Observation of the Higgs Boson in HZZ4L Channel and its Mass and Width Measurements Using the CMS Detector at the LHC

MISSING IMAGE

Material Information

Title:
Observation of the Higgs Boson in HZZ4L Channel and its Mass and Width Measurements Using the CMS Detector at the LHC
Physical Description:
1 online resource (166 p.)
Language:
english
Creator:
Cheng, Tongguang
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
MITSELMAKHER,GUENAKH
Committee Co-Chair:
KORYTOV,ANDREY
Committee Members:
RAMOND,PIERRE
FRY,JAMES N
ACOSTA,DARIN E
GROISSER,DAVID JOEL

Subjects

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

Notes

Abstract:
The properties of a Higgs boson candidate in the HZZ4L decay channel, with L as an electrons or a muon, are studied using data from proton-proton collisions at the LHC corresponding to an integrated luminosity of 5.05 inverse femtobarn at center-of-mass energy at 7 TeV and 19.7 inverse femtobarn at at 8 TeV, recorded with the CMS detector. The new boson is observed as a narrow resonance with a local significance of 6.8 standard deviations. The analysis uses the matrix element method, which allows for enhancing the search sensitivity by about 15 percents at the low mass range and for establishing spin and parity quantum numbers of the observed boson, which are found to be consistent with the expectations for the Standard Model Higgs boson. The presence of an additional Standard Model like Higgs boson with a mass between 114.5 GeV and 119.0 GeV or between 129.5 GeV and 832.0 GeV is ruled out at a 95 percent confidence level. The production cross section of the new boson times the branching fraction to four leptons is measured to be consistent with that is predicted by the Standard Model. Per-event four-lepton mass uncertainties are used in evaluation of the mass and width of the observed Higgs boson candidate and are shown to improve the precision of these measurements by about 10 percents. The mass of the observed boson is measured to be 125.6 GeV with 0.4 GeV statistical uncertainty and 0.2 GeV systematic uncertainty. And its total width is constrained to be less than 3.4 GeV at the 95 percent confidence level.
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.
Statement of Responsibility:
by Tongguang Cheng.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: MITSELMAKHER,GUENAKH.
Local:
Co-adviser: KORYTOV,ANDREY.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2014
System ID:
UFE0046693:00001


This item is only available as the following downloads:


Full Text

PAGE 1

OBSERVATIONOFTHEHIGGSBOSONINHZZ4LCHANNELANDITSMASSANDWIDTHMEASUREMENTSUSINGTHECMSDETECTORATTHELHCByTONGGUANGCHENGADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2014

PAGE 2

c2014TongguangCheng 2

PAGE 3

IdedicatethisdissertationtomycolleguesthatcontributetotheHiggsanalysisattheLHC. 3

PAGE 4

ACKNOWLEDGMENTS First,IshouldthankMattSnowballforhishelpthatbroughtmequicklystartingworkingontheanalysisandforhisstrongandpatienttechnicalsupport.AndIreallyappreciateMingshuiChen,PredragMilanovicandAurejiusRinkeviciusfortheirfruitfuldiscussionsonthephysicsandstatisticspartsoftheanalysis.Especially,IreallyappreciatemyadvisorsGuenakhMitselmakherandAndreyKorytovforprovidingmethechanceandbenecialsuggestionstoworkontheHiggsanalysiswhichisextremelyexcitingandfruitful.AndnallyIthankmyparentsfortheirstrongsupport. 4

PAGE 5

TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 13 CHAPTER 1THEHIGGSBOSONWITHINTHESTANDARDMODEL ............ 15 1.1OverviewoftheStandardModel ....................... 15 1.2HiggsMechanismandElectroweakSymmetryBreaking .......... 16 1.3ProductionsandDecaysoftheHiggsBoson ................ 19 1.4MassoftheHiggsBoson ........................... 21 1.5Conclusion ................................... 22 2OVERVIEWOFTHECMSDETECTORATTHELHC .............. 24 2.1TheLHCMachine ............................... 24 2.2ColliderPhysicsattheLHC .......................... 25 2.3TheCompactMuonSolenoidDetector .................... 26 2.3.1TrackingSystem ............................ 27 2.3.2ElectromagneticCalorimeter ..................... 27 2.3.3HadronicCalorimeter .......................... 28 2.3.4SuperconductingMagnet ....................... 29 2.3.5MuonSystem .............................. 29 2.3.5.1DriftTube ........................... 30 2.3.5.2CathodeStripChambers .................. 30 2.3.5.3ResistivePlateChambers .................. 30 2.3.6CMSTriggerSystem .......................... 30 2.3.6.1L1Trigger ........................... 31 2.3.6.2HighLevelTrigger ...................... 31 3PHYSICSOBJECTS ................................. 35 3.1Electrons .................................... 35 3.1.1ElectronReconstructionandIdentication .............. 35 3.1.2Isolation ................................. 37 3.1.3ImpactParameterSelection ...................... 38 3.1.4ElectronMomentumAssignmentandEnergyRegression ..... 38 3.1.5ControlofElectronEnergyScaleandResolution .......... 39 3.1.6ElectronScaleLinearityMeasurement ................ 40 3.2Muons ...................................... 41 5

PAGE 6

3.2.1MuonReconstructionandIdentication ............... 41 3.2.2IdenticationandRemovaloftheGhostMuons ........... 42 3.2.3DerivationoftheMuonScaleandResolutionCorrections ..... 43 3.2.4MuonScaleandResolutionMeasurements ............. 44 3.2.5ImpactParameterSelection ...................... 45 3.2.6Isolation ................................. 45 3.3Photons ..................................... 46 3.4Jets ....................................... 47 4ANALYSISSTRATEGY ............................... 56 4.1DatasetandMonteCarloSamples ...................... 56 4.2EventSelection ................................. 58 4.3FinalStateRadiationRecovery ........................ 59 4.4EventYieldEstimation ............................. 62 4.5SignalYieldEstimationandtheUncertainties ................ 62 4.5.1TotalSignalCrossSectionandBranchingRatio .......... 62 4.5.2SignalAcceptance ........................... 63 4.5.3SignalEfciency ............................ 64 4.6IrreducibleBackgroundEstimation ...................... 64 4.7ReducibleBackgroundEstimation ...................... 66 4.7.1MethodUsingOpposite-signedDileptonControlRegion ...... 66 4.7.2MethodUsingSame-SignedDileptonControlRegion ........ 68 4.7.3EventYieldPrediction ......................... 70 4.7.4ClosureTestUsingData ........................ 70 4.8Double-PartonScatteringEstimation ..................... 71 5OBSERVABLES ................................... 81 5.1Four-LeptonInvariantMass .......................... 81 5.1.1ModelingofSignal ........................... 81 5.1.2ModelingofIrreducibleBackground .................. 85 5.1.3ModelingofReducibleBackground .................. 86 5.2MatrixElementbasedKinematicDiscriminant ................ 87 5.2.1Introduction ............................... 87 5.2.2ComparisontoSingleVariableDiscriminant ............. 88 5.2.3MEKDinSearchingforStandardModelHiggsBosonandSpin-ParityHypothesisTests ............................ 89 5.3DiscriminantforVBFandVHEvents ..................... 90 5.3.1EventCategorization ......................... 90 5.3.2VBFandVHDiscriminationintheDijetCategory .......... 91 5.3.3VBFandVHDiscriminationinthe0/1JetCategory ......... 91 6OBSERVATIONOFTHEHIGGSBOSON ..................... 101 6.1SummaryoftheObservation ......................... 101 6.1.1EventYields ............................... 101 6

PAGE 7

6.1.2EventDistributions ........................... 101 6.2StatisticalMethodology ............................ 102 6.3ExclusionLimits ................................ 103 6.4SignicanceoftheExcessintheLowMassRegion ............. 104 7PER-EVENTMASSRESOLUTIONASANOBSERVABLE ........... 108 7.1CalibrationofPer-EventMassResolution .................. 109 7.1.1CalibrationofSingleLeptonResolution ................ 110 7.1.2CorrectionsfromDileptonResonances ................ 112 7.2EstimationofCalibratedPer-EventMassResolution ............ 113 7.3DataDrivenValidationofPer-EventMassResolution ........... 114 7.4ClosureTestsonHiggsMonteCarloEvents ................. 116 7.5ModelingofPer-EventMassResolutionDistribution ............ 116 7.6StatisticalMethodologyforMassMeasurement ............... 118 8RESULTSONMassANDWIDTHMEASUREMENTS .............. 132 8.1ExpectedMassResults ............................ 132 8.2ObservedMassResults ............................ 133 8.3ResultsonWidthMeasurement ........................ 135 9OTHERPROPERTIESOFTHEOBSERVEDHIGGSBOSON .......... 142 9.1SignalStrengthandConstraintsonProductionModes ........... 142 9.2ResultsofSpinandParityHypothesisTests ................. 143 9.2.1ResultsforSpinandParityHypothesisTesting ........... 144 9.2.2ResultsofCPViolationMeasurement ................ 144 10CONCLUSION .................................... 149 APPENDIX AVALIDATIONONSIGNALMASSSPECTRUMPARAMETERINTERPOLATION 150 A.1ParameterInterpolationofSignalMassSpectrumModel .......... 150 A.2ValidationoftheSignalModelInterpolation ................. 150 BANALYTICALAPPROXIMATIONFORTHEDOUBLE-SIDEDCRYSTALBALLANDBREIT-WIGNERCONVOLUTION ...................... 157 REFERENCES ....................................... 162 BIOGRAPHICALSKETCH ................................ 166 7

PAGE 8

LISTOFTABLES Table page 3-1OptimizedcutvaluesontheBDToutputforelectronswith510GeV. .... 36 4-1Rate,purityandefciencygainforsignalandZZbackground .......... 62 4-2SignalacceptanceAfordifferentQCDscales. .................. 63 4-3MethodApredictionofreduciblebackground ................... 68 4-4MethodAApredictionofreduciblebackground .................. 70 4-5Combinedpredictionofreduciblebackground ................... 70 4-6AcceptanceofZ+DYDPS .............................. 72 5-1Listofdiscriminantsusedspin-parityanalyses .................. 90 6-1Thenumberofestimatedbackgroundandsignaleventsandnumberofobservedcandidatesinfullmassrange ............................ 101 6-2Thenumberofestimatedbackgroundandsignaleventsandnumberofobservedcandidatesfocusingona9GeVrangearound125GeV(121.5
PAGE 9

LISTOFFIGURES Figure page 1-1Higgsproductionmechanisms ........................... 23 1-2Higgsproductionsanddecays ........................... 23 2-1Demonstrationofhadroncollision ......................... 32 2-2Compactmuonsolenoid ............................... 32 2-3Layoutofsiliconstripsinthetrackingsystem ................... 33 2-4EncapofECALsub-detector ............................ 33 2-5Muonsystem ..................................... 33 2-6PrincipleofmuonCSCsystem ........................... 34 2-7L1triggerworkow .................................. 34 3-1ElectronBDToutputdistribution .......................... 49 3-2ROCcurveofelectronMVAID ........................... 49 3-3Electronparticleowisolationasafunctionofnumberofvertices ........ 50 3-4Higgsmassregression ............................... 50 3-5Electronsmearing .................................. 51 3-6Electronenergyscaleandresolutionindifferentcatergorise ........... 51 3-7Z!e+e)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(resolutionasafunctionofnumberofvertices ............. 52 3-8Electronenergyscalesummaries .......................... 52 3-9Muonenergyscale .................................. 53 3-10Muonresolution ................................... 54 3-11Efciencyofparticleowisolation ......................... 55 4-1GainofFSRrecovery ................................ 73 4-2Instrumentaluncertaintiesrelatedtodata-to-MCdifferencesin7TeVdata ... 74 4-3Instrumentaluncertaintiesrelatedtodata-to-MCdifferencesfor8TeVdata .. 75 4-4PDF+suncertainties ................................ 76 4-5QCDscaleuncertainties ............................... 76 9

PAGE 10

4-6FakeratesmeasuredforprobemuonswhichsatisfythelooseselectioncriteriainZ(`1`2)+sample ................................ 77 4-7FakeratesmeasuredforprobeelectronswhichsatisfythelooseselectioncriteriainZ(`1`2)+esample ................................ 77 4-8Invariantmassdistributionoftheeventsselectedinthe2P2Fcontrolsampleinthe8TeVdata ................................... 78 4-9Thecorrelationbetweenthefakerateandthefractionoflooseelectronsforwhichthetrackhasonemissinghitinthepixeldetector ............. 78 4-10Averagefakeratecomparison ............................ 79 4-11Closuretestsofreduciblebackgroundestimation ................. 79 4-12Effectivecrosssection ................................ 80 5-1Fitsofthesignalm4`distributions .......................... 93 5-2Systematicsofthesignalm4`distributions ..................... 93 5-3Highmasssignalshape ............................... 94 5-4Modelofhighmasssignalshape .......................... 94 5-5Fitsoftheirreduciblem4`distributions ....................... 95 5-6Fitsofthereduciblem4`distributionsZ2!e+e)]TJ ET 0 G 0 g BT /F1 11.955 Tf 291.32 -356.63 Td[(................. 95 5-7Alternativetsofthereduciblem4`distributionswhereZ2!e+e)]TJ ET 0 G 0 g BT /F1 11.955 Tf 384.33 -380.54 Td[(....... 96 5-8Shapeofthereduciblem4`distributionZ2!+)]TJ ET 0 G 0 g BT /F1 11.955 Tf 300.62 -404.45 Td[(................ 96 5-9Decayvariables ................................... 97 5-10Singlevariablediscriminant ............................. 98 5-11ComparisonofdifferentROCcurves ........................ 99 5-12mjjandjj ...................................... 99 5-13VBFdiscriminant ................................... 100 6-1Four-leptoninvariantmassm4`distribution ..................... 105 6-2KinematicdiscriminantDkinbkgdistribution ...................... 106 6-3ThepTandFisherdiscriminant ........................... 106 6-4Limits ......................................... 107 6-5Signicance ...................................... 107 10

PAGE 11

7-1Singleelectronresolution .............................. 121 7-2Singlemuonresolution ............................... 121 7-3Leptons'pulldistribution ............................... 122 7-4Four-electronmassshape .............................. 122 7-5Twoapproachesforper-eventmassresolutioncalculation ............ 123 7-6Examplesofdimuontsforper-eventmassresolutionvalidation ........ 124 7-7Examplesofdielectrontsforper-eventmassresolutionvalidation ....... 124 7-8Per-eventmassresolutionvalidationusingZevents ............... 125 7-9Zmassresolutionbasedonleptons'pseudorapidity ............... 125 7-10Zmassresolutionbasedonelectrons'qualities .................. 126 7-11Closuretestusingsignalevents .......................... 127 7-12Signalper-eventmassresolutiondistribution ................... 128 7-13Per-eventmassresolutiondistributionoftheirreduciblebackground ...... 128 7-14Per-eventmassresolutiondistributioninthecontrolregions ........... 129 7-15Per-eventmassresolutiondistributionofthereduciblebackground ....... 130 7-16Per-eventtailparameters .............................. 131 8-1Closuretestofper-eventmassresolutionmodel ................. 137 8-2Pulldistributionofexpectedmassmeasurements ................. 137 8-3DistributionoftheuncertaintyonthettedmassoftheHiggsbosonfortoyMonteCarlosamples ................................ 138 8-4Observedlikelihoodscanasafunctionofmassforthedifferenttsandfordifferentchannels .................................. 138 8-5Channelcompatibilityamongdifferentchannels .................. 139 8-6Channelcompatibilitywithrespecttothethecombinationofthethreechannels 139 8-7Observed1Dlikelihoodscanasafunctionofmassfordifferentlikelihoodtmethodsforthecombinationofallnalstates ................... 140 8-8Observedwidth .................................... 140 8-9Observedandexpectedwidthupperlimits ..................... 141 11

PAGE 12

9-1Likelihoodcontoursonthesignalstrengthmodiers ............... 146 9-2DistributionofDbkg .................................. 146 9-3DistributionsofDJP .................................. 147 9-4Resultoffa3measurement ............................. 148 A-1Linearandconstanttsoftheparametersdescribingthesignalf(m4ljmH)modelasafunctionofmHformH<400GeVat7TeV .............. 151 A-2Linearandconstanttsoftheparametersdescribingthesignalf(m4ljmH)modelasafunctionofmHformH<400GeVat8TeV .............. 152 A-3Linearandconstanttsoftheparametersdescribingthesignalf(m4ljmH)modelasafunctionofmHformH400GeVat7TeV .............. 153 A-4Linearandconstanttsoftheparametersdescribingthesignalf(m4ljmH)modelasafunctionofmHformH400GeVat8TeV .............. 154 A-5Probabilitydensityfunctionsf(m4ljmH)fortheHiggsbosonmasswhenmH<400GeVatthereconstructionlevelafterthefullleptonandeventselectionsareapplied ...................................... 155 A-6Probabilitydensityfunctionsf(m4ljmH)fortheHiggsbosonmasswhenmH400GeVatthereconstructionlevelafterthefullleptonandeventselectionsareapplied ...................................... 156 B-1DecompostionofaCrystalBallfunction ...................... 160 B-2ApproximateCrystalBallfunction .......................... 160 B-3ComparisonbetweenapproximateandexactCrystalBallfunction ....... 161 12

PAGE 13

AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyOBSERVATIONOFTHEHIGGSBOSONINHZZ4LCHANNELANDITSMASSANDWIDTHMEASUREMENTSUSINGTHECMSDETECTORATTHELHCByTongguangChengMay2014Chair:GuenakhMitselmakherCochair:AndreyKorytovMajor:PhysicsThepropertiesofaHiggsbosoncandidateintheHZZ4Ldecaychannel,withLasanelectronsoramuon,arestudiedusingdatafromproton-protoncollisionsattheLHCcorrespondingtoanintegratedluminosityof5.05inversefemtobarnatcenter-of-massenergyat7TeVand19.7inversefemtobarnatat8TeV,recordedwiththeCMSdetector.Thenewbosonisobservedasanarrowresonancewithalocalsignicanceof6.8standarddeviations.Theanalysisusesthematrixelementmethod,whichallowsforenhancingthesearchsensitivitybyabout15percentsatthelowmassrangeandforestablishingspinandparityquantumnumbersoftheobservedboson,whicharefoundtobeconsistentwiththeexpectationsfortheStandardModelHiggsboson.ThepresenceofanadditionalStandardModellikeHiggsbosonwithamassbetween114.5GeVand119.0GeVorbetween129.5GeVand832.0GeVisruledoutata95percentcondencelevel.TheproductioncrosssectionofthenewbosontimesthebranchingfractiontofourleptonsismeasuredtobeconsistentwiththatispredictedbytheStandardModel.Per-eventfour-leptonmassuncertaintiesareusedinevaluationofthemassandwidthoftheobservedHiggsbosoncandidateandareshowntoimprovetheprecisionofthesemeasurementsbyabout10percents.Themassoftheobservedbosonismeasuredtobe125.6GeVwith0.4GeVstatisticaluncertaintyand0.2GeV 13

PAGE 14

systematicuncertainty.Anditstotalwidthisconstrainedtobelessthan3.4GeVatthe95percentcondencelevel. 14

PAGE 15

CHAPTER1THEHIGGSBOSONWITHINTHESTANDARDMODEL 1.1OverviewoftheStandardModelTheStandardModel,thehistoryofwhichcanbetracedbacktothe1920's,explainsthreefundamentalinteractionintheuniverse.InteractionsintheStandardModelaredescribedbyforcesthataretransmittedthroughparticlescalledgaugebosons,theelementaryparticlesthatareinvolvedintheinteractionsmediatedbygaugebosonsareknownasfermions,suchaselectrons.Thestronginteraction,carriedbygluonsholdsfermionsknownasquarkstogethertoformnewmassiveparticlesknownashadrons.Theresidualstronginteraction,so-callednuclearforce,furtherbindsprotonsandneutronstogethertoformnuclei.Theelectromagneticforcewhichdescribestheinteractionbetweenchargedparticles,carriedbyphotons,pusheselectronsintoorbitalsaroundnucleitoformatoms.TheweakforceisresponsibleforboththeradioactivedecayandnuclearfusionofsubatomicparticlescausedbytheemissionorabsorptionofbosonW+,W)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(andZgaugebosons.Differentfromstronginteractionandelectromagneticinteraction,theW+,W)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(andZgaugebosonsthatcarrytheweakforcearemassivewhilegluonsandphotonsaremassless.FermionsoftheStandardModelareclassiedaccordingtothetypeofinteractioninwhichtheyareinvolved.Therearesixquarksformsthreegenerationofup-typequarks(upu,charmc,topt)anddown-typequarks(downd,stranges,bottomb),threegenerationsofchargedleptons,andthreegenerationsofneutralleptonpartnerknowasneutrinos(electrone,electronneutrinoe,muon,muonneutrino,tauon,tauonneutrino)Thechargedparticlescaninteractthroughtheelectromagneticforcemediatedbygaugebosonsknownasphotons.Inadditiontoelectriccharge,quarksalsocarrycolorchargeandinteractviathestrongforcethroughgaugebosonscalledgluons.Theeightfoldmultiplicityofgluonsislabeledbyacombinationofcolorandanti-colorcharge.Becausegluonshaveaneffectivecolorcharge,theycanalsointeractwith 15

PAGE 16

themselves.Thegluonsandtheirinteractionsaredescribedbythetheoryofquantumchromodynamics.Aphenomenoncalledcolorconnementresultsinquarksbeingperpetuallyboundtooneanotherthroughstronginteractioncarriedbygluons,formingcolor-neutralcompositeparticles(hadrons)containingeitheraquarkandanantiquark(mesons)orthreequarks(baryons).Themostwellknownexamplesofbaryonsaretheprotonandtheneutron. 1.2HiggsMechanismandElectroweakSymmetryBreakingAuniedtheoryofelectromagnetismandweakinteractionswasproposedbySheldonGlashow,StevenWeinberg,andAbdusSalam,forwhichtheysharedthe1979NobelPrizeinPhysics.TheirelectroweaktheorypostulatednotonlytheWbosonswhichwerenecessarytoexplainbetadecay,butalsoanewZbosonthathadneverbeenobserved.TheseparticlesareaccuratelydescribedbyanSU(2)gaugetheory.Theyhavetobemassivetoexplaintheshortrangeoftheweakinteraction.TheHiggsmechanism,whichwasforwardedbyPeterHiggsandothersinthemid1960's,breaksthegaugesymmetryspontaneouslyandpredictstheexistenceanewparticle:Higgsboson[ 1 3 ].TheHiggsmechanismisrealizedbyaddingadoubletofcomplexscalareldsintotheelectroweaksectoroftheStandardModelas[ 4 ]:L=jDHj2)]TJ /F8 11.955 Tf 13.15 8.08 Td[(1 2l2jj2)]TJ /F8 11.955 Tf 13.15 8.08 Td[(1 2v22)]TJ /F8 11.955 Tf 13.15 8.08 Td[(1 4FaFa, (1)whereH=0B@H+H01CA=1 p 20B@H1+iH2H3+iH41CA (1)andD=@)]TJ /F4 11.955 Tf 11.96 0 Td[(iga 2Wa)]TJ /F4 11.955 Tf 11.95 0 Td[(ig0Y 2B,Fa=@Wa)]TJ /F3 11.955 Tf 11.95 0 Td[(@Wa+gabcWbWc(a,b=1,2,3). (1) 16

PAGE 17

isacomplexscalareldwithfourrealdegreesoffreedomandalsoaspinorinSU(2)anddenethehyperchargeYcarriedbytobeequalto1.Thepotentialofhasmexicanhatpotential(whenv2>0)withvacuumatjHj=v.ChoosingthevacuumtobehHi=0=1 p 20B@0v1CAwiththeeldh(x)astherealexcitationaroundthevacuumexpectationvalue.WritingtheeldHasH=U(x)0B@0v+h1CA=exp()]TJ /F12 11.955 Tf 16.4 11.35 Td[(Xi=1,2,3i(x)i 2)1 p 20B@0v+h1CA (1)onecanseethattheabovechoiceofthevacuumdoesn'tlosegeneralitybecauseonecanalwayspluginthenewformatoftheeld,andthederivativesofthethephaseU(x)ofcanbeabsorbedintoWthroughagaugetransformation:W0XiW0ii 2=)]TJ /F4 11.955 Tf 9.3 0 Td[(iUy@U+UyW (1)CallingtheeldW0W,thepartoftheLagrangianrelevanttothebecomes jDj2=)]TJ /F4 11.955 Tf 10.5 8.09 Td[(ig 2aWa)]TJ /F4 11.955 Tf 13.15 8.09 Td[(ig0 2B2=1 80B@gW3+g0Bp 2gW)]TJ /F6 7.97 Tf -1.93 -7.29 Td[(p 2gW+)]TJ /F4 11.955 Tf 9.3 0 Td[(gW3+g0B1CA0B@0v1CA2+f(h(x))=1 2gv2W+W)]TJ /F6 7.97 Tf -1.94 -7.89 Td[(+1 8v2(W3B)0B@g2)]TJ /F4 11.955 Tf 9.3 0 Td[(gg0)]TJ /F4 11.955 Tf 9.3 0 Td[(gg0g021CA0B@W3B1CA+f(h(x)). (1) ThechargedWgaugebosonmassisgivenbyMW=gv=2.Themassmatrixinthe(W3,B)basishaszerodeterminant,indicatingoneofthestateshastobemasslesswhichturnsouttobethephoton.TheothermassiveeigenstateistheZboson.IntroducingcosWg p g2+g02,sinWg0 p g2+g02,whereWis 17

