapeofZZ .TheprocedureisidenticaltotheoneusedinVBFsignal forPDFandscalevariations. ShapeofZZfromsingle-Zspectrum .ForZZcompletecalculationofre-summation effectsarenotavailable.Thereforecontrolsamplesindatafromsingle-Z productionareused[ 3 ].ThespectraforthesedatasamplesareshowninFigure 4-15 andcomparedto POWHEG MC.Thedata/MCdifferenceistwithalinear functionandthisdifferenceisusedtore-weightthe POWHEG spectrumtoobtaina systematicuncertainty. Figure4-14. 2D pT 4 vs m 4 templatesfor q q ZZ (left)and gg ZZ (right)at8TeV. 4.4.2.3Reduciblebackground pT 4 model Thefractionofreduciblebackgroundfor m H > 2 m Z islow,howeverinthelow massregionadetaileddescriptionisnecessary.However,theamountofstatisticsin thecontrolregionsthatwouldgenerallyusedtomodela Z + XpT 4 areinsufcient tollatwodimensionaltemplate.Therefore,thelineardependenceofthe Z + XpT 4 on m 4 hasbeenexploited.Figure 4-16 showsthislineardependenceof pT 4 / m 4 vs 152

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Figure4-15. Datato POWHEG comparisonfordatainthe Z productionanalysisat7TeV [ 3 ]. m 4 .Therefore,thefullcontrolsampledistributioncanbettedwithamodiedTsallis function(usedtomodelFONLLresultsforheavyavors[ 82 ]). T ( x = pT 4 / m 4 ) x n 1 e bx 1 1+ + x 2 + m 2 % m n 2 T 2 n 2 (48) Thetforthe8TeVsampleisshowninFig. 4-17 .Thetemplateisthenlledwith thevaluestakenbythisfunctionat pT 4 / m 4 ,where pT 4 and m 4 arethecentersofa 2D-templatebin.Uncertaintiesonreduciblebackgroundareobtainedbypropagatingthe uncertaintiesonthettedparametersoftheTsallisfunction.Theupperpanelsshowt results,inlinearandlogscales,whilethelowerpanelisthetpull((data-PDF)/ # data ). 153

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Figure4-16. Proledistributionofthevariable pT 4 / m 4 versus m 4 forreducible backgroundat8TeV,ttedwithaconstantline. 4.5BackgroundEstimation Therearetwomainsourcesofbackgroundinthe H ZZ 4 search.Theseare 1. IrreducibleBackground arisingfrom q q ZZ 4 and gg ZZ 4 production.Theseareestimatedfromsimulationandveriedthroughacross sectionmeasurementindata.ShapePDF'saretakenfromsimulation. 2. ReducibleBackground arisingfromprocesseswhichcontainoneormore non-promptleptonsinthenalstate.Thisisdominatedby Z + jets events andthereforeisreferredtoas Z + X ,howeverthereisacontributionfrom t t WZ + jets ,andsingletopproduction.Theseareestimatedfromdatausinga fake ratio methodofextrapolatingestimatesfrom Z + X enrichedcontrolregions(CR's), backtothesignalregion.ShapePDF'saretakenfromCR's. Thefollowingsectionsdescribethebackgroundestimatemethodsanduncertainties indetail. 4.5.1IrreducibleBackgroundModel Theirreducible q q ZZ and gg ZZ backgroundsareestimatedfromsimulation. Forthe q q ZZ production,the POWHEG generatorisusedtoproduce q q ZZ 4 eventsatNLO.Inthecaseof gg ZZ ,thereisnoNLOgeneratoravailable,therefore adedicatedLOgeneratorcalled gg2ZZ isusedtoproduce gg ZZ 4 events. Theshapesofthesebackgroundsaremodeledwithempiricalfunctions(described 154

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Figure4-17. Fittothe pT 4 / m 4 distributionafterselectionforreduciblebackgroundata center-of-massenergyof8TeV. later)whicharethenxedinthelikelihoodcalculation.Theyieldsaredetermined fromsimulationandareallowedtooataccordingtotheassignedtheoreticaland experimentaluncertainties.Inthissection,onlythetheoreticaluncertaintieswillbe discussed. 4.5.1.1CrossSectionandUncertainties TheexpectedrateforagivenmassrangeiscalculatedfromMCas ZZ@NLO: dN dm 4 = 3 i C i ( m 4 ) N MC ( m 4 ) F ZZNLO ( m 4 ), (49) 155

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gg ZZ: dN dm 4 = 3 i C i ( m 4 ) N MC ( m 4 ) F gg 2 ZZ ( m 4 ). (410) wherethedata-to-MCcorrectionfactors C i ( m 4 ) areassumedtobethesameasfor theHiggseventswith m H = m 4 PDF + s andQCDuncertaintiesfor pp ZZ 4 atNLOand gg ZZ 4 areevaluatedusing MCFM [ 83 ].Atthetimetheseuncertaintieswereevaluated, MCFM onlyallowedthe2e2 nalstateandthusthisnalstatewasusedwiththefollowing ducialcuts: m ee > 12GeV m > 12GeV electron pT > 7GeVand | % | < 2.5 muon pT > 5GeVand | % | < 2.4 Theminimalallowedjet-leptonandlepton-lepton # R min wererelaxedtozero. CrosssectionswerecalculatedinclusivelyinthenumberofjetsfoundatNLO.The uncertaintiesareassessedbothfor7TeVand8TeVseparately.Perreference[ 84 ], thePDF + s andQCDscaleuncertaintiesaretreatedasuncorrelated.However, uncertaintiesbetween7TeVand8TeVareassumed100%correlated. ForestimationofthePDF + s systematicerrors,thePDF4LHCprescriptionis used[ 85 ].ThethreePDFsetsusedareCT10[ 74 ],MSTW08[ 86 ],andNNPDF[ 87 ]. TheobtainedresultsaresummarizedinFigure 4-18 wherethepointsareevaluated uncertainties,andthecurvesarethetsystematicerror 1 ( m 4 ) tobeusedinthe statisticalanalysis.Thefour-leptonmassdependentPDF + s systematicerrors,forboth 7TeVand8TeV,areparametrizedas ZZ@NLO: 1 ( m 4 )=1+0.0035 $ ( m 4 % 30) (411) gg ZZ: 1 ( m 4 )=1+0.0066 $ ( m 4 % 10). (412) 156

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Figure4-18. PDF + s uncertaintiesfor pp ZZ 4 (left)atNLOand gg ZZ 4 (right). ToestimatetheQCDscalesystematicerrors,variationsinthedifferentialcross section d # / dm 4 ,astherenormalizationandfactorizationscalesarechangedbyafactor oftwoupanddownfromtheirdefaultsetting( R = F = m Z .Figure 4-19 summarizes theresults.Thefour-leptonmassdependentQCDscalesystematicerrors,forboth7 TeVand8TeV,areparameterizedasfollows ZZ@NLO: 1 ( m 4 )=1.00+0.01 $ ( m 4 % 20) / 13 (413) gg ZZ: 1 ( m 4 )=1.04+0.10 $ ( m 4 +40) / 40) (414) 4.5.1.2ShapeModel Thetsforboth gg ZZ and q q ZZ aredonewithempiricalfunctions.Equation 415 showstheformforthetfunctionfor q q ZZ ,whileequation 416 showsthet functionfor gg ZZ .Alltsareperformedonsimulation. F ZZNLO ( m 2 a 2 b 2 c )= ( f 1 + f 2 + f 3 ) (415) F gg 2 ZZ ( m 2 a 2 b 2 c )= ( f 1 + f 2 ) (416) where 157

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Figure4-19. QCDscaleuncertaintiesfor pp ZZ 4 (left)atNLOand gg ZZ 4 (right)processes. f 1 ( m 2 a )= 0.5+0.5erf m % a 1 a 2 .. a 4 1+ e ( m a 1 ) / a 3 (417) f 2 ( m 2 b )= 0.5+0.5erf m % b 1 b 2 .. b 4 1+ e ( m b 1 ) / b 3 + b 6 1+ e ( m b 1 ) / b 5 (418) f 3 ( m 2 c )= 0.5+0.5erf m % c 1 c 2 .. c 4 1+ e ( m c 1 ) / c 3 (419) The ZZ backgroundshapetsareshowninFigure 4-20 .Therearefoundto benosystematicuncertaintiesthatwoulddistortthe ZZ 4 massdistributions inasubstantialwayoverthemassrangecorrespondingtotheHiggsbosonwidth. Therefore,alluncertaintiesonthe ZZ -backgroundareincludedasuncertaintiesin normalization,whoseabsolutescalemaydependontheHiggsbosonmass m H being probedinthesearch. ForagivenhypothesisofHiggsbosonmass,thesignalisalocalizedpeakinthe m 4 distribution.Largevariationsinthesignalshapeinthenarrowregionsunderthe Higgsbosonpeakarenotexpected.Thisisconrmedbylookingatthelocalshape changesduetoQCDscaleandPDFvariationsandholdstrueevenforthehighHiggs bosonmasshypothesiswherenaturalwidthofthebosonisquitebroad.Therefore,no uncertaintiesonthe ZZ backgroundlineshapeareapplied. 158

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Figure4-20. Fitsofsimulationusingthechosenempiricaltfunctionfor q q ZZ (left) and gg ZZ (right). 159

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4.5.2ReducibleBackgroundModel Thereduciblebackground,dominatedby Z + jets andreferredtoas Z + X for thisreason,isnoteasilyestimatedfromMC.Inthecaseofthethis Z + X background, eventsareselectedduetomisconstructionofjetsasleptons,orfakeleptonsasthey're called.Toestimatethisbackground,afakeratiomethodisemployed.Thebasicmethod startswithdeningcontrolregionswhichcontaintwo tight leptonswhichpresumably comefromaprompt Z andatleastonefakelepton.Todenethesefakeleptons, certainvariablesareinverted,suchasRelPFIso,ID,andsometimes SIP 3 D .Thissection describesthederivationofthereduciblebackgroundyieldandshapeestimatesusedin theanalysis. Thereduciblebackgroundisevaluateddirectlyfromdatausingtwostatistically independentmethodswithpartiallyuncorrelatedsystematicuncertainties.Thetwo methodsstartfromtheobservednumberofeventsindifferentfour-leptoncontrol regionsandestimatetheexpectedcontributioninthesignalregionusinglepton misidenticationprobabilities f ( pT | % | ) thataredenedasprobabilitiesforalepton (electronormuon)whichpassestherelaxedidentication/isolationcriteriatoalsopass thenalselectioncriteria. Inbothmethodsmisidenticationprobabilities f ( pT | % | ) aremeasuredas functionsofleptontransversemomentum pT and % usingthree-leptoncontrolregions Z + loose .Theseregionsaredenedbyrequiringtwoleptonstohaveinvariantmass consistentwiththe Z bosonmassandtosatisfytightleptonselectioncriteria,while thethirdlepton loose isrequiredtosatisfyrelaxedidentication/isolationcriteria.To reducethecontaminationfrom WZ eventswiththreepromptleptons,themodulus ofthetransversemissingmomentumvector, MET ,computedasthenegativeofthe vectorsumofallreconstructedtransversemomentaofparticlesidentiedwiththePF algorithm,isrequiredtobelessthan25GeV.Theinvariantmassoflepton loose and 160

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oppositesignleptonfromthe Z candidateshouldsatisfy m 2 > 4GeVtomatchthe samerequirementusedinthefour-leptoneventselection. 4.5.2.1MethodusingOppositeSignLeptons Inthisapproach,theleptonpairformingthe Z candidateisrequiredtohavean invariantmass | m !! % m Z | < 10GeV.Thisstrictrequirementsuppressesthecontribution of Z + ( FSR eventswithasymmetricFSRphotonconversions,wheneitherelectron orpositronintheconversionpairhasalowmomentumandisnotreconstructed.The misidenticationprobability f ( pT | % | ) rangesfrom5-10%(1-15%)dependingonthe muon(electron) pT and % Thismethodusestwoseparatefour-leptoncontrolregionswhichsatisfyallsignal selectioncriteriaexceptthatinoneregionbothleptonsformingthe Z 2 candidateare requiredtofailnalleptonselectioncriteria(region2P2F),whileintheotherregion, exactlyoneofthesetwoleptonsisrequiredtofailnalleptonselection(region3P1F). The2P2Fcontrolregion,containing N 2P2F events,isusedtoestimatecontribution frombackgroundsthatintrinsicallyhaveonlytwopromptleptons( Z + lightjets, Zb b t t ).Theestimateofthesebackgrounds'contributiontothesignalregionisobtainedby weightingeachevent i inthe2P2Fcontrolregionbyfactor f i 3 1 f i 3 f i 4 1 f i 4 ,where f i 3 and f i 4 are misidenticationprobabilities,or fakerates ,forleptonsfailingthenalselection. The3P1Fcontrolregion,containing N 3P1F events,isusedtoestimatecontribution frombackgroundswiththreepromptleptonsandonemisidentiedlepton( WZ + jets Z ( + jets withasymmetricconversion).First,eachevent j inthe 3 P 1 F regionisweighted byfactor f j a 1 f j a ,where f j a isthefakeratefortheleptonfailingnalselection( a =3or4 ).A smallnumberof ZZ events,whereoneofthefourpromptleptonsfailsthenalselection, alsocontributetothe3P1Fregionandshouldnotbecountedintheextrapolation.This number, n ZZ 3P1F ,isestimatedfromsimulationandthetotalpredictionisthenreducedby factor (1 % n ZZ 3P1F / N ZZ 3P1F ) .Moreover,2P2F-typeeventscontributetothe3P1Fregion aswell.Theircontributioncanbeestimatedas / i ( f j 3 1 f i 3 + f j 4 1 f i 4 ) .Afterbeingweighted 161

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byeither f j 4 1 f i 4 or f j 3 1 f i 3 ,theseeventswouldresultinanover-predictionby / i (2 f i 3 1 f i 3 f i 4 1 f i 4 ) whichhastoberemoved.Therefore,thenalexpectedyieldforreduciblebackground becomes: N reducible SR = 1 % n ZZ 3P1F N ZZ 3P1F N 3P1F 0 j f j a 1 % f j a % N 2P2F 0 i f i 3 1 % f 3 f i 4 1 % f i 4 (420) Predictionsforthenumberofeventsinthethreenalstates(4e,4 ,2e2 )aswell asforthe7and8TeVdatasetsareobtainedseparately.Thisformulaisalsousedfor predictingthenumberofreduciblebackgroundeventsinvariousdistributionsusedinthe analysis. Figure4-21. Fakeratesmeasuredforprobemuonswhichsatisfythelooseselection criteria,measuredina Z ( "" )+ sampleinthe7TeVdata(left)andthe8 TeVdata(right). 162

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Figure4-22. Fakeratesmeasuredforprobeelectronswhichsatisfythelooseselection criteria,measuredina Z ( "" )+ e samplewithin | M inv ( 1 2 ) % M Z | < 10 GeV,inthe7TeVdata(left)andthe8TeVdata(right). 163

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4.5.2.2MethodusingSameSignLeptons Inthisapproach,thefakerate f ( pT | % | ) ismeasuredinaphasespacethat isascloseaspossibletothesignalregion.The Z + loose sampleisselectedwitha di-leptoninvariantmasscriterion | m !! % m Z | < 40GeV.Insuchasample,thecontribution fromradiatedFSRphotonstotheelectronfakerate f ( e pT | % | ) isdifferentthaninthe controlregionwherethefakeratesareapplied.Totakethisintoaccount,thecorrelation between f ( e pT | % | ) andthefraction r miss ( pT | % | ) oflooseelectronsforwhichthetrack hasonemissinghitinthepixeldetectorismeasured.Thisisdoneusingsampleswith differentFSRcontributionsobtainedbyvaryingcriteriaon | m !! % m Z | and | m !! e loose % m Z | Thecorrected f ( e pT | % | ) isthencomputedusingthevalue r miss ( pT | % | ) measuredin thecontrolsamplewhereweapplythemethod. Thismethodusesonefour-leptoncontrolregionwhichsatisesallsignalselection criteriaexceptthatthetwoleptonsformingthe Z 2 candidatearerequiredtosatisfy relaxedidentication/isolationcriteriaandtobeofsamesign(region 2P2L SS ). Theexpectednumberofreduciblebackgroundeventsinthesignalregionisthen obtainedas: N reducible SR = r OS / SS N 2P2L SS 0 i f i 3 f i 4 (421) where N 2P2L SS isthenumberofobservedeventsintheregion 2P2L SS ,and r OS / SS istheratioofthenumberofeventsinthe 2P2L OS and 2P2L SS controlregionsobtained fromsimulation. 164

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Figure4-23. Averagefakeratestobeappliedtothecontrolsample(closedreddots), comparedtothefakeratesmeasuredinthefakeratesample(closedblack dots)andintheOSfakeratesample(opensquares).Thefakerates correspondingtoBarrel(Endcap)electronsforthe7TeV(right)and8TeV (left)dataareshown. 165

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4.5.2.3Combinedresultsanduncertainties Predictionsofthetwomethodsfortheexpectedyieldofreduciblebackgroundsare showninTable 4-5 andagreewithinstatisticaluncertainties.Thedominantsourcesof theseuncertaintiesarethelimitednumberofeventsin3P1F,2P2Fand 2P2L SS control regions,aswellasintheregionwherewecomputethecorrectionfactorfor f ( e pT | % | ) Sincethesedominantsourcesaremutuallyindependent,resultsofthetwomethodsare combinedassumingfullyuncorrelatedstatisticaluncertainties.Thecombinedresultsare showninthelastrowofTable 4-5 Table4-5. Reduciblebackgroundyieldspredictedbybothmethodsandassociated statisticaluncertainties. Channel 4e 4 2e2 4e 4 2e2 collisionenergy 7TeVdata 8TeVdata MethodusingOSleptons1.6 0.31.1 0.42.5 0.56.2 0.73.1 0.88.4 1.2 MethodusingSSleptons1.2 0.40.5 0.11.9 0.45.9 0.93.1 0.59.4 1.0 Combinedestimate1.4 0.20.6 0.12.3 0.36.1 0.63.1 0.59.2 0.7 Thedominantsystematicuncertaintyofthemethodarisesfromfactthatbackground compositionintheregionwherethefakeratesaremeasuredisnotthesameasin regionswheretheyareapplied.Forthisreason,simulationisusedtoidentifydifferent typesoffour-leptonprocesseswithmisidentiedleptonsinthenalstate,tomeasure fakeratesineachoftheseprocessesandtomeasuretheirrelativeproportionin differentcontrolregions.Theeffectofbackgroundcompositiononthenalyield predictionandthesystematicuncertaintyofthemethodareestimatedbasedonthese measurements. 4.5.2.4LineShape The m 4 lineshapeforthereduciblebackgroundisobtainedforthemethod describedinsection 4.5.2.1 ,byttingthe m 4 distributionsof2P2F-likeand3P1F-like contributionsseparatelyusingempiricalfunctionalforms.Systematicuncertaintyon the m 4 shapeisdeterminedastheenvelopethatcoversallinvestigatedalternative 166

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Figure4-24. Predictionforthereduciblebackgroundinallthreechannelstogether (blackdots)ttedusinganempiricalshape(bluecurve)withindicatedtotal uncertainty(yellowband)(left).Contributionsfromthe2P2F-like(green) and3P1F-like(red)processesarettedseparately. functionalforms.Itisconvertedintoadditionalsystematicuncertaintiesontheexpected eventyieldnearagiven m 4 Thetotalsystematicuncertaintiesarecomprisedofsystematicuncertaintieson themethodandonthe m 4 shape,andareestimatedtobe20%,25%,40%forthe 4e,2e2 ,4 nalstate,respectively.Thecombinedpredictionoftheexpectedyields ofthisbackgroundwithcombinedstatisticalandsystematicuncertaintiesisgiven insection 4.9.1 andalsoshowninFigure 4-24 (left).Validationofthemethodusing controlsample Z 1 + e & isshownontheright.Theobservedinvariant m 4 distribution, predictionofthereduciblebackgroundandexpectedcontributionsfrom ZZ areshown withblackdots,greenhistogramandbluehistogram,respectively. Validationofmethodshavebeenperformedusingsamplesofeventsthathave passedthestandardanalysisselectionwithexceptionthatthe Z 2 candidateisformed outofoppositeavorleptonpair(region Z 1 + e & ).Thepredictedcontributionof reduciblebackgroundinthiscontrolregionisfoundtobeinagreementwiththe observednumberofeventswithintheuncertainties.Figure 4-24 (right)showsthe 167

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validationofthemethoddescribedinsection 4.5.2.1 .Figure 4-25 showsabreakdown ofthecontributionsfromthe2P2Fand3P1Fregionforthechannelswithelectronfakes. Thesearetheshapesusedinthestatisticalanalysis. A B C Figure4-25. Fitsofthe m 4 distributionsforchannelswithelectronfakesforthe(a)2P2F component,(b)3P1Fcomponent,and(c)thesumofthetwofunctions. 168

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4.6SignalModel 4.6.1LowMassSignalModel ForStandardModelHiggsmasshypotheses m H < 400GeV,thenarrow-width resonancehypothesisholds,sothesignallineshapefor f ( m 4 l | m H ) ismodeledasa Breit-Wignerfunctiondescribingthetheoreticallineshape,convolutedwithanempirical resolutionfunctionthataccountsforexperimentalscalebiasandresolution. TherelativisticBreit-Wignerfunction, f BW ( m H | m H ) ,isthefollowing: f BW ( m 4 l | m H )= % gg ( m 4 l ) % ZZ ( m 4 l ) m 4 l ( m 2 4 l % m 2 H ) 2 + m 2 4 l % 2 ( m 4 l ) (422) whiletheresolutionfunctionhasbeenchosenasthesimplestfunctionthataccounts fortheGaussianresolutionofthecoreofthe m 4 distributionandthetailsinducedby radiativeeffectsforthemuonsandenergyleakageintheelectromagneticcalorimeter,a DoubleCrystal-Ballfunction f dCB ( m 4 | m H ) : dCB ( 3 )= N 4 5 5 5 5 6 5 5 5 5 7 A ( B + | 3 | ) n L ,for 3 <' L A ( B + | 3 | ) n R ,for 3 >' R exp % 3 2 / 2 # ,for L $ 3 $ R (423) where 3 =( m 4 % m H % # m H ) / # m .Thisfunctionhassixindependentparameters,andis intendedtocapturetheGaussiancore( # m )ofthefour-leptonmassresolutionfunction, systematicmassshift # m H ofthepeak,andtheleft-andright-handtailoriginatingfrom leptonsemittingbremsstrahlungradiationinthetrackermaterial.Thisispresentfor bothelectronsandmuons,andfromthenon-Gaussianmis-measurementsspecicto interactionsofelectronswiththedetectormaterial(twoparameters, n and ,foreach sideofthemean).Theprominenceoftheleft-,right-handtailisdenedbythepower n L n R ,respectively.Theparameters L R denewherethesplicingofthetailsandthe corearemade,inunitsof # m .Ithasbeenfoundthattherighttailisdescribedwellforall themasshypotheseswithaconstantparameter n R =20.Parameters A and B arenot 169

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independent.Theyaredenedbyrequiringthecontinuityofthefunctionitselfandits rstderivatives. N isthenormalizingconstant. TheactualsignalPDFisbuiltthroughtheconvolution: f ( m 4 | m H )= DCB ( m 4 | m H ) ) pdf 1 ( m H | m H ) (424) TheBreit-WignerpdfisfullydeterminedbytheHiggsbosonmass,whilethe parametersofthedoubleCrystal-ballareobtainedfromtsofsimulatedsignalevents, afterthefullleptonandeventselectionsareapplied.Figure 4-26 showthetsfor4 ,4e and2e2 (right)eventssimulatedwith + s = 8TeVforaHiggsbosonwith m H = 126 GeVandforaHiggsbosonwithmassabovethe2 m Z 0 massthreshold( m H = 200 GeV).Lineshapesfor7TeVareverysimilar. Figure4-26. Probabilitydensityfunctions f ( m 4 l | m H ) forasignalwith m H = 126GeV (top)or m H = 200GeV(bottom)atthereconstructionlevelafterfulllepton andeventselectionsareappliedfor4 (left),4e(center)and2e2 (right) events. 170

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Aftertheparametersofthesignalmodelareobtainedforallthesimulatedsamples, theparametersarettedasafunctionof m H withpolynomialstoobtainthesignalmodel parameterizationforallmassvalues.In B ,inFigures B-1 (7TeV)and B-2 (8TeV)thesix doublecrystal-ballparameterswithinterpolationareshownforallthesimulatedmasses for7TeVand8TeV,respectively.Thevaluesfromthislastparametrizationareusedfor allmasses,regardlessofwhethertheyhavethecorrespondingsamplessimulatedor not.ThismeansthatthestatisticalanalysiscanbeperformedforanygivenHiggsmass, regardlessofexistingMC.ThevalidationoftheinterpolatedPDFsforsomediscrete masspointsareshownintheappendixinFigure B-5 ,wheretheinterpolatedPDFin superimposedontothedistributionoftheactualsimulationpoints. IthasalsobeencheckedthatauniquePDF,extractedfromtheggHMCdistribution, isvalidforalltheproductionmechanismsandbothdi-jettaggedanduntaggedcategory. InFigure 4-27 ,thedistributionsfortheotherproductionmodesareshown(VBF, WH,ZH, t t H)intheuntaggedcategory,andcomparedwiththeggHproduction distributionandtheparameterizationderivedforit(fromtheinterpolationdescribed above).The t t Hproductionhasnegligiblestatisticsinthiscategorysincethejets associatedtothe t t causemostoftheeventsendupinthedi-jetcategory.Emptypoints representthedistributionforinclusivecategoryggHproduction,usedtoderivethe parameterization(greenline).Fromlefttoright:4 ,4e,and2e2 channels,andtopto bottom:ggH,VBF,WH,ZH,and t t Hproductions. TheonlyexceptionforwhichthedistributionbetweentheggHandthealternative productionaredifferentistheZH,where Z "" ,becausethecombinatoricsfromthe Z notfromtheHiggsdecaycreatesasecondarypeakathigher m 4 .Giventhatthe fractionoftheseeventswiththewrongcombinatoricsissmallwithrespectthecorrect combinatorics,givesamasspeakaroundtheexpectedvalue,andthefactthatthis productionrepresentsatinysignalyieldwiththecurrentluminosity,nospecialPDFis used. 171

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Figure4-27. Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmass m H = 126GeVatthereconstructionlevelafterfullleptonandeventselections areappliedfordifferentproductionmodesintheUntaggedCategory(black points). Figure 4-28 showsthe m 4 massdistributions,dividedbytheproductionmodes andcomparedwiththeparameterizedPDFfromggH.Alsointhiscase,withthesame 172

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exceptionofZHassociatedproduction,whichisverysmall,thesamePDFcanbe safelyusedforalltheproductions.Emptypointsrepresentthedistributionforinclusive categoryggHproduction,usedtoderivetheparameterization(greenline).From lefttoright:4 ,4e,2e2 channels,andtoptobottom:ggH,VBF,WH,ZH,and t t H productions. 173

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Figure4-28. Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmass m H = 126GeVatthereconstructionlevelafterthefullleptonandevent selectionsareappliedfordifferentproductionmodesintheDi-JetCategory (blackpoints). 174

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4.6.2SignalModelUncertaintiesfor m H < 400GeV Theuncertaintiesaffectingtheshapeofthesignal,forHiggsmasshypotheses m H < 400GeV,arethefollowing: 1. Theoreticaluncertaintiesonthetheoreticallineshape f BW ( m 4 l | m H ) 422 Sinceforthelowmassregionthetheoreticalwidthismuchsmallerthanthe experimentalresolution,theshapeisnotsensitivetosystematicuncertaintieson thetheoreticalsignallineshape. 2. Instrumentaluncertaintiesonthedetectorresolutionfunction f dCB ( m 4 | m H ) 423 .Thelargestsystematicsfromexperimentalsourcesonthesignalmodelis thenonperfectknowledgeoftheleptonscaleandresolution,thatpropagatesto thecomputationofthe4 invariantmass. Sincealargesampleof Z "" ,where = e ,isusedtocalibratethelepton scaleanduncertainty,whichcoversamomentumrangebetween30-50GeVwith highstatistics,thelargestsystematicremainsfromthedependencyofthescale andresolutionfrom pT % andrunconditions(pile-upvariationsacrossthells). Thesedependenciesformuonsareshowninsection 3.2.7 .Afterthemuon correctionstheresidualdependency(differentiallywithrespectthesimulation)is lessthan0.1%,whichpropagatestoabout0.1%onthe4 massforboth4 and 2e2 events.Theuncertaintyontheresolutionisestimatedtobe20%relativeto the # dCB Forelectrons,thedependencyon pT ofthescalerelativetosimulationis higher,becauseofthecontributionofbothECALandtrackerinthemomentum measurementwithdifferentweightdependingonthe pT .Thisdependency isshown,subdividedintwoelectroncategories,differentiallywithrespectthe simulationinsection 3.1.8 .Thedependenciesofthescaleasafunctionof otherquantities(pile-up)arefoundtobeminimal,soasystematicerrorisnot needed,giventhesmalluncertaintyontheintegratedcorrectiondonewiththe Z ee .Thescaledependencyon pT iscorrectedfortheresidualnonlinearity indata/MonteCarlo,butaconservativeestimateofthesystematicsofthescale dependencyisdoneassumingthatthereisnobetterknowledgethantheobserved data-to-simulationdiscrepancy.Toestimateit,theexpectedshiftisappliedtothe electronsinaHiggsMonteCarlosamplewith m H = 126GeV,andtheinvariant massisrecomputed.ThenattothemassdistributionwithaDoubleCrystalBall functionisdonetakingthedifferenceinthettedmeanbetweenthenominaland theshifteddistributionaseventsystematicduetothiseffect.Thedistributionsfor 2e2 and4eareshowninFigure 4-29 for8TeV. Thesystematicsduetothiseffectappliedarethenasfollows: 4 e nalstate:extra0.4%systematic 2 e 2 nalstate:extra0.2%systematic 175

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Figure4-29. Fourleptoninvariantmassdistributionwiththenominallepton momentum(black)andaftertheextrascaleshiftsareappliedtothe MonteCarlo(blue)withthedoubleCrystalBalltsuperimposed,for the4e(left)and2e2 (right)nalstatesfor8TeVsimulationwith m H = 126GeV. wheretheeffectontheinvariantmassisbetterthantheworstshiftseenper electronbecausethecoreofthedistributionisdominated,forkinematicand efciencyreasons,byelectronswithmoderate pT inthebarrelregionwherethe scaleismoreprecise. 4.6.3HighMassSignalModel ForaStandardModelHiggswithmass # 400GeV,thelineshapewidthbecomes verylarge( > 70GeV).Theproblemhasbeendiscussedindetailsinreference[ 88 ], andamorecorrectapproachtodescribetheHiggsinvariant-massdistributionhas beenproposed,knownas ComplexPoleScheme(CPS) .ThetotalHiggsproduction cross-sectionhasbeenrecomputedbytheHiggsCross-SectionWorkingGroupto includecorrectionsduetoCPSathighHiggsmass[ 89 ].Thoseupdatedvaluesforthe totalcross-sectionhavebeenusedinconjuctionwithanewfunctionalitydevelopedin POWHEG [ 69 ]inordertore-weightHiggssignalsamplestomatchtheHiggslineshape predictedintheCPSapproach. 176

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AthighHiggsmasstheinterferencebetweentheHiggssignalandthe gg ZZ backgroundbecomesverylarge,asdiscussedinreference[ 90 ].Theeffectof interferencehasbeenshowntobeconstructivebelowtheHiggsmasspeakand destructiveabove.Itthereforehasanegligibleeffectonthetotalcross-section(1-2%) butitstronglybiasestheinvariantmassdistribution.Moreovertheinterferencehas beencomputedonlyatLO,whilethesignalisknownatNNLO.Thisanalysisfollowsthe approachproposedinreference[ 90 ]toestimatetheuncertaintyduetomissinghigher perturbativeorderontheinterference.GiventhesignalatNNLO( S NNLO = S LO K )and theinterferenceatLO( I ),threealternativeestimationofsignal + interferencecanbe considered: S LO K + I (425) S LO K + I K # (426) ( S LO + I ) K (427) respectivelycalledadditive,intermediateandmultiplicativerecipes.Theintermediate recipeisbuiltconsideringtheratio( K # )betweenNNLOHiggs-diagramswithonly gg initialstateandLOHiggs-diagrams: K = S NNLO ( gg Hg + qg Hq + qq Hg ) S LO ( gg H ) = K # + K rest (428) K # = S NNLO ( gg Hg ) S LO ( gg H ) (429) Inthisanalysis,theHiggslineshapehasbeenre-weightedtoincludetheeffectof theinterferenceasdescribedbytheintermediaterecipe.Alternativelineshapesare alsobuiltwiththeadditiveandmultiplicativerecipestoestimatetheuncertaintyonthe missinghigherperturbativeordersontheinterferencecalculation. 177

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TheeffectoftheCPSandinterferencecorrectionsonthe H ZZ invariantmass distributionandtherelateduncertaintiesareshowninFigure 4-30 .Thetwobounding shapesenclosingthelledbandrepresentsthelineshapeuncertaintyusedinthet. Figure4-30. Fourleptoninvariantmassdistributionatgeneratorlevelbeforeandafter theCPS+interferencecorrectionsforaHiggsmassof900GeVproduced ingluonfusion(left)orinvectorbosonfusion(right). Giventhepeculiaritiesofthesignallineshapein m H # 400GeVrange,thesignal modelhastobemodiedwithrespectthelowmassrangesearch.Afterthere-weighting describedabove,insteadofusingthetypicalformusedforlowmassin 422 amodied versionoftheBreit-Wignerwiththefollowingformisused f HM BW ( m 4 l | m H )= m 4 l ( m 2 4 l % m 2 H ) 2 + m 2 4 l % 2 ( m 4 l ) (430) lettingthe % parametertooatinthet.Althoughthisapproachwilllosethecorrelation ofthe % parameterwiththephysicalHiggswidth,itallowstogetagoodt.Systematics onthelineshapeareestablishedbyvaryingtheweightsusedtore-weightthesignal eventsby 1 # AconvolutionofthishighmassBreit-WignerwiththeDoubleCrystall-Ball, describedinequation 423 isthenusedasthetfunction.Inordertogetasmoothly (andmonotonically)varyingfunctionof % fromtheBreit-Wignerand # dCB ,aconstrained likelihoodttothesignalMonteCarloisperformed,assumingthatthephysicalwidth 178

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oftheHiggsfor m H # 400GeVislargerthantheexperimentalresolution,whichis regulatedby # dCB .Figure 4-31 showsthetsfor m H = 600GeVfor8TeV.Lineshapes for7TeVareverysimilar. Figure4-31. Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmassatthe reconstructionlevelafterthefullleptonandeventselectionsareappliedfor m H = 600GeVat8TeVfor4 (left),4e(center)and2e2 (right)events. Thisalsogivesaparameterizationofthesignalthatcanbeinterpolatedwitha polynomialasisdoneforthelowmass.Theinterpolationoftheparametersisshown intheAppendix B inFigure B-4 forthe8TeVcase.ValidationoftheinterpolatedPDFs forsomediscretemasspointsisshownintheappendixinFigure B-6 ,wherethe interpolatedPDFissuperimposedontothedistributionoftheactualsimulationpoints. 4.6.4SignalModelUncertaintiesfor m H # 400GeV BeyondtheuncertaintiesduetomissingtermsintheperturbativeQCDexpansion andimpreciseknowledgeofpartondistributionfunctions,thefollowingelectroweak(EW) correctionsalsogainlargeimportanceathighHiggsmass: EWcorrectionsintheHiggsproduction,includedinthetotalcross-section,( < 10 % upto1TeVHiggsmass)whiletheeffectontheHiggslineshapeisnegligible. EWcorrectionsforcomplexpole,includedinlineshapeuncertainty EWuncertaintyforthedecay,includedinlineshapeuncertainty ForHiggsmasseslargerthanthetopmass( m t )anadditionaluncertaintyshouldbe considered:thecomputationoftheNNLOHiggscross-sectionaswellasthegeneration 179