PAGE 18

calledtheweakangle,onecanexpressA=cosWB+sinWW3 (1)andZ=cosWW3)]TJ /F8 11.955 Tf 11.96 0 Td[(sinWB (1)withMW MZ=1 2gv v 2p g2+g02=cosW. (1)WhatweseefromaboveisthattheLagrangianstillpreservestheSU(2)XU(1)symmetrywhilethevacuumdoesn't;thegaugesymmetryisspontaneouslybroken.Moreover,thevacuumisstillinvariantundera3 2+Y=2(Y=1)transformation.Asaresult,thegaugebosoncorrespondingtothissymmetrystillstaysmassless,correspondingtothephotonthatcarrieselectromagneticforce.TheeldsondescribingthephaseoftheeldbecomethethelongitudinalpolarizationmodesofthemassiveWandZbosons.TheHiggsbosonisrepresentedbytheeldh,describingtheuctuationaroundthevacuum.TheHiggsbosondecidesthevacuumstructureoftheelectroweaksector,providingmasstotheWandZbosons.Furthermore,theoriginofmassforfermionscanbealsoexplainedbytheirinteractionswiththeHiggseld.Left-handedleptonanditsneutrinopartnerformanSU(2)doubletasL=0B@i`i1CA,sodoleft-handeddown-typequarkandup-typequark.TheYukawacouplingbetweenHiggseldandfermionsintroducedas:LleptonYukawa=i(^Liyeiiei+^Qiydiidi)H?+i^QiUijyujjui2H+c.c.. (1)^Li=LT2,iisthegenerationindexand2=0B@0)]TJ /F4 11.955 Tf 9.3 0 Td[(ii01CAisoneofPaulimatricesthatformSU(2)algebra.TheretermsarenotonlyinvariantunderSU(2)XU(1)symmetry 18

PAGE 19

andbutalsoinvariantunderLorentzsymmetrybyintroducinganantileft-handedfermion(eLforleptons,dLanduLfordown-andup-typequarks,respectively).AfterspontaneousbreakingofSU(2)XU(1)gaugesymmetry,theaboveYukawainteractionsbecomeLleptonYukawa=i p 2(v+h)(y[e]11eyReL+y[]11yRL+y[]11yRL)+c.c., (1)wheretheright-handedleptoneRisrelatedtoantileft-handedleptoneLeL=)]TJ /F3 11.955 Tf 9.29 0 Td[(2eR. (1)MorealgebraworkisneededforquarksinceinEquation( 1 ),Uijdoesnotnecessarilyformarealdiagonalmatrix.Asaresult,extraunitarytransformationsareneededtoexpresstheYukawacouplingintermsofquarkmasseigenstates.Finally,similarformcanbederivedastheYukawainteractionforleptons.Asonecansee,themasstermisgeneratedasthecouplingrelatedtotheleft-handedpartandright-handedpartofafermionandthemasstermisproportionaltotheYukawacouplingyandthevacuumexpectationvaluevoftheHiggseld.Soingeneral,themassforafermioncanbeexpressasmf=1 p 2yfv. (1)ThestrongerafermioninteractswithHiggsboson,theheaviermassthisfermionwouldhave.Neutrinosarekeptmasslessbecausethereisnoright-handedneutrinointheStandardModel. 1.3ProductionsandDecaysoftheHiggsBosonAspredictedintheStandardModel,theHiggsbosondecaysnearlyinstantly.Asaresult,thereshouldbenoexistingHiggsbosonsinnature.TosearchforthislastmissingpieceoftheStandardModel,weneedtoproducetheHiggsbosonandlookfortheevidencebyreconstructingitsdecayproducts.TheLargeHadronCollider(LHC),isa 19

PAGE 20

proton-protoncolliderdesignedtolookformanynewtypesofphysics,mostnotablytheHiggsboson.TherearethreemainproductionmechanismsattheLHC,thecorrespondingdiagramsareshowninFigure 1-2 .Thedominantoneisgluonfusion(ggH).GluonshavenodirectcouplingtotheHiggsboson,buttwogluonscanfuseintoaHiggsbosonthroughquarkloop.ThecouplingbetweenHiggsoffermionsiscalledYukawacouplingwhichisproportionaltothefermion'smass.Asaresult,thedominantquarksinthelooparetopquarksbecausetheyhavethelargestmassamongallquarks.Onetheotherhand,theHiggsbosonhassizablecouplingsonlytotheW+/W)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(andZbosonsintheStandardModel,soinsteadofviathetopquarkYukawacoupling,Higgsbosonscanbeproducedviatheirgaugebosoncouplings.ThisinducestheVBFproductionmechanismswhichisweakbosonfusionwheretwoincomingquarkseachradiateaWorZbosonwhichmergeandformaHiggsboson.Inaddtion,HiggscanbealsoproducedinassociationwitheitheraWorZboson,oratop-antitopquarkpair.ThecrosssectionsfordifferentproductionmechanismsasafunctionofHiggsmassmHforaproton-protoncenterofmassenergyof7TeVareshowninFigureAofFigure 1-2 .ThecrosssectionofggHisabouttentimeshigherthantherestproductioncrosssectionespecialatlowmHbecausegluondensityinsideprotonsdominateinthelowmomentumregion.Vectorbosonfusionhasnexthighestcrosssection.Althoughtheassociateproductionhaslowcrosssection,theW,Zandtop-antitopquarkprovideasignaturetoidentifytheproductionofHiggsfrombackgroundprocesses,thereforetheyarealsousedtosearchforaStandardModelHiggsboson.TheHiggsdecaybranching[ 6 ]ratiosasafunctionofHiggsmassmH,areshowninFigureBofFigure 1-2 .Onecanseethatinthelowmassregion,Higgsdecaystobottom-antibottompairsalmost80%ofthetime.However,theQCDbackgroundinthischannelismanyordersofmagnitudelargerthanthatoftheHiggs.WWandZZchannelshavemoderatebranchingratioswhenmHisabove100GeVandbecome 20

PAGE 21

crucialwhenmHisabovetwiceoftheWorZmass.TheWWbranchingratioisabouttwiceofZZbecausethepermutationoftwoZbosonsdoesnotmakeanalstatewhilepermutationbetweenW+andW)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(does. 1.4MassoftheHiggsBosonTheStandardModeldoesn'tprovidedirectconstraintsonthemassoftheHiggsbosonwhichisafreeparameter.TherehavebeenmanyexperimentaleffortsbeforetheLHCandtheoreticalstudiestogiveconstraintsonthemassoftheHiggsboson.ThedirectexperimentalconstraintscomefromsearchesfortheSMHiggsbosonatLEPandtheTevatron.TheseexcludeaHiggsmassmH<114.4GeV[ 7 ]andbetween160and170GeV[ 8 ]atthe95%condencelevel(CL).Furthermore,theHiggsbosoncangivequantumcorrectionstotheelectroweaksectoroftheStandardModelasitcanappearasavirtualparticle.Asaresult,theHiggsmasscanenterintoelectroweakprecisiontestsofsomephysicalvariables.ThecontributiontotheHiggslikelihoodfunctioncomesfromaglobalttoelectroweakprecisiondatawithintheStandardModel,andfavorsmH<158GeV[ 9 ].Ontheotherhand,theconsiderationpurelyfromtheorycanalsogiveconstraintsontheHiggsmass,mainlyfromtheconsistencyoftheStandardModelatthequantumlevel.ThetrivialityargumentprovidesanupperlimitontheHiggsmass.V()=j2j(y)+(y)2. (1)Thescalarquarticcouplingevolvesasd=dt=32=42,t=ln(2=20). (1)Here0issomereferencescale,whichcouldaswellbethevacuumexpectationvaluev.Thesolutionoftheaboveequationis()=(0) 1)]TJ /F5 7.97 Tf 13.15 5.48 Td[(3(0) 42ln2 20. (1) 21

PAGE 22

Thismeansthereexitsapolewhichiscalledthe`Landaupole'.Inordertoremainperturbativeatallscalesoneneedstohave=0,thusmakingthetheorytrivial.IfoneconsiderstheStandardModelisvalidwhentheenergyscaleislessthansomecutoff,thenneedstobegreaterthanzerowhen<.IfonesetstobeequaltotheGrandUnicationscale,mHislessthan160GeV.Inreality,oneneedstocalculatefromacompleteLagrangianincludingtheotherpiecesoftheStandardModeltogettherunningof.Vacuumstabilityisbasedontherequirementthatthepotentialisalwaysboundedfrombelow.Thismeans(Q)hastoremainpositiveatanyenergyscaleQ,whichinturngivesrisetoalowerboundontheHiggsmass.IftheHiggsmassistoosmall,i.e.,isverysmall,thenthetopquarkcontributiondominateswhichcandrivetoanegativevalue,meaningthevacuumisnotstable.ThevacuumstabilitycanprovideconstrainonmassofthestandardModelHiggsbosonbyrequiringthecouplingstayspositiveuptoascale.ThedetaileddiscussioncanbefoundinReference[ 10 ]. 1.5ConclusionInthischapter,anoverviewoftheStandardModelispresented.Aswecansee,theHiggsbosonplaysauniqueroleintheStandardModel,byexplainingthestructureoftheelectroweakinteraction.ThesignicanceofmassoftheHiggsbosonisnotonlythelastunknownparameterintheStandardModel,butalsoitcansteerapathbetweentheStandardModelandphysicsbeyondtheStandardModel.Fromthissense,themeasurementofthemassoftheHiggsbosoncouldrevealthefateoftheStandardModel. 22

PAGE 23

Figure1-1. ThegureshowtheHiggsbosonproductionmechanisms. A BFigure1-2. Thegureshowstheproductioncrosssectionsat7TeVanddecaybranchingratiosasafunctionofmH. 23

PAGE 24

CHAPTER2OVERVIEWOFTHECMSDETECTORATTHELHC 2.1TheLHCMachineTheLargeHadronCollider[ 11 ],a.k.a.theLHC,istheworld'slargestandhighest-energyparticleaccelerator.TheprimemotivationoftheLHCistondtheoriginofelectroweaksymmetrybreakingforwhichtheHiggsmechanismispresumedtoberesponsible.TheLHCcanbealsousedtotestconsistencyoftheStandardModelatenergyscalesaboveabout1TeVandsearchfornewphysicsbeyondStandardModel.TheLHCiscontainedinacircularundergroundtunnelwithacircumferenceof27kilometers.Thereare1,232dipolemagnetskeepthebeamsontheircircularpath,whileanadditional392quadrupolemagnetsusedtokeepthebeamsfocusedtomaximizethechancesofinteractionbetweentheparticlesinthefourintersectionpoints,wherethetwobeamswillcross.Liquidheliumisusedtokeepthesuperconductingmagnets,madeofcopper-cladniobium-titanium,attheiroperatingtemperatureof1.9K.Beforebeinginjectedintothemainring,theprotonsareacceleratedbyaseriesofsystemsthatsuccessivelyincreasetheirenergy.First,theprotonsaregeneratedwith50MeVenergyatthelinearparticleacceleratorLINAC2.ThentheprotonsentertheProtonSynchrotronBooster(PSB),wherethetheyareacceleratedto1.4GeVandfurtheracceleratedto26GeVintheProtonSynchrotron(PS).Finally,theSuperProtonSynchrotron(SPS)isusedtofurtherincreasetheirenergyto450GeVbeforetheyareatlastinjectedintothemainring.Ratherthancontinuousbeams,theprotonswillbebunchedtogether,into2,808bunches,115billionprotonsineachbunchsothatinteractionsbetweenthetwobeamswilltakeplaceatdiscreteintervalsnevershorterthan25nsapart,correspondingtoabunchcollisionrateof40MHz.ThedesignluminosityoftheLHCis1034cm2s1.Thecollidertunnelcontainstwoadjacentparallelbeampipes,eachcontainingaprotonbeam,whichtravelinoppositedirectionsaround 24

PAGE 25

theringthatintersectatfourpointswherefourdetectorsexit:ALICE,ATLAS,CMSandLHCb.Besidesprotonprotoncollisions,heavy-ioncollisionsareincludedintheprogram.Whilelighterionsareconsideredaswell,thebaselineschemedealswithleadions.TheleadionswillberstacceleratedbythelinearacceleratorLINAC3,andtheLow-EnergyIonRing(LEIR)willbeusedasanionstorageandcoolerunit.TheionswillthenbefurtheracceleratedbythePSandSPSbeforebeinginjectedintoLHCring,wheretheywillreachanenergyof2.76TeVpernucleon. 2.2ColliderPhysicsattheLHCProtonsarenotelementaryparticles,theyaremadeupofpartonswhicharequarksandgluons.Duetothehighenergiesofthecollisions,hardscatteringtakesplacebetweenthepartonsthatconstitutetheprotons,describedbymomentumdistributionsthatdependontheenergyscaleatwhichtheprotonisprobed.Theprotonremnants,notdirectlytakingpartinthehardinteraction,giverisetotheso-calledunderlyingevent.BeforeandafterthehardinteractionthepartonscanundergoinitialandnalstateradiationasdemonstratedinFigure 2-1 .Thetwopartonsenteringthehardinteractioncarryfractionsx1andx2oftheprotonmomentum.TheprobabilitydistributionfunctionforapartonoftypeitoacquireafractionalmomentumxandvirtualityorsquaredfourmomentumQ2iscalledthepartondensityfunctionfip(x,Q2)oftheproton.Factoringoutthehardpartonic2!ninteraction,thetotalhadroniccrosssectionofahardscatteringiscalculatedbyconvolutingtheprobabilityfunctionsf1andf2withthecrosssectionofthepartonicinteraction,dpp!n=Z10dx1Z10dx2f1p(x1,Q2F)f2p(x2,Q2F)d1+2!n(^s). (2)ThescaleQ2Fplaystheroleofseparatingthehardperturbativepartonicinteractionwhichcanbecalculated,andthesoftnon-perturbativelong-distanceeffectsinthe 25

PAGE 26

protonwhichareparametrizedbythepartondensityfunctions.Thepropertyofasymptoticfreedomofthestronginteractionisreectedintheconnementofquarksincolor-neutralhadrons.Asaconsequence,barequarkscannotbeobserveddirectly.Quarksandgluonsmanifestthemselvesexperimentallyasjetsofparticles.Aftertheirproductioninthehardinteractionororiginatingfromtheprotonremnants,quarksandgluonsundergopartonbranchingfromtheirinitialenergydowntoscaleswherethecouplingofthestronginteractionbecomestoolargeandperturbativecalculationsbreakdown.Thenon-perturbativeprocessofjetformationthroughfragmentationandhadronizationatlowenergyscalesisdescribedwithphenomenologicalmodels.Productioncrosssectionsforwidevarietyofprocessesspan12-13ordersofmagnitudefromproton-protoninelasticscattering(100mb)todibosonproduction(100pb). 2.3TheCompactMuonSolenoidDetectorTheCompactMuonSolenoid(CMS)detectorisamulti-purposeexperimentaldetectorattheLHC[ 12 ].ThelayoutofCMSisshowninFigure 2-2 :FigureAisa3DviewandFigureBistheviewoftheCMScrosssectiononthetransverseplane(i.e.,theplaneperpendiculartothebeamline).Thefollowingcoordinateconventionisused:thezaxisisplacedalongthebeamline,andthexandyaxesdenethetransverseplace,perpendiculartothebeam.Thesphericalcoordinates(r,,)arereplacedby(r,,).ristheradialdistance,istheazimuthalangleinthetransverseplane,isthepolaranglewithrespecttothez-axis.Thepseudorapidityisdenedas =)]TJ /F8 11.955 Tf 11.29 0 Td[(ln(tan(=2))(2)Sections??willdescribethesubstructureoftheCMSdetectorfrominsidetooutside. 26

PAGE 27

2.3.1TrackingSystemTheCMStrackeriscomposedofasiliconpixeldetectorwiththreebarrellayersatradiibetween4.4cmand10.2cmandasiliconstriptrackerwith10barreldetectionlayersextendingoutwardstoaradiusof1.1m.Thepixeldetectorcoversapseudorapidityrangefrom-2.5to2.5,matchingtheacceptanceofthecentraltracker.Threelayersofsiliconpixeldetectors[ 13 14 ]areplacedclosetotheinteractionregiontoimprovethemeasurementoftheimpactparameterofcharged-particletracks,aswellasthepositionofsecondaryvertices.Atthedesignluminosity,ameanofabout20inelasticcollisionswillbesuperimposedontheeventofinterest.Pixeldetectorsaredesignedtoalsohelpreconstructinteractionpointswhichoccurfromdifferentbunchcrossingsknownaspileup.Thenextlayersofsiliconmicro-stripdetectors[ 15 16 ]extendtoanouterradiusof1.1m.ThesiliconstriplayersconsistofthreepartsasshowninFigure 2-3 :thetrackerinnerbarrel(TIB),thetrackerouterbarrel(TOB)andthetrackerendcaps(TEC)providingafullcoverageofpseudorapidityrangefrom-2.5to2.5. 2.3.2ElectromagneticCalorimeterTheelectromagneticcalorimeter(ECAL)usesleadtungstate(PbWO4)crystals[ 17 ]withcoverageinpseudorapidityupto3.0.Theadvantageofleadtungstate(PbWO4)isthatithasfasttimingresponse,highdensityandstrongradiationresistance.ThescintillationdecaytimeisofthesameorderofmagnitudeastheLHCbunchcrossingtime:about80%ofthelightisemittedin25ns.Itsdensityis8.28g=cm3)withshortradiationlength(0.89cm)andsmallMoliereradius(2.2cm),resultinginanegranularityandacompactstructure.TheECALiscomposedofofthreeprimarysubcomponents:thebarrel(EB),theendcap(EE)asshowninFigure 2-4 ,andthepreshower(ES).ThebarrelpartoftheECAL(EB)coversthepseudorapidityrangejj<1.479.Thecrystallengthis230mmcorrespondingto25.8radiationlengthwithataperedshape,slightlyvaryingwith 27

PAGE 28

positioninjj.Theyaremountedinaquasi-projectivegeometrytoavoidcracksalignedwithparticletrajectories,makingasmallangle(3o)withrespecttothevectorfromthenominalinteractionvertex.Theendcaps(EE)covertherapidityrange1.479
PAGE 29

differentregime:(E(GeV) E(GeV))2=(90% p E(GeV))2+(4.5%)2,forHBandHE, (2)(E(GeV) E(GeV))2=(172% p E(GeV))2+(9.0%)2,forHF. (2) 2.3.4SuperconductingMagnetThesuperconductingmagnetforCMShasbeendesignedtoreacha3.8-Teslamagneticeldinafreeboreof6-mdiameterand12.5-mlengthwithastoredenergyof2.6GJatfullcurrent.Thestrongmagneticeldinthesolenoidprovideslargebendingpoweronchargeparticles,whichallowsthecharge/massratioofparticlestobedeterminedfromthecurvedtrackthattheyfollowinthemagneticeld.Anironyokeisstaggeredwithlayersofthemuonchambers,providingthedetectorwithstructuralsupportinadditiontofeedinga2-Teslareturnmagneticeldwhichallowsadditionalcurvatureforthemuonmomentummeasurements. 2.3.5MuonSystemAsisimpliedbytheexperiment'smiddlename,thedetectionofmuonsisofcentralimportancetoCMS.Preciseandrobustmuonmeasurementwasacentralthemefromitsearliestdesignstages.MuondetectionisapowerfultoolforrecognizingsignaturesofinterestingprocessesovertheveryhighbackgroundrateexpectedattheLHCwithfullluminosity.Forexample,HiggsbosondecaysintoZZorZZ,whichinturndecaysintofourleptons.Thebestfour-leptonmassresolutioncanbeachievedifalltheleptonsaremuonsbecausemuonsarelessaffectedthanelectronsbyradiativelossesinthetrackermaterial.Therearefourmuonstations,eachstationconsistsofseverallayersofaluminumdrifttubes(DT)inthebarrelregionandcathodestripchambers(CSC)intheendcapregion,complementedbyresistiveplatechambers(RPC)asshowninFigure 2-5 29

PAGE 30

2.3.5.1DriftTubeThedrifttubes(DT)arelongaluminumcellsofafewcentimeterswide,lledwithgas,andwithananodewireinthecentrethatcollectsionizationchargeswhenachargedparticletraversesthetube.InaDTchambermanyofthesedrifttubecellsarearrangedinthreesuper-layers.Twoofthesesuper-layershaveanodewiresparalleltothebeamline,providingameasurementoftherandcoordinates;thethirdsuper-layerisplacedperpendicularbetweentheothers,andprovidesthez-coordinatemeasurement. 2.3.5.2CathodeStripChambersThecathodestripchambers(CSC)areusedintheendcapregions,wherethehighernon-uniformityofthemagneticeldmakesthedrifttubessub-optimal.TheCSCsaremulti-wireproportionalchamberscomprisedof6anodewireplanesinterleavedamong7cathodepanels.Wiresrunazimuthallyanddeneatrack'sradialcoordinate,stripsaremilledoncathodepanelsandrunlengthwiseatconstantwidth.Byinterpolatingchargesinducedoncathodestripsandavalanchepositiveionsnearawire,onecanobtainapreciselocalizationofanavalanchealongthewiredirection[ 19 ]asshowninFigure 2-6 2.3.5.3ResistivePlateChambersTheresistiveplatechambers(RPC)detectorsinCMSconsistofdouble-gapchambers,with2mmspacingslledwithgas.ThepositionresolutionfromtheRPC'siscoarserthanfortheDT'sandCSC's,butthecollectionofchargesonthestripsisveryfast,with3nstimeresolution.Therefore,thesechambersservemainlyasthetrigger,wheretheyprovideinformationcomplementarytotheDTandCSC. 2.3.6CMSTriggerSystemTheLHCprovidesproton-protonandheavy-ioncollisionsathighinteractionrates.Forprotonsthebeamcrossingintervalis25ns,correspondingtoacrossingfrequencyof40MHz.Sinceitisimpossibletostoreandprocessthelargeamountof 30

PAGE 31

dataassociatedwiththeresultinghighnumberofevents,adrasticratereductionhastobeachieved.Moreover,asshowninthecrosssectionhierarchyofproton-protoncollisions,theproton-protoninelasticscatteringdominatesifnopreselectionsareapplied.Sincethecrosssectionoftheprocessespeopleareinterestedinisordersofmagnitudesmallerthantheinelasticscattering,triggersareneededtoidentifytheinterestingeventsandstorethem. 2.3.6.1L1TriggerTheLevel-1Triggerconsistsofcustom-designed,largelyprogrammableelectronics,designedtoreduceeventratetoabout100kHz.TheworkowofL1triggerisshowninFigure 2-7 .TheL1Triggerhaslocal,regionalandglobalcomponents.Atthebottomend,thelocaltriggers,alsocalledTriggerPrimitiveGenerators,arebasedonenergydepositsincalorimetertriggertowersandtracksegmentsorhitpatternsinmuonchambers,respectively.Regionaltriggerscombinetheirinformationandusepatternlogictodeterminerankedandsortedtriggerobjectssuchaselectron,photonandmuoncandidates.Therankisdeterminedasafunctionofenergyormomentumandquality,whichreectsthelevelofcondenceattributedtotheL1parametermeasurements.TheGlobalCalorimeterandGlobalMuonTriggersdeterminethehighest-rankcalorimeterandmuonobjectsacrosstheentireexperimentandtransferthemtotheGlobalTrigger. 2.3.6.2HighLevelTriggerTheHighLevelTrigger(HLT)processesalleventsthatareacceptedbytheLevel-1triggerinasingleprocessorfarmwithseveralthousandnodes.ItisintendedtobringtheeventratefromtheLevel-1outputdowntoO(100Hz),whichcorrespondstotheavailablebandwidthtowardsmassstorageforanexpectedeventsizeofabout1MB.ThereconstructionatHLTisdesignedtobeclosetothenalofinereconstructionbutalsosaveCPU. 31

PAGE 32

Figure2-1. Demonstrationofhadroncollision. A BFigure2-2. Compactmuonsolenoid.FigureAshowsa3DpointofviewandtheFigureBshowsthetransversecrosssectionoftheCMSdetector. 32