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oftheNLOMonteCarlosamplesusedinthisanalysisaredoneintheapproximation ofaneffectivetheorywith m t "( (HQapproximation).Thisapproximationbreaks downatlargeHiggsmass,butitisexpectedtohavenegligibleeffectonthetotal cross-sectionandontheHiggslineshape.TheeffectoftheHQapproximationandof theEWcorrectionsintheHiggsproduction,previouslymentioned,havebeenstudied atNLOwithanewversionof POWHEG whichimplementsCPS,EWproductionandHQ corrections. WhiletheeffectoftheEWcorrectionsandoftheinterferenceontheHiggsline shapemaybedifferentinggHandVBF,inthepresentinclusiveanalysisthe gg H line shapeisusedtodescribeboththecasessincethegluon-gluoncontributiondominates inmostoftheHiggsmassspectrum. Figure 4-30 (bottom)showsthesizeoftheuncertaintiesontheshapegivenby thehighmasscorrections.Inordertopropagatethissystematiceffectonthelimits andp-valuecalculations,thesignalshapefunctionisre-twiththetwoalternative hypotheses.Inthist,alltheparametersdescribingthesignalPDFarexedtothe valuesobtainedfromthenominalt,exceptthe % oftheBreit-Wignerfunction.This way,theuncertaintyonthehigh-masscorrectedshapesispropagatedtotheparameter representingthewidthofourtheoreticalPDF.Oncethetstothetwoalternative hypothesesareperformed,thedifferencebetweenthenominalvalueof % andthe valuedeterminedbythealternativetsiscalculated.Theuncertaintyon % orthe largestvariationbetweenthetwoarethenconsideredasasystematic.Thisprocedure isperformedforallmasspointsandsystematiceffecton % between3%and5%is observedamongthewholespectrum.Aconservativesystematicof5%foranyHiggs masshypothesishasbeenchosen. 4.6.5SignalNormalizationUncertaintyandSystematics Inthissection,thesystematicsappliedonthenormalizationofthesignalandon thereducibleandirreduciblebackgroundsusedforthecrosssectionmeasurement 180

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= # /# SM aredescribed,aswellasforallthepropertiesmeasurementsofthelow massHiggsboson. 4.6.5.1TotalSignalCrossSection Systematicerrorsonthesignaltotalcrosssectionfor each productionmechanism andforallHiggsbosonmassesarefullydenedelsewhere[ 75 ].Theycomefrom PDF + s systematicerrorsandfromtheoreticaluncertaintiesevaluatedbyvaryingQCD renormalizationandfactorizationscales( R and F ). Assuggestedbyreference[ 84 ],thePDF + s andQCDscaleuncertaintiesare treatedascompletelyuncorrelated.The7and8TeVuncertaintiesareassumedtobe 100%correlated. 4.6.5.2BranchingratioBR ( H 4 ) Theuncertaintyon BR ( H 4 l ) istakentobe2%andassumedtobe m H -independent. 4.6.5.3SignalAcceptance DependingontheHiggsbosonmass,theleptonkinematiccutsrestrictthesignal acceptanceto A / 0.6-0.9[ 91 ].Theacceptanceuncertainties 4 A / A areevaluatedby using MCFM .Forcalculations,the pp H ZZ 2e2 processwasusedat7TeV withthefollowingcuts: m ee > 12GeV m > 12GeV electron pT > 7GeVand | % | < 2.5 muon pT > 5GeVand | % | < 2.4 Theminimalallowedjet-leptonandlepton-lepton # R min wererelaxedtozero.Cross sectionswerecalculatedinclusivelyinthenumberofjetsfoundatNLO.Uncertaintieson acceptanceat8TeVarefoundtobethesameasat7TeVandare100%correlated. Thesensitivityofthesignalacceptancetotherenormalizationandfactorization scalesisevaluatedbyvaryingthembyafactoroftwoupanddown.Theresultsare 181

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showninTable 4-6 .Theacceptanceerrorsareverysmall(0.1-0.2%)andtherefore,can besafelyneglected. Table4-6. Signalacceptance A fordifferentQCDscales. Higgsbosonmass m H (GeV)120200400500600 Default A 0 ( R = F = m H / 2 )0.54210.73180.81200.84210.8637 A up ( R = F = m H ) 0.54170.73170.81280.84270.8644 A down ( R = F = m H / 4 )0.54300.73280.81190.84180.8632 4 A / A =max | # A| / A 0 0.17%0.14%0.11%0.07%0.08% ForestimationofthePDF + s systematicerrors,thePDF4LHCprescription[ 85 ] isused.ThethreePDFsetsusedareCT10[ 74 ],MSTW08[ 86 ],NNPDF[ 87 ].The resultistheenvelopecontainingallvariationsforthethreesetsofPDFs.A2% mass-independentuncertaintyhasbeenassignedtoaccountfortheseuncertainties. Perreference[ 84 ],theacceptanceandtotalcrosssectionuncertaintiesaretreated asuncorrelated.PaststudieshaveshownaverylittlecorrelationforthelowHiggs bosonmass.Forthehighmass,anegativecorrelationseemstodevelop,whichimplies thatbyleavingthesecorrelationsoutmakestheanalysisresultsmoreconservative. Forsimplicity,thesameuncertaintyisassignedtoallproductionmechanismsanditis assumedthattheyare100%correlated,whichisalsoconservative. 4.6.5.4SignalEfciency Leptonsinthesignal H ZZ 4 arepromptandtheirtriggerandreconstruction/ID efcienciesaswellastheimpactparameterandisolationcutefcienciescanbereadily evaluateddirectlyfromdatabyinvokingthetag-and-probe(T&P)methodappliedon Z "" events.Theresultsofthesemeasurementsarereportedinsections 3.1.9 and 3.2.8 ,forelectronsandmuonsrespectively. Inthissection,resultsofpropagatingthemeasuredper-leptonefciencies(andtheir errors)tothe 4 phasespaceselectionarediscussed. Theobserveddata/MonteCarlodiscrepancyintheleptonreconstructionand identicationefcienciesmeasuredwiththedata-driventechniquesisusedtocorrect 182

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theMonteCarloonanevent-by-eventbasis.Theuncertaintiesonthisefciency correctionarepropagatedindependentlytoobtainasystematicuncertaintyonthenal yieldsforsignalsandZZbackground. Inpractice,theper-leptondata-to-MCratiosaremultipliedtogiveweighttoan individualevent.Toobtainsystematicerrors,vehundredtoyMCexperimentsarerun foreacheventintheMCsample.Ineachtoyexperiment,avaluefromaGaussian distributionwithmeangivenbythecentralvalueofthedata-to-MCratioandthewidth givenbytheassociatederrorissaved.ThesystematicuncertaintyistakenastheRMS ofthedistributionofthetotalnumberofexpectedeventsinthevehundredtoys. TheresultingsystematicsarereportedintheFigures 4-32 and 4-33 forthe7and8 TeVanalysisrespectively. Figure4-32. Instrumentaluncertaintiesin7TeVdatarelatedtodata/MCdifferencesin efcienciesinreconstruction,identication,isolationand SIP 3 D asa functionof m H ,for(topleft)4echannel,(topright)4 channel(bottomleft) 2e2 channel(electrononlyuncertainties),(bottomright)2e2 channel (muononlyuncertainties). 183

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Figure4-33. Instrumentaluncertaintiesin8TeVdatarelatedtodata/MCdifferencesin efcienciesinreconstruction,identication,isolationand SIP 3 D asa functionof m H ,for(topleft)4echannel,(topright)4 channel(bottomleft) 2e2 channel(electrononlyuncertainties),(bottomright)2e2 channel (muononlyuncertainties). Inaddition,1.5%uncertaintyrelatedtotriggerisaddedinquadrature. 184

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4.7Event-by-Event(EbE)Uncertainties D mass Itispossibletobuildanuncertaintyonthemassforeachindividualevent. BecausetheresolutionoftheHiggssignaleventsareexpectedtobeslightlybetter thanthebackground,thiscanhelpincreasediscriminationpowerbetweensignaland backgroundeventsinthemassandwidthmeasurements.UsingEbEuncertainties alsomakesthesemeasurementsmore"correct",becauseinsteadofusinganaverage resolutionfunctionforeveryevent,theexactresolutioniscalculatedandusedforeach eventrespectively.Thissectiondiscussedtheprocesstoderive,correct,andvalidate theEbEuncertainties. Theseevent-by-event(EbE)massuncertaintiesarebuiltfromuncertaintieson individualleptonmomentummeasurements.Formuons,theuncertaintyisderived fromafullerrormatrixobtainedfromthemuontrackt.ForECAL-drivenelectrons,the uncertaintyisestimatedfromacombinationoftheECALandtrackermeasurement, neglectinguncertaintyonthetrackdirectionfromtheGSFt.Fornon-ECAL-driven electrons,asimpleparameterizationoftheECALenergyerrorhasbeencreated,and iscombinedwiththetrackermomentumerrorasisdoneforECAL-drivenelectrons.For FSRphotons,theparticleowparameterizationisused. Thisinformationcanthenbepropagatedtothefullfourleptonmassinoneoftwo wayscurrentlyused. 1. Theindividualleptonmeasurementserrorsareextendedtothefull4 measurement usingananalyticalerrorpropagationthatincludesallcorrelations. 2. Aslightlysimplerapproachistoextendtheindividualerrorstothefull4 measurementbutignoringerrorsonmeasurementsoftheanglesformuons. Eachindividual 4 m iscalculatedseparately,andthenmeasuredresolutiononthe fourleptonmassistakenasthequadraturesumofthefourindividual 4 m as m 0 = F ( p T 1 1 % 1 ; p T 2 2 % 2 ; p T 3 3 % 3 ; p T 4 4 % 4 ) (431) 185

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4 m i = F ( ...; p Ti + 4 p Ti i % i ;... ) % m 0 (432) 4 m = + 4 m 2 1 + 4 m 2 2 + 4 m 2 3 + 4 m 2 4 (433) Thetwomethodsarefoundtoagreewithin1%orless.Figure 4-34 showsa comparisonofthetwomethods. Figure4-34. Comparisonoffour-leptonmasserrorscalculatedfromthetwoapproaches tocomputetherelativeper-eventerror D mass on8TeVHiggsMCsample with m H = 125GeVfor4e(topleft),4 (topmiddle),2e2 (topright),4 + ( (bottomleft)and2e2 + ( (bottomright). 186

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4.7.1CalibrationofEbEUncertainties BeforetheEbEuncertaintiescanbeusedintheanalysis,theyneedtobecalibrated andveriedindata. AfterstudyingtherawEbEuncertaintiesinsimulatedHiggseventsaswellas Z and J / eventsindata,itwasdeterminedthatthecalibrationoftheGaussiancore oftheper-leptonresolutiondoesnotachieveacorrectmodelingofthefour-lepton invariantmassuncertainty.Thiscouldbeduetoseveralreasons:thecontributionof non-GaussiantailsfromtheindividualleptonstoaGaussiancoreofthemulti-lepton resolution,unrecoverednalstateradiation,orthenon-uniformenergyscalebiasesasa functionofleptonkinematics. Calibrationfactorsforper-leptonmomentumresolutionsarefoundbysplitting reconstructed Z decaysindataandsimulationinseveralregionsofpseudorapidityand thenttingtheseinvariantmassdistributions.Formuons,correctionfactorsforthelow pT regionaredeterminedfrom J / and decaysindataandsimulation. Tondthecalibrationfactorforaparticularbinin( pT % ),bothleptonsfromthe Z "" eventsarerequiredtobeinthegiven( pT % )bin.The m !! massisthentwith aBreit-Wignerfunctionwhichdescribesthenominal Z shapeconvolutedwithaCrystal BallFunctiontodescribethedetectorresolution.TheBreit-Wignerfunctionparameters arexed,withthemeansettothenominal Z massandwidthsettothenatural Z width.TheCrystalBall # CB issettobeaproductbetweenamultiplier and 4 m ,where 4 m istheEbEmassresolutionincludingthecorrectionontheper-leptonmomentum uncertainties.Themultiplier thenbecomesthecorrectionfactorforleptonsinthe corresponding( pT % )bin. Table 4-7 summarizestheper-leptonmomentumcorrectionfactors.Muoncorrection factorsrangefrom5-15%,whileelectroncorrectionfactorsareabouttwicethat,which isexpectedduetothelargernon-Gaussiantailsandnon-uniformityoftheenergyscale forelectrons.Formuons,thesecorrectionsareontopoftheonesderivedfrompull 187

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distributionsatthesingleleptonlevel.Forelectronsin2012data,aslightlydifferent binningin | % | isused, [0.0,1.0,1.5,1.9,2.5] ,asityieldsamoreuniformcorrectionfactor withineachbin. Table4-7. Correctionfactorsfortheper-leptonmomentumuncertaintiesderivedfrom Z (high pT muonsandall pT electrons)and J / events(low pT muons)indata andsimulations. Geometry2011Data2011Sim.2012Data2012Sim. muons: p T < 20 GeV | % | < 0.8 1.00 1.06 1.04 1.02 0.8 < | % | < 1.60.98 1.07 1.04 1.01 1.6 < | % | < 2.40.96 1.07 1.03 0.99 muons: p T > 20 GeV | % | < 0.8 1.09 1.16 1.14 1.11 0.8 < | % | < 1.61.16 1.03 1.11 1.05 1.6 < | % | < 2.40.95 0.99 1.26 1.01 electrons | % | < 0.8 1.25 1.27 1.17 1.13 0.8 < | % | < 1.51.16 1.11 1.20 1.17 1.5 < | % | < 2.01.30 1.30 1.20 1.14 2.0 < | % | < 2.51.16 1.24 1.17 1.10 4.7.2Modelingofthe D mass Inordertouse D mass toincreasediscriminationbetweensignalandbackground, theexpecteddistributionforbothsignalandbackgroundmustbemodeledversusHiggs mass,justlikethesignallineshape.ThisisdonebyttingeventsfromMCanddata controlregionsforsignalandbackground.Allchannelsandbothsignalandbackground componentsaremodeledwithaPDFcomposedofaLandauplusaGaussian. P ( D mass )= x Landau( 4 rel m 4 ld # ld )+(1 % x ) Gaussian( 4 rel m 4 gs # gs ) (434) Figure 4-35 showsanexampleofthetfora126GeVHiggsMCsample,while Figure 4-36 showsthetsfor qq ZZ and gg ZZ backgroundsamples. Anexampleoftheinterpolationofthetparametersforthe8TeV,4 channelis giveninFigure 4-37 188

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Forreduciblebackground,acontrolregionwithrelaxedcutstogainstatistics isused.Thenthe D mass distributionfromthecontrolregioniscomparedwith ZZ backgroundand Z + jets MCsamples.Theeventsinthecontrolregionarere-weighted accordingtothe pT and % dependentfakeratesaswell.The4eand2e2 Z + jetsD mass distributionsarettedwithaLandautimesGaussian.Figure 4-38 showsthesetsfora m 4 rangeof120-130GeV. 189

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Figure4-35. Four-leptonrelativemasserrordistributions D mass (points)andtsforsignal MonteCarlosampleat8TeVwith m H = 126GeVfor4 (left),4e(middle), and2e2 (right)events. Figure4-36. Four-leptonrelativemasserrordistributions D mass (points)andtsfor qq ZZ (top)and gg ZZ MonteCarlosamplesat8TeVfor4 (left),4e (middle),and2e2 (right)events. 190

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Figure4-37. InterpolationoftheparametersfortheLandau+Gaussianusedtodescribe D mass in 434 for4 channelat8TeV.Topleft: ld ,topright: # ld ,bottom left: gs ,bottomright: # gs Figure4-38. Four-lepton D mass distributionfrom8TeVdata(7TeVissimilar)control regionforZ+Xbackgroundfor4 (left),4e(middle)and2e2 (right),with tssuperimposed. 191

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4.7.3ValidationoftheEbEUncertaintiesinData Whilethegoalofthecalibrationdiscussedintheprevioussectionistomatchthe predictedresolutionwiththemeasuredresolution,itmustbeexplicitlycheckedbefore itcanbeused.ToquantifythelevelofaccuracytowhichthefourleptonEbEmass resolutioncanbepredicted, Z "" eventsindataaresplitintocategoriesaccording theirpredictedmassresolutions.Thenerbinnedthecategorization,thecloserthatthe averagemassresolutioninthecategorywillbetotheEbEmassresolution.Forthistest, 10binsarechosen. The m !! distributionsfortheseeventsarethenttedwithaBreit-Wigner(xed parametersasbefore)convolutedwithaCrystalBallfunction.Themeasured D mass isthencomparedtothepredicted D mass foreachcategory.Figure 4-39 showsthese correlationplotsforallcategories.Thedashedlinesrepresentthesystematicerror assignedtothemomentumresolutionforbothmuonsandelectrons,20%inthiscase. Figure4-39. Correlationbetweenthepredictedper-eventmasserrorfromthelepton uncertaintyandthemeasuredmasserror,throughtsto Z + (left) and Z e + e (right)in8TeVdataandsimulation. Thisclosuretestindicatesthatthepredictedresolutionisingoodagreementwith themeasuredresolutionwithinthe20%systematicuncertaintyassigned.TheEbE 192

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uncertaintiescanthenbesafelyusedintheanalysis.Theonlyplacetheywillbeusedin thestatisticalanalysisininthemassandwidthts. 4.8KinematicDiscriminants Justastheuseof D jet and pT 4 canincreasediscriminationpowerinthedi-jet and0/1jetcategoriesbetweenVBFandnon-VBFlikeevents,adiscriminantbuiltfrom kinematicvariablescanbeusedinthelikelihoodttoincreasediscriminationpower betweensignalandbackgroundlikeevents,aswellastoseparatedifferentsignal hypotheses.Inthissection,theformulationofthesekinematicdiscriminants, K D are discussed,aswellastheirimplementationintheanalysis. KinematicsoftheHiggsdecayto ZZ nalstatehasbeenextensivelystudied intheliteratureinapplicationtothestudiesoftheHiggsbosonornewexoticboson properties,seeforexamplereferences[ 4 92 93 94 95 94 96 97 98 99 100 101 102 103 104 105 92 106 97 101 102 107 108 104 109 110 ].TheCMS experimenthasintroducedthematrixelementlikelihoodapproach(MELA)which reliesonprobabilitiesforaneventtocomeeitherfromsignalorbackgroundwitha setofobservableswhichfullycharacterizetheeventtopologyinitscenter-of-mass frame[ 111 112 ].Theseobservablescouldbechosenforexampleas ( m 4 m 1 m 2 2 ( ) where 2 ( areveanglesdenedinreference[ 4 ].Equivalently,thefour-vectorsofthefour leptonscarryfullinformationabouttheevent,butcareneedstobetakentodenethose inthecenter-of-massframe.Here,thelongitudinalortransverseboostofthefour-lepton systemisarenotconsideredbecausetheydependonproductionmechanismsand couldbemoreeffectivelyusedasaseparatesetofobservables. Severalimplementationsofthematrixelementapproach,aswellasmachine trainedtechniques(MVA's)havebeenexaminedinthisanalysis.Theprimaryresults areobtainedwithamatrixelementapproachfromthe JHUGEN [ 4 103 ]using MCFM for ZZ background[ 83 ],andmustbeinalmostperfectagreementwithresultsobtained withthe MEKD package[ 113 ],whichisbasedonMadGraph[ 114 ]withFeynRules.Both 193

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Figure4-40. IllustrationofaHiggsproductionanddecay ab H Z 1 Z 2 4 withthe twoproductionangles ) and $ 1 shownintheHiggsrestframeandthree decayangles ) 1 ) 2 ,and $ showninthe Z ( ) restframes[ 4 ]. JHUGEN and MEKD allowafullLOmatrixelementapproachincludingnalstatelepton interference.Allothermethodsareexpectedtoyieldsimilarresultsandareusedto strengthencondenceinthenominalresults.Theseincludeananalyticalapproach tothematrixelementfromMELA[ 4 103 104 ]andmachinetrainedtechniques includingBoostedDecisionTrees(BDT's)andBayesianNeuralNetworks(BNN's). Asanadditionallayerofscrutiny,thepurematrixelementsforsignalandbackground musthaveverygoodcorrelationbetween JHUGEN and MEKD Givenseveralsignal(SMand J P )andbackground( q q ZZ and gg ZZ ) hypotheses,thereareseveraleffectiveprobabilitiesthatonecancalculateforeach 194

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event: P SM = P kin SM ( 2 ( m 1 m 2 | m 4 ) P mass sig ( m 4 | m H ) (435) P J P = P kin J P ( 2 ( m 1 m 2 | m 4 ) P mass sig ( m 4 | m H ) (436) P q qZZ = P kin q qZZ ( 2 ( m 1 m 2 | m 4 ) P mass q qZZ ( m 4 ) (437) P ggZZ = P kin ggZZ ( 2 ( m 1 m 2 | m 4 ) P mass ggZZ ( m 4 ), (438) where P kin istheprobabilityasafunctionofangularandmassobservables ( 2 ( m 1 m 2 ) andcalculatedwiththematrixelementapproach,while P mass istheprobabilityas afunctionofthefour-leptonreconstructedmassandiscalculatedusingthe m 4 parameterizationusedinthecross-sectionanalysis.Parameterizationofkinematicsfor instrumentalbackground Z + X doesnotexistfromrstprinciplesandthisbackground istreatedempiricallyinanalysis.TheassumptionoftheHiggsbosonmass m H = 126 GeVisusedinthisanalysis,butcanbeadjustedtoanyhypothesismass.Theseare thecompletedescriptionsofprobabilitiesdenedinthecenter-of-massframeofthe 4 system.Boostobservableasafunctionofthe 4 system(suchas pT andrapidity Y )arenotincludedintothe K D sincethosedependonproductionmechanismandare moreoptimallyusedoutsideofthekinematicdiscriminantcalculation. Fromtheaboveprobabilities,severalobservablescanbecreated,suchas D kin bkg = P kin SM P kin SM + c P kin q qZZ = 8 1+ c ( m 4 ) P kin q qZZ ( m 1 m 2 2 ( | m 4 ) P kin SM ( m 1 m 2 2 ( | m 4 ) 9 1 (439) D bkg = P SM P SM + c P bkg = 8 1+ c ( m 4 ) P kin bkg ( m 1 m 2 2 ( | m 4 ) P mass bkg ( m 4 ) P kin SM ( m 1 m 2 2 ( | m 4 ) P mass sig ( m 4 | m H ) 9 1 (440) D J P = P SM P SM + c J P P J P = 8 1+ c J P P kin J P ( m 1 m 2 2 ( | m 4 ) P kin SM ( m 1 m 2 2 ( | m 4 ) 9 1 (441) D ggZZ = P kin ggZZ P kin ggZZ + c ggZZ P kin q qZZ = 8 1+ c ggZZ ( m 4 ) P kin q qZZ ( m 1 m 2 2 ( | m 4 ) P kin ggZZ ( m 1 m 2 2 ( | m 4 ) 9 1 (442) 195

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wheretheconstants c x aretunedtoadjustrelativenormalizationofprobabilities,forthe optimalappearanceoftheeventdistributionsafterthedetectoracceptanceeffects.The D kin bkg and D bkg observablesemphasizeseparationofsignalfrombackground.Theydiffer onlybyinclusion( D bkg )ornot( D kin bkg )ofthe m 4 probability.The D kin bkg isdesignedtobe usedtogetherwith m 4 inalikelihoodt,while D bkg canbeusedstand-aloneforoptimal backgroundrejectionpower.The D ggZZ isusedonlyasacross-checkofthe q q ZZ and gg ZZ backgroundcontributionsathighmass.Finally, D J P canbecalculated foranumberofalternativespin-parity J P signalhypotheses.Foracompletelistofall discriminantsusedinanalysis,seeTable 4-8 .Itcanbeshownthattheaboveapproach retainsallinformationabouttheeventforoptimalhypothesistesting. Theabovehypothesistestingapproachcanalsobeextendedtomodelswhich areindependentofproductionmechanisms.Thiscanbeachievedbyconsideringthe unpolarized X -bosonproductionbyeitheraveragingoverthespindegreesoffreedomof theproduced X -boson,orequivalently,integratingoverthetwoproductionangles cos ) and $ 1 inthe J P x probabilityexpectation P J P x [ 4 ].Thisleadstothespin-averagedmatrix elementsquaredforthe X -decayastheprobability P inthekinematicdiscriminant. Thismethodisalsoappliedtocalculatethe D dec bkg discriminantforsignal-to-background separation. D dec bkg = 8 1+ c ( m 4 ) 1 4 : d $ 1 dcos ) P kin bkg ( m 1 m 2 2 ( | m 4 ) P mass bkg ( m 4 ) P kin SM ( m 1 m 2 2 ( | m 4 ) P mass sig ( m 4 | m H ) 9 1 (443) D dec J P = 8 1+ c J P 1 4 : d $ 1 dcos ) P kin J P ( m 1 m 2 2 ( | m 4 ) P kin SM ( m 1 m 2 2 ( | m 4 ) 9 1 (444) Thismethodappliestoanypossiblehypothesiswithnon-zerospin.Thespin-zero kinematicsarealreadyindependentoftheproductionmechanismduetolackofspin correlationsforanyspin-zeroparticle,sincetheresult cos ) and $ 1 distributionsare isotropicforanyproductionmodel.Smallpotentialdifferencesintheproduction-independent 196

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discriminantdistributionsduetodetectoracceptanceeffectsaretreatedassystematic uncertainties. Table4-8. Listofkinematicdiscriminantsusedinthecross-sectionandspin-parity analyses. Discriminant Note Observablesusedinthe p -valueanalysis m 4 four-leptoninvariantmass,mainbackgrounddiscrimination D bkg discriminateSMHiggsbosonagainst ZZ background D jet Fisherdiscriminant,usejetinformationtoidentifyVBFtopology D pT pT todiscriminateproductionmechanisminthenon-jetcategory Observableusedasacross-checkofbackgroundmodel D ggZZ discriminate gg ZZ against q q ZZ SMEWproduction Observablesusedinthespin-parityanalyses D bkg discriminateSMHiggsbosonagainst ZZ background,include m 4 D 0 pseudo-scalar( 0 ),discriminateagainstSMHiggsboson D 0 + h BSMscalarwithhigherdimoperators( 0 + h ) D 1 Exoticvector( 1 ), q q X D 1 + Exoticpseudo-vector( 1 + ), q q X D gg 2 + m KKGraviton-likewithminimalcouplings( 2 + m ), gg X D q q 2 + m KKGraviton-likewithminimalcouplings( 2 + m ), q q X D gg 2 + b KKGraviton-likewithSMinthebulk( 2 + b ), gg X D gg 2 + h BSMtensorwithhigherdimoperators( 2 + h ), gg X D gg 2 h BSMpseudo-tensorwithhigherdimoperators( 2 h ), gg X Production-independentobservablesusedinthespin-parityanalyses D dec bkg discriminateagainst ZZ background,include m 4 ,exclude cos ) $ 1 D dec 1 Exoticvector( 1 ),decay-onlyinformation D dec 1 + Exoticpseudo-vector( 1 + ),decay-onlyinformation D dec 2 + m KKGraviton-likewithminimalcouplings( 2 + m ),decay-onlyinformation Inthecaseofthenominalsearchanalysis,wherediscriminationofsignalversus backgroundiskey,twodimensionaltemplatesof K D versus m 4 areused.Figure 4-41 showsanexampleofthesetemplatesforggHsignaland q q ZZ withdataoverlaid. 197

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Figure4-41. D bkg fora m H = 126GeVHiggs(topleft), q q ZZ (topright)inthelow massregion,and q q ZZ inthehighmassregion(bottom)withdata eventsoverlaid. 198

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4.9SearchResults Theprevioussectionshavediscussedallthetoolsandpiecesneededtoform nalresultsinthesearchfortheHiggsbosoninthe H ZZ 4 decaychannel.In thissection,thepiecesofthepuzzlehavebeenassembledandtheresults[ 115 ]are presentedbeginningwithexpectedeventyields,theneventdistributions,kinematic distributions,andnally K D distributions. 4.9.1Yields Table 4-9 showsthenumberofestimatedsignalandbackgroundeventsaswell astheobservedcandidatesindata,afternalinclusiveselection.Countsareshown separatelyfor7TeVand8TeV,aswellascombined.Signaland ZZ backgroundare estimatedfromMonteCarlosimulation,while Z + X isestimatedfromdata. Sinceanewbosonhasbeenobservednear125GeV,dataeventcountscompared withsignalexpectationina9GeVrangearound125GeV(121.5 < m 4 < 130.5GeV) aregiveninTable 4-10 .Countsareshownseparatelyfor7TeVand8TeV,aswellas combined. 199

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Table4-9. Thenumberofestimatedbackgroundandsignaleventsandnumberof observedcandidates,afternalinclusiveselection,inthefullmeasurement range100 < m 4 < 1000GeV. Channel 4e 4 2e2 5.1fb 1 at7TeV ZZ background 14.9 2.022.4 2.835.4 4.5 Z + X 1.4 +0.3 0.3 0.6 +0.2 0.2 2.3 +0.6 0.6 Allbackgroundexpected16.2 2.022.9 2.837.7 4.5 m H =125GeV 0.6 0.11.1 0.11.5 0.2 m H =126GeV 0.7 0.11.2 0.11.7 0.2 m H =500GeV 0.8 0.11.1 0.11.8 0.2 m H =800GeV 0.1 0.00.1 0.00.2 0.0 Observed 15 19 48 19.7fb 1 at8TeV ZZ background 62.5 8.797.4 12.8155.8 20.1 Z + X 6.1 +1.2 1.2 3.1 +1.2 1.2 9.2 +2.3 2.3 Allbackgroundexpected68.6 8.8100.5 12.8165.0 20.3 m H =125GeV 3.0 0.45.8 0.77.4 0.8 m H =126GeV 3.3 0.56.3 0.78.1 0.9 m H =500GeV 4.3 0.55.9 0.710.3 1.1 m H =800GeV 0.6 0.10.8 0.11.3 0.1 Observed 74 115 199 5.1fb 1 at7TeVand19.7fb 1 at8TeV ZZ background 77.4 10.7119.8 15.6191.2 24.6 Z + X 7.4 +1.5 1.5 3.6 +1.5 1.5 11.5 +2.9 2.9 Allbackgroundexpected 84.8 +10.8 10.8 123.5 +15.6 15.6 202.7 +24.8 24.8 m H =125GeV 3.6 0.56.9 0.88.9 1.0 m H =126GeV 4.0 0.67.5 0.99.8 1.1 m H =500GeV 5.16 0.646.97 0.7912.17 1.36 m H =800GeV 0.67 0.080.89 0.11.55 0.18 Observed 89 134 247 200

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Table4-10. Thenumberofestimatedbackgroundandsignaleventsandnumberof observedcandidates,afternalinclusiveselection,inthefullmeasurement range121.5 < m 4 < 130.5GeV. Channel 4e 4 2e2 5.1fb 1 at7TeV ZZ background 0.2 0.00.5 0.00.7 0.0 Z + X 0.2 +0.0 0.0 0.1 +0.0 0.0 0.3 +0.1 0.1 Allbackgroundexpected 0.4 +0.0 0.0 0.5 +0.0 0.0 0.9 +0.1 0.1 m H =125GeV 0.5 0.11.0 0.11.3 0.2 m H =126GeV 0.6 0.11.2 0.11.5 0.2 Observed 0 2 3 19.7fb 1 at8TeV ZZ background 0.8 0.12.1 0.22.6 0.2 Z + X 0.6 +0.1 0.1 0.3 +0.1 0.1 1.1 +0.3 0.3 Allbackgroundexpected 1.5 +0.2 0.2 2.4 +0.2 0.2 3.6 +0.3 0.3 m H =125GeV 2.4 0.45.3 0.66.4 0.7 m H =126GeV 2.8 0.45.9 0.77.3 0.8 Observed 4 6 10 5.1fb 1 at7TeVand19.7fb 1 at8TeV ZZ background 1.1 0.12.5 0.23.2 0.2 Z + X 0.8 +0.2 0.2 0.4 +0.2 0.2 1.3 +0.3 0.3 Allbackgroundexpected 1.9 +0.2 0.2 2.9 +0.2 0.2 4.6 +0.4 0.4 m H =125GeV 3.0 0.46.4 0.77.7 0.9 m H =126GeV 3.4 0.57.1 0.88.8 1.0 Observed 4 8 13 201

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4.9.2EventDistributions Thereconstructedfourleptoninvariantmassdistributionsforthefulldatasetare showninFigure 4-42 .Theanalysisusesthemassrange100-1000GeVonlyforthe Higgssearch,whiletherange50-100GeVisusedforthe Z 4 analysistobe discussedinChapter 6 .Figures 4-43 and 4-44 showthesamemassdistributionssplit bynalstatefor7TeVand8TeVrespectively. Figure 4-45 showstheinvariantmassdistributionsforthereconstructed Z 1 and Z 2 intheHiggsanalysis,aswellasthecorrelationbetweenthetwoforaHiggsat126GeV. Figure4-42. Distributionofreconstructedinvariantfourleptonmass.Blueis ZZ MC, greenisfromdatadriven Z + X ,andredis m H = 126GeVHiggsMC. 202

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Figure4-43. Distributionofreconstructedinvariantfourleptonmasssplitbychannelfor 7TeVdataandMC.Blueis ZZ MC,greenisfromdatadriven Z + X ,and redis m H = 126GeVHiggsMC. Figure4-44. Distributionofreconstructedinvariantfourleptonmasssplitbychannelfor 8TeVdataandMC.Blueis ZZ MC,greenisfromdatadriven Z + X ,and redis m H = 126GeVHiggsMC. 203

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Figure4-45. Distributionofreconstructedinvariant Z 1 (left)and Z 2 (right)mass,aswell astheircorrelationforeventswith121.5 > m 4 > 130.5GeV(bottom).Blue is ZZ MC,greenisfromdatadriven Z + X ,andredis m H = 126GeV HiggsMC. 204