PAGE 33

Figure2-3. Layoutofsiliconstripsinthetrackingsystem. Figure2-4. EncapofECALsub-detector. Figure2-5. Muonsystem.ThegureshowsthelongitudinalcutoftheCMSMuonSystem. 33

PAGE 34

Figure2-6. PrincipleofmuonCSCsystem.TheCSCoperationisdonebyinterpolatingchargesinducedoncathodestripsbyavalanchepositiveionsnearawire.Thenonecanobtainapreciselocationofanavalanchealongthewiredirection. Figure2-7. L1triggerworkow. 34

PAGE 35

CHAPTER3PHYSICSOBJECTS 3.1Electrons 3.1.1ElectronReconstructionandIdenticationTheelectronsarereconstructedinCMS[ 21 23 ]bycombiningECALandtrackerinformationwhichstartsfromthereconstructionofclustersintheECAL.ElectronshowersdeposittheirenergyinseveralcrystalsintheECAL.Approximately94%oftheincidentenergyofasingleelectronorphotoniscontainedin3-by-3crystals,andabout97%in5-by-5crystals.Thepresencematerialinfrontofthecalorimeterresultsinbremsstrahlungandphotonconversions.Becauseofthestrongmagneticeld,theenergyreachingthecalorimeterisspreadindirection.Thespreadenergyisclusteredbybuildingaclusterofclustercalldsupercluster,whichisextendedin.Superclustersarethenusedtoselecttrajectoryseedsbuiltbythecombinationoftrackerhitsintheinnermosttrackerlayers.AGaussiansumlter(GSF)tisappliedtoestimatetheelectrontrackparametersateachmeasurementpoint,modelingtheenergylossbyasuperpositionofGaussiandistributions.TheidenticationofelectronsusesonaBoostedDecisionTree(BDT)withmultivariateanalysistechnique[ 24 ]whichcombinesseveralobservablessuchastheamountofbremsstrahlungalongtheelectrontrajectory,thegeometricalandmomentummatchingbetweentheelectrontrajectoryandassociatedclusters,aswellasshower-shapeobservables.ThemultivariateidenticationistrainedusingHiggsbosonMonteCarlosampleassignalagainstW+1-fakeelectrondatasampleasbackground.ThedistributionoftheoutputoftheBDTforthefakeelectronsinthetrainingsamplesW+jetsandtestsamplesZ+jetsdataandforrealpromptelectrons(electronsfromfromZ!e+e)]TJ /F1 11.955 Tf 7.08 -4.34 Td[()areshowninFigure 3-1 .Thedistributionshowsverygoodagreementbetweenthetrainingandapplicationsampleintheanalysisandthegooddiscriminationpowerbetweenpromptandfakeelectrons. 35

PAGE 36

Theimprovementoftherejectionpoweragainstfakes,testedonthedatacontrolsamplesdescribeabove,isvisibleinawiderangeofefciencieswithrespectacutbasedapproach.Foratypicallooseworkingpointthegaininefciencyatthesamebackgroundrejectionpointisabout10%perleptonforpT>20GeVanditbecomesevenlargerforlowerpT.ROCcurves(signalvsbackgroundefciency)areshowninFigure 3-2 .AnoptimizationfortheworkingpointusedintheanalysishasbeenperformedscanningthecutvaluesforeachcategoryusedinthetrainingoftheBDTperformingtheanalysisforeachscenarioandoptimizingtheexpectedsignicanceoftheone-dimensional,two-dimensionalandthreedimensionalt.Sincepartofthecontributiontotheexpectedsignicancecomesfromthemuonchannels(4and2e2),inthecasethesignicanceoftwoscenariosisthesame,wechosetheoptimalpointforthe4echannelonly,whichisthemostsensitivetoelectronidentication.TheoptimizedcutvaluesontheBDToutputfor510GeVaresummarizedinTable 3-1 andTable 3-2 ,respectively. Table3-1. OptimizedcutvaluesontheBDToutputforelectronswith50.470.80.004jj>1.479BDT>0.295 Table3-2. OptimizedcutvaluesontheBDToutputforelectronswithpT>10GeV. Electrons'jjcutBDToutputcutvalue jj<0.8BDT>-0.340.8-0.65jj>1.479BDT>0.60 36

PAGE 37

3.1.2IsolationParticlebasedisolation,bycalculatingthescalarsumofthetransversemomentumoftheparticleowcandidatesreconstructedinaRconeof0.4,denedas: RelPFiso=PchargedhadronpT+PneutralhadronpT+PphotonpT pleptonT(3)Isolationissensitivetopileupconditionbecausepileupleadstoextraenergydepositedinthedetector,leadingtotheriseofthemeanisolationvalues.Therefore,theefciencyofthecutonisolationvariablesstronglydependsonpile-upconditions.Thedegradationofisolationperformancesduetopile-upcanbepartlymitigatedassociatingthechargedparticleowcandidatestotheprimaryvertices.Wedothisthroughthisassociationwithso-calledpfNoPileupassociation,whichconsistsinlteringthesampleofchargedparticleowcandidatesassociatedwiththeotherprimaryverticesexcludingtheonewiththehighestPp2Toftheassociatedtracks.However,theneutralcomponent(neutralhadronandphotons),forwhichthisassociationcannotbetriviallydone,needaspecialtreatment.Amongseveralcorrectionmethods,theoneusingFastJet[ 25 26 ]energydensity()intheeventhasbeenchosentoestimatethemeanpile-upcontributionwithintheisolationconeofalepton.Thevariableisdenedforeachjetinagiveneventandthemedianofthedistributionforeacheventistaken.Thecorrectiontotheneutralcomponentoftheisolationvariableisthenappliedaccordingtotheformula: rcorrXneutralpT=max(uncorrXneutralpT)]TJ /F3 11.955 Tf 11.96 0 Td[(Ae,0GeV)(3)wheretheeffective(Ae)ofagivencomponentisdenedastheratiobetweentheslopeoftheaverageisolationandasafunctionofnumberofvertices.TheelectronAearecomputedonselectedZ!eeeventsondatainbinstocopewiththetruncationoftheisolationconeintheencap.Weshowtheaverageisolationsumsforuncorrectedandcorrectedparticleow(PF)isolationinFigure 3-3 37

PAGE 38

Afterthecorrectionsfortheneutralcomponenttheaverageisolationbecomesalmostindependentonthenumberofvertices. 3.1.3ImpactParameterSelectionInordertoensurethattheleptonsareconsistentwithacommonprimaryvertexwerequirethattheyhaveanassociatedtrackwithasmallimpactparameterwithrespecttotheeventprimaryvertex.Weusethesignicanceoftheimpactparametertotheeventvertex,jSIP3D=IP IPj,whereIPistheleptonimpactparameterinthreedimensionsatthepointofclosestapproachwithrespecttotheprimaryinteractionvertex,andIPtheassociateduncertainty.Hereafter,aprimaryleptonisaleptonsatisfyingjSIP3Dj<4. 3.1.4ElectronMomentumAssignmentandEnergyRegressionTheelectronmomentumisestimatedfromthecombinedmeasurementofECALclusterenergyandfromthetrackmomentum.SincetheenergyresolutionimproveswiththemomentumfortheECALwhiledecreasesforthetracker,thecombinationdependsontheenergyitself,butalsoontheclusterandthetrackquality.Toimprovetheresolution,anenergyregressionisappliedtodeterminethemomentumoftheelectronusingamultivariateapproach.Differentsetsofinputvariablesareusedtotraintheregressiondependingonwhethertheelectronisdetectedinthebarrelortheendcapoftheelectromagneticcalorimeter.Inordertotestagainstover-training,thesesampleswereexplicitlydividedintwo.Onlyonehalfisusedfortraining,whiletheremaininghalfisusedtotesttheperformanceoftheregression.Thetargetoftheregressionischosentobetheratioofthegeneratedenergytotherawenergyofthesuperclusterforbarrelelectrons,andtheratioofthegeneratedenergytothesumofthesuperclusterrawenergyandthepreshowerenergyforendcapelectrons.AverygoodimprovementinresolutionwithrespectthestandardcorrectionsoverawiderangeofpTspectrumandpseudorapidity.Finally,theregressioncorrectedECALenergyislinearlycombinedwiththetrackmomentumusinganotherregressioninordertobenetfrombothmeasurementsinthenalmomentumestimation.Theinformationofanumberof 38

PAGE 39

qualityvariablesofbothclusterandtrackisusedintheregression,signicantlyimprovetheresolutionofthemeasurement.TheapplicationoftheregressiontoHiggsbosonmassreconstructionisshowninFigure 3-4 .ThecomparisonofthereconstructedHiggsbosonmassforthefourelectronsandtwoelectronstwomuonsnalstateshowsanimprovementintheresolutionofmorethan10%. 3.1.5ControlofElectronEnergyScaleandResolutionTheresolutionofelectronmomentumissignicantlyimprovedfromtheregressiononECALandECAL-trackcombination.However,theabsoluteenergyscalehasalsotobecalibratedtodatabecausetheregressionistrainedusingMCevents.Whatismoreimportantfortheanalysis,themeasurementoftheHiggsmassdependscruciallyontheenergyscaleanditsuncertaintythatweneedtoassigntotheleptons.Weshowinthissectionthederivationofthecorrectionsthathavetobeappliedonsimulationtoachieveagoodmatchingoftheenergyresolutionobservedindatathroughtheapplicationofextrasmearingandthederivationofcorrectionstothescaletobeappliedtothedatatoremovethedetectorbiases.BoththecorrectionsarederivedonZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(controlsample.TheprocedureisdescribedinReference[ 27 ],anditisrepeatedherefortheparticularenergyregressionusedinthisanalysis.Theprocedureconsistsoftwosteps.First,thesuperclusterenergyscaleistunedandcorrectedvaryingthescaleinthedatatomatchtheMonteCarloinZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(events;second,theelectronsuperclusterenergyismodiedbyapplyingaGaussianmultiplicativefactorcenteredin1+Pandwitharesolution,wherePistheenergyscalecorrectionandistheadditionalconstanttermintheenergyresolution.Aftertheseoverallcorrections,datatosimulationdifferencesstillexistsbecauseofthedifferentkinematicsandphasespacedifferencesbetweenthecalibrationsample(Z!e+e)]TJ /F1 11.955 Tf 7.09 -4.33 Td[()andthesampleHiggsdecay. 39

PAGE 40

Forelectrons,Z!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(invariantmasscanbebuiltindifferentcategoriesinandseparatingwellandbadmeasuredelectronsusingtheelectronclassication.ThisclassicationdescribestheamountofenergyradiatedbyBremsstrahlungandthequalityofreconstruction,thereforeseparatingdifferentmomentumresolutions.Eventsarelookedatinlowandhighpileupregimes.ThedistributionsarettedwithaBreit-Wignerwithxedparameters)convolutedwithaCrystalBallwithparametersthatareallowedtooat.Figure 3-6 showstheresultsobtainedthiswayusing2012dataandcomparingtoMCexpectations.Systematicuncertaintiesonelectronenergyscalecanbeextractedfortheseresults.ItisestimatedasthemaximumdeviationbetweendataandMCofttedZ!e+e)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(peakpositionindifferentcategoriesofpseudorapidityandelectronclasses.Overall,dataandMCagreeswithin0.4%.SplittingbyECALregion,wereach0.1%forelectronintheBarrel,andupto0.4%forelectronsintheECALendcaps.Wehavealsocheckedthedependencyoftheelectronmomentumscalewithrespecttopile-up.ThereconstructedZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.33 Td[(isbuiltfordifferentslicesofnumberofvertices,inbothdataandMC,andarettedasdescribedabove.TherearenosignicantvariationoftheZpeakwiththenumberofvertices,andtheMCdistributionwellfollowsthedata,ascanbeappreciatedontheFigure 3-7 3.1.6ElectronScaleLinearityMeasurementThestudiesdescribedabovewasmainlycheckingthescaleforelectronswithrelativelyhighmomenta.Wemayaccountasasystematicafurtherpossiblenon-linearityinthemomentumestimationdifferentiallywithrespecttheMonteCarlowhenpropagatingtheelectroncalibrationestimatedattheZscaletothescaletypicaloftheelectronsofanHiggswithmassmH125GeV.ToestimatethisweperformtstotheZ!e+e)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(invariantmassdistributiondifferentiallyinpTandjjoftheprobeelectron,whilethetagisintegratedoverallthepossiblephasespace.Ineachtthesignalmodelisdescribedwithatemplatebuilton 40

PAGE 41

Drell-YanMonteCarlo,andsmoothedinthecasesoflowstatistics.ThenthetemplatetisperformedallowingonesinglescaleparametertooattomatchdataandMonteCarlo.Theprocedureisvalidatedallowingalsoanextrasmearinginthet:withthesetemplatetswegetextrasmearingthatarecompatiblewiththeofcialonesreportedabove.SincethepurityandstatisticsisnotgoodforpT<15GeV,thescaleismeasuredwithboostedJ=and(1S)eventsthatcanbeselectedondatawithdielectrontriggersandtheelectronselectionusedinthisanalysis.Thetopologyofthissample(nonisolated)issuchthattheycannotbeusedforefciencymeasurements,butstillthescaleisreliableandtheycancompletethegapinthepTrangefrom7to15GeV.The(2S,3S)cannotberesolved,sotheycannotbeusedtoestimatetheelectronscale.ThettothemainpeakisperformedwithaCrystalBallfunction.WesummarizethisextrashiftsasafunctionofpTandjjinFigure 3-8 forthe7and8TeVdata.Theyshowthattheextrashiftisnegligiblearoundthepointwherethecalibrationwasdone,whilethereisanextrashiftwhengoingtolowerpT.Themaximumdriftisabout0.1%inthebarrelandabout0.3%intheenedcapforboth7and8TeVdata. 3.2Muons 3.2.1MuonReconstructionandIdenticationInCMSreconstruction,muonsarebuiltfromtheirtrackreconstructionindifferentsub-detectors.Themuons'tracksarerstreconstructedindependentlyintheinnertracker(socalledtrackertrack)andinthemuonsystem(socalledstandalonemuontrack).Correspondingly,tworeconstructionapproachesareused[ 28 ]:globalmuonsandtrackermuons.Inglobalmuonreconstruction,foreachstandalonemuontrack,amatchingtrackertrackisfoundbycomparingparametersofthetwotrackspropagatedontoacommonsurface,andthetrackfortheglobalmuonisttedbycombininghitsfromthetracker 41

PAGE 42

trackandstandalonemuontrack,usingtheKalmanltertechnique[ 29 ].Intrackermuonreconstruction,alltrackertrackswithpT>0.5GeVandtotalmomentump>2.5GeVareconsideredaspossiblecandidatesthenextrapolatedtothemuonsystemincludingthemagneticeldeffect,energylosses,andmultiplescatteringthroughthedetectormaterial.Ifatleastonemuonsegmentinthemuonsystem(ashorttrackstubmadeofDTorCSChits)matchestheextrapolatedtrack,thecorrespondingtrackertrackwillbequaliesasatrackermuon. 3.2.2IdenticationandRemovaloftheGhostMuonsTrackerMuonreconstructionismoreefcientthantheGlobalMuonreconstructionatlowmomenta,p.5GeV,becauseitrequiresonlyasinglemuonsegmentinthemuonsystem,whereasGlobalMuonreconstructionisdesignedtohavehighefciencyformuonspenetratingthroughmorethanonemuonstationandtypicallyrequiressegmentsinatleasttwomuonstations.Thecombinationofdifferentalgorithmsprovidesarobustandefcientmuonreconstruction.Agivenphysicsanalysiscanachievethedesiredbalancebetweenidenticationefciencyandpuritybyapplyingaselectionbasedonvariousmuonidenticationvariables.ForthisanalysiswechoosetheParticleFlowMuonselection.TheParticleFlowMuonsareselectedamongthereconstructedmuontrackcandidatesbyapplyingminimalrequirementsonthetrackcomponentsinthemuonsystemandtakingintoaccountamatchingwithsmallenergydepositsinthecalorimeters.MoredetailsoftheParticle-FlowMuonselectionaredescribedinReference[ 30 ].Ontheotherhand,themuonreconstructionleadstothecreationofghostmuonsintwocases.Intherstcase,thetrackertrackofamuonisbrokenintwo,andbothtracksareidentiedasmuons.Thesignatureisasfollows:thetrackssharemuonsegments,haveasmallR,andhavethesamecharge.Inthesecondcase,thetrackofanotherparticleintheeventisfoundtobecompatiblewiththesamemuonhits.Thesignatureissharedsegments.Theseghostmuonshavealmostnoinuenceinthe 42

PAGE 43

signalregionthankstotheapplicationofParticleFlowMuonIdenticationcriteriathatrejectsmostofthem.However,inthebackgroundcontrolregionwherethesecriteriaarerelaxed,theycouldperturbtheestimationofreduciblebackground.Thensimplecriteriaareappliedtoremovethiscontribution.MuonsarerequiredtohaveR>0.02whichrejectssplittracks(andsomelowmassresonances).TrackerMuonsthatarenotreconstructedasGlobalMuonsarerequirethetobearbitratedwhichremovesalargefractionofthemismatchtracks.Afterthesecuts,theresidualcontaminationofghostmuonsinthebackgroundcontrolregionisestimatedtobefrom4%to9%ofthetotalevents.Inaddition,weaddanrequirementtokilltheremainingmismatchtrackseventswhereamuonistaggedasghostifithasmorethan50%ofsharedsegments.ThepreferenceisalwaysgiventothemuonspassingthePFmuonidenticationcriteria.Forsame-signmuonswithR<0.03,wepickthebestaccordingto(pT)=pT.Forothercases,wepickthemuonwiththelargestnumberofsegments.Finalambiguities,ifany,areresolvedbychosingthemuonwithhighestpT.AGlobalMuonorTrackerMuonwithwithtwoarbitratedmatchesisnevercleaned. 3.2.3DerivationoftheMuonScaleandResolutionCorrectionsTheprecisemeasurementofleptonmomentumisoneofthemaingoalsforthisanalysiswhichaimsatreconstructingthemassoftheHiggsbosoncandidateswiththebestpossibleaccuracy.Forthisreason,thereconstructedmomentaofthemuonswerecorrectedbothindataandinsimulationinordertoremoveremaininglocalbiasesinthemeasuredpT,mainlyduetothenon-perfectknowledgeofthethedetector,aswellasmagneticeldsandthepresenceofmaterialinfrontofthesensors.CorrectionswerederivedwiththeMuScleFit[ 28 ]toolkitonsamplesofrealandsimulatedZ!+)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(eventsbothat7and8TeV.Inthethisapproach,thebiasesinthemuonpTmeasurementaredeterminedfromthepositionoftheZmasspeakasafunctionofmuonkinematicvariables.MuScleFitisbasedonanun-binned 43

PAGE 44

maximumlikelihoodt.withareferencemodeltocorrectthemomentumscale,wherethecorrectionfactorisparametrizedbyanansatzfunctionofmuonkinematicsvariables.Afterapplyingcorrections,thereisstillaresidualmismatchintheresolutionbetweendataandMC.TheMuScleFitcorrectionpackageaddsanextrasmearingformuonmomentainMCevent,basedonthedifferencebetweenthettedresolutionindataandMC. 3.2.4MuonScaleandResolutionMeasurementsThemomentumscaleandresolutionafterthecalibrationarevalidatedindatausingdimuonfromJ=,andZdecays,tocoverthefullmomentumrangerelevantfortheanalysis.PFmuonswithpT>5GeVareconsidered,andforZdecaysthePFisolationandSIPcriteriausedintheanalysisarealsoapplied.TheeventsareseparatedincategoriesaccordingtotheaveragepTandjjofthetwomuons,andthedimuonmassdistributionsineachcategoryarettedtoextractthemassscaleandresolution.Asthesignalline-shapefortheH!4`searchisextractedfromsimulatedevents,onlytherelativedifferencebetweendataandsimulationinthemomentumscaleandresolutionisrelevantfortheresult,andthereforetheresultsarepresentedintermsofthetwoquantities M M=Mdata)]TJ /F4 11.955 Tf 11.96 0 Td[(Msim. Msim., =(M)data)]TJ /F3 11.955 Tf 11.95 0 Td[((M)sim. (M)sim..(3)ForJ=decays,thesignalismodeledwithaCrystalBallfunctionandthebackgroundwithathirdorderBernsteinpolynomial.ThemassscaleandresolutionareestimatedfromthemeanandsigmaoftheCrystalBallfunction.ForZdecays,theparametrizationusedisanumericalconvolutionofaBreit-WignerandaCrystalBallfunctionwhilethebackgroundisneglected.Fordecaysindata,thedimuondistributionismodeledasthesumofthreeCrystalBallsfunctionscorrespondingtothe1S,2Sand3Sstates,constrainingthemassseparationbetweenthethreepeakstotheirnominalvalues[ 20 ]andassumingaconstant(M)=Mforthethree.Thebackgroundis 44

PAGE 45

modeledwithafourthorderBernsteinpolynomial.Forsimulatedevents,onlythe1Sstateisused,modeledwithasingleCrystalBallfuntion.TheresultsforthemomentumscaleandresolutionareshowninFigure 3-9 andFigure 3-10 ,respectively.In2011,afterthecalibrationtherelativemomentumscaleisstabletowithin0.1%,andtheresolutionwithinabout10%.Thecalibrationfor2012dataisstillpreliminary,andslightlylessaccurateatlowmomentumthantheonefor2011data. 3.2.5ImpactParameterSelectionThesameimpactparameterselectionisappliedonmuonsasfortheelectrons,i.e.,jSIP3DIP IPj<4. 3.2.6IsolationIsolationformuonsisalsotheparticleowisolation,asdescribedfortheelectrons.Allreconstructedparticleowcandidatesidentiedaselectronsormuonsarevetoedinthecalculationoftheisolationdeposit.InthiswayweremovethecontributionfromthemuonitselfandweachievethecleaningfromthecontributionoftheotherleptonsoftheHiggsdecay.Thepileupcorrectionstrategyisdifferentthanfortheelectroncase:ithasbeenshownthatthesocalledcorrectionsworkinthesamewayastheeffectiveareasandithastheadvantagenottorequirethecomputationoftheAeff.Thecorrectedisolationisthendenedasfollows: RelPFIso=PchargehadronpT+max(PneutralhadronET+PphotonET)]TJ /F8 11.955 Tf 11.95 0 Td[(,0) pleptonT,(3)wherePchhadpTisthesumofthetransversemomentumofthechargedhadronsoriginatingfromtheprimaryvertex,whilePneutralhadronETandPphotonETarerespectivelythetransverseenergyoftheneutralhadronsandthetransverseenergyofthephotons.istheestimationoftheenergydepositofneutralparticles(hadronsandphotons)ofpile-upvertices:=1 2PchhadPUpTwhichiscomputedfromthetracksnotassociated 45

PAGE 46

withtheprimaryvertexofthecollision,thusgivinganper-eventestimateofthepile-upcontribution.Thefactor1/2correspondstoanaiveaverageofneutraltochargedparticles,measuredinjetsinReference[ 32 ].TheaveragecorrectedparticleowisolationformuonsindataisshowninFigure 3-11 .Sincetheperformanceofthecorrectiontotheisolationisalmostidenticaltotheeffectiveareacorrection,thesameworkingpointfortheisolationhasbeenchosen,i.e.,RelPFiso<0.4. 3.3PhotonsAZdecayintoaleptonpaircanbeaccompaniedbynalstateradiation(FSR).Ifthephoton'spTisrequiredtoexceed2GeV,about8%(15%)ofthedecaysintomuons(electrons)areaffected.Forelectrons,themeasuredenergiesautomaticallyincludetheenergyofalargefractionoftheemittedphotonsintheassociatedelectromagneticsuper-cluster.However,themeasurementonmuons'momentadoesnotincludetheemittedphotons.FinalstateradiationisthereforeexpectedtodegradetheZmassresolutionwhenmeasuredwiththesolemuonpairs,andinturndegradetheHiggsbosonmassresolutioninthe4andinthe2e2nalstates.Inadditiontobeingcollinearwiththeleptons,nalstateradiationalsotendstofavorlowenergyphotonemissioncollineartothelepton.ToIdentifyinglowenergyphotonsoverlappingwithotherparticlesisincludedintheparticle-owconceptdevelopedinCMS[ 31 ].Photonsareidentiedandreconstructedwiththeparticle-owreconstructionwithaspecicclusteringalgorithm,efcientdowntoanenergyofabout230MeVintheECALbarreland600MeVintheECALend-caps.Thedeterminationofthephotonenergiesanddirectionsismonitoredinthedatawith0!decays,andisshowntobeaccurate,reliable,andinagreementwiththepredictionsfromsimulation[ 32 ].Theparticleowreconstructionincludesanidenticationofshoweringmuons,tunedforenergeticmuons.Intherarecasesinwhichsuchashoweringmuonis 46