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CHAPTER5 STATISTICALANALYSIS Inthischapter,themethodologyandresultsofthestatisticalanalysisaredescribed. Allmethodsdiscussedaredescribedindetailinreference[ 116 ]. Totakefulladvantageofallthepropertiesavailableinthe H ZZ 4 search,a multi-dimensionallikelihoodtisperformed.Duetotherelativelysmallnumberofevents expectedintheHiggspeak,themassdimensioninun-binnedandtheresolutionmodel isusedasdescribedinsection 4.6 .Togetthemostsensitivityoutofthemaximum likelihoodt,threevariablesordimensionsareused. 1. Thefour-leptonmass, m 4 2. Thekinematicaldiscriminant K D 3. Theproductionmodediscriminant D jet ( pT 4 )inthedi-jettagged(0/1jet)category Toincludethekinematicdiscriminant,a2Dhistogramtemplateofthe K D vs m 4 is implementedasdescribedinsection 4.8 .Thistemplateistwodimensionaltoaccount forthestrongcorrelationofthekinematicdiscriminantwiththemass.ThetotalPDFis thendenedas L 2 D ( m 4 K D )= L ( m 4 ) L ( K D | m 4 ), (51) wherethersttermcorrespondstothe1DmassPDFandthesecondtermtothe 2Dtemplateofmassvskinematicdiscriminant.Theconditionalvariableinthesecond termisimplementedinthetemplatebynormalizingallybinsorstripscorresponding tothesamemass,tothesamevalue.The2Dtemplatethendoesnotincludeany informationpertainingtothemass,howeverreturnsinformationonthe K D givensome mass. Forimplementingthethirddimension( D jet or pT 4 )asimilarprocedureisimplemented. Both D jet and pT 4 havesomecorrelationwiththemass.Inbothcasesthecorrelations 205

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aretakenintoaccountbyintroducingtwodimensionalconditionaltemplatesasinthe caseofthekinematicdiscriminant. Thethreedimensionallikelihoodisthendenedas L 3 D ( m 4 K D D jet )=( L ( m 4 ) L ( K D | m 4 )) L ( D jet | m 4 l ), (52) whereonemoreconditionalpdfisadded.Thetwojetcategoriesandthethreenal statesarecombinedasdifferentdatasetstoprovidethemodelforthesimultaneoust. The( m 4 K D D jet )un-binneddistributionsoftheselectedeventsaresplitintosix categoriesbasedonthreenalstates(4 ,4e,2e2 )andtworunningperiods(7and 8TeV).Theseeventsareexaminedfor187hypotheticalHiggsbosonmasses m H ina rangebetween110GeVand1000GeV,wherethemassstepsareoptimizedtoaccount fortheexpectedwidth, % H ,andresolutionformeasurementof m H [ 116 ]. Section 5.0.3 summarizesthesystematicuncertaintiesusedinthemaximum likelihoodt.Section 5.0.4 presentstheexclusionlimits,whilesection 5.0.5 quanties thesignicanceoftheobservedexcess.Finally,section 5.1.2 describesthedifferent measuredsignalstrengths, 5.0.3SummaryofSystematicUncertainties Thesummaryofsystematicuncertaintiesusedinthemaximumlikelihoodt arepresentedinTables 5-1 5-2 ,and 5-3 for7TeVand8TeVrespectively.All systematicuncertaintiesare100%correlatedbetween7and8TeV,exceptthe luminositysystematicuncertainty.Log-normaluncertaintieson Z + X normalizationare correlatedbetween7and8TeV,howevertheyareuncorrelatedbetweendifferentnal states.Uncertaintiesfromtag-and-probemeasurementsonmuonsandelectronsare correlatedbetweennalstatesthatcontainthoseobjects.Uncertaintiesonthe K D are incorporatedasuncertaintiesoftheshapesofthe2Dtemplatesbyusingalternatively shapedtemplateswhichrepresent1sigmachanges.Thetthen"morphs"between thesealternativetemplates. 206

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Table5-1. Systematicuncertaintiesinpercentfor7TeV. Uncertainty Type Process ggHVBFWHZH t t HqqZZggZZZ+X Luminosity lnN2.22.22.22.2 2.2 2.2 2.2 PDFAcceptance H 4 lnN2 2 2 2 2 gg PDF+ S lnN7-14 8.3-13.5 6.6-20.9 qq / q q PDF+ S lnN 1.5-122.3-52.3-5.5 2.9-10.9 QCDScaleforggH lnN6-8.5 QCDScaleforVBF lnN 0-3.3 QCDScaleforWH lnN 0.9-1.8 QCDScaleforZH lnN 1.8-4 QCDScalefor t t H lnN 2.6-12.5 BR( H 4 ) lnN2 2 2 2 2 QCDScaleforqqZZlnN 2.6-8.7 QCDScaleforggZZlnN 22.7-55 ElectronEff.(TnP) lnN 3.1-11.1 MuonEff.(TnP) lnN 1.5-4.3 CBmean param. 0.4 CBsigma param. 20 CBtailN param. 5 207

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Table5-2. Systematicuncertaintiesinpercentfor8TeV. Uncertainty Type Process ggHVBFWHZH t t HqqZZggZZZ+X Luminosity lnN2.62.62.62.6 2.6 2.6 2.6 PDFAcceptance H 4 lnN22 2 2 2 gg PDF+ S lnN7-12 8-12 6.6-20.9 qq / q q PDF+ S lnN 2.5-62.2-4.62.1-5 2.9-10.9 QCDScaleforggH lnN5-9 QCDScaleforVBF lnN 0-1.1 QCDScaleforWH lnN 0.9-1.7 QCDScaleforZH lnN 1.8-4.5 QCDScalefor t t H lnN 3.5-12.5 BR( H 4 ) lnN22 2 2 2 QCDScaleforqqZZlnN 2.6-8.7 QCDScaleforggZZlnN 22.7-55 ElectronEff.(TnP) lnN 0.8-3 MuonEff.(TnP) lnN 1.5-4.7 CBmean param. 0.4 CBsigma param. 20 CBtailN param. 5 208

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Table5-3. Normalizationuncertaintyinpercentplacedon Z + X estimateforboth7and 8TeV. 4e 4 2e2 -40+60-20+20-25+25 5.0.4ExclusionLimits Inthissection,theexclusionlimitsforaStandardModelHiggsdecayingto fourleptonsthroughtwointermediate Z bosonsarepresented.Thefullstatistical methodologyasusedbybothCMSandATLASfortheHiggssearchisdescribedin detailinreference[ 116 ].Resultspresentedhereareinaccordancewiththosesetforth bytheLHCHiggsCombinationgroup.Resultsontheexclusionlimitsarepresentedin termsofthesignalstrength, isdenedastheratiooftheobservedcrosssection dividedbytheexpectedcrosssectionfromaStandardModelHiggs( = ) ) SM ).Ifthe observedlimitcrossesbelowthe = 1lineatagiven m H ,thentheobservedcross sectionexcludesaStandardModelHiggsatthegiven m H at95%condencelevel. Figure 5-1 showstheobservedandexpectedexclusionlimitsforthe3Dstatistical analysis( m 4 K D D jet or pT 4 ).FromFigure 5-1 ,itcanbeconcludedthataStandard ModelHiggsisexpectedtobeexcludedinthemassrange m H = [115-700]GeV giventhecurrentsensitivityoftheanalysisandtheamountofdatataken.Giventhe observeddata,aStandardModelHiggsisexcludedat95%condencelevelinthe range m H = [114.5-119]GeVand[129-800]GeV.Thegreen(yellow)bandaroundthe expectedlimitsrepresentsthe68%(95%)rangeofexpectationforthebackgroundonly hypothesis. 5.0.5SignicanceofExcess Toquantifytheobservedexcessindata,thebackgroundonlyhypothesis p -value isused.Thisistheprobabilityofthebackgroundtouctuategivinganexcessofevents aslargeorlargerthantheobservedexcess.Again,thefullmethodologythathas beenadoptedhereisfullydescribedinreference[ 116 ].Thewidelyacceptedstandard thresholdfordiscoveryis5 # excess. 209

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(GeV) H m 110120130140150160170180 SM 4l) ZZ (H / 95% CL 4l) ZZ (H -1 10 1 10 CMS -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s Observed Expected 1 Expected 2 Expected (GeV) H m 100 200 300 400 1000 SM 4l) ZZ (H / 95% CL 4l) ZZ (H -1 10 1 10 CMS -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s Observed Expected 1 Expected 2 Expected Figure5-1. Observedandexpected95%CLupperlimitontheratiooftheproduction crosssectiontotheSM-likeexpectation.7TeVand8TeVdatasamplesare used. Figure 5-2 showsacomparisonofthe1D( m 4 ),2D( m 4 K D ),and3D( m 4 K D D jet or pT 4 )model p -values.Thedashedlineshowstheexpectedsignicancefor StandardModelHiggsateach m H giventhesensitivityoftheanalysisandtheamountof datacollected.Themaximumobservedsignicanceof7.1 # isobservedat m H = 125.7 GeV,whiletheexpectedsignicanceis7.0 # .Observedandexpectedsignicancefor thesethreemodelsaresummarizedinTable 5-4 Table5-4. Signalexpectedandobservedsignicance( # )attheminimumofthep-value (125.7 GeV )for7+8TeVcombineddata,for3Dt(nominal),2Dtand1D t. L 1 D ( m 4 ) L 2 D ( m 4 K D ) L 3 D ( m 4 K D D jet or pT 4 ) expected5.6 # 6.8 # 7.0 # observed5.0 # 6.8 # 7.1 # 210

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Figure5-2. Signicanceofthelocaluctuationswithrespecttothestandardmodel expectationasafunctionoftheHiggsbosonmassforanintegrated luminosityof5.1fb 1 at7TeVand19.7fb 1 at8TeVinthelowmassrange 110-180GeVontheleftandinthewholemassrange100-1000GeVonthe right. 211

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Withanobservedsignicanceabove5 # ,theobservedexcessqualiesasa discoveryofanewbosondecayingtofourleptonswithamassnear125GeV. With adiscoveryconrmed,thefocusnowturnstowardsmeasuringthepropertiesofthenew bosonsuchasitsmass,width,signalstrengthandspin-parityproperties. 5.1PropertiesMeasurement 5.1.1Mass Themassmeasurementmakesuseofthreemodelsthathavebeendiscussedin previoussections:thesignallineshapemodel,theevent-by-eventmassuncertainties D mass ,andnallysignalversusbackground K D .Thenominalresultusedisthe3D likelihoodusingallthreeofthesemodelstotforthebesttmass. Figure 5-3 showsthe2Dlikelihoodscanintheplane ( m H ) foralikelihoodt usinga3Dmodel( L ( m 4 l D mass K D ) ).The3Dtuses K D resultinginamildmodel dependence.Thesolidellipsesrepresent68%CLcontours( 2 #ln Q =2.3 for ndof =2 ). Allthenuisanceparametersofthetareproledforeachpointofthescan.Thebestt massvaluesareshowninTable 5-5 Figure5-3. Twodimensionallikelihoodscanformass m H versussignalstrength = # /# SM forthe3Danalysis L 3 D ( m 4 D mass K D ) 212

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Figure 5-4 showsthe1Dlikelihoodscansversus m H for1D( L 1 D ( m 4 ) ),2D ( L 2 D ( m 4 D mass ) )and3D( L 3 D ( m 4 D mass K D ) )models.Allsystematicerrorsare includedandproled,alongwith ,foreachpointinthescan.Toestimatetheeffect ofsystematicuncertaintyonthefullstatisticalplussystematicuncertaintyonthe bestt,aseparatelikelihoodscanhasbeencompletedexcludingnormalization andshapesystematicuncertainties.Theresultinguncertaintyfromthetisthenthe statisticaluncertaintyonthebesttvalue.Thesystematicuncertaintyisestimatedas thedifferenceinquadraturebetweenthefulluncertaintyandthestatisticaluncertainty. Figure5-4. 1Dlikelihoodscanasafunctionofmassincludingstatisticalandsystematic uncertaintiesfor1D(left)analysis,2D(middle)and3Danalysis(right). Figure 5-5 showsthe1Dlikelihoodscansversus m H comparing1D,2D,and3D modelsforeachchannel,4e,4 ,and2e2 separately.Acomparisonof1D,2D,and3D modelsforallnalstatescombinedisshowninFigure 5-6 ThebesttmassesforthedifferentchannelsandmodelsareshowninTable 5-5 Thenominalresultscomefromthebestexpecteddetermination,whichisthecombined 3Dt,forwhichthettedvalueis125.6 0.4(stat.) 0.2(syst.)GeV. Table 5-6 representsacrosscheckthatthecontributionofthesystematic fromtheleptonmomentumscaleiswhatitisexpectedtobe.Thecontributionsare around0.07%,0.17%and0.11%inthecaseof4 ,4eand2e2 ,respectively.Thisis compatiblewiththepropagationoftheleptonscaleuncertaintytothe4 nalstate. 213

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Figure5-5. 1Dlikelihoodscanasafunctionofmassforthedifferenttscenariosfor4 (left),4e(middle)and2e2 (right)nalstates. Table5-5. Besttvaluesforthemassofthenewbosonandforthe Z boson,both measuredinthe4 " = e nalstates,with1D,2Dand3Dt,respectively, asdescribedinthetext. Channel1D: L ( m 4 ) (GeV)2D: L ( m 4 D mass ) ( GeV )3D: L ( m 4 D mass K D ) (GeV) 4 125.01 +0.73 1.23 (tot.)125.08 +0.62 1.05 (tot.)125.05 +0.60 0.79 (stat.) +0.15 0.34 (syst.) 4e126.55 +1.45 1.41 (tot.)126.56 +1.54 1.73 (tot.)126.15 +1.70 1.38 (stat.) +0.76 1.12 (syst.) 2e2 126.62 +1.08 0.91 (tot.)126.34 +1.05 0.70 (tot.)126.32 +0.96 0.65 (stat.) +0.24 0.11 (syst.) 4 125.72 +0.52 0.49 (tot.)125.69 +0.50 0.45 (tot.)125.63 +0.47 0.39 (stat.) +0.09 0.18 (syst.) Table5-6. Besttvaluesforthemassofthenewbosonmeasuredinthe4 " = e nalstates,with3Dt,showingthecontributionoftheleptonscale uncertaintyinthetotalmassuncertainty. Channel 3D: L ( m 4 D mass K D ) (GeV) 4 125.05 +0.60 0.79 (stat.) +0.11 0.08 (scalesyst.) +0.11 0.33 (othersyst.) 4e126.15 +1.70 1.38 (stat.) +0.25 0.20 (scalesyst.) +0.72 1.10 (othersyst.) 2e2 126.32 +0.96 0.65 (stat.) +0.14 0.11 (scalesyst.) +0.19 0.08 (othersyst.) 214

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Figure5-6. 1Dlikelihoodscanasafunctionofmassforthedifferenttscenariosforthe combinationofallnalstates,7and8TeVdata. Figure5-7. BesttvaluefortheHiggsmassinthedifferentchannels(points)andforthe combinationofthethreechannels(line,withbarrepresentingthe1 # uncertainty)forthedifferenttcongurations:1D( L ( m 4 l ) )ontheleft,2D ( L ( m 4 l D mass ) )onthemiddle,3D( L ( m 4 l K D ), D mass )ontheright. 215

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5.1.2SignalStrength Thesignalstrength( = ) ) SM )neartheobservedexcessisshowninFigure 5-8 (left). Itismeasuredtobe =0.93 +0.26 0.23 (stat.) +0.13 0.09 (syst.)atthebesttmassof125.6GeV.The signalstrengthcanbedoneseparatelyforthedi-jetand0/1jetcategoryaswell.Figure 5-8 (right)showsthesignalstrengthobservedinboththedi-jetand0/1jetcategories. The0/1jetcategory ismeasuredtobe =0.83 +0.31 0.25 whilethedi-jetcategory is measuredtobe =1.45 +0.89 0.62 .Whilestillstatisticallylimited,allmeasured arefoundto beconsistentwiththeStandardModelexpectationforaHiggsnear125.6GeV. [GeV] H m 110115120125130135140145 SM / Best fit -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 CMS -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s 68% CL band Figure5-8. Signalstrengthversus m H neartheobservedexcess(left)andsignal strengthinthedi-jetand0/1jetcategories(right). Becauseoftheuseofthedi-jetand0/1jetcategories,thesignalstrengthcanbe speciedseparatelyfordifferentproductionmechanismstoprobetherelativecross sectionsofthosemechanismscomparedtotheStandardModelexpectation.Anatural separationoftheproductionmechanismswouldbetodeneacommonsignalstrength fortheonesthatarefermioninduced( F )andasignalstrengthfortheonesthatare W / Z induced V .Assumingthemultidimensionalpdfforeachproductionmodeisgiven by f i ( x ) where x isavectorofthedimensionsusedinthetandtheexpectedyieldfrom 216

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StandardModelisgivenby N i ,thesignalpartofthelikelihoodismodiedas L H = F N ggH f ggH ( x )+ V N qqH f qqH ( x )+ V N ZH f ZH ( x ) + V N WH f WH ( x )+ F N ttH f ttH ( x ) (53) Toextractthevaluesof ( V F ) amaximumlikelihoodtisperformedusingthe3D model L 3 D ( m 4 K D D jet or pT 4 ) inthedi-jetand0/1jetcategories. Figure5-9. Likelihoodcontoursonthesignalstrengthmodiersassociatedwith fermions( F )andvectorbosons( V )shownat68%and95%CL. Figure 5-9 showsa2Dcontourofthebesttvaluesoftheparametersofinterest andtwocondenceintervalsof68%and95%thathavebeenderivedbyvaryingthe likelihoodby # NLL = 1.15and # NLL = 2.995respectively. Eachparametercanbemeasuredbyprolingtheothergivingtheresult V =1.7 +2.2 2.1 F =0.80 +0.46 0.36 wheretheerrorisgivenbya68%CLinonedimensionderivedbyvaryingthenegative loglikelihoodby # NLL = 0.5.Whilestatisticsarestillfairlylow,theresultsarevery consistentwiththeexpectationforaStandardModelHiggs. 217

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5.1.3Width Figure 5-10 showsthescanofthe3DlikelihoodversusthewidthoftheSM-like Higgsbosonwithanarbitrarywidth.Inthisscan,themassandthesignalstrength are proled,asallothernuisanceparameters.Theobservedbesttwidthof % H = 0.00 +1.3 0.00 GeVisconsistentwithanarrowwidthresonanceaspredictedbyaStandardModel Higgswithanupperlimitonthewidthofthenewresonanceof3.4GeVata95%CL,for anexpectedupperlimitof2.8GeV. Figure5-10. 1DlikelihoodscanasafunctionofHiggsdecaywidthwiththe3Dlikelihood t. 218