PAGE 47

identied,theenergiesoftheparticleowclusterslinkedtothemuondonotgiverisetoseparateparticles.Forthetransversemomentaofinterestinthelow-massHiggsbosonsearch,however,theshoweringprobabilityisvanishinglysmall,whichleadstothelossofanotentirelynegligiblefractionofcollinearFSRphotons.ParticleowECALclusterslinkedtoidentiedshoweringmuonsarethereforeidentiedasanothertypeofphotonsintheanalysis.Thephotonisolationisdeterminedfromthechargedhadrons,photonsandneutralhadronsidentiedbytheparticle-owreconstructioninaconeofsizeR=0.30aroundthephotondirection.Inthiscone,allchargedhadronscompatiblewithoriginatingfromthesignalprimaryvertexandwithapTlargerthan200MeV,allphotonsandneutralhadronswithapTlargerthan500MeVareincludedintheisolationdeposits.Theabsolutephotonisolationisdenedasthesumofthetransversemomentaofalltheseiso-deposits.Todiscriminateagainstphotonsthatareproducedinpileupinteractions,anadditionalisolationdepositisdenedthatcorrespondstothechargedparticlesumfromtheverticesotherthantheprimaryvertex.Finally,thepileup-correctedrelativeisolationisobtainedbydividingtheabsoluteisolationbythephotontransversemomentum,pTwhichcanbeexpressedas: I=Ich+I+Ineut+IPU pT.(3) 3.4JetsJetsusedinthisanalysisarereconstructedbycombiningtheenergymeasuredinthecalorimetersandtracksfromchargedparticlesonthebasisofthestandardCMSparticleowalgorithm[ 31 ]andusingtheAnti-kT[ 33 ]clusteringalgorithmwithdistanceparameterR=0.5.Thejetsareusedtotagjetsfromvectorbosonfusion(VBF)andassociatedproductionmechanismsoftheHiggsboson.Jetsareonlyconsiderediftheyhavejj<4.7.Duringthejetclustering,constituentsthatoriginatefrompileuparealsoclusteredwithconstituentsfromthehardscattering. 47

PAGE 48

Tocorrectthepile-upcontributiontothejetenergyscale,thecontributionfrompile-upisestimatedbytheL1Fastjetmethodwhichreliesonthedenitionofajetarea[ 34 ]fromwhichamediandensity(,inGeV/Area)pereventcanbedened.ThecorrectionsubtractstothejetpTequalsArea.ThestandardL2andL3jetenergyscalefactors[ 35 ]areappliedontopofthisL1correction.TheselectedjetsarerequiredtohavepT>30GeVafteralltheabovecorrectionsareapplied.Jetscomingfrompile-upeventsareidentiedbyamultivariateanalysis(MVA)techniquebasedontheBoostedDecisionTree(BDT)method.Adiscriminantisbuiltbasedonthenumberofverticesintheevent,thejetkinematics(pT,,),compatibilityofthejettothehardinteractionvertexbasedonchargedconstituentsforjetswithinjj<2.75,theneutralandchargedconstituentsmultiplicities,andseveraljetshapeproperties(jetradiusweightedbytherelativepTcontributionoftheconstituentsandthepTfractioninringsaroundthejetaxis).Amongthethreeworkingpointsdened,weusetheloosestoneinthepresentanalysis. 48

PAGE 49

A BFigure3-1. ElectronBDToutputdistribution.ThegureshowsthedistributionofelectronBDToutputfortrainingsampleW+jets,testsampleZ+jetson2012dataandpromptelectronsinZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(simulationinthebarrel(FigureA)andendcap(FigureB). A BFigure3-2. ROCcurveofelectronMVAID.ThegureshowsROCcurvesfortheelectronmultivariateidentication(BoostedDecisionTrees)comparedwiththecut-basedselectionworkingpoints.SignaleventsarefromDrell-YanMCsample.BackgroundeventsarefromjetsfakingelectronsinadatasampledominatedbyZ+jetsprocess.ElectroncandidateswithpT>20GeVareshown.FigureAisforelectronsinthebarrelregion,andFigureBisforelectronsintheendcapregion. 49

PAGE 50

A BFigure3-3. Electronparticleowisolationasafunctionofnumberofvertices.FigureAshowstheaverageestimateofeventenergydensityintheevent,andparticleowcomponentsasafunctionofthenumberofreconstructedvertices.Thechargedparticlesareassociatedtotheprimaryvertex.FigureBshowstheeffectoftheeffectiveareascorrectiononthetotalparticleowisolation.ElectronsareselectedwithpT>20GeVandinadatasampledominatedbyZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(events. A BFigure3-4. Higgsmassregression.ThegureshowsthecomparisonofthereconstructedHiggsbosonmassdistributionsafterapplyingMonteCarlo-to-datacorrectionsforthestandardelectronmomentumassignmentandtheregressionassignment,forthe4e(FigureA)and2e2(FigureB)channel.AtissuperimposedandtheparameterestimatingthecoreresolutionisshownDCB.TheeffectiveRMSofthedistribution,includingthetailsinthemassrangeshownisalsoreported. 50

PAGE 51

A BFigure3-5. Electronsmearing.Thegureshowsthedata-to-simulationcomparisonforZ!e+e)]TJ /F1 11.955 Tf 12.63 0 Td[(events.Redlledhistogramrepresentstheun-smearedsimulation.Blackhistogramrepresentsthesimulationafterthesmearingshavebeenapplied,andthepointsrepresent8TeVdata. A BFigure3-6. Electronenergyscaleandresolutionindifferentcatergorise.ThegureshowsZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(eventscategorizedregardingtheelectronsclassicationforthebestcategoryofevents,withbothnon-showeringelectronsinthebarrelandtheworstcategory,withbothshoweringelectronsintheendcap.Reddotsare2012datawithatsuperimposed.Bluesquaresaresimulationwithanothertsuperimposed. 51

PAGE 52

Figure3-7. Z!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(resolutionasafunctionofnumberofvertices.ThegureshowsZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.33 Td[(peakpositiondifferencesbetweendataandMCdividedbythepeakpositioninMCasafunctionofthenumberofvertices. A BFigure3-8. Electronenergyscalesummaries.Thegureshowstheextradata-to-MonteCarloshiftsasafunctionofelectronpTfor7TeVdata(FigureA)and8TeVdata(FigureB)computedusingJ=,andZintotwoelectronresonances. 52

PAGE 53

A B C DFigure3-9. Muonenergyscale.ThegureshowstherelativedifferencebetweenthedimuonmassscaleindataandMCextractedfromJ=,andZdecays,asfunctionoftheaveragemuonpT(FigureA)andjj(FigureB)forthe2011data(FigureC)and2012data(FigureD).MarkersfordifferentpTandjjbinsareslightlydisplacedhorizontallyforlegibilitypurposes.Theuncertaintiesshownarestatisticalonly. 53

PAGE 54

A B C DFigure3-10. Muonresolution.ThegureshowstherelativedifferencebetweenthedimuoninvariantmassresolutionsindataandMCextractedfromJ=,andZdecays,asfunctionoftheaveragemuonpT(FigureA)andjj(FigureB)forthe2011data(FigureC)and2012data(FigureD).MarkersfordifferentpTandjjbinsareslightlydisplacedhorizontallyforlegibilitypurposes.Theuncertaintiesshownarestatisticalonly. 54

PAGE 55

A BFigure3-11. Efciencyofparticleowisolation.ThegureshowstheefciencyofuncorrectedparticleowisolationandcorrectedparticleowisolationforbothandEffectiveAreacorrectedisolationasafunctionofthereconstructednumberofverticesinZ!+)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(eventsselectedondata. 55

PAGE 56

CHAPTER4ANALYSISSTRATEGYTheHiggsbosonsearchinH!ZZ!4`istheprocesswhereHiggsdecaysintotwoZbosons,oneorbothorthemcouldbeofftheZmasspeak,andZbosonsdecayintodi-leptonpairs.SincethenalstateparticlesthatarerelevanttoHiggsdecayareallleptons,thisprocesshasverysmallbackgroundcontaminationduetoQCD.ComparedwithH!WW!2`2,therearenoneutrinosinthenalstatethatcan'tbedirectlydetected.ThenalstatecanbecompletelyreconstructedbyidentifyingfourleptonsfromZdecays.Thebackgroundmainlycomesfromfour-leptonsdecayfromZZorZproducedbyquarkanti-quarkannihilationandgluon-gluonfusionthroughboxdiagram.AnothersourceofbackgroundcontributionsisfromfromZbbandttwherenalstatescontaintwoisolatedleptonsandtwoleptonsinthejets,aswellasinstrumentalbackgroundsfromZ+jetsandWZ+jetswherejetsaremis-identiedasleptons.SotheanalysisstrategyisaimedatndingfourleptonswhicharefromZbosonsthatarefromHiggsdecay. 4.1DatasetandMonteCarloSamplesThedatasampleusedinthisanalysiswasrecordedbytheCMSexperimentduring2011(runrangefrom160431to180252)andduring2012(runrangefrom190645to208686),whichcorrespondtoL=5.05fb)]TJ /F5 7.97 Tf 6.59 0 Td[(1in2011at7TeVandL=19.7fb)]TJ /F5 7.97 Tf 6.59 0 Td[(1in2012at8TeVisusedinthisanalysis.Theluminosityisknownwithaprecisionof2.2%in2011and4.4%in2012[ 36 ].ThedataareproducedcentrallyandcombinevariouscollectionsofHighLevelTriggers.Forthe2011data,theanalysisreliesontheso-calledDoubleElectronandDoubleMuonprimarydatasets.TheyareformedbyanORbetweenvarioustriggerswithsymmetricorasymmetricpTthresholdsforthetwoleptons,withorwithoutadditionalidenticationandisolationrequirements.Inthe2012data,electron-muoncross-triggersareaddedtorecoverafewpercentofinefciencyinthe2e2nalstate 56

PAGE 57

atlowfour-leptonmassregime,formingtheso-calledMuEGprimarydataset.Wealsousetri-electrontriggerswithalowerpTthresholdforboth2011and2012datatorecoverinefciencyofDoubleElectrontrigger.Everysingleeventisuniquelyidentiedbyitsrunnumber,eventnumberandalumi-sectionnumberwhichstandsforasub-sectionofarunduringwhichtheinstantaneousluminosityisunchanged.Foreventsexitinmorethanoneprimarydataset,thesethreenumbersareusedtoremoveduplicateeventstomakesurenoeventsarecountedmorethanonce.TheHiggsbosonMonteCarlo(MC)samplesusedinthecurrentanalysisaregeneratedwithPOWHEG[ 37 ]whichincorporatesNLOgluonfusion(gg!H)andweak-bosonfusionqq!qqH.ThepTdistributionoftheHiggsbosonismatchedtothecalculationfromHRes[ 38 ]whichcombinesthecalculationofthecrosssectionforStandardModeHiggsbosonproductionuptoNNLOinQCDperturbationtheoryincludingenhancedcontributionsatsmalltransversemomenta.TheCTEQ6M[ 39 ]andCT10[ 40 ]partondistribution(PDF)setsareusedforgeneration7and8TeVHiggsMCsampleswiththeHiggsbosonwidthstakenfromReference[ 5 ].AdditionalsampleswithWH,ZHandttHassociatedproductionareproducedwithPYTHIA[ 41 ].TheHiggsbosonisforcedtodecaytotwoZ-bosons,whichareallowedtobeoff-shell,andbothZ-bosonsareforcedtodecayviaZ!2`.Totestdifferentspin/parityhypotheses,eventswithalternativemodelsoftheHiggsbosonaregeneratedusingJHUGEN[ 42 ].qq!ZZ()!4lisalsoproducedwithPOWHEG[ 37 ],includingthecompleteNLOsimulation,interfacedtoPYTHIA[ 41 ]forpatronshower,hadronization,unstableparticledecaysandtheunderlyingevent.Thegluon-inducedZZbackground,althoughtechnicallyofNNLOcomparedtotherstorderZ-pairproduction,amountstoanon-negligiblefractionofthetotalirreduciblebackgroundatmassesabovethe2MZthreshold.Thiscontributionsareestimatedbyusingthededicatedtoolgg2ZZ[ 43 ],whichcomputesthegg!ZZ()!4`atLO,whichisoforder2s,comparedto0sforthe 57

PAGE 58

LOqq!ZZ()!4l.Thehardscatteringgg!ZZ()!4`eventsarethenshoweredandhadronizedusingPYTHIA[ 41 ].TosimulatethebackgroundwhereatleastofonetheleptonsisnotfromZdecay,Z+jetssamplesaregeneratedwithMadGraph[ 44 ].Bothlight(q=d,u,s)andheavy-avor(q=c,b)jetsareincludedinthesample.Toseparatethecontributionfromheavy-avorjets(referredtoastheZ+bbsample)theZ+jetssample,generatedusingMadGraph[ 44 ],waspartitionedinZ+lightjetsandZ+heavyavorjetsusingalterselectingeventswithtwob-jetsortwoc-jetsinthenalstate.Thett!2`22bsample,anothermajorsourceofreduciblebackgroundisgeneratedwithPOWHEG[ 37 ]eventgenerator. 4.2EventSelectionTherequirementthattheeventspasstheelectronandmuontriggersmentionedinisconsistentlyappliedindataandMCevents.Giventheveryhightriggerefciency,withrespecttheofineselectionofthedoubleleptontriggersandtheintroductionofthetri-leptontriggers,itisnotneededtoapplyadatatosimulationefciencyscalefactor.Eventselectionafterthepassingtriggerselectionstartsbytherequiringatleastonegoodprimaryvertex(PV)satisfyingthefollowingcriteria:highnumberofdegreeoffreedom(NPV>4),collisionsrestrictedalongthez)]TJ /F1 11.955 Tf 9.3 0 Td[(axis(zPV<24cm)andsmallradiusofthePV(rPV<2cm).Twotypesofleptonsonwhichtheselectionstepsactonaredened.Thersttypeislooselepton.Electronsarerequiretobewithintheacceptanceofjej<2.5,withpeT>7GeVandhaveequalorlessthanoneexpectedmissinginnerhits.Andmuonsarerequiretosatisfyjj<2.4,pT>5GeV.Bothelectronsandmuonsshouldsatisfyrequirementsonthetransverse(dxy<0.5cm)andlongitudinal(dz<1cm)impactparameterwithrespecttotheprimaryvertex.GhostmuonsareremovedasdescribedinSection 3.2.1 .Inaddition,itisrequiredthatR>0.02betweentheleptons.Theothertypeistightlepton.Inaddtiontolooseleptoncriteria,electronsshouldpassthe 58

PAGE 59

electronidenticationcriteriaasdescribedinSection 3.1.1 ,andmuonsshouldmeetthePFMuonsrequirements(seeSection 3.2.1 ).Furthermore,leptonisolationshouldsatisfyrelativePFIso<0.4andthesignicanceofthethree-dimensionalimpactparametertotheeventvertex,SIP3D,isrequiredtosatisfyjSIP3Dj<4.ThefourleptoncandidatesareselectedbysearchingforleptonpairingwhichareexpectedtobefromrealorvirtualZbosonfromHiggsdecay.TheselectionstartsfromsearchforrstZ(Z1).Theeventshouldhaveapairoftightleptoncandidatesofoppositechargeandsameavor(i.e.,e+e)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(,+)]TJ /F1 11.955 Tf 7.08 -4.34 Td[()withinvariantmassclosesttothenominalZbosonmassiskeptanddenotedasZ1.Theselectedpairshouldsatisfy4020GeVandpT>10GeV.InordertosuppressQCDbackground,thereconstructionmassofopposite-signandsame-avorleptonpairmustsatisfym`+`)]TJ /F3 11.955 Tf 11.04 -.3 Td[(>4GeV.Finally,mZ1isrequiredtobegreaterthan40GeV,mZ2isrequiredtobegreaterthan12GeVandandm4`isrequiredtobegreaterthan100GeV. 4.3FinalStateRadiationRecoveryThefour-leptoncandidateselectionusesleptonspassingallselectioncriteria,includingisolationtoconstructtwoZsfromHiggsdecay.However,therecouldbeachancethattherearephotonsradiatedfromelectronsinthenalstatewhichhappentobenotincludedintheelectronreconstruction.Theprobabilityforphotonstoberadiatedfrommuonsismuchsmallerthantheelectronbecausethemuon'smassisathousandstimeslargerthanelectrons,though,onceitoccurs,thenalstateradiatedphotonsfrom 59

PAGE 60

muonsarebyconstructioncompletelyignoredinthemuon'sreconstruction.Asaresult,itisnecessarytoincludethenalstateradiated(FSR)photonsintotheselection.IncaseanFSRphotoncandidateisselectedintheevent,theisolationsummayhavetoberecalculatedtoremovethecontributionoftheFSRphoton.Moreover,thebuildingofZcandidatesneedstobemodiedtoincludeFSRphoton'scontributiontotheinvariantmass.Inthepresentanalysis,onlyphotonswithpTinexcessof2GeVandwellwithininthetrackeracceptance(jj<2.4)areconsidered,andassignedtoaleptonandtoaZfromthecandidateHiggsbosondecay.PhotonsareconsideredonlyiftheminimumRdistancewithrespecttoanyoftheZleptonsissmallerthanR<0.5.Ifthedistanceofthephotontotheclosestleptonisbetween0.07and0.50,theprobabilitythatthisphotonarosefrompile-upor,toalesserextent,fromtheunderlyingevent,becomesappreciable,becauseofthelargeannulusarea.ToenrichthephotonsampleingenuineFSRphotons,thepTcutistightenedto4GeVandthephotonisrequiredtobesomewhatisolatedfromotherparticles.TherelativePFisolationincludingpile-upcontributionisrequiredtobesmallerthan1.0.ForbothZcandidates,onlythephotonsthatmakeamasswithaleptonpairclosertothenominalZmass(takenheretobe91.2GeV)butwithamaximumm``<100GeVarekept.Afterthephotonshavebeenselectedwiththeabovecriteria,ifthereisatleastonephotonwithpT>4GeVtheonewiththehighesttransversemomentumisassociatedtotheZboson;ifthereisnophotonwithpT>4GeVtheclosestphotontoanyoftheleptonsisassociatedtotheZboson.Theinvariantmassiscalculatedusingthefour-vectordenedbythesumofthefour-vectorsofthetwoleptonsandthephoton.IfnoFSRphotoncandidateisselected,thedefaultfourleptonanalysisapplies.Otherwise,theselectedphotonsareremovedfromthecorrespondingleptonisolationcones(ifintheisolationcones),andthedefaultfourleptonanalysisowproceedswiththemodiedleptonisolations,andwiththeZcandidatemassesdeterminedwiththecorrespondingleptonpairandtheassociated 60

PAGE 61

photon.Finally,theHiggsbosoncandidatemassisdeterminedfromthemomentaofthefourleptonsandallFSRphotoncandidates.TheFSRidenticationalgorithmistestedonsimulatedHiggssignaleventswithamassof125GeVwithanaveragepileupof20interactions.ThetotalefciencyiscomparedbyrunningthefullselectionwithandwithouttheFSRalgorithmapplied.Figure 4-1 showsthecomparisonoftheinvariantmassdistributionbeforeandafterFSRrecoveryforeventswithanidentiedFSRphotonandoverallevents.TheFSRalgorithmrecoversperformancebymovingtheeventsfromtheFSRtailbacktotheHiggspeakbulkdistribution.Inaddition,duetotheisolationrequirementsandthenewdenitionofthemassesoftheZbosons,moreeventsareintroducedinthenalselectionafterFSRrecovery.InthecaseofHiggssignal,thetailsarereducedandthearithmeticRMSisimprovedfrom7.1%to6.9%whiletheGaussianRMSisnotmodiedshowingthattheeffectonthewidthdistributionduetotheimpurityisnegligible.InthecaseoftheZZcontinuumtheperformanceisexpectedtobesimilar.TheperformancemetricsareusedtoquantifytheperformanceofFSRreconstruction.TherateisdenedasthenumberofeventswithidentiedFSRphotonsdividedbythetotalnumberofeventsafterallselectionrequirements.ThepurityisdenedasthenumberofeventswithidentiedFSRphotonswherethemassofthesystemconsistingoftheleptonsandthephotonsisnearertothenominalmassofthestudiedresonancewithrespecttothemassoftheleptonsalone.TheefciencygainisdenedasthenumberofeventsafterallselectionrequirementsafterapplyingtheFSRrecoveryalgorithmdividedbythenumberofeventsafterallselectionrequirementswithoutapplyingtheFSRrecoveralgorithm.TheresultsarepresentedinTable 4-1 .TheeffectofFSRonelectronsismuchsmallerduetotheabsorptionofnearbyFSRphotonsintheelectromagneticsuper-cluster,thereforethefourmuonnalstateisaffectedthemost.Anincreaseinthetotalefciencyof2%isexpectedandthisismainly 61

PAGE 62

Table4-1. Rate,purityandefciencygainforsignalandZZbackground ProcessRate(%)Purity(%)Gain(%) H!ZZ(all)6.0802.0H!ZZ!49.1823.0H!ZZ!2e25.0780.6H!ZZ!4e1.4721.8SMZZ(all)6.7812.1SMZZ!410.1833.0SMZZ!2e26.5770.6SMZZ!4e1.8721.8 attributedtothesubtractionofthephotonfromtheisolationannulusoftheleptonsandtotheincreasedefciencyofthedileptonmassrequirementsafterincludingthephoton. 4.4EventYieldEstimation 4.5SignalYieldEstimationandtheUncertaintiesThesignalyieldcanbeestimatedbycombiningthecrosssectionSMfromtheoryandacceptanceAandefciencyasNsigSR=C(mH)sSMA, (4)whereC(mH)isthedata/MCefciencycorrectionfactorasafunctionofHiggsmassmHand,denotedassignalstrength,servingasamultiplieronthecrosssectionsigmaSMpredictedwiththeStandardModel. 4.5.1TotalSignalCrossSectionandBranchingRatioThecrosssectionisestimatedastheproductoftheHiggsproductioncrosssectionandHZZ4LbranchingratioBR(H!4l).SystematicuncertaintiesonthesignaltotalcrosssectionforeachproductionmechanismandforallHiggsbosonmassescanbefoundinReference[ 5 ].Theycomefrompartondensityfunction(PDF)andQCDcouplingssystematicuncertaintiesandfromtheoreticaluncertaintiesevaluatedbyvaryingtheQCDrenormalizationscaleRandfactorizationscaleF.ThePDFplussandQCDscaleuncertaintiesaretreatedasuncorrelated.Thesystematicuncertainties 62

PAGE 63

in7and8TeVareassumedtobe100%correlated.TheuncertaintyonBR(H!4l)istakentobe2%andassumedtobemH-independent. 4.5.2SignalAcceptanceDependingontheHiggsbosonmass,theleptonkinematiccutsrestrictthesignalacceptancetoAfrom60%to90%.TheacceptanceuncertaintiesA=AareevaluatedusingMCFM[ 45 ].Forcalculations,weusedthepp!H!ZZ!e+e)]TJ /F3 11.955 Tf 7.09 -4.34 Td[(+)]TJ /F1 11.955 Tf -417.26 -28.25 Td[(processat7TeVwiththecuts:me+e)]TJ /F3 11.955 Tf 12.2 -.3 Td[(>12GeV,m+)]TJ /F3 11.955 Tf 12.2 -.3 Td[(>12GeV,electrons'pT>7GeVandjj<2.5,andmuons'pT>5GeVandjj<2.4.Theminimaljet-leptonandlepton-leptonRmin-distancewererelaxed,i.e.settozero.ThecrosssectionsarecalculatedinclusivelyinthenumberofjetsfoundatNLO.Weassumethatuncertaintiesonacceptanceat8TeVarethesameasat7TeVandare100%correlated.Thesensitivityofthesignalacceptancetotherenormalizationandfactorizationscalesisevaluatedbyvaryingthembyafactoroftwoupanddown,wherethedefaultacceptanceisestimatedwhentherenormalizationandfactorizationscalesareequaltothehalfoftheHiggsbosonmass.Theuncertaintyturnsouttobe(0.1-0.2%)asshowninTable 4-2 Table4-2. SignalacceptanceAfordifferentQCDscales. mH(GeV)A0AupAdownmaxjAj=A0 1200.54210.54170.54300.17%2000.73180.73170.73280.14%4000.81200.81280.81190.11%5000.84210.84270.84180.07%6000.86370.86440.86320.08% ForestimationofthePDF+ssystematicuncertainties,weusethePDF4LHCprescription[ 46 ].ThethreePDFsetsusedareCT10[ 40 ],MSTW08[ 47 ],NNPDF[ 48 ].TheresultisanenvelopeofallvariationsforthethreesetsofPDFsassigninga2%mass-independentuncertainty. 63

PAGE 64

4.5.3SignalEfciencyLeptonsinHZZ4LarerealleptonsfromZdecays.Theirtrigger,reconstructionandidenticationefciencies,aswellastheimpactparameterandisolationcutefcienciescanbeevaluateddirectlyindataandMCbyinvokingthetag-and-probemethodappliedtoZ!``events.Thedata-to-MCdiscrepancyintheleptonreconstructionandidenticationefcienciesmeasuredwiththedata-driventechniquesisusedtocorrecttheMonteCarloonanevent-by-eventbasis.TheuncertaintiesonthisefciencycorrectionarepropagatedindependentlytoobtainasystematicuncertaintyonthenalyieldsforsignalandZZbackground.Theper-leptondata-to-MCratioisusedtoweightindividualeventstocorrectyieldsforanydata/MCdifference.ForeachMCsample,vehundredtoyMCexperimentsaregenerated.Ineachexperiment,thedata/MCcorrectionareoatedoncewithaGaussianhypothesis,wherethemeanisthecentralvalueofthedata/MCratioandthewidthistheassociateduncertaintyoftheratio.ThesystematicuncertaintyistakenastheRMSofthedistributionofthetotalnumberofexpectedeventsinthevehundredtoys.TheresultingsystematicsarereportedintheFigure 4-2 andFigure 4-3 forthe7and8TeVanalysisrespectively.Inaddition,a1.5%uncertaintyisassignedontheuncertaintyofefciencyrelatedtotrigger. 4.6IrreducibleBackgroundEstimationWeestimatetheyieldofqq!ZZandgg!ZZbasedoncorrespondingMCsamples.Theestimateisusedastheinitialvalueforthet,forwhichweuseamodelderivedfromanNLOgenerationofqq!ZZ!4`usingthePOWHEGgenerator.Forgg!ZZinsteadthereisnotanNLOcalculationavailable,andweusethepredictionfromthegg2ZZgenerator.WhilethemodelsusedinthetsarexedtotheMCestimate,theyieldisallowedtovarywithintheuncertaintyduringstatisticalanalysis.ThePDF+sandQCDuncertaintiesforpp!ZZ!4`atNLOandgg!ZZ!4`areevaluatedusingMCFM[ 45 ].Weusethe2e2nalstateandtheducialcutsforleptonsme+e)]TJ /F3 11.955 Tf 10.1 -.3 Td[(>12GeV,m+)]TJ /F3 11.955 Tf 10.11 -.3 Td[(>12GeV,electronpT>7GeVandjj<2.5,andmuon 64

PAGE 65

pT>5GeVandjj<2.4.Theminimaljet-leptonandlepton-leptonRmin-distancearesettozero.ThecrosssectionsarecalculatedinclusivelyinthenumberofjetsfoundatNLO.Theuncertaintiesareassessedbothfor7and8TeV.ThePDF+sandQCDscaleuncertaintiesaretreatedasuncorrelated,whileuncertaintiesbetween7and8TeVareassumedtobe100%correlated.ThePDF4LHCprescription[ 46 ]isusedtoestimatePDF+ssystematicerrorsusingthreePDFsets:CT10[ 40 ],MSTW08[ 47 ],NNPDF[ 48 ].TheobtainedresultsaresummarizedinFigure 4-4 .ThefourleptonmassdependentPDF+ssystematicerrors,forboth7and8TeV,canbeparametrizedasfollows:ZZ@NLO:(m4`)=1+0.0035p (m4`)]TJ /F8 11.955 Tf 11.96 0 Td[(30) (4)gg!ZZ:(m4`)=1+0.0066p (m4`)]TJ /F8 11.955 Tf 11.95 0 Td[(10) (4)ForestimationofQCDscalesystematicerrors,wecalculatevariationsinthedifferentialcrosssectiond=dm4`aswechangetherenormalizationandfactorizationscalesbyafactoroftwoupanddownfromtheirdefaultsettingR=F=mZ.TheobtainedresultsaresummarizedinFigure 4-5 .ThefourleptonmassdependentQCDscalesystematicerrors,forboth7and8TeV,canbeparametrizedasfollows:NLOZZ:(m4`)=1.00+0.01p (m4`)]TJ /F8 11.955 Tf 11.95 0 Td[(20)=13 (4)gg!ZZ:(m4`)=1.04+0.10p (m4`+40)=40) (4)NLOZZ:(m4`)=1.00+0.01p (m4`)]TJ /F8 11.955 Tf 11.95 0 Td[(20)=13 (4)gg!ZZ:(m4`)=1.04+0.10p (m4`+40)=40) (4) 65

PAGE 66

4.7ReducibleBackgroundEstimationBesidestheirreduciblebackgroundwheretherearefourrealleptonsfromZ()decays,thereareeventswhicharisefromprocesseswhichcontainoneormorefakeleptonsinthefour-leptonnalstate.Themainsourcesoffakeleptonsareleptonswhicharenon-isolatedelectronsandmuonscomingfromdecaysofheavy-avormesons,mis-reconstructedjets(usuallyoriginatingfromlight-avorquarks)orelectronsfromphotonconversions.Therateofthesebackgroundprocessesisestimatedbymeasuringtheprobabilityforfakeleptons,whichmeetpredenedlooseselectioncriteria,topassthenalselectioncriteria.Theseprobabilities,referredtoasfakerates,areappliedontheobservationinsomededicatedcontrolsamplesindatatoextracttheyieldinthesignalregion.Twomethodsareusedtopredictthereduciblebackground,differingbythechoiceofcontrolregionandthecorrespondingwaytoestimatethefakerate. 4.7.1MethodUsingOpposite-signedDileptonControlRegionInordertomeasuretheleptonfakeratios,datawithZ(``)+eandZ(``)+topologyareused,wheretheeventsareexpectedtobedominatedbynalstateswhichincludeaZbosonanafakelepton.Theseeventsarerequiredtohavetwosameavor,opposite-signleptons,withpT>20/10GeVpassingthetightselectioncriteria,whichareexpectedtoformtheZcandidate.Furthermore,thetightrequirementjMinv(`1,`2))]TJ /F4 11.955 Tf -453.17 -23.9 Td[(MZj<10GeVisappliedtoreducethecontributionfromphotonconversions.Inaddition,thereshouldbeanextraleptonpassingthelooseselectioncriteriaandtheSIP3Dcut.Thisleptonwillbeusedastheprobeleptontomeasurethefakerate.TheinvariantmassofthislooseleptonandtheoppositesignleptonfromthereconstructedZcandidateshouldsatisfym2l>4GeV.EacheventisrequiredtohavemissingtransverseenergyEmissT<25GeVtosuppressthecontaminationduetopromptleptonsfromWbosondecaysandfromWZandttprocesses. 66

PAGE 67

Thefakeratiosarethenmeasuredinbinsoftransversemomentumofthelooseleptonandintwobinsofpseudo-rapidityfor2011dataand2012data,respectively.ThemuonfakeratesareshowninFigure 4-6 andelectronfakeratesareshowinFigure 4-7 .TwocontrolsamplesareobtainedbyrequiringthatatleaseoneofthetwolooseleptonswhichformZ2candidatedonotpassthenalidenticationandisolationcriteria.TheonewithtwolooseleptonsisdenotedasPrompt+2Fake(2P2F)andtheotheronewithexactlyonelooseleptonisdenotedasPrompt+1Fake(3P1F)controlsample.The2P2FcontrolsamplesareexpectedtobedominatedbyeventsthatintrinsicallyhaveonlytworealleptonssuchasZ+lightjets,Zbbandtt.Theinvariantmassdistributionofeventsselectedinthe2P2FcontrolsampleisshowninFigure 4-8 forthe8TeVdataset.Forchannelswithfakeelectrons,the2P2FcontrolsampleisreasonablywelldescribedbytheMC.ThefakeratesforthetwoleptonsareusedtoextractthecontributioninsignalregionN2P2FSRasN2P2FSR=X(fi 1)]TJ /F4 11.955 Tf 11.96 0 Td[(fifj 1)]TJ /F4 11.955 Tf 11.96 0 Td[(fj)N2P2F, (4)wherefiandfjarethefakeratesforthetwolooseleptonsandN2P2Fisthenumberofobservedeventsinthe2P2Fcontrolsample.The3P1Fcontrolsamplesisexpectedtobepopulatedwiththetypeofeventsthatpopulatethe2P2FregionwhereoneofthelooseleptonpassthetightselectioncriteriaaswellaswithWZeventsthatintrinsicallyhavethreepromptleptons.Moreover,therecouldbecontributionfromZZwhereoneofthefourtrueleptonshappenstobeidentiedasalooselepton.Hencethecontributionsfrom2P2FcontrolsampleandZZprocessneedtoberemovedwhenusingfakeratiostoextrapolatefromthe3P1Fcontrolregiontothesignalregion.Thecontributionofthe3P1Fcontrolsampleinthesignal 67

PAGE 68

regioncanbeexpressedasN3P1FSR=Xfi (1)]TJ /F4 11.955 Tf 11.95 0 Td[(fi)(N3P1F)]TJ /F4 11.955 Tf 11.95 0 Td[(Nbkg3P1F)]TJ /F4 11.955 Tf 11.96 0 Td[(NZZ3P1F) (4)wherefiisthefakeratesforthelooseleptons,NZZ3P1FisthecontributionfromZZtakenfromMCsamplesandNbkg3P1Fisthecontributionfromthe2P2Fcontrolsample,denedasNbkg3P1F=X(fi 1)]TJ /F4 11.955 Tf 11.96 0 Td[(fi+fj 1)]TJ /F4 11.955 Tf 11.95 0 Td[(fj)N2P2F. (4)FinallytheexpectedyieldsfromreduciblebackgroundisthesumofN2P2FSRandN3P1FSR.Table 4-3 showstheexpectednumberofeventsinthesignalregionsfromthereduciblebackgroundprocesses,bothforthe7and8TeVdata.Thersterroristhestatisticaluncertainty,whichisdominatedbythelargestatisticaluncertaintyofthe3P1Fcomponent.Theseconderrorisasystematicuncertaintyduetothestatisticaluncertaintyofthefakerates. Table4-3. ThenumberofeventsfromZ+Xexpectedinthesignalregion(m4`>100GeV)inthe7and8TeVdata,aspredictedfromMethodA.Thersterrordenotestheuncertaintyduetothelimitedstatisticsofthecontrolregions,thesecondonedenotesthesystematicuncertaintyduetothestatisticaluncertaintyofthefakerates. DataYieldof4eYieldof4Yieldof22eYieldof2e2 7TeV1.60.30.11.10.40.12.20.40.10.30.30.18TeV6.20.70.23.10.80.26.90.90.21.50.70.2 4.7.2MethodUsingSame-SignedDileptonControlRegionInthismethod,theleptonfakerateisstillcalculatedusingZ+eandZ+eventsindata,buttherequirementonMinv(`1,`2)isrelaxedto40
PAGE 69

reconstructedinvariantmassoftheSS-SFleptonshastosatisfythesamecutsasthesignalregion.Thereconstructedfour-leptoninvariantmassisrequiredtosatisfym4`>100GeVandtheQCDsuppressioncutisapplied.Thenalreduciblebackgroundinthesignalregionisestimatedas:NZ+X=NDATAOS SSMCf1f2 (4)whereNDATAisthenumberofeventsinthecontrolregion,OS SS)MCisacorrectionfactorbetweenoppositesign(OS)andsamesign(SS)controlsamplesandf1andf2arethefakeratesofeachadditionallooseleptonparameterizedasafunctionofpTand.WhiletherequirementjMinv(`1,`2))]TJ /F4 11.955 Tf 12.68 0 Td[(MZj<10GeVlargelysuppressesFSRofphotonsradiatedofftheleptonlegs,theseradiationsoccuratamuchlargerrateinthisphasespace.Eventswherearadiatedphotonmakesanasymmetricconversion,whereonelowpTlegisnotidentied,contributetotheZ+esamplethatisusedtomeasuretheelectronfakerate.However,therelativefractionofFSRconversionsisnotthesameinthesamplethatfakeratesaremeasuredandinthecontrolsamplewherethefakeratesareapplied.Tocorrectthisdifference,fakeratesaremeasuredinsamplesenrichedinFSRconversionsbyrequiringjMinv(`1,`2,e))]TJ /F4 11.955 Tf 12.77 0 Td[(MZj<5GeV.Inagiven(pT,)bin,oneexpectsalineardependenceofthefakeratewithrespecttotheaveragenumberoftrackmissinghitsinthepixeldetector.ThislinearbehaviorisdemonstratedinFigure 4-9 .Finally,thecorrectionfactorisappliedonthefakeratesfromtheratiooftheaveragenumberofmissinghitsinthepixeldetectorinthecontrolregionandtheintheregionwherefakeratesaremeasured.Theeventyieldsexpectedinthesignalregion,inthemassrangem4`>100GeV,aresummarizedinTable 4-4 .Thersterrorcorrespondstothestatisticaluncertainty,theseconderrordenotesthesystematicsuncertainty,whichincludestheuncertaintyofthefakeratesandtheuncertaintyoftheOS-to-SSratios. 69

PAGE 70

Table4-4. ThenumberofeventsfromZ+Xexpectedinthesignalregion(m4`>100GeV)inthe7and8TeVdata,aspredictedfromMethodAA.Thersterrordenotestheuncertaintyduetothelimitedstatisticsofthecontrolsample,theseconderrordenotesthesystematicuncertaintyduetotheOS-to-SSratioandtotheuncertaintyofthefakerates. DataYieldof4eYieldof4Yieldof22eYieldof2e2 7TeV1.20.00.40.50.10.11.50.00.40.40.10.18TeV5.90.10.93.10.20.57.00.20.92.40.20.4 4.7.3EventYieldPredictionThepredictionsforthereduciblebackgroundfromthetwomethodsusingdifferentcontrolregionsareinreasonableagreement.Thestatisticaluncertaintiesofthetwomethods,duetothenitestatisticsofthecontrolsamples,arefullyuncorrelatedbecausethecontrolsamplesareorthogonalwithrespecttoeachother.Intheaveraging,thesourceofcorrelationbetweentheerrorsofmethodAandthoseofmethodAA,whichisduetothenitesizeofthesampleswherethefakeratesaremeasured,canbeneglected.Hence,theerrorsgiveninTable 4-3 andinTable 4-4 canbetreatedasfullyuncorrelatedinthecombination.ThenalestimatesforthereduciblebackgroundaregiveninTable 4-5 Table4-5. ThepredictedyieldsforthereduciblebackgroundobtainedbycombiningtheresultsofmethodAandmethodAA.ForthechannelswhereZ2!,thesystematicuncertaintyduetothebackgroundcompositionofthecontrolsamplesisindicatedseparately,astheseconderrorquoted.Itisthedominantsourceofuncertainty. DataYieldof4eYieldof4Yieldof22eand2e2 7TeV1.40.20.580.110.232.290.310.178TeV6.10.63.090.451.249.250.720.94 4.7.4ClosureTestUsingDataAnotherclosuretesthasbeenperformedformethodAA,usingsamplesofZplustwooppositeavorleptons(e,).AspecialsignalsampleisselectedusingtheselectionandkinematiccutsofthebaselineHiggsphasespace,butwrongavorpairing,i.e.e,isusedtomaketheZ2candidate.Thissignalsampleisexpectedto 70

PAGE 71

bedominatedbyeventswheretheZ2candidateismadefromtwofakeleptons,whichcanbeobtainedbyapplyingmethodAAtoacontrolsampleofZ1plustwolooseleptonsofoppositesignandoppositeavor(Z1+e).33eventsareobservedinthe2012Z1+esignalsample.Thecorrespondingfour-leptoninvariantmassdistributionisshowninFigure 4-11 .ThereduciblebackgroundcomponentobtainedfrommethodAAisshownasthegreenhistogram.Thetotalexpectedbackgroundof27.12.0eventscompareswellwiththenumberofobservedevents.TheclosuretestsbasedondatashownoevidencethatthesystematicuncertaintyneedstobeenlargedforthechannelswheretheZ2candidateismadefromtwoelectrons.AndthelowstatisticsintheZ2!channelsinthesame-signclosuretestdoesnotallowtoreducethe40%uncertaintyobtainedfromtheMCstudies. 4.8Double-PartonScatteringEstimationTheirreduciblebackgroundsmentionedabovearefromtheso-calledsingle-partonscatteringprocesseswhereinvolveonepartonineachprotoncollidingviaahardinteraction.Therecouldexitprocesseswheretwopartonsinoneprotoncollidewithtwopartonsintheotherproton,whichisknownasdoublepartonscattering(DPS)/citedps.ThemostrelevantDPSprocesstoH!ZZ!4`analysisisZ+DYprocess,whereonehardinteractionisZbosonproductionandleptonicdecayandtheotherhardinteractionisDrell-Yan(DY)process(wheretheintermediateparticlecouldbeeitheraZbosonorvitalphoton).SincethisZ+DYprocessalsoleadstofourleptonswhichcanformZ1andZ2pair,itcancompletelymimictheNLOpp!ZZandgg!ZZbackgrounds.TheleadingordercrosssectionforaDPSprocessisproportionaltotheproductofcrosssectionsofthecorrespondingsingle-partonscatteringprocessesas[ 52 53 ]Z+DYDPS=ZDY e, (4)whereeisexpectedtobeprocessandkinematiccutindependent.Naively,itcanberelatedtothegeometricalsizeoftheproton.Thiseffectivecrosssectionis 71

PAGE 72

measurementusingW!`+2jetseventscollectedatATLASdectorandtheresultis111(stat.)+3)]TJ /F5 7.97 Tf 6.58 0 Td[(2(syst.)mb[ 54 ]whichisconsistentwithlowenergyexperimentsasshowninFigure 4-12 .ToextractthecontributionfromZ+DYDPSprocess,wegenerateDPSeventswithPYTHIA8[ 55 ]withoutfurtherdetectorsimulationtoestimatetheyieldsofthePDSprocess.ForEquation( 4 ),thecrosssectionofZ+DYDPSprocessis0.27fbwithmZbetween40and120GeVandm2`>12GeVforDYprocesswherethecrosssectionsforthecorrespondingsinglepartonscatteringprocessesarecalculatedusingPYTHIA8[ 55 ]).TheacceptancewithpT>5GeV,jj<2.4areestimatedbasedonthegeneratedDPSeventsandsummarizedinTable 4-6 whereonecanseethattheacceptanceforZ+DYDPSprocessisapproximatelytheproductionofacceptanceofZandacceptanceofDYprocess. Table4-6. AcceptanceofZ,DYandZ+DYDPSprocesses. ProcessAcceptance Z(4012GeV)34%Z+DY18% Assumingtheducialcrosssection(thecrosssectionwithinthephasespacedenebyleptonpTandjjcutsandcutsonmZ1andmZ2)forthreenalstatestogetherisvetimescrosssectionin4nalstate,thetotalexpectedyieldofthisDPSprocessbeforeanyleptonefciencycorrectionisabout0.6eventat7TeV(about5fb)]TJ /F5 7.97 Tf 6.59 0 Td[(1data)inthefullm4`rangeusingthesamekinematiccutastheH!ZZ!4`analysis.Iffocusingonthelowmassregion(m4`inbetween100and170GeV),theyieldwillbe0.3eventwhichisabout20%ofthecorrespondingreduciblebackground,safelycoveredbythereduciblebackgrounduncertainties.HencethebackgroundduetioDPSisnotincludedasaseperatebackground. 72

PAGE 73

Figure4-1. TheguresshowstheinvariantmassreconstructionoftheHiggscandidateoftheeventswithanidentiedFSRphoton(FigureA)andallevents(FigureB)forHiggssignalwithmH=126GeV. 73

PAGE 74

A B C DFigure4-2. Instrumentaluncertaintiesrelatedtodata-to-MCdifferencesin7TeVdata.Thegureshowstheinstrumentaluncertaintiesrelatedtodata-to-MCdifferencesinefcienciesinreconstruction,identication,isolationandSIPasafunctionofmH,for4echannel(FigureA),4channel(FigureB)and2e2channelforelectrononlyuncertainties(FigureC)and2e2channelformuononlyuncertainties(FigureD).Resultsarefor7TeVdata. 74

PAGE 75

A B C DFigure4-3. Instrumentaluncertaintiesrelatedtodata-to-MCdifferencesfor8TeVdata.Thegureshowstheinstrumentaluncertaintiesrelatedtodata-to-MCdifferencesinefcienciesinreconstruction,identication,isolationandSIPasafunctionofmH,for4echannel(FigureA),4channel(FigureB)and2e2channelforelectrononlyuncertainties(FigureC)and2e2channelformuononlyuncertainties(FigureD).Resultsarefor8TeVdata. 75

PAGE 76

A BFigure4-4. PDF+suncertainties.ThegureshowsthePDF+suncertaintiesforpp!ZZ!4`atNLO(FigureA)andgg!ZZ!4`(FigureB)processes.Thepointsareevaluateduncertainties.Thecurvesaretheparamitrizedsystematicerror(m4`)tobeusedinthestatisticalanalysis. A BFigure4-5. QCDscaleuncertainties.ThegureshowstheQCDscaleuncertaintiespp!ZZ!4`atNLOand(FigureA)gg!ZZ!4`(FigureB)processes.Thepointsareevaluateduncertainties.Thecurvesarethetsystematicerrortobeusedinthestatisticalanalysis. 76

PAGE 77

A BFigure4-6. FakeratesmeasuredforprobemuonswhichsatisfythelooseselectioncriteriainZ(`1`2)+sample.Thegureshowsthefakeratesmeasuredforprobemuonswhichsatisfythelooseselectioncriteria,measuredinaZ(`1`2)+sampleinthe7TeVdata(FigureA)andthe8TeVdata(FigureB)wherejMinv(`1,`2))]TJ /F4 11.955 Tf 11.62 0 Td[(MZj<10GeV.Theblue(red)symbolscorrespondtomuonswithinjj<1.2(jj>1.2). A BFigure4-7. FakeratesmeasuredforprobeelectronswhichsatisfythelooseselectioncriteriainZ(`1`2)+esample.ThegureshowsthefakeratesmeasuredforprobeelectronswhichsatisfythelooseselectioncriteriainZ(`1`2)+esampleinthe7TeVdata(FigureA)andthe8TeVdata(FigureB)wherejMinv(`1,`2))]TJ /F4 11.955 Tf 11.95 0 Td[(MZj<10GeV.Theblue(red)symbolscorrespondtoelectronswithinjj<1.45(jj>1.45). 77

PAGE 78

A BFigure4-8. Invariantmassdistributionoftheeventsselectedinthe2P2Fcontrolsampleinthe8TeVdata.Thegureshowstheinvariantmassdistributionoftheeventsselectedinthe2P2Fcontrolsampleinthe8TeVdata,combiningthe4eand22echannels(FigureA)andcombiningthe4and2e2channels(FigureB). A BFigure4-9. Thecorrelationbetweenthefakerateandthefractionoflooseelectronsforwhichthetrackhasonemissinghitinthepixeldetector.Thegureshowtheexamplesofthecorrelationbetweenthefakerateandthefractionoflooseelectronsforwhichthetrackhasonemissinghitinthepixeldetector.EachdotshowsthemeasurementsmadeinagivenZ+looseesample. 78

PAGE 79

A BFigure4-10. Averagefakeratecomparison.ThegureshowtheaveragefakeratestobeappliedtothecontrolsampleofMethodAA(closedreddots),comparedtothefakeratesmeasuredintheAAfakeratesample(closedblackdots)andintheAfakeratesample(opensquares).Thefakeratescorrespondingtobarrelelectronsforthe7TeVdata(FigureA)andendcapelectronsforthe8TeVdata(FigrueB)areshown. A BFigure4-11. Closuretestsofreduciblebackgroundestimation.ThegureshowstheclosuretestsofmethodAA,usingsame-signleptons(FigureA)andopposite-signoppositeavorleptons(FigureB).Thedotsshowtheinvariantfour-leptonmassdistributionforthe2012data.TheexpectationfromZplustwofakeleptonsaspredictedbymethodAAisshownbythegreenhistogram.AlsothecontributionsfromZZevents(bluehistogram),andfromWZproduction(yellowhistogram)areshown. 79

PAGE 80

Figure4-12. Effectivecrosssection.Thecentre-of-massenergysdependenceofeextractedindifferentprocessesindifferentexperiments,foranenergyrangebetween63GeVand7TeV. 80