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5.1.4SpinParity GiventhediscoveryofanewbosonobservedattheLHC,itiscrucialtodetermine thespinandquantumnumbersofthenewparticle,anditscouplingstotheStandard Modeleldsasaccuratelyaspossible.Thebasicstrategyforthespin-paritymeasurements havebeendiscussedinsection 4.8 .Table 4-8 listsallthedifferenthypothesismodels whichhavebeentested. Forspin-paritystudies,theeventcategorizationbasedonjetsisnotusedinorder toreducethedependenceontheproductionmechanism.Consequently,thefour-lepton pT 4 and D jet ,arenotusedeither,resultinginthe L J P 2 D ( D bkg D J P ) modeldenedin equation 54 .Twoobservablescanbecreatedforeachevent, D J P and D bkg .The rstobservableemphasizedsignal-signalseparationandthesecondemphasizes signal-to-backgroundseparation,eachonebeinganoptimalobservableforsuchatask. Eventsinthemassrange106 < m 4 < 141GeVareusedtoperformthesestudies. Signalmassisassumedtobe m H = 126GeV.The2D PDFs forsignalandbackground forthepairofdiscriminants, P ( D J P |D bkg ) inequation 54 ,areobtainedfromsimulation forsignalandirreduciblebackground,whilefor Z + X theyareobtainedfromcontrol regionsindata.TotesteachhypothesisversustheStandardModel,2Dtemplates areusedasdiscussedinsection 4.8 .Theprobabilityforthedatatobeconsistentwith eithertheStandardModelHiggsbosonhypothesisoranalternative J P modelisthen calculated. L J P 2 D ( D bkg D J P )= P ( D bkg | m H ) P ( D J P |D bkg ). (54) Technicaldetailsarediscussedbelow. 5.1.4.1FractionofCP-violatingeventsinthepeak Thespin-zero J P models 0 + 0 + h ,and 0 correspondtotheterms a 1 a 2 ,and a 3 respectively,appearinginthedecayamplitudeforaspin-zerobosondenedinequation 219

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55 A ( H ZZ )= v 1 ; a 1 m 2 Z 0 1 0 2 + a 2 f (1) + f (2), + + a 3 f (1) + f (2), + < (55) where f ( i ), + ( f ( i ), + )isthe(conjugate)eldstrengthtensorofa Z bosonwithpolarization vector 0 i .Notationforspin-1andspin-2amplitudecouplingscanbefoundinreference[ 103 ]. Inadditiontohypothesisseparationtests,atforacontinuousparametercalled f a 3 isalsodone.Thefractionof CP -oddcontributionisdenedunderassumption a 2 =0 as f a 3 = | a 3 | 2 # 3 | a 1 | 2 # 1 + | a 3 | 2 # 3 where # i istheeffectivecross-sectionoftheprocesscorrespondingto a i =1, a j = i =0 Resultsof f a 3 Measurement InFigure 5-11 themeasurementoftheCP-violatingcontributiontothedecay amplitudeisshown,expressedasthefractiontothedecayrate f a 3 = 0.00 +0.15 0.00 ,or equivalently f a 3 < 0.47at95%CL. a3 f 00.20.40.60.81 lnL -2 0 2 4 6 8 10 12 14 Expected Observed CMS -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s Figure5-11. Scanof % 2ln L in1D(left)asafunctionof f a 3 ,where f a 3 isthefractionof observed 0 eventsinthedataset.ExpectationwithAsimovdatasetisalso showninthe1Dprojection. 220

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5.1.4.2Alternativespin-paritymodels ThenumberofexpectedSMHiggsbosoneventsineachchannel i =1,..,6 (where thesixchannelscorrespondto2e2 ,4e,4 in7or8TeVsamples)isestimatedwithfull CMSSWMCsimulationandincludesalldetectoreffectsandleptoninterferenceinthe 4eand4 channels.Thisnumberisdenotedas N SM exp ( i ) Thenumberofexpectedevents N J P exp ( i ) inthealternativespin-parityhypothesis J P needstobecorrectedforbothdetectoreffectsandleptoninterferenceduetodifferent kinematics.Thefractionof2e2 events f J P 2 e 2 changesfrommodeltomodelandisless than50%intheSMdueconstructiveinterferencein4eand4 .Itislargerthan50% inothermodelsconsideredduetodestructiveinterference.Also,acceptanceeffects aredifferent.Therefore,ifthesameproductioncross-sectionisassumedforthe2e2 nalstateofanon-SMbosonasoftheStandardModelHiggs,thenumberofexpected eventshastobecorrectedineachchannelindependentlyasfollows N J P exp ( i )= N J P reco N Gen f 0 + 2 e 2 f J P 2 e 2 (56) where N J P reco ( i ) isthenumberofeventsselectedwiththesimulatedMCsampleforthe J P modelinagivenchannel i ,assumingthesametotalcross-sectionasaSMHiggs,and N J P Gen isthetotalnumberofeventssimulated,then N J P Gen = / i N J P Gen ( i ) Ontheotherhand,ifonewantstopreservethetotalexpectedyieldafteralldetector effects,therenormalizedyieldisexpectedtobescaledbyaconstantfactorforeach model N J P norm ( i )= norm ( i ) N 0 + exp ( i ) (57) Where norm ( i ) iscomputedas norm ( i )= N J P exp ( i ) N 0 + exp ( i ) / N 0 + exp ( j ) / N J P exp ( k ) (58) 221

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Theformermethodisusedinthecaseofhypothesistestingof 0 vs 0 + m ,using N J P exp ( i ) directlysothatthereisnoassumptionthattheacceptanceonthesetwomodels isthesame.Allotherhypothesismodelsusethelattermethod, N J P norm ( i ) .Thisnumberis usedasthemeanexpectednumberofeventswhentoyMCexperimentsaregenerated. ThealternativesetoftoyMCexperimentsisgeneratedwhenallexpectedeventyields arescaledbytheobservedvalueof = # Obs / # SM Equation 59 denesthecorrectionfactorthataccountsforthechangeinyielddue onlytointerferenceeffects,whileequation 510 denesthe factorthatincludesboth interferenceandacceptanceeffectsonthenalsignalyields.Thesecorrectionfactors canbefoundforallsignalhypothesismodelsinTables 5-7 and 5-8 ideal ( i )= f 0 + 2 e 2 1 % f J P 2 e 2 1 % f 0 + 2 e 2 1 f J P 2 e 2 = # 0 + 2 e 2 # J P i # J P 2 e 2 # 0 + i (59) exp ( i )= N J P exp ( i ) N 0 + exp ( i ) (510) ResultsforSpin-ParityHypothesisTesting Torunthehypothesistests,2Dtemplatesarebuiltusingthe( D bkg D J P )distribution, insteadofthe( D m 4 )asinthecross-sectionanalysis,otherwisetheapproachisvery similar.Inthiscase, D bkg includesinformationonthe m 4 lineshapeprovidingafew percentincreasedsensitivity. InFigure 5-12 adistributionsofthe D bkg observablesandtheproductionindependent D dec bkg observableareshown. InFigure 5-13 the D J P observablesforalltestedhypothesesareshown,fromtopto bottomandlefttorightare:rstrow: J P =0 ,1 ,2 + m ( gg ) ;secondrow: 0 + h ,1 + ,2 + m ( q q ) ; thirdrow: J P =2 + b ,2 h ,2 + h ;fourthrow:productionindependenttests J P =1 ,1 + ,2 + m 222

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Figure5-12. Distributionof D bkg indataandMCexpectationsforthebackgroundandfor asignalresonanceconsistentwithSMHiggsbosonat m H = 125.6GeV (left)andthe D dec bkg distributionfortheproductionindependentscenario (right). Tondtheexpectedandobservedseparationbetweentwomodels,theparameter 2ln( L 1 / L 2 ) isconstructedwiththelikelihood L evaluatedforthetwomodels.Thesignal strengthinthetisleftfreetooatasnuisanceparameter.Allsystematicuncertainties includedinthenominalanalysisareincorporatedinthehypothesisseparationanalysis aswell.Theuncertaintyonthemassdistributionofthesignalcomingfromthescale andresolutionoftheleptonsisincludedbycreatingalternativetemplatesscalingand smearingthevalueof m 4 ininputtothe D bkg calculation.Morphingbetweenthenominal andalternativetemplatestakesthisintoaccountwhencalculatingthelikelihoodsduring thestatisticalanalysis.Inasimilarfashion,anuncertaintyontheshapeofthetemplate forthe Z + X backgroundisapplied. Thedistributionof q = % 2ln( L J P / L SM ) isexaminedwithgeneratedsamplesof backgroundandsignaloftwotypes(SM 0 + and J P )for m H = 125.6GeV.Herethe likelihoods L arecalculatedwiththesignalratesallowedtooatindependentlyforeach signaltype,andthenuisanceparametersaretreatedasindependent.Theexpected distributionsaregeneratedwithsignalcross-sectionequaltothatoftheStandardModel, 223

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whichisconsistentwithobservation.Theexpectedeventyieldsinthealternativemodels arecorrectedforacceptanceandleptoninterferenceasdiscussedabove.Theexpected andobservedteststatistic q isshowninFigure 5-14 forallthehypothesestested. Table 5-9 showsexpectedandobservedteststatisticforthetwelvemodelstested. Theexpectedseparationisquotedfortwoscenarios,whenthesignalstrengthforeach hypothesisispre-determinedfromthettodataandwheneventsaregeneratedwith SMexpectationforthesignalyield( =1).Theobservedseparationquotesconsistency oftheobservationwiththe 0 + modelor J P model,andcorrespondstothescenario whenthesignalstrengthispre-determinedfromthettodata.Thelastcolumnquotes CL s criterionforthe J P model.TheresultsallfavoraStandardModelHiggsbosonwithin thestatisticsavailable. 224

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Table5-7. Correctionfactorsandeventyieldsinthedifferentchannelsofthealternative spin-parityhypotheses. channel + sf J P i $ ideal ( i ) % reco ( i ) $ exp ( i ) N J P exp ( i ) $ norm ( i ) N J P norm ( i ) model: 0 + m 4e7TeV0.2591.00.2551.00.6811.00.681 4 7TeV0.2591.00.3911.01.061.01.06 2e2 7TeV0.4821.00.3061.01.521.01.52 4e8TeV0.2591.00.2091.02.831.02.83 4 8TeV0.2591.00.3841.05.201.05.20 2e2 8TeV0.4821.00.2791.07.021.07.02 model: 0 4e7TeV0.2380.8450.2200.7310.4980.8480.577 4 7TeV0.2380.8450.3760.8120.8590.9420.996 2e2 7TeV0.5241.00.2980.9751.481.131.72 4e8TeV0.2380.8450.1830.7372.090.8552.42 4 8TeV0.2380.8450.3590.7894.100.9154.76 2e2 8TeV0.5241.00.2690.9636.761.127.84 model: 0 + h 4e7TeV0.2460.8980.2720.9590.6530.9340.636 4 7TeV0.2460.8980.4210.9511.010.9270.980 2e2 7TeV0.5081.00.3401.121.711.091.66 4e8TeV0.2460.8980.2240.9702.750.9462.68 4 8TeV0.2460.8980.4130.9635.010.9394.88 2e2 8TeV0.5081.00.3061.097.681.077.48 model: 1 4e7TeV0.2400.8540.1280.4290.2930.8920.608 4 7TeV0.2400.8540.2070.4480.4740.9310.985 2e2 7TeV0.5211.00.1670.5500.8371.141.74 4e8TeV0.2400.8540.1000.4071.150.8462.40 4 8TeV0.2400.8540.2030.4512.350.9384.88 2e2 8TeV0.5211.00.1470.5283.711.107.71 model: 1 + 4e7TeV0.2500.9040.1520.5390.3670.9070.618 4 7TeV0.2500.9040.2520.57780.6110.9731.03 2e2 7TeV0.5071.00.1980.6510.9911.101.67 4e8TeV0.2470.9040.1200.5191.470.8742.48 4 8TeV0.2470.9040.2430.5732.980.9645.02 2e2 8TeV0.5071.00.1780.6354.461.077.51 225

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Table5-8. Correctionfactorsandeventyieldsinthedifferentchannelsofthealternative spin-parityhypotheses. channel + sf J P i $ ideal ( i ) % reco ( i ) $ exp ( i ) N J P exp ( i ) $ norm ( i ) N J P norm ( i ) model: 2 + m ( gg ) 4e7TeV0.2370.8360.2270.7460.5080.8660.590 4 7TeV0.2370.8360.3690.7850.8310.9120.965 2e2 7TeV0.5271.00.2970.9721.481.131.72 4e8TeV0.2370.8360.1870.7452.110.8652.45 4 8TeV0.2370.8360.3620.7854.080.9114.74 2e2 8TeV0.5271.00.2670.9646.771.127.86 model: 2 + m ( q q ) 4e7TeV0.2370.8360.1810.5940.4040.8550.582 4 7TeV0.2370.8360.2990.6360.6730.9160.969 2e2 7TeV0.5271.00.2440.8011.221.151.75 4e8TeV0.2370.8360.1510.6031.710.8672.46 4 8TeV0.2370.8360.2850.6183.220.8904.63 2e2 8TeV0.5271.00.2190.7845.511.137.93 model: 2 + h 4e7TeV0.2450.8950.2240.7910.5390.9180.623 4 7TeV0.2450.8950.3570.7990.8460.9270.981 2e2 7TeV0.5091.00.2870.9471.441.101.67 4e8TeV0.2450.8950.1890.8012.270.9292.63 4 8TeV0.2450.8950.3430.7944.130.9214.79 2e2 8TeV0.5101.00.2590.9356.571.097.62 model: 2 h 4e7TeV0.2430.8760.2060.7160.4880.9030.615 4 7TeV0.2430.8760.3370.7490.7920.9451.00 2e2 7TeV0.5151.00.2610.8531.301.081.64 4e8TeV0.2430.8760.1730.7352.080.9272.63 4 8TeV0.2430.8760.3310.7503.900.9474.92 2e2 8TeV0.5151.00.2380.8485.961.077.52 model: 2 + b 4e7TeV0.2340.8180.2220.7250.4940.8700.593 4 7TeV0.2340.8180.3590.7430.7860.8910.943 2e2 7TeV0.5321.00.2930.9581.461.151.75 4e8TeV0.2340.8180.1850.7392.090.8872.51 4 8TeV0.2340.8180.3470.7313.800.8774.56 2e2 8TeV0.5321.00.2650.9466.641.137.97 226

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0 D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 1 2 3 4 5 6 7 8 9 Data + 0 =0 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D 1 D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 1 2 3 4 5 6 7 8 9 Data + 0 =1 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D m + 2 gg D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 2 4 6 8 10 Data + 0 (gg) m + =2 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D h + 0 D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 2 4 6 8 10 Data + 0 h + =0 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D + 1 D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 1 2 3 4 5 6 7 8 9 Data + 0 + =1 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D m + 2 q q D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 2 4 6 8 10 Data + 0 ) q (q m + =2 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D b + 2 gg D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 2 4 6 8 10 12 Data + 0 (gg) b + =2 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D h 2 gg D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 1 2 3 4 5 6 7 8 Data + 0 (gg) h =2 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D h + 2 gg D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 1 2 3 4 5 6 7 8 9 Data + 0 (gg) h + =2 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg D 1 dec D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 2 4 6 8 10 Data + 0 dec =1 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg dec D + 1 dec D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 1 2 3 4 5 6 7 Data + 0 dec + =1 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg dec D m + 2 dec D 00.10.20.30.40.50.60.70.80.91 Events / 0.05 0 1 2 3 4 5 6 7 8 9 Data + 0 (gg) m (dec) + =2 P J ZZ/Z Z+X CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s > 0.5 bkg dec D Figure5-13. Distributionsof D J P witharequirement D bkg > 0.5.Distributionsindata (pointswitherrorbars)andexpectationsforbackgroundandsignalare shown. 227

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) + 0 /L P J -2 ln(L -40 -20 0 20 40 60 0 any + h 0 any 1 X q q 1 any + 1 X q q + 1 any + m 2 X gg + m 2 X q q + m 2 any + b 2 X gg + h 2 X gg h 2 X gg CMS -1 = 8 TeV, L = 19.7 fb s ; -1 = 7 TeV, L = 5.1 fb s CMS data Median expected 1 + 0 1 P J 2 + 0 2 P J 3 + 0 3 P J Figure5-14. (Top)Distributionof q = % 2ln( L J P / L SM ) fortwosignaltypes( 0 + representedbytheyellowhistogramandalternative 0 hypothesisbythe bluehistogram)for m H = 125.6GeV.(Bottom)Asummaryofthetwelve alternativehypothesestested. 228

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Table5-9. Listofmodelsusedinanalysisofspin-parityhypothesescorrespondingto thepurestatesofthetypenoted. J P expected( =1)obs. 0 + obs. J P CL s 0 2.4 # (2.7 # )-1.0 # +3.8 # 0.05% 0 + h 1.7 # (1.9 # )-0.3 # +2.1 # 4.5% 1 2.6 # (3.3 # )-1.4 # +4.7 # 0.002% 1 + 2.1 # (2.7 # )-1.5 # +4.1 # 0.02% 1 dec 2.5 # (3.3 # )-1.8 # +4.9 # 0.001% 1 + dec 2.0 # (2.6 # )-2.1 # +4.8 # 0.004% 2 + mgg 1.9 # (1.7 # )-1.1 # +3.0 # 0.9% 2 + mq q 1.7 # (2.0 # )-1.7 # +3.8 # 0.2% 2 + mdec 1.5 # (1.6 # )-1.6 # +3.4 # 0.7% 2 + b 1.6 # (1.9 # )-1.4 # +3.4 # 0.5% 2 + h 3.8 # (4.1 # )+1.8 # +2.0 # 2.3% 2 h 4.2 # (4.5 # )+1.0 # +3.2 # 0.09% 229