PAGE 81

CHAPTER5OBSERVABLES 5.1Four-LeptonInvariantMassTheHiggsbosoninvariantmassspectrumformsaresonancestructure.Accordingtoenergy-momentumconservation,theHiggsboson'sfour-momentumcanbereconstructedbyaddingallitsdecayproducts'four-momenta.Thefour-leptondecaychannelhasthebenetthatallthefourleptonscanbefullyreconstructedandmeasuredwithgoodprecision.Hencetheshapeoffour-leptoninvariantmasswillbeveryclosetoadeltafunction.Ontheotherhand,thereisnoresonancestructureinneitherqqZZ=ggZZbackgroundnorreduciblebackgrounds.Asaresult,theshapeoffour-leptoninvariantmasscanbeusedtoenhancethesignal-to-backgroundseparation. 5.1.1ModelingofSignalForSMHiggsbosonmasshypothesesmH<400GeVthenarrowwidthresonancehypothesisholds,sowemodelthesignalline-shapeforf(m4ljmH)asaBreit-Wignerfunctiondescribingthetheoreticalline-shape,convolutedwithanempiricalresolutionfunctionthataccountsforexperimentalscalebiasandresolution.TherelativisticBreit-WignerfunctionisfBW(mHjmH)is:fBW(m4ljmH)=)]TJ /F5 7.97 Tf 6.78 -1.8 Td[(gg(m4`))]TJ /F5 7.97 Tf 6.78 -1.8 Td[(ZZ(m4l)m4l (m24`)]TJ /F4 11.955 Tf 11.95 0 Td[(m2H)2+m24l)]TJ /F5 7.97 Tf 6.78 3.45 Td[(2(m4`). (5)whiletheresolutionfunctionhasbeenchosenasadouble-sidedCrystalBall(DCB)functionfDCB(m4`jmH):DCB()=N8>>>><>>>>:A(B+jj))]TJ /F7 7.97 Tf 6.59 0 Td[(nL,forRexp)]TJ /F2 11.955 Tf 5.48 -9.69 Td[()]TJ /F3 11.955 Tf 9.3 0 Td[(2=2,forLR, (5)where=(m4`)]TJ /F4 11.955 Tf 12.68 0 Td[(mH)]TJ /F8 11.955 Tf 12.68 0 Td[(mH)=m.Thisfunctionhassixindependentparameters,includingtheGaussiancore(m)ofthefour-leptonmassresolutionfunction,systematicmassshiftmHofthepeak,andtheleft-andright-handtailoriginatingfromleptons 81

PAGE 82

emittingbremsstrahlunginthetrackermaterial,presentforbothelectronsandmuons,andfromthenon-Gaussianmis-measurementsspecictointeractionsofelectronswiththedetectormaterial(twoparameters,nand,foreachsideofthemean).Theprominenceoftheleft-,right-handtailisdenedthepowernL,nR,respectively.TheparametersL,Rdenewherethesplicingofthetailsandthecorearemade,inunitsofm.IthasbeenfoundthattherighttailisdescribedwellforallthemasshypotheseswithaconstantparameternR=20.Finally,thesignalprobabilitydensityfunction(PDF)isbuildbytheconvolution:f(m4`jmH)=DCB(m4`jmH)pdf1(mHjmH) (5)TheBreit-WignerfunctionisfullydeterminedbytheHiggsbosonmass,whiletheparametersoftheDCBfunctionareobtainedfromthetofsignalMCeventsafterthefullselectionweightedbydata-to-MCcorrection.Figure 5-1 showthetsfor4,4eand22e(right)eventssimulatedwithp s=8TeVforaHiggsbosonwithmH=126GeV.Lineshapesfor7TeVsignalMCeventsareverysimilarto8TeV.TheparameterevolutionarettedasafunctionofmHwithpolynomialstoobtainthesignalmodelparameterizationalsofortheintermediarymassvalues.Thevaluesfromthisparametrizationareusedforallthemassbins,regardlesswhethertheyhavethecorrespondingsamplessimulatedornot.ThevalidationoftheinterpolationcanbefoundintheAppendix A .Thedistributionsfortheminorproductionmodes:VBF,WH,ZH,ttHintheuntaggedcategory,andcomparewiththeggHproductiondistributionandtheparameterizationderivedforit(fromtheinterpolationdescribedabove).ThettHproductionhasnegligiblestatisticsinthiscategorysince,duetothejetsassociatedtothettdecay,mostoftheeventsendupinthedijetcategory.TheonlyexceptionforwhichthedistributionbetweentheggHandthealternativeproductionaredifferentistheZH,wheretheZ!``,becausethecombinatoricsfromtheZnotfromtheHiggsdecaycreatesa 82

PAGE 83

secondarypeakathigher4`masses.Giventhatthefractionoftheseeventswiththewrongcombinatoricsissmallwithrespectthecorrectcombinatoricsgivingamasspeakaroundtheexpectedvalue,andthefactthatthisproductionrepresentsatinysignalyieldwiththecurrentluminosity,nospecializedmodelisusedforthiscomponent.TheuncertaintiesaffectingtheshapeofthesignalistheuncertaintiesonthedetectorresolutionfunctionfDCB(m4`jmH)inEquation( 5 ).Thelargestsystematicsfromexperimentalsourcesonthesignalmodelisthenonperfectknowledgeoftheleptonscaleandresolution,whichoriginatesfromthedependencyofthescaleandresolutiononpT,andfromrunconditions.Formuon,theenergyscaleuncertaintyislessthan0.1%,whichpropagatestoabout0.1%onthe4`massfor4events.Theuncertaintyontheresolutionisestimatedtobe20%.ForelectronsthedependencyonpTofthescalerelativetothesimulationishigher,becauseofthecontributionofbothECALandtrackerinthemomentummeasurementwithdifferentweightdependingonthepT.Thedependenciesofthescaleasafunctionofotherquantitiesarefoundtobeminimal,soasystematicsisnotadded,giventhesmalluncertaintyontheintegratedcorrectiondonewiththeZ!e+e)]TJ /F1 11.955 Tf 7.09 -4.34 Td[(.ThescaledependencyonpTiscorrectedfortheresidualnonlinearityindataorMC,butweconservativelyestimatethesystematicsonthatassumingthatwehavenobetterknowledgethantheobserveddata-to-simulationdiscrepancy.ToestimateitweapplytheexpectedshifttotheelectronsinaMonteCarlosampleofHiggswithmH=126GeV,andrecomputingtheinvariantmass.Wethentthemassdistributionwithadouble-sidedCrystalBallfunctionandwetakethedifferenceinthettedmeanbetweenthenominalandtheshifteddistributionaseventsystematicduetothiseffect.Thedistributionsfor2e2and4eareshowninFigure 5-2 .Thesystematicsduetothiseffectareextra0.3%systematicfor4enalstateandextra0.2%systematicfor2e2nalstate 83

PAGE 84

AsthemassofaStandardModelHiggsgoesbeyond400GeV,itsnaturalwidthbecomesverylarge(>70GeV).Asaresult,thenarrowwidthapproximation,i.e.,theresonanceduetoaaStandardModelHiggscanbeexpressedasarelativisticBreit-Wignerfunctionisnotvalidanymore;abetterapproximationisproposetodescribetheHiggsinvariant-massdistribution,knownasComplexPoleScheme(CPS)[ 49 ].Correspondingly,thetotalHiggsproductioncross-sectionisrecomputedtoincludecorrectionsduetoCPSathighHiggsmassandPOWHEG[ 37 ]hasupdatedtoincludeCPSapproach.TheHiggsMCsamplesandcorrespondingcrosssectionsathighmassHiggsregimealreadyincludetheeffectaccordingtoCPSapproach,sonoextracorrectionisneededtoeithercorrectcrosssectionsorreweighttheMCsamples.Moreover,theinterferencebetweentheHiggssignalandthegg!ZZbackgroundbecomesmorecrucialasdiscussedinReference[ 50 ].ThedifcultyfromtheoreticalsidetoestimatetheeffectofinterferenceisthattheinterferencecanbecomputedonlyatLOwhilethesignalisknownatNNLO.Asaresult,theregularxed-ordercalculationcannotbeapplied.InthisanalysiswefollowtheapproachproposedinReference[ 50 ]toestimatetheinterferenceeffectanditsuncertaintyduetoincompleteknowledgeonhigherordercorrectionontheinterference.Intheapproach,theKfactor,deneastheratiobetweenNNLOandLOdifferentialcrosssectiond=dm4`,isusedtoestimatetheNNLOinterferenceeffectfromLOinterferenceeffectas(S+I)NNLO=SLOKNNLO+ILOKggNNLO, (5)However,thisKfactorbasedapproachisonlyanapproximatewaytoestimateinterferenceeffect.Toestimatetheuncertainty,twoalternativeapproachesareusedcalledadditiveandmultiplicativerecipes.TheeffectoftheCPSandinterferencecorrectionsontheH!ZZinvariant-massdistributionandtherelateduncertaintiesareshowninFigure 5-3 84

PAGE 85

ToparametrizethesignalshapeincludingtheCPSandinterferenceeffect,amodiedBreit-WignerfunctionisusedtomodeltheinvariantmassatgeneratorlevelasfHMBW(m4`jmH)=m4` (m24`)]TJ /F4 11.955 Tf 11.95 0 Td[(m2H)2+m24`)]TJ /F5 7.97 Tf 6.78 3.46 Td[(2(m4`), (5)where)]TJ /F1 11.955 Tf 10.09 0 Td[(parametertooatinthet.ThismodiedBreit-Wignerfunctionisthenusedtoconvolutewiththedouble-sidedCrystal-BallfunctiontodescribethemassspectrumatreconstructionlevelasshowninFigure 5-4 .Finally,similartowhatisdoneinlowmassregime,themodelisparametrizedasafunctionofHiggsmassbyinterpolatingfromdiscretemasspointswherethereareMCsamples.ThevalidationoftheparametrizationcanbefoundinAppendix A 5.1.2ModelingofIrreducibleBackgroundThetheshapeofinvariantmassforpp!ZZ!4`backgrounds(NLOandgg!ZZ)aremodeledusing:NLOZZdN dm4`=C(m4`)NMC(m4`)FZZNLO(m4`), (5)gg!ZZdN dm4`=C(m4`)NMC(m4`)FggZZ(m4`). (5)wheretheoveralldata-to-MCcorrectionfactorsC(m4`).ThefunctionsFNLOZZ(m4`)andFgg!ZZ(m4`)areparameterizedseparatelyfor4e,4,and2e2usingthesimulateddistributionsasfollows:f1(m,~a)=0.5+0.5erfm)]TJ /F8 11.955 Tf 11.95 0 Td[(a1 a2a4 1+e(m)]TJ /F7 7.97 Tf 6.58 0 Td[(a1)=a3 (5)f2(m,~b)=0.5+0.5erfm)]TJ /F8 11.955 Tf 11.96 0 Td[(b1 b2b4 1+e(m)]TJ /F7 7.97 Tf 6.58 0 Td[(b1)=b3+b6 1+e(m)]TJ /F7 7.97 Tf 6.58 0 Td[(b1)=b5 (5)f3(m,~c)=0.5+0.5erfm)]TJ /F8 11.955 Tf 11.95 0 Td[(c1 c2c4 1+e(m)]TJ /F7 7.97 Tf 6.59 0 Td[(c1)=c3 (5) 85

PAGE 86

FNLOZZ(m,~a,~b,~c)=f1+f2+f3 (5)Fgg!ZZ(m,~a,~b,~c)=f1+f2 (5)TheZZbackgroundshapetsat7TeVaresummarizedinFigure 5-5 .Similarresultsarederivedfor8TeVaswell. 5.1.3ModelingofReducibleBackgroundTheamountofreduciblebackgroundwithinagivenm4`rangeisobtainedfromthepredictedbackgroundinthefullmassrange(m4`>100GeV),andfromtheshapeofthem4`distribution.ThelatterisextractedfromtstothecontrolsamplesusedinMethodA.ThecontrolsamplesinMethodAAwillgivetheanswerwhichagreeswithMethodAwithinuncertainties.Forthedeterminationoftheshapeofthem4`distributionforthechannelswhereZ2!ee,thetwochannels4eand22earetreatedtogether.Themassdistributionoftheeventsobservedinthe2P2Fcontrolregion,weightedbyfi 1)]TJ /F7 7.97 Tf 6.58 0 Td[(fifj 1)]TJ /F7 7.97 Tf 6.59 0 Td[(fj,isttedrst.ThiscorrespondstothesecondterminEquation( 4 ).Thefunctionchosentotthis2P2FcomponentistheproductofaLandauwiththeexponentialofarstdegreepolynomial.Themassdistributionoftheeventsobservedinthe3P+1Fsample,aftersubtractionoftheexpectedZZcontributionandofthebackgroundfromZplustwofakeleptons,isttedbyaLandaufunction.Theshapeisgivenbyweightedsumofthetwottedfunctions.Thetteddistributionsforthe2P2Fand3P1FsamplesandthesumofthetwofunctionsareshowninFigure 5-6 .Alternativetshavebeenperformedinordertoassesstheuncertaintyofthisshape,whichareshowninFigure 5-7 .Theuncertaintyofthem4`shapeisdrivenbythatofthe3P1Fcomponent,ofwhichthestatisticsislimited.Tosimplifythestatisticalanalysis,theuncertaintyofthem4`shapeistreatedasaglobalnormalizationuncertaintyof20%. 86

PAGE 87

Withinthelimitedstatistics,the3P1FcontrolsampleinchannelswheretheZ2candidateismadefromtwomuonsdoesnotindicatethepresenceofabackgroundsourcethatwouldbebadlyestimatedbythe2P2FcomponentofmethodAandthatwouldhaveaspecicm4`shape.Hence,themassshapeisjustobtainedfromthedistributionoftheeventsinthe2P2Fcontrolregion,mergingthechannels4and2e2,weightedbyfi 1)]TJ /F7 7.97 Tf 6.59 0 Td[(fifj 1)]TJ /F7 7.97 Tf 6.59 0 Td[(fj.ALandaufunctiondescribeswellthedistribution,asshowninFigure 5-8 .Theshapeisratherwellconstrained,andanyuncertaintyonthem4`distributionisabsorbedinthelargesystematicuncertaintyof40%setontheeventyields.Thechannels2e2(wheretheZ1ismadefromtwoelectrons)and22e(wheretheZ1ismadefromtwomuons)aretreatedtogether.Themassshapeusedforthischannelistheaverageofthetwoshapespresentedabove,weightedbytheeventyieldsexpectedinthetwochannels,andaglobalnormalizationuncertaintyof25%isused. 5.2MatrixElementbasedKinematicDiscriminantKinematicsoftheHiggsdecaytoZZnalstatehasbeenextensivelystudiedintheliteratureinapplicationtothestudiesoftheHiggsbosonornewexoticbosonproperties[ 56 70 ].Theseobservablescouldbechosenforexampleasm1,m2,~),where~areveanglesdenedinReference[ 65 ].Equivalently,thefour-vectorsofthefourleptonscarryfullinformationabouttheevent,butsomecareneedstobetakentodenethoseinthecenter-of-massframe.Andweconcentrateontheconstructionthekinematicdiscriminantsfrommatrixelements. 5.2.1IntroductionInadditiontofour-leptoninvariantmass,detailsofthekinematicstructureofthefour-leptonnalstatecanbeusedtofurtherseparatesignalwithbackground.Forexample,mZ2canserveasagoodcandidate.Fromphysicspointofview,theleptonsinsignaleventscomefromeitherrealorvirtualZbosonsdecays,ontheotherhand,theleptonsinsignaleventscomenotonlyfromrealorvirtualZbosons,butalsofromvirtual 87

PAGE 88

photondecay.mZ1isprobablytherealZineithersignalandbackgroundprocessesbyconstruction(sincemZ1ischosentobeclosertonominalZmassthanmZ2),mZ2easilywilleasilypickupthevirtualZbosonsinsignalprocessbutbothvirtualZbosonsandvirtualphotonsinbackgroundevents.Therefore,mZ2willtendtohavehighervaluesinsignaleventsthanbackgroundevents.ThegreatadvantageoftheH!ZZ!4`channelisthatthenalstatecanbefullyreconstructedanwellmeasured.Besidesm4`andmZ2,fully-reconstructedfour-bodynalstatesprovideeightobservablesinthecenterofmassframe(notincludingthepTandrapidityYofthefour-leptonsystemandnotcountingtheirrelevantazimuthalorientation)asshowninFigure 5-9 ;theyaremZ1,mZ2andveangularvariablesdescribetheH!ZZdecayandtwoZ!`+`)]TJ /F1 11.955 Tf 10.41 -4.33 Td[(decays. 5.2.2ComparisontoSingleVariableDiscriminantThedistributionofvedecayanglesandmZ1andmZ2forH!ZZ!4`eventsandqq!ZZ!4`areshowninFigure 5-10 .WecanconstructtwoprobabilitydensityfunctionsPs(x)andPb(x)foreachofthesevariables(herexstandsforeithermZ2oror)thentaketheratiooftheseprobabilitiestoconstructdiscriminants.ReceiverOperatingCharacteristic(ROC)curveisusedtorepresentthepowerofeachdiscriminantbasedonsinglevariableKDandMEKD.TheROCcurveiscreatedbyplottingthefractionofsignaleventsversusthefractionofbackgroundeventsatvariousthresholdsetbythecorrespondingdiscriminant.ThesethreeROCcurvesareshowninFigure 5-11 ,alongwiththeROCcurveconstructedusingtheMEMKD(H;ZZ)calculatedusingtheMadGraphmatrixelement.OnecanseethattheanalysisutilizingKD(H;ZZ)basedonthematrixelementisthemostsensitive.MEKDmaximallyunitizesthekinematicinformationofthenalstate,includesallthesevenvariablesandtheircorrelations.ThisalsostronglymotivatestheusageofMultivariateAnalysis(MVA).TheadvantageofMEMisthatisthatitusesmatrixelementsquare(tobuilddiscriminant) 88

PAGE 89

whichhasaclear,wellunderstoodphysicsmeaningwhileMVArequiresanadhoctrainingonMCsampleswithlargestatistics. 5.2.3MEKDinSearchingforStandardModelHiggsBosonandSpin-ParityHypothesisTestsSincematrixelementsquareisproportionaltotheprobabilityfunctionofnalstatekinematics,wecanbuildtheMatrixElementbasedkinematicdiscriminant(MEKD)asa(monotonic)functionofratiobetweenmatrixelementsquarewithsignalhypothesisandbackgroundhypothesisasDkinbkg=PkinSM PkinSM+cPkinqqZZ="1+c(m4`)PkinqqZZ(m1,m2,~jm4`) PkinSM(m1,m2,~jm4`)#)]TJ /F5 7.97 Tf 6.58 0 Td[(1, (5)wherePkinSMandPkinqqZZarematrixelementsquareswithsignalandqqZZbackgroundhypotheses,respectively,andc(m4`)takescareoftherelativenormalizationbetweensignalandbackgroundmatrixelements.Foreventswithnalstateradiatedphoton,thephoton'sfourmomentumisaddedtothenearestlepton.ThedistributionofMEKDfavorsathigherMEKDvalueforsignaleventsandatlowMEKDvalueforbackgroundevents.HenceMEKDcanbeusedasanobservableofwhichthedistributioncanbeusedtofurtherseparatesignalwithrespecttobackgroundontopofdistributionofm4`.Moreover,theMEKDusedtoseparatesignalofStandardModelHiggswithrespecttoqqZZbackgroundcanbeextendedtoseparatedifferentspin/parityhypothesesonHiggsboson.SimilartoDkinbkg,MEKDforspin/parityhypothesistestcanbedenedasDJP=PSM PSM+cJPPJP="1+cJPPkinJP(m1,m2,~jm4`) PkinSM(m1,m2,~jm4`)#)]TJ /F5 7.97 Tf 6.59 0 Td[(1. (5)Acompletelistofalldiscriminantsusedforspin/parityhypothesistestcanbefoundinTable 5-1 .However,therearebothsignaleventsandbackgroundeventsinobserveddata,oneneedsnotonlyDJPtoseparatedifferentspin/parityhypothesesbutalsoDkinbkgtoseperatesignalandbackgroundevents.Toenhancethepowertoseparatesignaland 89

PAGE 90

Table5-1. Listofdiscriminantsusedspin-parityanalyses.Thethreeobservablesm4`,Djet,andDpT(notconsideredaskinematicdiscriminants)arelistedforcompleteness. ObservableAnalysisstratergy DbkgSeperationofSMHiggsbosonagainstZZbackground,includem4`D0)]TJ /F1 11.955 Tf 18.71 -.3 Td[(Pseudoscalar(0)]TJ /F1 11.955 Tf 7.09 -4.34 Td[(),discriminateagainstSMHiggsbosonD0+hBSMscalarwithhigherdimoperators(0+h)D1)]TJ /F1 11.955 Tf 18.71 -.3 Td[(Exoticvector(1)]TJ /F1 11.955 Tf 7.09 -4.34 Td[(),qq!XD1+Exoticpseudovector(1+),qq!XDgg2+mKKGraviton-likewithminimalcouplings(2+m),gg!XDqq2+mKKGraviton-likewithminimalcouplings(2+m),qq!XDgg2+bKKGraviton-likewithSMinthebulk(2+b),gg!XDgg2+hBSMtensorwithhigherdimoperators(2+h),gg!XDgg2)]TJ /F10 5.978 Tf 6.64 -6.42 Td[(hBSMpseudotensorwithhigherdimoperators(2)]TJ /F7 7.97 Tf 0 -8.28 Td[(h),gg!XDdecbkgSeperationagainstZZbackgroundincludingm4`andexcludingcos,1Ddec1)]TJ /F1 11.955 Tf 20.61 1.39 Td[(Exoticvector(1)]TJ /F1 11.955 Tf 7.09 -4.34 Td[()withdecay-onlyinformationDdec1+Exoticpseudovector(1+)withdecay-onlyinformationDdec2+mKKGraviton-likewithminimalcouplings(2+m)withdecay-onlyinformation backgroundevents,theinformationofm4`distributionsofStandardModelHiggsandqqZZareembeddedintoDkinbkgtoformamuchstrongerdiscriminantDbkg=PSM PSM+cPbkg="1+c(m4`)Pkinbkg(m1,m2,~jm4`)Pmassbkg(m4`) PkinSM(m1,m2,~jm4`)Pmasssig(m4`jmH)#)]TJ /F5 7.97 Tf 6.58 0 Td[(1. (5) 5.3DiscriminantforVBFandVHEvents 5.3.1EventCategorizationFortheStandardModelHiggs,asmallfractionofthecrosssectioncomesfromvectorbosonfusion(VBF),andassociatedHiggsproductionwithaWoraZboson(VH).SeparatingthegluonfusionandVBForVHcontributionsisparticularlyrelevantforHiggscouplingmeasurementandforcompatibilitytestwithrespecttotheHiggsbosonspredictedintheStandardModel.TheVBFmechanismcanbeprobedexperimentallybyexploitingthedistinctdijetsignature.HencetheeventsarecategorizedbasedonthenumberofreconstructedjetspassingtheselectionmentionedinSection 3.4 .Jetsthat 90

PAGE 91

overlapwithanyofthefour-leptoncandidatesandadditionalFSRphotonsbyR<0.5arerejectedanddonotcontributetothecategorization.Twocategoriesaredenedbasedonthejetmultiplicity.Eventswithlessthantworeconstructedjetsaredenedtobein0/1jetcategory.Andeventswithatleasttwojetsaredenedtobeindijetcategory.FormH=125GeVAbout50%oftheVBFeventshavetwojetsinthenalstatewhileinthecaseofthegluonfusionthisisvalidfor8%oftheevents.IntheWHandZHproduction,afractionofeventsof25and40%respectivelycontributetothedijetcategory. 5.3.2VBFandVHDiscriminationintheDijetCategoryInthecaseofVBFthetwojetsmustformalargepseudorapiditygapandsincetheytendtobeproducedbacktoback,theirinvariantmassisexpectedtobelargeaswell.Ontheotherhand,inthecaseofgluonfusion,thejetstendtobenear(dominatedbygluonsplittingorapairofgluons)andtheirmassfollowsafallingspectrum.FinallyinthecaseofVHthedijetmasspeaksneartheWandZnominalmassandthevectorbosonsystemdecayingtodijetsisboosted.Themainvariablestodiscriminatebetweentheproductionmechanismsinthedijetcategoryarethepseudorapiditygapbetweenthetwojets(denotedasjj)andtheinvariantmassofthetwojets(mjj).Thelinearcombinationofthetwovariablesthatmaximizetheseparationbetweenvectorbosonfusionandgluonfusionisgivenby:Djet=0.18jj+1.9210)]TJ /F5 7.97 Tf 6.59 0 Td[(4mjj (5)FigureAinFigure 5-13 showsthedistributionofthelineardiscriminantforthedifferentproductionmechanismsandZZbackground.Thoseshapesareexploitedtoseparatetheproductionmechanismsinthedijetcategory. 5.3.3VBFandVHDiscriminationinthe0/1JetCategoryInthe0/1jetcategorytherearelessthantwojetsthatarereconstructedalongwiththefourleptonsystem.Inabout50%ofthecasesfortheVBFproductionthere 91

PAGE 92

isatleastonejetreconstructedintheevent.AdditionaldiscriminationbetweengluonfusionandVBFcanbeachievedbyexploitingthetransversemomentumofthefourleptonsysteminthe0/1jetcategory.FigureBinFigure 5-13 showsthedistributionofthetransversemomentumspectrumfordifferentHiggsproductionmodesandZZbackground. 92

PAGE 93

A B CFigure5-1. Fitsofthesignalm4`distributions.Thegureshowstheprobabilitydensityfunctionsf(m4ljmH)forsignalwithmH=126GeVatthereconstructionlevelafterthefullleptonandeventselectionsareapplied.Thedistributionsobtainedfrom8TeVMCsamplesarettedwiththemodeldescribedinthetextfor4(FigureA),4e(FigureB)and22e(FigureC)events. A BFigure5-2. Systematicsofthesignalm4`distributions.Thegureshowsthefour-leptoninvariantmassdistributionwiththenominalleptonmomentum(black)andaftertheextrascaleshiftsareappliedtotheMCwiththedoubleCrystalBalltsuperimposed,forthe4e(FigureA)and2e2(FigureB)nalstatesinthecaseof8TeVsimulationwithmH=126GeV. 93

PAGE 94

A BFigure5-3. Highmasssignalshape.Thegureshowsthefour-leptoninvariantmassdistributionatgeneratorlevelbeforeandaftertheCPSandinterferencecorrectionsforanHiggsmassof900GeVproducedingluonfusion(FigureA)orinvectorbosonfusion(FigureB).Thetwoboundingshapesenclosingthelledbandrepresentsthelineshapeuncertaintyusedinthet. A B CFigure5-4. Modelofhighmasssignalshape.Thegureshowstheprobabilitydensityfunctionf(m4ljmH)fortheHiggsbosonmassatthereconstructionlevelafterthefullleptonandeventselectionsareappliedformH=600GeVat8TeV.Thedistributionsarettedwiththemodeldescribedinthetextfor4(FigureA),4e(FigureB)and22e(FigureC)events. 94

PAGE 95

A B C D E FFigure5-5. Fitsoftheirreduciblem4`distributions.Thegureshowsthetsofsimulationusingthechosenempiricaltfunction. A B CFigure5-6. Fitsofthereduciblem4`distributionsZ2!e+e)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(].Thegureshowthetsofthem4`distributionsforchannelswithelectronfakes,whereFigureAisthetofthe2P2Fcomponent,FigureBisthetofthe3P1FcomponentandFigureCisthesumofthetwofunctions. 95

PAGE 96

A BFigure5-7. Alternativetsofthereduciblem4`distributionswhereZ2!e+e)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(.Thegureshowstheshapeofthem4`distributionforthereduciblebackground,forthe4eand22echannels,inanextendedmassrange(FigureA)andfor100GeV
PAGE 97

Figure5-9. Decayvariables.ThegureshowsanillustrationofaparticleHproductionanddecaya+b!H!Z1Z2!4`withthetwoproductionanglesand1shownintheHrestframeandthreedecayangles1,2,andshownintheZ()restframes.HstandseitherforaSMHiggsboson,anexoticparticle,oringeneralthe4`system. 97

PAGE 98

A B C D E FFigure5-10. Singlevariablediscriminant.ThegureshowsthedistributionofHiggssignaleventswithmH=120GeV(solidred)andbackgroundZZevents(dashedblue)intherange100
PAGE 99

Figure5-11. ComparisonofdifferentROCcurves.ThegureshowsthecomparisonofdifferentROCcurvesbasedonMEKD(redcurve),mZ2(bluecurve),(magentacurve),and(blackcurve). A BFigure5-12. mjjandjj.Thegureshowsthecomparisonofpseudorapiditygap(FigureA)andinvariantmassofthetwotaggedjets(FigureB)inthedijetcategoryfordifferentHiggsproductionmechanismsandZZbackground. 99

PAGE 100

A BFigure5-13. VBFdiscriminant.Thegureshowsthecomparisonofthelinearsherdiscriminantshapesofthedominantproductionmechanismsinthedijetcategory(FigureA)andcomparisonofthetransversemomentumshapesofdifferentproductionmechanismsinthe0/1jetcategories(FigureB). 100

PAGE 101

CHAPTER6OBSERVATIONOFTHEHIGGSBOSON 6.1SummaryoftheObservation 6.1.1EventYieldsThenumberofestimatedbackgroundandsignaleventsandnumberofobservedcandidatesafternalinclusiveselectionindatainthefullsearchrangefrom100to1000GeV,isgiveninTable 6-1 ,separatelyfor2011(7TeV)and2012(8TeV)andcombined. Table6-1. Thenumberofestimatedbackgroundandsignaleventsandnumberofobservedcandidates,afternalinclusiveselection,inthefullmeasurementrange100
PAGE 102

Table6-2. Thenumberofestimatedbackgroundandsignaleventsandnumberofobservedcandidates,afternalinclusiveselection,inthefullmeasurementrange121.50.5)areobserved. 6.2StatisticalMethodologyTousethemaximuminformation,weusealltheobservablesinthemaximumlikelihoodt:thefour-leptonmassm4`,thekinematicaldiscriminant(KD)andtheproductionmodediscriminantVD(DjetorDpTinthedijettaggedoruntaggedcategory.Thesystematicuncertaintiesofthesignalandbackgroundmodelareparametrizedasnuisanceparametersandareproledwhenmaximizingthelikelihoodt.Themodelingofthethekinematicdiscriminantisimplementedasa2DhistogramtemplateoftheontheKDvaluevsthem4`plane,whichautomaticallyincludesthestrongcorrelationofthekinematicdiscriminantwiththemass.Thenthelikelihoodusing 102

PAGE 103

m4`observablealonecanbeextendedas: L2D(m4`,Dkinbkg)=L(m4`)L(Dkinbkgjm4`),(6)wherethersttermcorrespondstothe1Dmassprobabilitydensityfunction(PDF)andthesecondtermtothe2Dtemplateofmassvskinematicdiscriminant.Theconditionalterminthesecondtermisimplementedinthetemplatebynormalizingallycolumnscorrespondingtothesamemasstothesamevalueeach.Thereforethe2DtemplaterepresentsaconditionalPDFofthekinematicdiscriminant.ForimplementingthethirddimensionVD,asimilarprocedureisimplemented,andthecorrelationswithmassaretakenintoaccountbyintroducingtwodimensionalconditionaltemplatesasinthecaseofthekinematicdiscriminant.Giventheaboveathreedimensionallikelihood(e.ginthecaseofVDforthetaggedcategory)isdenedas: L3D(m4`,Dkinbkg,VD)=(L(m4`)L(Dkinbkgjm4`))L(VDjm4`),(6)whereonemoreconditionalPDFisadded.Thetwojetcategoriesandthetreenalstatesarecombinedasdifferentdatasetstoprovidethemodelforthesimultaneoust. 6.3ExclusionLimitsAsearchforaStandardModel-likeHiggsbosonisconducteduptom4`=1TeV.ForeachHiggsbosonmasshypothesis,weperformasimultaneouslikelihoodtfor(m4`,Dkinbkg,VD)distributionsusingthestatisticalapproachesdiscussedinReference[ 71 ].Asacross-check,westudythelimitfromone-dimensionalm4`distributionsandatwo-dimensionalm4`,KDt.WeadoptthemodiedfrequentistconstructionCLs[ 71 72 ]astheprimarymethodforreportinglimits.Apartfromthelowmassexcessaround126GeVcorrespondingtothenewobservedboson,nosignicantexcessisobserved.Figure 6-4 thereforeshowstheexclusionlimitsobtainedwiththemethodologydescribedabove.AStandardModellike 103

PAGE 104

Higgsbosonisexcludedat95%C.L.intherangesfrom114.5GeVto119GeVandfrom129.5GeVto832GeVforanexpectationof115GeVto700GeV. 6.4SignicanceoftheExcessintheLowMassRegionThep-valueorequivalently,thesignicance,isusedtoquantifytheobservedexcess.InFigure 6-5 weshowthesignicanceofthelocaluctuationwithrespecttothebackgroundonlyexpectation,combining7and8TeVdata,whereabeyond5excessisobservedatabout125.7GeVwhilenoothersignicantexcessisobserved.Table 6-3 showstheexpectedandobservedsignicanceatmH=125.7GeVfor7and8TeVdataforthe3D,2Dand1Dlikelihoodt.ThesignicantgaininsensitivitytosearchforaStandardModel-likeHiggsbosoncanbeseenbycomparingtheexpected2Dand1Dlocalsignicance.Moreover,thereisagoodagreementinexpectationandobservationforlikelihoodtusingDkinbkg. Table6-3. Signalexpectedandobservedsignicance()attheminimumofthep-value(125.7GeV)for7and8TeVcombineddata,for3Dt(nominal),2Dtand1Dt. 1D2D3D Expectation5.66.56.7Observation5.06.86.8 104

PAGE 105

A BFigure6-1. Four-leptoninvariantmassm4`distribution.Thegureshowsthedistributionofthefour-leptonreconstructedmassforthefulldataset,comparedtoStandardModelbackgroundexpectationsinfullmassrange(FigureA)andlow-massrange(FigureB). 105

PAGE 106

A BFigure6-2. KinematicdiscriminantDkinbkgdistribution.ThegureshowsthedistributionofthekinematicdiscriminantDkinbkgversusthefour-leptonreconstructedmassm4`inthelow-massregion(100to180GeV).Thecontoursrepresenttheexpectedrelativedensityofbackground(FigureA)andsignal(FigureB)events,forhypothesismH=126GeV.Thepointsshowdatawithmeasuredinvariantmassuncertainties. A BFigure6-3. ThepTandFisherdiscriminant.ThegureshowsthedistributionofVBFandVHdistribution.FigureAshowsthedistributionofpTinthe0/1-jetcategory.FigureBshowsthedistributionofFisherdiscriminantinthedijetcategory.Pointsrepresentthedatawhichareinthemassregion121.5m4l130.5GeV,shadedhistogramsrepresentthebackgroundandtheunshadedhistogramthesignalexpectation. 106

PAGE 107

A BFigure6-4. Limits.Thegureshowstheobservedandexpected95%C.L.upperlimitontheratiooftheproductioncrosssectiontotheSM-likeexpectation.7and8TeVdata-samplesareused.The68%and95%rangesofexpectationforthebackground-onlymodelarealsoshownwithgreenandyellowbands,respectively.FigureAshowslowmassrangeonly,comparing1D,2Dand3Dt.Thebandscorrespondtothe3Dt.ThethefullmassrangeresultsisshowninFigureB. A BFigure6-5. Signicance.ThegureshowsthesgnicanceofthelocaluctuationswithrespecttotheStandardModelexpectationasafunctionoftheHiggsbosonmassinthelowmassrangefrom110to180GeV(FigureA)andinthewholemassrangefrom110to1000GeV(FigureB).DashedlineshowsthemeanexpectedsignicanceoftheSMHiggssignalforagivenmass.Resultsforthe3Dmodel(m4`,Dkinbkg,VD)areshowninblack,1Dmodel(m4`)inredand2Dmodel(m4`,Dkinbkg)inblue. 107

PAGE 108

CHAPTER7PER-EVENTMASSRESOLUTIONASANOBSERVABLEInthischapter,wewillshowtheproceduresandresultsofthemeasurementofthemassandwidthoftheHiggsbosonthatisobservedinthelowmassregion,withafocusonusingtheper-eventmassresolution.Theresolutionisanestimatorofthedifferencebetweenthetrueandmeasuredvalue.Theleptonresolutioncanbemeasuredusingdileptonresonances.Ontheotherhand,thedileptonmassresolutioncanbepredictedusingtheinformationprovidedbyCMSsoftware.Ifthepredictionofthemulti-leptonmassresolutioncanmatchtheobservedmassresolution,thenwecanusethepredictionofthemassresolutionasanobservabletoseparatewellmeasuredeventsfrompoorlymeasuredevents.Thewellmeasuredevents,i.e.,withgoodmassresolution,havealargerprobabilitytobeclosetothetruevalueofthemass.Soiflargerweightisgiventothewellmeasuredevents,thenalresulthaslargerprobabilitytobeclosertothetruth.Thisisthemotivationforusingper-eventmassresolutiontoincreasetheaccuracyoftheHiggsbosonmassmeasurement.ThequalityofthemomentummeasurementforbothelectronsandmuonsstronglydependsontheircharacteristicssuchaspT,,numberofreconstructedhitsformuonsoramountofbremsstrahlungforelectrons,etc..TheelectronresolutionisshowninFigure 7-1 asafunctionofelectronmomentumwheretheE-pcombinationisthenalestimationoftheelectronmomentumresolution.Thetracker-onlyresolutiondominatesinthelowmomentumregionandbecomesworsewhenthemomentumincreasesbecausetheelectronbendslessinthemagneticeldwhenithaslargertransversemomentum.TheECAL-onlyresolutiondominatesinthehighmomentumregionandbecomesbetterasthemomentumincreases.TheE-pcombinationresolution,asacombinationoftheECAL-onlyandthetracker-onlyresolutioncanspreadnearlyafactorof2overthemomentumregionfrom10to100GeV.ThemuonresolutionasafunctionofmuonjjandpTisshowninFigure 7-2 .EventsaretakenfromasimulatedHiggs 108

PAGE 109

sample(mH=126GeV).Theresolutionisdenedasthesigmaofdouble-sidedCrystalBallfunctionthatdescribesthereconstructedpTdistributionaroundthetruepT,wherethemuonmomentumresolutioncanspreadasafactorof3(about1%to3%).Asthesingle-leptonmomentumresolutionpropagatestothemulti-leptonsystem,thefour-leptoninvariantmassresolutionforH!4`decayscanspreadasmuchasafactorof2-3.Indiscriminatelycombiningeventswithwellandpoorlymeasuredfour-leptonmasseswilldilutethesensitivityoftheHiggsbosonmassmeasurements;theeventswithgoodresolutionshouldhavelargerweighttothenalresultsbecausetheyprovidemeasurementsclosertothetruevaluethantheeventswithbadresolution.Wecanmakeasimpleexampletodemonstratethebenetofweightingdifferentmeasurementsbytheirresolutions.Assumingtherearetwomeasurementsx1andx2ofthesamevariablexwithresolution1and2.Anaiveestimatorofxwillbetheaverageofthetwomeasurements, ^x=1 2(x1+x2).(7)Theoptimizedestimateisbuiltbytheweightedsumofthetwomeasurementsaccordingtotheirresolution ^x=22 (21+22)x1+21 (21+22)x2.(7) 7.1CalibrationofPer-EventMassResolutionIndividualleptonuncertaintyonmomentummeasurementscanbeprovidedbytheCMSsoftwareframework:muontracktsprovidethefulluncertaintyofthecovariancematrixfromthemomentummeasurement;forelectrons,themomentumuncertaintyisestimatedfromthecombinationoftheECALandtrackeruncertaintiesiftheelectronsareECALdriven.Fornon-ECALdrivenelectrons,aparametrizationoftheECALenergyuncertaintyisusedandthencombinedwiththeuncertaintyfromtrackermomentummeasurement.Asaresult,theresolutionoffour-leptoninvariantmasscanbepredictedonanper-eventbasisbypropagatingsingleleptonuncertaintytothefour-leptonsystem. 109

PAGE 110

However,oneneedstocheckwhetherthepredictionproperlyrepresentstheobservedresolution.TheproceduretocalibratethepredictedmassresolutiontomatchtheobservedmassresolutionusingdileptonresonancesindataandMCeventscanbefactorizedintotwosteps.Intherststep,acalibrationonsingleleptonresolutionisderivedfromthemomentumpulldistributionusingDrell-YanMC1events,followedbythesecondstepwheretheresidualcorrectionfactorisextractedbyttingthedileptonresonancestoincludenon-Gaussianeffectontheresolutionanddata-to-MCdiscrepancy. 7.1.1CalibrationofSingleLeptonResolutionForanyobservableO,onecandenethepullofthisobservableastheratiobetweendifferenceofmeasuredandtruevalue,andtheuncertaintyofmeasurementwhichisanestimationoftheresolution. pullO=(Omeasure)]TJ /F4 11.955 Tf 11.96 0 Td[(Otrue)=O.(7)IftheuncertaintyOisaproperestimationoftheresolution,thepullofOshouldhaveaGaussiandistributionwithstandarddeviation=1(andmean=0ifthereisnobiasinthemeasurements).TotestwhetherthepredictedmomentumuncertaintyprovidedbytheCMSsoftwareframeworkproperlyreectssingleleptonresolution,Drell-YanMCeventswithfullsimulationofCMSdetectorareusedtoderivethepulldistributionofleptons'momentum.FigureAinFigure 7-3 showstheinverseoftherootmeansquare(RMS)forthepulldistributionof1=pinZ!+)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(MCeventswherebothmuonsareinthesamebinonthepT)-242(jjplane.1=pisusedinsteadofpTsinceitsdistributionismoreGaussianlike,asaresult,theRMSofthepulldistributionisequivalenttotheofthecorresponding 1TheprocesswhereaZbosonorvirtualphotonisproducedfromproton-protoncollisionsandthendecaystodileptonnalstates. 110

PAGE 111

Gaussiandistribution.Thereasonthatthepulldistributionshavepullwithdeviatingfrom1isthatthemuonenergyscaleandresolutioncorrectionsapplyacorrectionfactorandextrasmearingonmuonmomentum.Asaresult,theyonlycorrecttheobservedresolutioninZ!+)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(,whilethepredictionoftheresolutionisnotaffected.ThepredictiononmomentumuncertaintyofmuonsarecalibratedbytheinverseofRMSinthecorrespondingpT-jjbin.ThismakesthepulldistributionGaussianwithastandarddeviationof1.Thecorrectionfactorsrangefromabout0.7toabout1.5andarelargerforhigherpTmuons,becausetheresolutioninthelowmomentumregionisdominatedbymultiplescattering,whichisfairlywellmodeledinthesimulationandthuslylessaffectedbythecalibrationonresolution.Thesameprocedure,inprinciple,shouldbealsoappliedonelectrons.However,aswearegoingtosee,thislevelofcalibrationisnotquitenecessarysincetheenergyregressionandcalibrationproceduresresultinestimatedenergyuncertaintiesthatcorrectlydescribethecoreoftheenergyresolution.Asanexample,FigureBinFigure 7-3 showsthepTpullforsingleelectroninZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.33 Td[(eventsin7TeVDYMCsample,wherebothelectronpTarebetween35and45GeV,andjjisbetween0.8and1.0.Thepulldistributionisasymmetricandhasnon-Gaussiantails,andhencecannotbesimplydescribedbyaGaussiandistribution.Fittingthepulldistributionbyadouble-sidedCrystalBallfunction,onendsthatofthepulldistributionisveryclosetoone,indicatingthatthecoreresolutionoftheelectronmomentumiswellpredicted.Ontheotherhand,thepulldistributionisasymmetricandhasnon-Gaussiantails.SimilardeviationwithrespecttoaGaussiandistributionisalsoobservedinthemuons'pulldistribution,butnotasmuchaselectrons.Severalfactorscouldcontributetothisdiscrepancy.Theunderestimationoroverestimationnalstateradiation,andthepresenceofnon-uniformenergyscalebiasesasafunctionoftheleptonkinematicsandquality.Thenexttaskistoincludecalibrationonthepredicteduncertaintyforthecontributionofthenon-Gaussianfeatureoftheleptonmeasurement. 111

PAGE 112

7.1.2CorrectionsfromDileptonResonancesStudiesonsimulatedsignaleventsandonZandJ/eventsindatashowthatacalibrationoftheGaussiancoreoftheper-leptonresolutionisnotsufcienttoachieveacorrectmodelingoftheinvariantmassdistributionfrommultipleleptons.Severalfactorscontributetothisdiscrepancy.Thecontributionofthenon-Gaussiantailsatsingle-leptonleveltotheGaussiancoreofthemulti-leptonresolution,theunrecoverednalstateradiation,andthepresenceofnon-uniformenergyscalebiasesasafunctionoftheleptonkinematicsandquality.AsanexampleshowninFigure 7-4 ,atofthemassspectrumfora125GeVHiggsdecaytofourelectronsisperformedwithadouble-sidedCrystalBallfunctionwherealltheparametersareallowedtooatexceptthesigmaoftheGaussiancorewhichisxedtobetheper-eventmasserrorwithoutanycorrection.Theplotshowsthatthemodelcannotdescribetheline-shapeifusingtheper-eventmassresolutionwithoutcorrection.Acalibrationfactorfortheestimatedper-leptonmomentumresolutionisthereforedeterminedfromtstotheinvariantmassdistributionofreconstructedZdecaysindataandsimulation,inseveralregionsofpseudorapidity.Inthecaseofmuons,correctionfactorsforlowpTaredeterminedfromJ/events,wheretheresidualcorrectionsareshownindifferentpT,jjbins.Togetthecalibrationonmassresolution,ZeventsineitherdataormcareusedbyrequiringbothleptonsareinthecorrespondingpTandjjbin.WemodelthedileptonmassspectrumbytheBreit-WignerfunctiondescribingthegeneratorlevelZshapeconvolutedwithaCrystalBallfunctiondescribingthedetectoreffects.TheBreit-WignerfunctionparametersarexedbysettingthemeantobetheZmassandwidthtobethenaturalZwidth.IntheCrystalBallfunction,theCBissettobeequaltotheproductbetweenamultiplierandm,wheremistheper-eventmassresolutionincludingthecorrectionontheper-leptonmomentumuncertainties.Themultiplierisextractedby 112

PAGE 113

ttingtheabovemodeltotheline-shape.AndthiswillbeusedasthecorrectionfactorforleptonsinthecorrespondingpTandjjbin.Thesecalibrationfactors,giveninTable 7-1 andTable 7-2 areinthe5%to15%rangeformuons,andabouttwicethatsizeforelectrons,asexpectedgiventhelargernon-Gaussiantailsandthelargernon-uniformityoftheenergyscaleintheelectroncase.ThecalibrationwillbeappliedonsingleleptonmomentumresolutioninthecorrespondingpT)-304(jjbinandthenpropagatedtocalibratepredictedmulti-leptonmasses. Table7-1. Correctionfactorsfortheper-leptonmomentumuncertaintiesderivedfromZ(highpTmuonsandallpTelectrons)andJ=events(lowpTmuons)in7TeVdataandMC.Formuons,thesecorrectionsareontopofthecorrectionfactorsderivedfromsingleleptonmomentumpulldistributions. LeptonkinematicselectionDataMC MuonpT<20GeV,jj<0.81.001.06MuonpT<20GeV,0.820GeV,jj<0.81.091.16MuonpT>20GeV,0.820GeV,1.6
PAGE 114

Table7-2. Correctionfactorsfortheper-leptonmomentumuncertaintiesderivedfromZ(highpTmuonsandallpTelectrons)andJ=events(lowpTmuons)8TeVindataandMC.Formuons,thesecorrectionsareontopofthecorrectionfactorsderivedfromsingleleptonmomentumpulldistributions. LeptonkinematicselectionDataMC MuonpT<20GeV,jj<0.81.041.02MuonpT<20GeV,0.820GeV,jj<0.81.141.11MuonpT>20GeV,0.820GeV,1.6
PAGE 115

ofsingleleptonmeasurement.Andnally,themassresolutioncanbeestimatedbypropagatingcalibratedsingleleptonmomentumuncertainties.However,thisisnotenoughtoassertthatthepredictedmassresolutionreectsthetrueresolutiononanevent-by-eventbasis.WhathasbeendonesofaristomakesurethepredictedmassresolutionreectstheaverageresolutionwhenleptonsareinaparticularpT)]TJ /F3 11.955 Tf 12.52 0 Td[(bin.Tofurtherquantifythelevelofaccuracythatwecanpredictthemassresolutiononanevent-by-eventbasis,wecategorizetheZ!``dataandMCeventsbasedontheirpredictedmassresolution.Thenercategorizationonthepredictedmassresolution,thecloserthataveragemassresolutioninthecorrespondingcategorywillbetotheper-eventmassresolution.Inpractice,thetestisdonebyclassifyingtheZ!`+`)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(eventsintotencategoriesbasedonwhat(average)massresolutionwewouldpredictfortheeventsineachcategory.TheobservedresolutionisextractbyttingtheZmassshapeineachcategorywiththeconvolutedBreit-WignerandCrystalBallfunctionplusexponentialfunctionasthebackgroundmodel.ThedimuonanddielectroninvariantmassspectrumwiththeirtsareshowninFigure 7-6 andFigure 7-7 usingdataandMCZevents.FigureAinFigure 7-8 showstheobservedrelativemasspeakshiftandrelativeinstrumentalwidthforthedielectronZevents.FigureBinFigure 7-8 showstheobservedrelativemasspeakshiftandrelativeinstrumentalwidth(CrystalBallparametersdividedbythenominalZmass)forthedimuonZevents.Thedashedlinesrepresentthesystematicuncertaintythatweneedtoassigntoper-eventmassresolution.Wecansafelydrawtheconclusionthattheper-eventmassresolutioncanbepredictedwithin20%uncertaintyaroundtheobservedmassresolution.Furthermore,wedivideZeventsintotwothreecasesaccordingtothetwoleptons'pseudorapidity:barrel-barrel,barrel-endcapandendcap-endcap.Ineachcase,werepeatdividingeventsintotencategoriesaccordingtotheirpredictedmassresolution. 115