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CHAPTER6 USING Z 4 The Z 4 decaysgiveacleanresonantpeakinthefour-leptoninvariantmass distribution,whichcanbeusedasa"standardcandle"inthecontextoftheHiggsboson searchinthe H ZZ 4 decaymode[ 117 ].Thenumberofeventsinthe Z 4 peakat m 4 = m Z isatleast5timeslargerthantheexpectednumberofeventsfor theSMHiggsbosonwithamassnear125GeV.Therefore,the Z 4 peakcanbe usedfora direct validationofourunderstandingofthefour-leptonmassscaleandthe four-leptonmassresolutioninthesamephasespaceastheHiggsbosonfour-lepton decays.Toenhancethepeak,thelowendofthe m Z 2 -cutcanberelaxed.Hereafter, three Z 4 phasespacecongurationsaredesignatedfortheanalysis:Higgs Selection( m Z 2 > 12GeV),Nominal( m Z 2 > 4GeV),andRelaxed( m Z 2 > 0GeV).The MCforthe Z 4 signalistechnicallylimitedtohaving m Z 2 nolowerthan4GeVdue tosimulationconstraints.Eachcongurationusethesameselectionrequirementsasfor the H ZZ 4 analysis,exceptthechangein m Z 2 andfortherelaxedandnominal congurations,therequirementonfouroutofsixpossibleoppositecharge,sameavor leptons m !! > 4GeVisexcluded(asthe m Z 2 requirementsisatorbelow4GeV). Inthetfunction,theirreduciblebackgroundshapeistakenfroma pp ZZ 4 simulationwherethes-channel Z 4 peakisnotpresent,withtheoverall normalizationoatinginthemassandwidtht.The Z + X normalizationandline shapeisestimatedthesamewayasdiscussedinsection 4.5.2.1 ,exceptwithlowered m Z 2 cutstomatchthoseusedinthisanalysis.Thesignalshapeisaconvolution oftheBreit-WignerandCrystalBallfunctions.Thecentralvalueandwidthofthe Breit-Wignerfunctionarexedatthe Z bosonmass m Z andwidth % Z [ 57 ].TheCrystal Ballparametersarefreeinthet.Inthischapter,theprocessofusingthe Z 4 peak tovalidatetheHiggspeakmass,width,andspin-paritymeasurementswillbediscussed. 230

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6.0.5ValidationofHiggsMassandWidth TherststepinvalidatingtheHiggsmassandwidthmeasurementsisndinga functionalformtobeusedinthetofthe Z 4 peak.Thesamefunctionalformas usedintheHiggsmassandwidthtisused,whichisaBreit-Wignerfunctionconvoluted withaCrystalBallfunction(inthiscase,singlesidedinsteadofdoublesided)asshown below. f BW ( m 4 | m Z )= % gg ( m 4 ) % ZZ ( m 4 ) m 4 ( m 2 4 % m 2 Z ) 2 + m 2 4 % 2 ( m 4 ) (61) CB ( 3 )= N 4 5 6 5 7 A ( B + | 3 | ) n L ,for 3 <' L exp % 3 2 / 2 # ,for 3 # L (62) f ( m 4 | m Z )= CB ( m 4 | m Z ) ) f BW ( m 4 | m Z ) (63) Next,thesimulationmustbecheckedtomakesuretherearenobiasesintroduced inthe Z 4 peakthatmightaffecttheresultsofthemassandwidtht.AtoftheMC withaBreit-WignerfunctionatGENlevelisshowningure 6-1 .Inthist,themassof theBreit-WignerisallowedtooatandthewidthissettothePDGvalue( % Z 0 = 2.4956 GeV).TheredoesnotappeartobeanysystematicshiftsintheGENlevelMC.Anysmall shifts(order50MeV)seenarewellcoveredbysystematicsusedintheanalysis. JustasintheHiggsmasst,thereconstructionlevelMCmustnowbetforthe resolutionparametersintheCBwhilexingtheBWparameterstothenominal Z mass andwidth.Thisisdoneforeachofthethreenalstatesand7and8TeVseparately. Figure 6-2 showsthesetsandthetvaluesfortheparametersofinterest.These parameterswillthenbexedintheCBfortsondata. UsingthesamemethodasintheHiggsmassandwidtht,amaximumlikelihoodt isperformedonthe Z 4 peak.Figure 6-3 showsthe1Dlikelihoodscansversus m Z withtheircorrespondingmassdistributionsoverlaidwiththettedfunction. 231

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Themassdistributionsalsolistthevaluesanduncertaintiesforthemassandwidth measurements. Table6-1. Resultsforthemasstofthe Z 4 peakforindividualchannelsandthe cumulative 4 channelwiththeiruncertainties. Channel 4 4 4e 2e2 HiggsConguration91.12 0.2390.99 0.4192.83 1.7791.30 1.03 NominalConguration91.16 0.2391.00 0.2693.67 1.0991.24 0.46 RelaxedConguration91.15 0.2391.00 0.1591.64 0.6791.54 0.26 Insummary,the Z 4 massandwidthmeasurementsareinverygood agreementwiththoseexpectedfromtheStandardModel.Themassmeasurement showsexcellentagreementforallthreecongurationsused,validatingthatthe momentumscalecalibrationsusedinthefour-leptonanalysisareaccurateand stablewithregardtodifferent M Z requirements.Thisprovidescondenceinthescale calibrationprocedureandthemassmeasurementmethodusedinthe H ZZ 4 analysis.Similarly,themeasuredwidthofthe Z 4 peakiswithin2standard deviationsforallcongurations,excepttherelaxedconguration,whichmeausres slightlymorethan2standarddeviationsawayfromtheexpectedvalue.Thisis acceptablewiththelimitedstatisticsavailableandprovidesanexcellentvalidationof the H ZZ 4 widthmeasurementmethod. 232

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[GeV] 4l m 88899091929394 a.u. 0 500 1000 1500 2000 2500 3000 3500 0.0069 BW_mean = 91.2447 CMS Simulation [GeV] 4l m 88899091929394 a.u. 0 500 1000 1500 2000 2500 3000 3500 0.0069 BW_mean = 91.2337 CMS Simulation [GeV] 4l m 88899091929394 a.u. 0 100 200 300 400 500 600 700 800 900 0.014 BW_mean = 91.270 CMS Simulation [GeV] 4l m 88899091929394 a.u. 0 200 400 600 800 1000 0.013 BW_mean = 91.254 CMS Simulation [GeV] 4l m 88899091929394 a.u. 0 200 400 600 800 1000 0.019 BW_mean = 91.286 CMS Simulation [GeV] 4l m 88899091929394 a.u. 0 200 400 600 800 1000 0.019 BW_mean = 91.268 CMS Simulation [GeV] 4l m 88899091929394 a.u. 0 200 400 600 800 1000 1200 1400 1600 1800 0.014 BW_mean = 91.244 CMS Simulation [GeV] 4l m 88899091929394 a.u. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0.013 BW_mean = 91.241 CMS Simulation Figure6-1. Four-leptonmassdistributioninthe7TeV(left)and8TeV(right)GENMC for Z 4 (toprow), Z 4 e (secondrow), Z 2 2 e (thirdrow),and Z 2 e 2 (lastrow)ttedwithaBreit-Wigner. 233

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(GeV) 4l m 5060708090100110 a.u. 0 50 100 150 200 250 0.060 = 1.063 0.026 = 0.012 RECO Z0 m 0.031 = 1.017 RECO # CMS Simulation (GeV) 4l m 5060708090100110 a.u. 0 50 100 150 200 250 300 0.048 = 1.101 0.021 = -0.0200 RECO Z0 m 0.026 = 1.126 RECO # CMS Simulation (GeV) 4l m 5060708090100110 a.u. 0 10 20 30 40 50 60 70 0.13 = 1.75 0.034 = -0.0124 RECO Z0 m 0.043 = 2.505 RECO # CMS Simulation (GeV) 4l m 5060708090100110 a.u. 0 10 20 30 40 50 60 70 0.071 = 1.376 0.036 = -0.0681 RECO Z0 m 0.043 = 2.223 RECO # CMS Simulation (GeV) 4l m 5060708090100110 a.u. 0 20 40 60 80 100 120 140 0.087 = 1.254 0.044 = -0.0480 RECO Z0 m 0.053 = 1.786 RECO # CMS Simulation (GeV) 4l m 5060708090100110 a.u. 0 20 40 60 80 100 120 140 160 180 0.069 = 1.248 0.037 = -0.0263 RECO Z0 m 0.045 = 1.832 RECO # CMS Simulation (GeV) 4l m 5060708090100110 a.u. 0 20 40 60 80 100 0.17 = 1.68 0.040 = 0.045 RECO Z0 m 0.055 = 1.755 RECO # CMS Simulation (GeV) 4l m 5060708090100110 a.u. 0 20 40 60 80 100 0.20 = 1.66 0.042 = -0.0232 RECO Z0 m 0.058 = 1.718 RECO # CMS Simulation Figure6-2. Four-leptonmassdistributioninthe7TeV(left)and8TeV(right)GENMC for Z 4 (toprow), Z 4 e (secondrow), Z 2 2 e (thirdrow),and Z 2 e 2 (lastrow)ttedwithaBreit-WignerconvolutedwithaCBwith oating ,and # 234

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(GeV) Z m 888990919293949596 ln L -2 0 1 2 3 4 5 6 7 8 9 10 CMS preliminary -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s Combined 4e Z 4 Z 2e2 Z (GeV) Z m 888990919293949596 ln L -2 0 1 2 3 4 5 6 7 8 9 10 CMS preliminary -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s Combined 4e Z 4 Z 2e2 Z (GeV) Z m 888990919293949596 ln L -2 0 1 2 3 4 5 6 7 8 9 10 CMS preliminary -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s Combined 4e Z 4 Z 2e2 Z (GeV) l 4 m 5060708090100110 Events / 2 GeV 0 5 10 15 20 25 30 35 Data Z Z+X GeV -0.37 +0.37 = 91.12 Z M GeV -0.83 +1.00 = 3.60 Z CMS Preliminary -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s (GeV) l 4 m 5060708090100110 Events / 2 GeV 0 10 20 30 40 50 60 70 80 Data Z Z+X GeV -0.23 +0.23 = 91.16 Z M GeV -0.50 +0.54 = 2.98 Z CMS Preliminary -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s (GeV) l 4 m 5060708090100110 Events / 2 GeV 0 50 100 150 200 250 Data GeV -0.14 +0.14 = 91.15 Z M GeV -0.29 +0.30 = 3.55 Z CMS Preliminary -1 = 8 TeV, L = 19.7 fb s -1 = 7 TeV, L = 5.1 fb s Figure6-3. 1Dlikelihoodscansofthe Z masstswithHiggsconguration,nominal conguration,andrelaxedcongurationfromlefttoright(toprow). Correspondingmassdistributionswithoverlaidts(bottomrow). 235

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6.0.6ValidationofSpinParity OncethemassoftheHiggsisknowntoareasonablecertainty,itisnaturalto proceedtomeasurementsofthespinandparity.ThestandardHiggsspin-parity analysisisdescribedindetailinreference[ 115 ].Thesameanalysiscanberepeated usingthe Z 4 peaktoprovideausefulconrmationofthemethodonrealdatafrom awellknownresonance.Todothis,amatrixelementcalculationmustbeprovidedfor gg H 4 q q Z 4 ,and q q ZZ 4 .Forthesecalculations, MEKD [ 113 ]hasbeenusedtodiscriminatebetweenthesemechanisms.Fromthesematrix elementswecanformprobabilityratiosrestrictedtotherange[0,1].Theformulafor theseprobabilityratiosfortwoprocessesAandBareshowninequation 64 C hereis aconstantontheorderof100chosentomakethedistributionsmorevisuallypleasingin 1Danddoesnotaddorsubtractinformation.Itispurelyamonotonictransformation. P = |M A | 2 |M A | 2 + C |M B | 2 (64) Figure 6-4 (top)showstheseprobabilityratioswhereprocessAis gg H 4 andprocessBis q q ZZ 4 ,whileFigure 6-4 (bottom)showstheseprobability ratioswhereprocessAis gg H 4 andprocessBis q q Z 4 .Inthestandard Higgsspin-parityanalysis,massinformationfrom pdf ( m 4 ) wouldbeincorporatedinto theprobabilityratioswhereprocessAis gg H 4 andprocessBis q q ZZ 4 Thisisperformedtogainseparationpowerontheorderof5-8%sincethesignalin thecaseofHiggsisanarrowpeakontopofaatbackgroundspectrumandthereis alowsignalrate.Inthecaseof Z 4 ,thisisnotnecessarysincethepresenceof q q ZZ 4 underthe Z 4 peakisontheorderofpercentlevelorsmaller,and thesignalrateismuchhigherthanaStandardModelHiggsaround126GeVforthe nominalanalysis(massof Z 2 requirementhasbeenloweredfrom12to4GeV).Instead, the m 4 rangeisrestrictedto m Z 5 GeV.Oneotherrequirementisaddedforselected events,thatallofthe m !! combinationshavemassgreaterthan4GeV,whicheliminates 236

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eventswhichwouldlikelycomefromcascadedecaysofheavyquarksandgenerally makestheselectionascleanaspossible.Allbackgroundshavebeenrecalculatedwith theserequirements. ME ProbRatio 00.10.20.30.40.50.60.70.80.91 Normalized 0 0.02 0.04 0.06 0.08 0.1 0.12 H MC ZZ MC ME ProbRatio 00.10.20.30.40.50.60.70.80.91 Normalized 0 0.02 0.04 0.06 0.08 0.1 0.12 H MC ZZ MC ME ProbRatio 00.10.20.30.40.50.60.70.80.91 Normalized 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 H MC ZZ MC ME ProbRatio 00.10.20.30.40.50.60.70.80.91 Normalized 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 H MC ZZ MC ME ProbRatio 00.10.20.30.40.50.60.70.80.91 Normalized 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 H MC ZZ MC ME ProbRatio 00.10.20.30.40.50.60.70.80.91 Normalized 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 H MC ZZ MC Figure6-4. ProbabilityratioswhereprocessAis gg H 4 andprocessBis q q ZZ 4 (top)andprobabilityratioswhereprocessAis gg H 4 andprocessBis q q Z 4 (bottom)for4e(left),4 (middle),and2e2 (right). FollowingthestandardHiggsspin-parityanalysis,theseprobabilityratiodistributions areusedtolltwo-dimensional templates thatareusedtotosspseudo-experiments forthelikelihoodanalysis.ThesetemplatesareshowninFigure 6-5 gg H 4 over q q ZZ 4 isusedfortheXaxis(toprowofFigure 6-4 )and gg H 4 over q q Z 4 isusedfortheYaxis(bottomrowofFigure 6-4 ).Aloglikelihood analysisisthenperformedwiththesetemplates.Theexpectedyieldfor gg H 4 at M 4 = M Z isassumedtobethesameasthe Z 4 expectedyield.Theteststatistic q = % 2ln ( L 0 + / L Z ) isshowninFigure 6-6 (left).Theobservedvalueisexactlyas 237

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expectedforaStandardModelZboson.Thelikelihoodscanofthefractionof 0 + events inthe Z 4 peakisshowninFigure 6-6 (right).Thismeasurementiscomparableto the f a 3 measurementinthestandardHiggsanalysis.Theupperlimitat95%CLonthe fractionof 0 + eventsinthe Z 4 peakis0.073withanexpectedupperlimitof0.075 foraStandardModelZ. Asafurthercheck,severalkinematicvariablescanbecomparedtosimulationfor both q q Z 4 andaHiggsat m Z .ThesecomparisonsareshowninFigure 6-7 for80GeV < m 4 < 100GeV.Allkinematicvariablesareingoodagreementwithathe StandardModelZboson.This,alongwiththespin-paritymeasurementperformedon the Z 4 peakprovidecondenceinthepropertiesmeasurementsperformedinthe H ZZ 4 analysis.The Z 4 peakcanthuslybeusedasacalibrationpeakfor themassandwidthmeasurementsinthe H ZZ 4 analysis,andthe H ZZ 4 spin-paritymeasurementmethodhasbeenvalidatedondatausingthe Z 4 decays. 238

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00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.01 0.02 0.03 0.04 0.05 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.01 0.02 0.03 0.04 0.05 0.06 0.07 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.02 0.04 0.06 0.08 0.1 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 0.012 0.014 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 0.012 0.014 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 0.012 0.014 00.10.20.30.40.50.60.70.80.91 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Figure6-5. Templatesusedinthe Z 4 spin-parityanalysisforggH(top), Z 4 (middletop),qqZZdoublyresonantonly(middlebottom),andZ+Xcontrol regiondata(bottom).Fromlefttoright:4e,4 ,2e2 239

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) Z /L + 0 ln(L -2 -1000-800-600-400-20002004006008001000 pseudo-experiments 0 0.02 0.04 0.06 0.08 0.1 0.12 Z + 0 CMS data -1 = 8 TeV, L = 19.7 fb s CMS Preliminary H f 00.020.040.060.080.1 lnL -2 0 1 2 3 4 5 6 7 8 9 10 -1 = 8 TeV, L = 19.7 fb s CMS Preliminary Exp Obs Figure6-6. Distributionofatest-statistic q = % 2ln ( L 0 + / L Z ) oftheZbosonhypothesis testedagainsttheSMHiggsbosonatat M Z hypothesis(left)." f a 3 "type measurementlikelihoodscan(right). Z1 Mass 405060708090100110120 Normalized to Data 0 2 4 6 8 10 12 14 16 18 H 91.2 ZZ/Z Data -1 = 8 TeV, L = 19.7 fb s CMS Preliminary Z2 Mass 0102030405060 Normalized to Data 0 10 20 30 40 50 60 H 91.2 ZZ/Z Data -1 = 8 TeV, L = 19.7 fb s CMS Preliminary Z2 Mass 05101520253035404550 Z1 Mass 40 45 50 55 60 65 70 75 80 85 90 H 91.2 ZZ/Z Data -1 = 8 TeV, L = 19.7 fb s CMS Preliminary max P 01020304050607080 Normalized to Data 0 10 20 30 40 50 H 91.2 ZZ/Z Data -1 = 8 TeV, L = 19.7 fb s CMS Preliminary 4l pT 0102030405060 Normalized to Data 0 10 20 30 40 50 60 H 91.2 ZZ/Z Data -1 = 8 TeV, L = 19.7 fb s CMS Preliminary ) cos( -1-0.8-0.6-0.4-0.200.20.40.60.81 Normalized to Data 0 10 20 30 40 50 60 70 H 91.2 ZZ/Z Data -1 = 8 TeV, L = 19.7 fb s CMS Preliminary Figure6-7. Kinematicvariablescomparison.Fromlefttoright:Top:MassZ1,MassZ2, MassZ1vsZ2.Bottom:Momentumofhighestmomentumlepton,pTof 4 system,cosineoftheanglebetweenZ2andthenearestlepton. 240

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CHAPTER7 CONCLUSIONS Inthisdissertation,asearchfortheHiggsbosoninthedecaychannel H ZZ 4 hasbeenperformedusingdatafrom pp collisionscorrespondingtoandintegrated luminosityof5.1 fb 1 atcenter-of-massenergy + s = 7TeVand19.7 fb 1 at + s = 8TeV data.Anewbosonhasbeenobservedasanarrowresonancewithalocalsignicance of6.8standarddeviations,ameasuredmassof125.6 0.4(stat.) 0.2(syst.)GeV, andatotalwidth $ 3.4GeVata95%condencelevel.Theproductioncrosssection ofthenewbosontimesthebranchingfractiontofourleptonshasbeenmeasuredtobe 0.93 +0.26 0.23 (stat.) +0.13 0.09 (syst.)timesthatpredictedbythestandardmodel.Itsspin-parity propertieswerefoundtobeconsistentwiththeexpectationsforthestandardmodel Higgsboson.Inaddition,measurementsofthe Z 4 massandwidthwerepresented. ThemassofZbosondecayingto4leptonswasfoundtobe91.16 0.23GeVwhilethe widthhasbeenfoundtobe2.98 +0.54 0.50 GeV.Spin-paritypropertiesoftheZbosonhave beenshowntobeconsistentwithexpectationfromtheStandardModel.Thusly,using the Z 4 decaysasacalibrationtoolprovidescondenceinthemethodandresultsof thepropertiesmeasurementsinthe H ZZ 4 analysis. 241

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APPENDIXA MUONDATA-MCSCALINGFACTORS TableA-1. Muonefciencynumbersfordata,simulationandforthedata/simulation scalefactor,for 5 < pT < 7.5 GeV. 5.00 < pT < 7.50 DataEff. errMCEff. errScaleFactor err % 2.40 < %< % 2.100.819 0.0110.816 0.0071.002 0.016 % 2.10 < %< % 1.600.826 0.0110.817 0.0071.011 0.016 % 1.60 < %< % 1.200.824 0.0110.813 0.0071.013 0.016 % 1.20 < %< % 0.900.817 0.0260.805 0.0221.015 0.042 % 0.90 < %< % 0.600.819 0.0260.806 0.0221.015 0.042 % 0.60 < %< % 0.300.819 0.0260.806 0.0221.015 0.042 % 0.30 < %< % 0.200.818 0.0260.806 0.0221.014 0.042 % 0.20 < %< 0.200.815 0.0260.804 0.0221.014 0.042 0.20 < %< 0.300.818 0.0260.806 0.0221.015 0.042 0.30 < %< 0.600.818 0.0260.806 0.0221.015 0.042 0.60 < %< 0.900.818 0.0260.806 0.0221.015 0.042 0.90 < %< 1.200.816 0.0260.804 0.0221.015 0.042 1.20 < %< 1.600.822 0.0110.811 0.0071.013 0.016 1.60 < %< 2.100.829 0.0110.818 0.0071.013 0.016 2.10 < %< 2.400.815 0.0110.815 0.0071.000 0.016 242

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TableA-2. Muonefciencynumbersfordata,simulationandforthedata/simulation scalefactor,for 7.5 < pT < 10 GeV. 7.50 < pT < 10.00 DataEff. errMCEff. errScaleFactor err % 2.40 < %< % 2.100.885 0.0040.881 0.0041.004 0.007 % 2.10 < %< % 1.600.893 0.0040.882 0.0041.012 0.007 % 1.60 < %< % 1.200.891 0.0040.878 0.0041.014 0.007 % 1.20 < %< % 0.900.859 0.0100.877 0.0090.979 0.015 % 0.90 < %< % 0.600.861 0.0100.879 0.0090.980 0.015 % 0.60 < %< % 0.300.861 0.0100.879 0.0090.980 0.015 % 0.30 < %< % 0.200.860 0.0100.879 0.0090.979 0.015 % 0.20 < %< 0.200.857 0.0100.877 0.0090.978 0.015 0.20 < %< 0.300.861 0.0100.879 0.0090.980 0.015 0.30 < %< 0.600.861 0.0100.879 0.0090.979 0.015 0.60 < %< 0.900.860 0.0100.879 0.0090.979 0.015 0.90 < %< 1.200.858 0.0100.876 0.0090.979 0.015 1.20 < %< 1.600.888 0.0040.875 0.0041.014 0.007 1.60 < %< 2.100.896 0.0040.883 0.0041.014 0.007 2.10 < %< 2.400.881 0.0040.880 0.0041.000 0.006 TableA-3. Muonefciencynumbersfordata,simulationandforthedata/simulation scalefactor,for 10 < pT < 15 GeV. 10.00 < pT < 15.00 DataEff. errMCEff. errScaleFactor err % 2.40 < %< % 2.100.915 0.0120.919 0.0020.994 0.014 % 2.10 < %< % 1.600.923 0.0120.920 0.0021.002 0.014 % 1.60 < %< % 1.200.921 0.0120.916 0.0021.004 0.014 % 1.20 < %< % 0.900.905 0.0060.914 0.0030.990 0.008 % 0.90 < %< % 0.600.908 0.0060.916 0.0030.991 0.008 % 0.60 < %< % 0.300.908 0.0060.916 0.0030.991 0.008 % 0.30 < %< % 0.200.907 0.0060.916 0.0030.990 0.008 % 0.20 < %< 0.200.904 0.0060.913 0.0030.989 0.008 0.20 < %< 0.300.907 0.0060.916 0.0030.990 0.008 0.30 < %< 0.600.907 0.0060.916 0.0030.990 0.008 0.60 < %< 0.900.907 0.0060.916 0.0030.990 0.008 0.90 < %< 1.200.904 0.0060.913 0.0030.990 0.008 1.20 < %< 1.600.918 0.0120.913 0.0021.004 0.014 1.60 < %< 2.100.926 0.0120.922 0.0021.004 0.014 2.10 < %< 2.400.910 0.0120.918 0.0020.990 0.014 243

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TableA-4. MuonEfciencynumbersfordata,simulationandforthedata/simulation scalefactor,for 15 < pT < 20 GeV. 15.00 < pT < 20.00 DataEff. errMCEff. errScaleFactor err % 2.40 < %< % 2.100.947 0.0010.952 0.0010.994 0.002 % 2.10 < %< % 1.600.956 0.0010.953 0.0011.003 0.001 % 1.60 < %< % 1.200.953 0.0010.948 0.0011.005 0.001 % 1.20 < %< % 0.900.933 0.0010.939 0.0010.994 0.002 % 0.90 < %< % 0.600.936 0.0010.941 0.0010.994 0.002 % 0.60 < %< % 0.300.936 0.0010.941 0.0010.994 0.002 % 0.30 < %< % 0.200.935 0.0010.941 0.0010.993 0.002 % 0.20 < %< 0.200.932 0.0010.938 0.0010.993 0.002 0.20 < %< 0.300.935 0.0010.941 0.0010.994 0.002 0.30 < %< 0.600.935 0.0010.941 0.0010.994 0.002 0.60 < %< 0.900.935 0.0010.940 0.0010.994 0.002 0.90 < %< 1.200.932 0.0010.938 0.0010.994 0.002 1.20 < %< 1.600.950 0.0010.946 0.0011.005 0.001 1.60 < %< 2.100.959 0.0010.954 0.0011.005 0.001 2.10 < %< 2.400.943 0.0010.950 0.0010.990 0.002 TableA-5. MuonEfciencynumbersfordata,simulationandforthedata/simulation scalefactor,for 20 < pT < 30 GeV. 20.00 < pT < 30.00 DataEff. errMCEff. errScaleFactor err % 2.40 < %< % 2.100.956 0.0010.961 0.0010.993 0.002 % 2.10 < %< % 1.600.968 0.0010.975 0.0010.992 0.001 % 1.60 < %< % 1.200.964 0.0010.972 0.0010.992 0.001 % 1.20 < %< % 0.900.960 0.0010.967 0.0010.993 0.002 % 0.90 < %< % 0.600.962 0.0010.968 0.0010.994 0.002 % 0.60 < %< % 0.300.957 0.0010.966 0.0010.991 0.002 % 0.30 < %< % 0.200.946 0.0020.960 0.0020.986 0.003 % 0.20 < %< 0.200.951 0.0010.963 0.0010.987 0.002 0.20 < %< 0.300.941 0.0030.953 0.0020.987 0.003 0.30 < %< 0.600.955 0.0010.965 0.0010.989 0.002 0.60 < %< 0.900.957 0.0010.964 0.0010.993 0.002 0.90 < %< 1.200.960 0.0010.967 0.0010.992 0.002 1.20 < %< 1.600.962 0.0010.966 0.0010.995 0.001 1.60 < %< 2.100.971 0.0010.977 0.0010.994 0.001 2.10 < %< 2.400.952 0.0010.961 0.0010.989 0.002 244

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TableA-6. MuonEfciencynumbersfordata,simulationandforthedata/simulation scalefactor,for 30 < pT < 40 GeV. 30.00 < pT < 40.00 DataEff. errMCEff. errScaleFactor err % 2.40 < %< % 2.100.964 0.0010.977 0.0010.986 0.001 % 2.10 < %< % 1.600.977 0.0000.985 0.0000.991 0.001 % 1.60 < %< % 1.200.978 0.0000.983 0.0000.995 0.001 % 1.20 < %< % 0.900.980 0.0000.984 0.0000.995 0.001 % 0.90 < %< % 0.600.983 0.0000.986 0.0000.997 0.001 % 0.60 < %< % 0.300.982 0.0000.986 0.0000.996 0.001 % 0.30 < %< % 0.200.972 0.0010.981 0.0010.991 0.001 % 0.20 < %< 0.200.979 0.0000.985 0.0000.994 0.000 0.20 < %< 0.300.973 0.0010.979 0.0010.993 0.001 0.30 < %< 0.600.983 0.0000.986 0.0000.996 0.001 0.60 < %< 0.900.981 0.0000.984 0.0000.997 0.001 0.90 < %< 1.200.979 0.0000.983 0.0000.996 0.001 1.20 < %< 1.600.974 0.0000.978 0.0000.995 0.001 1.60 < %< 2.100.980 0.0000.986 0.0000.994 0.001 2.10 < %< 2.400.961 0.0010.975 0.0010.984 0.001 TableA-7. MuonEfciencynumbersfordata,simulationandforthedata/simulation scalefactor,for 40 < pT < 100 GeV. 40.00 < pT < 100.00 DataEff. errMCEff. errScaleFactor err % 2.40 < %< % 2.100.965 0.0010.981 0.0010.983 0.001 % 2.10 < %< % 1.600.978 0.0000.988 0.0000.989 0.000 % 1.60 < %< % 1.200.982 0.0000.987 0.0000.995 0.000 % 1.20 < %< % 0.900.986 0.0000.990 0.0000.995 0.000 % 0.90 < %< % 0.600.989 0.0000.993 0.0000.996 0.000 % 0.60 < %< % 0.300.989 0.0000.993 0.0000.996 0.000 % 0.30 < %< % 0.200.980 0.0000.987 0.0000.993 0.001 % 0.20 < %< 0.200.986 0.0000.991 0.0000.994 0.000 0.20 < %< 0.300.980 0.0000.986 0.0000.994 0.001 0.30 < %< 0.600.989 0.0020.993 0.0000.996 0.002 0.60 < %< 0.900.987 0.0000.992 0.0000.995 0.000 0.90 < %< 1.200.985 0.0000.989 0.0000.996 0.000 1.20 < %< 1.600.978 0.0000.983 0.0000.995 0.000 1.60 < %< 2.100.982 0.0000.989 0.0000.993 0.000 2.10 < %< 2.400.963 0.0010.980 0.0010.981 0.001 245

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APPENDIXB SIGNALMODELDETAILS SignalModelParametersInterpolation :Figures B-1 (7TeV)and B-2 (8TeV) showthesixdoublecrystal-ballparametersinterpolationforallthesimulatedmassbins at7TeVand8TeV,respectively.Thepdfismodeledasadoublecrystal-ballfunction convolutedwiththerelativisticBreit-Wignerfunctiondescribedinthetext.Fromtherst rowtothelastone,thecrystal-ball'smean, # 1 n 1 ( n 2 isxedto20)parametersare shownrespectivelyfor4 (left),4e(center)and2e2 (right)simulatedevents. FigureB-1. Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdfasafunctionof m H for m H < 400GeVat7TeV. 246

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FigureB-2. Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdfasafunctionof m H for m H < 400GeVat8TeV. Thesameprocedureisappliedforthehighmasscase.Inthiscasethereisalso the % parameterofthemodiedBreit-Wignerfunction f HM BW describedinEq. 430 as aoatingparameterofthet,whichistheninterpolatedamongthedifferentmass points.Figures B-3 (7TeV)and B-4 (8TeV)showthesixdoublecrystal-ballparameters interpolationforallthesimulatedmassbinsat7TeVand8TeV,respectively.Thepdfis modeledasadoublecrystal-ballfunctionconvolutedwiththerelativisticBreit-Wigner functiondescribedinthetext.Fromtherstrowtothelastone,thecrystal-ball'smean, 247

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# ,BW % 1 ( n 1 isxedto5and n 2 isxedto20)parametersareshownrespectivelyfor 4 (left),4e(center)and2e2 (right)simulatedevents. FigureB-3. Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdfasafunctionof m H for m H # 400GeVat7TeV. 248

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FigureB-4. Linearandconstanttsoftheparametersdescribingthesignal f ( m 4 l | m H ) pdfasafunctionof m H for m H # 400GeVat8TeV. 249

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ValidationoftheSignalModelInterpolation :Figure B-5 showsthevalidation ofthePDF'sinterpolatedwiththefunction,describedintheprevioussection,forsome representativemassesintherange m H = 115-400GeVfor8TeVsamples(7TeV issimilar).Thepointsrepresentthedistributionsobtainedfromfullsimulationforthe someofthediscretemasspointsforwhichthereisMonteCarlo,whilethecurves superimposedarearetheinterpolatedPDF.Notisperformedhere.Agoodagreement isobservedbetweenthechosenanalyticalPDFandtheactualdistribution. Figure B-6 showsthevalidationofthePDFsinterpolatedwiththefunctiondescribed intheprevioussectionforsomerepresentativemassesintherange m H = 400-1000 GeVfor8TeVsamples(7TeVissimilar).Thepointsrepresentthedistributionsobtained fromfullsimulationforthesomeofthediscretemasspointsforwhichthereisMonte Carlo,whilethecurvessuperimposedarearetheinterpolatedPDF.Notisperformed here.AgoodagreementisobservedbetweenthechosenanalyticalPDFandtheactual distribution. Formasses m H # 800GeVtheagreementbetweentheinterpolatedPDFand theMCdistributionisnotverygoodonthetails,duetoanonsmoothbehaviorofthe tail.Thereisnotamorecomplicatedparameterizationforthesemassesbecause thedifferencebetweentheinterpolatedPDFandthedistributionissmallerthanthe theoreticalshapeuncertainty,whichisverylargeatsuchhighmass(seesection 4.6.3 ). 250

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FigureB-5. Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmassatthe reconstructionlevelafterthefullleptonandeventselectionsareapplied. 251

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FigureB-6. Probabilitydensityfunctions f ( m 4 l | m H ) fortheHiggsbosonmassatthe reconstructionlevelafterthefullleptonandeventselectionsareapplied. 252

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BIOGRAPHICALSKETCH MatthewSnowballisaphysicistnishinghisPh.D.inHighEnergyParticlePhysics. HewasborninDayton,OHandhaslivedthemajorityofhislifeintheSouth.He cametotheUniversityofFloridatostudyphysicsasanundergraduatein2005.After graduatingwithaB.S.inPhysicsin2009,hewasadmittedtograduateschoolto continuehisstudyofphysicswithaspecializationinHighEnergyParticlePhysics. HejoinedtheCMScollaborationin2009aswell,becomingpartofthegroupthat wouldgoontodiscoverthelonganticipatedHiggsbosoninJulyof2012.Throughthis experience,MatthewhasbecomeanexpertinhadroncolliderphysicsandontheHiggs analysis.Hewasanintegralpartofthediscoveryin2012andhispersonalworkwas evenfeaturedintheNobelPrizeceremonyinwhichPeterHiggsandFrancoisEnglert receivedtheNobelPrizeinPhysicsfortheirworkpredictingtheexistenceoftheHiggs boson.Aftergraduation,Matthewplanstocontinueworkinphysics,doingcuttingedge researchimportanttoadvancingourknowledgeoftheuniverse. 261