PAGE 116

AscanbeseeninFigure 7-9 ,theobservedmassresolutionarealsowithinthequotedsystematicsabove.ForZ!e+e)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(,besidesdividingeventsbasedonelectrons'jj,wealsocategorizetheeventsaccordingtothetwoelectrons'classication.Thebestcategoryismadeoftwoelectronswhichareboththeinbarrelandnon-showering.Theworstcategoryismadeoftwoelectronswhicharebothintheendcapandshowering.TherestoftheZeventsformthemediumcategory.Ineachcategory,wethenfurtherdivideeventsaccordingtothepredictedmassresolution.AscanbeseeninFigure 7-10 ,theobservedmassresolutionsarealsowithinthequotedsystematicuncertaintyabove,exceptthebestandworstcategory.However,thedieletroneventsinthesetwocategorizesarequiterarecomparedwiththeeventsintherestcategories,sothe20%isstillareasonableestimationforthesystematicsuncertainty. 7.4ClosureTestsonHiggsMonteCarloEventsAsonecansee,themeasuredandpredictedresolutionareingoodagreementwhichissafelywithinthe20%uncertaintyforZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(andZ!+)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(resolutionaftercalibration.Todemonstratewhethertheper-eventmassresolutioncalibrationfromZandJ/eventsworkfortheHiggseventswheretherearefourleptons,the8TeVHiggsMCsampleat125GeVisusedasanexampletoshowtheclosurebetweenpredictedandmeasuredresolutionanditsimprovementbythecalibration.AsshowninFigure 7-11 ,thepredictedandmeasuredresolutionhavebetteragreementaftertheper-leptonpTerrorcorrection. 7.5ModelingofPer-EventMassResolutionDistributionToincludetheper-eventmassresolutionintothestatisticalanalysis,thedistributionofper-eventmassresolutionismodeledforsignalandbackgroundfromMCeventsandfordatainthecontrolregion.Allchannelsandbothsignalandbackgrounddistributionsofper-eventmassresolutionarettedbyacombinationofLandauandGaussfunctions 116

PAGE 117

as P(m)=xLandau(relm4`,ld,ld)+(1)]TJ /F4 11.955 Tf 11.95 0 Td[(x)Gaussian(relm4`,gs,gs)(7)Figure 7-12 showsanexamplefora126GeVHiggssample,whileFigure 7-13 showsthetsforqq!ZZandgg!ZZbackgroundsamples.WethenparameterizettedparametersasafunctionofHiggsmassinordertointerpolateacrossthemassesforwhichwehavenofullsimulationwithsmoothpolynomialfunctions.Thedistributionsofper-eventmassresolutionforsignalandirreduciblebackgroundarederivedfromMCevents.Tocheckthedata-to-MCcompatibilityonper-eventmassresolutiondistribution,twocontrolregionsaredened,correspondingly.Z!4`decaysgiveacleanresonantpeakinthefour-leptoninvariantmassdistribution,whichcanbeusedasastandardcandleinthecontextoftheHiggsbosonsearchinthefour-leptondecaymode.TherstrowinFigure 7-14 showsthedistributionsofrelativemasserrordistributionfordataandMCinmasswindow80-100GeV,whereMCeventsareexpectedtobefavoredbyZ!4`events.ForZZ!4Lcontrolregion,thefour-leptonmasswindowischosentobein180-200GeVmasswindowasshowninthesecondrowinFigure 7-14 ,wherethedominanteventsareexpectedtobedibosondecay,whereMCeventsarefrom8TeVZZ2e2,ZZ4eandZZ4samples,anddatacorrespondto8TeVdataset.FromtheFigure 7-14 ,onecanseethatthereisnosignicantdiscrepancybetweendataandMCforthegivenstatistics.Forreduciblebackgrounds,weusethedataincontrolregion,weightingeacheventbyitsextrapolationfactorfromcontrolregiontosignalregionbuiltfromthesingleleptonfakerate.TheZ+X4eand2e2distributionsarettedwithacombinationofLandauandGaussianfunctions,showninFigure 7-15 usingeventsinthecontrolregionwithinamasswindowfrom120to130GeV. 117

PAGE 118

7.6StatisticalMethodologyforMassMeasurementSofar,therearethreeobservablesthatarerelevanttoHiggsmassmeasurement:four-leptoninvariantmass,matrix-element-basedkinematicdiscriminant(MEKD)andper-eventmassresolution.Forfour-leptoninvariantmass,thesignalshapeofthefour-leptoninvariantmassisdescribedastheconvolutionbetweenthedouble-CrystalBallfunctionandtherelativisticBreit-Wignerfunction.InthemassregionwheretheHiggsbosonisobserved,thenaturalwidthoftheHiggsbosonwithintheStandardModelisexpectedtobeafewMeV,muchsmallerthantheexpectedmassresolution(afewGeV).Tosimplifythemodel,theHiggsbosonisassumedtohavezerowidth,asaresult,therelativisticBreit-Wignerfunctionisreplacedbyadeltafunction.Thenthemodelofsignalfour-leptoninvariantmassshapecanbereducedto Psig(m4`jmH)=DCB(m4`jmH)pdf1(mHjmH)!DCB(m4`jmH).(7)Similartothestatisticalanalysisforexclusionlimitsandp-value,theinformationofMEKDcanbeincludedbytheproductionofp.d.f.offour-leptonmassandtwo-dimensionalDkinbkgvaluev.s.them4`template Psig(m4`DkinbkgjmH)=Pm4`sig(m4`jmH)PKDsig(Dkinbkgjm4`)(7) Pbkg(m4`Dkinbkg)=Pm4`bkg(m4`)PKDbkg(Dkinbkgjm4`),(7)wherem4`isaconditionalobservable,i.e.,PKD(Dkinbkgjm4`)isnormalizedforanygivenm4`value.Theintroductionoftheper-eventmassresolutionissomewhattricky.Forbackgroundmodel,onecansimplyignorethecorrelationbetweentheshapeofthemassspectrumandmassresolution.Becausetheshapeofthebackgroundmassspectrumisalmostatintherangethatweareinterestedin,aneventhasalmostidenticalprobabilitytomoveinoroutofanarrowmasswindowaroundagivenfour-leptonmassvalue.Therefore,thefullbackgroundmodelincludingper-eventmass 118

PAGE 119

resolutioncanbeexpressedas Pbkg(m4`,Dkinbkg,m4`)=Pm4`bkg(m4`)PKDbkg(Dkinbkgjm4`)Pm4`bkg(m4`jm4`)(7)Forsignal,anaiveconsiderationistoreplacetheofthedouble-sidedCrystal-Ballfunctionbyper-eventmassresolution Pm4`sig(m4`jmH,)!Pm4`sig(m4`jmH,m4`)Pm4`sig(m4`jmH).(7)However,thisisanimproperchoiceinthesensethatoncetheper-eventmassresolutionisabsorbedbyanintegralalongthem4`,thesignalp.d.f.usingper-eventmassresolutioncannotbereducedtotheoneusingaveragemassresolution.Thereasonforthisisthatthereissomecorrelationbetweenthetailofthedouble-CrystalBallfunctionandtheper-eventmassresolution.Toquantifythecorrelationbetweenthetailparametersandcoreresolution,eventsinsignalMCsampleswiththeHiggsmassat126GeVaresplitintofourcategoriesbasedontheirpredictedmassresolution.Themassspectrumineachcategoryisttedbyadouble-sidedCBfunctionallowingthe,LandRparameterstooat.Figure 7-16 showsthettedvaluesofL=Rasafunctionofthemassresolutionforthe4,4eand2e2channelsrespectively.ItcanbeseenthattheLandRparametersvarylinearlywiththemassresolution.Soaper-eventtailparametercanbeintroducedasebeL=aveLebe aveebeR=aveRebe ave, (7)whereaveL=R,avearetheaveragetailparametersandaveragecoreresolution,andebeistheper-eventmassresolution.Totestwhetherintroducingaper-eventtailparametercancreateamatchbetweenmodelsusingaverageresolutionandper-eventmassresolution,aclosuretestisperformedbygeneratingtoyMCdatasets:rstgeneratetoyssamplingtheper-event 119

PAGE 120

massresolutiondistribution,thenforeachtoy,generateamassinaccordancewiththedouble-sidedCBfunctionincludingbothper-eventmassresolutionandper-eventtail.TheresultsoftheclosuretestareillustratedinFigure 8-1 ,wherewecanseethatthetoydataagreeswiththeline-shapeobtainedbyttingthesignalMonteCarlosamplewithina10%variationofthemassresolutionparameter. 120

PAGE 121

Figure7-1. Singleelectronresolution.ThegureshowstheexpectedrelativeeforelectronsinthebarrelECALasafunctionofthemomentumfortheECAL-only,thetracker-only,andthecombinedestimations. A BFigure7-2. Singlemuonresolution.Thegureshowsthemuonmomentumresolutionasafunctionofjj(FigureA)andasafunctionofpT(FigureB)usingHiggsMCsamplewithmH=126GeVat8TeV. 121

PAGE 122

A BFigure7-3. Leptons'pulldistribution.ThegureshowstheRMSofmuons'1=ppulldistributiononpT)-222(jjplane(FigureA)anddistributionofelectrons'pTpulldistributionforelectronsinacerntainpT)-222(jjregion(FigureB). Figure7-4. Four-electronmassshape.Thegureshowsatofthelineshape(bluecurve)withuncorrectedper-eventmassresolutioncannotdescribemassspectrumdistribution. 122

PAGE 123

A B C D EFigure7-5. Twoapproachesforper-eventmassresolutioncalculation.Thegureshowsthecomparisonoffour-leptonmasserrorscalculatedfromthetwoapproacheson8TeV125GeVHiggssamplefor4e(FigureA),4(FigureB),2e2(FigureC),4+(FigureD)and2e2+(FigureE). 123

PAGE 124

A BFigure7-6. Examplesofdimuontsforper-eventmassresolutionvalidation.Thegureshowsthedimuoninvariantmassspectrum(points)andtswithconvolutedfunctionofBreit-WignerandCrystalBallfordataandMCZeventsusing8TeVDYMCsampleand8TeVdataset. A BFigure7-7. Examplesofdielectrontsforper-eventmassresolutionvalidation.Thegureshowsthedielectroninvariantmassspectrum(points)andtswithconvolutedfunctionofBreit-WignerandCrystalBallfordataandMCZeventsusing8TeVDYMCsampleand8TeVdataset. 124

PAGE 125

A BFigure7-8. Per-eventmassresolutionvalidationusingZevents.ThegureshowstheagreementbetweenobservedandmeasurementmassresolutionusingZ!e+e)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(dataandMC(FigureA)andZ!+)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(dataandMC(FigureB). A B C D E FFigure7-9. Zmassresolutionbasedonleptons'pseudorapidity.Thegureshowsthevalidationofthemuon(FigureA,BandC)andelectron(FigureD,EandF)momentumresolutionforbarrel-barrel(FigureAandD),barrel-endcap(FigureBandE)andendcap-endcap(FigureCandF)categoriesusingdataandMCevents. 125

PAGE 126

A B CFigure7-10. Zmassresolutionbasedonelectrons'qualities.Thegureshowsthevalidationoftheper-eventmassresolutionwhereelectronmomentumresolutionisdividedasbest(FigureA),medium(FigureB)andworst(FigureC)categoriesbasedonelectrons'qualitiesusingdataandMCevents. 126

PAGE 127

A B C D E FFigure7-11. Closuretestusingsignalevents.Thegureshowsthecorrelationbetweenmeasuredandpredictedmassresolutioninsignalevents.FigureA,BandCshowthecorrelationbetweenmeasuredandpredictedmassresolutionusingmassresolutionwithoutanyper-leptonresolutioncorrection,whileFigureD,EandFshowthecorrelationbetweenmeasuredandpredictedresolutionincludingper-leptoncorrectionformuonsandelectrons.Eventsarefrom8TeV125GeVHiggsMCsample. 127

PAGE 128

A B CFigure7-12. Signalper-eventmassresolutiondistribution.Thegureshowsthefour-leptonrelativemassresolutiondistributionsat8TeVwithmH=126GeVfor4channel(FigureA),4echannel(FigureB)and2e2channel(FigureC). A B C D E FFigure7-13. Per-eventmassresolutiondistributionoftheirreduciblebackground.Four-leptonrelativemassresolutiondistributionsandtsforqq!ZZ(FigureA,BandC)andgg!ZZMC(FigureD,EandF)samplesat8TeV. 128

PAGE 129

A B C D E FFigure7-14. Per-eventmassresolutiondistributioninthecontrolregions.Thegureshowstheper-eventmassresolutiondistributioninthecontrolregions.FigureA,BandCcorrespondtorelativemasserrordistributionfordataandmcinZ!4Lregionm4lfrom80to100GeV.FigureD,EandFcorrespondtorelativemasserrordistributionfordataandmcinZZ!4Lregionm4lfrom180to200GeV. 129

PAGE 130

A B CFigure7-15. Per-eventmassresolutiondistributionofthereduciblebackground.Thegureshowstheper-eventmassresolutiondistributionoftheredciblebackgroundfor4channel(FigureA),4echannel(FigureB)and2e2channel(FigureC). 130

PAGE 131

A B C D E FFigure7-16. Per-eventtailparameters.ThegureshowsthettedvaluesofL(left)andR(right)forthe4(FigureAandB),4e(FigureCandD),2e2(FigureEandF)channelfordifferentregionsofthemassresolution.Theerrorbarsonthex-axisindicatetherangeofmassresolutionwithinwhichsignaleventsareselectedandttedtoadouble-sidedCrystalBallfunctiontoextracttheparameters. 131

PAGE 132

CHAPTER8RESULTSONMASSANDWIDTHMEASUREMENTS 8.1ExpectedMassResultsTogettheexpectedbehaviorofmassmeasurement,toysaregeneratedaccordingtotheexpectedyieldsandprobabilitydensityfunctions(PDFs)oftheobservablesincludingm4`,Dkinbkgandper-eventmassresolutionm4`.Eachtoycanbeviewedasanensembleofobserveddata,sotheexpectationcanbeestimatedusingtheaverageoftheensembles.Tobeexplicit,weteachtoywiththelikelihoodusedforthemassmeasurementtoextractthecorrespondingbest-tmHanditsuncertaintymH,thentheaveragemHandtheaverageuncertaintyovertheensemblesareusedtodescribetheexpectedbehaviorofthemassmeasurement.ThedistributionofthepullofthettedmH,denedas(mH)]TJ /F4 11.955 Tf 13.43 0 Td[(mtrueH)=mHisusedtoestimatethebiasofthemodel.Figure 8-2 showsthedistributionofthepulldistributionforthemassmeasurementusingthe1D(L(m4l)),2D(L(m4l,m4`))and3D(L(m4l,m4`,Dkinbkg))likelihoodts.InTable 8-1 wesummarizethevaluesobtainedfromeachofthesetcongurationsforthethreechannelsseparatelyandthe4`combination.Theequivalentofthefull7and8TeVdataluminosityisassumedforthesestudies.Allarefoundtobeunbiased(withthebiasesbelow10%ofthetteduncertainty),andtheerrorsarewellestimated. Table8-1. MeanandstandarddeviationofthettedmHforthesinglechannelsandthedifferenttmethodsusinggeneratedtoys. Parameter1D(L(m4`))2D(L(m4`,m4`))3D(L(m4`,m4`,Dkinbkg)) 4mean0.000.02-0.050.02-0.050.0241.050.021.130.021.090.024emean0.070.020.050.020.010.024e0.960.021.030.031.020.032e2mean-0.070.050.010.02-0.020.022e20.970.031.080.021.070.024`mean-0.020.030.020.02-0.060.024`1.070.021.020.021.040.02 132

PAGE 133

Figure 8-3 showstheexpecteddistributionoftheuncertaintyonthettedmassmHforthecombinationofthethreechannelsforthecaseof1D(L(m4`)),2D(L(m4`,m4`))and3D(L(m4`,m4`,Dkinbkg))ts.Theimprovementfromtheinclusionoftheper-eventmassresolutionintheexpected,mostprobablevalueoftheuncertaintyisabout10%. 8.2ObservedMassResultsThelikelihoodscansovermH,whileprolingsignalstrengthasallothernuisanceparametersareshowninFigure 8-4 foralikelihoodtfor1D,2Dand3Dmodels.Foreachmodel,alikelihoodtisdonefordataseparatedinthreenalstates4e,4and2e2.Theresultofthemassmeasurementisquotedbythecentralvalueandthecorresponding1range.Thecentralvalueistakenasthebest-tvaluewhere)]TJ /F8 11.955 Tf 9.3 0 Td[(2lnL=0andthe1rangeoftheHiggsmassmeasurementcorrespondstotherangedeterminedby)]TJ /F8 11.955 Tf 9.3 0 Td[(2lnL=1.Todecomposethetotaluncertaintyintostatisticalcontributionandsystematiccontribution,alikelihoodscanwithoutprolingthenuisanceparametersisidentiedastheresultwithoutsystematicuncertaintyandthequadraturedifferencebetweenthelikelihoodwithandwithoutprolingthenuisanceparameterisusedtoestimatethesystematicuncertainty.TheresultoftheHiggsmassmeasurementissummarizedfordifferentmodelsoftsandfordataindifferentchannelsinTable 8-2 .For1DL(m4`)and2DL(m4`,m4`)t,thecentralvalueandthetotaluncertaintyarequoted.Theuncertaintyofthe3DL(m4`,m4`,Dkinbkg)tisdecomposedintosystematicuncertaintyandstatisticaluncertainty.Tounderstandthesourceofsystematicuncertainty,thesystematicuncertaintyduetoelectronandmuonenergyscaleisturnedoff,andthesystematicuncertaintyduetoleptonenergyscalealoneistakenasthequadraturedifferencebetweensystematicuncertaintywithandwithoutleptonenergyscaleuncertainty.TheresultissummarizedinTable. 8-3 astheratiobetweenthesystematicuncertaintyduetoleptonenergyscaleuncertaintyandthecentralvalueoftheHiggsmass.Thesearefoundbeberoughlyconsistentwiththeleptonenergyscaleuncertaintiesthatareput 133

PAGE 134

intothemodel,0.1%formuonsand0.3%forelectrons.Moreover,onecanseethattheleptonenergyscaledominatesthesystematicuncertainty.Thisisexpectedbecauseitdeterminesuncertaintyonthepositionofthepeakofthefour-leptonmassspectrum,whichwilltranslateintotheuncertaintyontheHiggsbosonmass. Table8-2. Best-tvaluesforthemassoftheHiggsbosonmeasuredinthe4`,`=e,nalstates,with1D,2Dand3Dlikelihoodt,respectively.Forthe1Dand2Dt,onlythetotaluncertaintyisgiven,whileforthe3Dtweseparatethecontributionfromstatisticalandsystematicuncertainty. Channel1D:L(m4`)(GeV)2D:L(m4`,m4`)(GeV)3D:L(m4l,m4`,Dkinbkg)(GeV) 4125.01+0.73)]TJ /F5 7.97 Tf 6.58 0 Td[(1.23(tot.)125.08+0.62)]TJ /F5 7.97 Tf 6.58 0 Td[(1.05(tot.)125.05+0.60)]TJ /F5 7.97 Tf 6.58 0 Td[(0.79(stat.)+0.12)]TJ /F5 7.97 Tf 6.58 0 Td[(0.13(syst.)4e126.55+1.45)]TJ /F5 7.97 Tf 6.58 0 Td[(1.41(tot.)126.56+1.54)]TJ /F5 7.97 Tf 6.58 0 Td[(1.73(tot.)126.15+1.53)]TJ /F5 7.97 Tf 6.58 0 Td[(1.62(stat.)+0.40)]TJ /F5 7.97 Tf 6.58 0 Td[(0.34(syst.)2e2126.62+1.08)]TJ /F5 7.97 Tf 6.58 0 Td[(0.91(tot.)126.34+1.05)]TJ /F5 7.97 Tf 6.58 0 Td[(0.70(tot.)126.32+0.86)]TJ /F5 7.97 Tf 6.58 0 Td[(0.61(stat.)+0.15)]TJ /F5 7.97 Tf 6.58 0 Td[(0.14(syst.)4`125.72+0.52)]TJ /F5 7.97 Tf 6.58 0 Td[(0.49(tot.)125.69+0.50)]TJ /F5 7.97 Tf 6.58 0 Td[(0.45(tot.)125.63+0.44)]TJ /F5 7.97 Tf 6.58 0 Td[(0.40(stat.)+0.15)]TJ /F5 7.97 Tf 6.58 0 Td[(0.17(syst.) Table8-3. SystematicuncertaintyduetoleptonenergyscaledividedbytheHiggsbosonmasscentralvaluein4e,4and2e2channel,respectively. 4e42e2 0.29%0.09%0.09% ThecompatibilitybetweenthetheHiggsmassmeasurementsindifferentnalstatesareshowninFigure 8-5 andmoreexplicitlyinFigure 8-6 .WecanseethattheresultofHiggsmassmeasurementsindifferentnalstatesareconsistentwiththeresultofcombiningallthreenalstateswithin1uncertainty.Finally,theresultcombingallnalstatesisshowninFigure 8-7 ,andthecentralvaluesandcorrespondinguncertaintiesaresummarizedinTable 8-4 .Theresultusingthe3D(L(m4`,m4`,Dkinbkg))likelihoodt,includingalltheinformationtomaximizethesensitivityonthemassmeasurementismH=125.6+0.4)]TJ /F5 7.97 Tf 6.59 0 Td[(0.4(stat.)+0.2)]TJ /F5 7.97 Tf 6.59 0 Td[(0.2(syst.)GeV. Table8-4. BesttvaluesforthemassoftheHiggsbosonmeasuredinthe4`,`=e,nalstates,with1D,2Dand3Dlikelihoodt,respectively.Forthe1Dand2Dt,onlythetotaluncertaintyisgiven,whileforthe3Dtweseparatethecontributionfromstatisticalandsystematicuncertainty. 1D:L(m4l)(GeV)2D:L(m4l,m4`)(GeV)3D:L(m4l,m4`,Dkinbkg)(GeV)125.72+0.52)]TJ /F5 7.97 Tf 6.58 0 Td[(0.49(tot.)125.69+0.50)]TJ /F5 7.97 Tf 6.59 0 Td[(0.45(tot.)125.63+0.44)]TJ /F5 7.97 Tf 6.58 0 Td[(0.40(stat.)+0.15)]TJ /F5 7.97 Tf 6.58 0 Td[(0.17(syst.) 134

PAGE 135

8.3ResultsonWidthMeasurementThemodelofthewidthmeasurementcanbeeasilyderivedbyextendingthemodelsofmassmeasurementthroughreplacingthedouble-sidedCBfunctionbytheconvolutionbetweentherelativisticBreit-Wignerfunctionandthedouble-sidedCBfunction.However,thepriceofthisstraightforwardextensioniscomputationallyintensiveness.TheconvolutionbetweentherelativisticBreit-Wignerfunctionandthedouble-sidedCBfunctioncannotbedoneanalytically.ThecurrentprocedureistousenumericconvolutionwithFouriertransformationimplementedbyFastFourierTransformationintheRooFitpackage[ 74 ].However,thisprocedureisshowntobethebottleneckinthecomputationespeciallyforthemodelsthatincludeper-eventmassresolution.Soinsteadofrelyingonnumericalcalculation,anapproximateevaluationoftheconvolutionintegralisproposed,whichsignicantlyreducesthecomputationtime.ThedetailscanbefoundinAppendix B .TheobservedresultsareshowninFigure 8-8 forthe1D,2Dand3Dts,intermsofa1Dlikelihoodscan,whenprolingthesignalstrengthandthemeasuredmass.Thenarrowwidthpredictionisverywellcompatiblewithdata.Thebesttresultforthe2Dand3D(especially3D,wheretheDkinbkgisused)isdifferentfromzero,whilethe1Dtoneiszero.Thisisinterpretedasbeingduetothehighweightthatsomeeventsfurtherfromthecentralvalueofthemass(125.6GeV)have,thuspullingthemeantowardshighervalues.Still,allthetsarewellconsistentwiththenarrowwidthexpectationfromSM.Thebesttwidthforthethreets,togetherwiththeupperlimitsat95%condencelevel(C.L.)arereportedinTable 8-5 .InthesameTablewealsoreporttheexpectedwidthresults,estimatedwith300toysmadebysamplingthebackgroundsfromfullsimulation.Theobservedandexpectedbest-tvaluesforwidth,togetherwiththeupperlimitsat95%C.L.arereportedinTable 8-5 ,whereonecanseethatthereisabout10%gainintheupperlimitbyincludingper-eventmassresolution.Totestthecompatibilitybetweenobservationandexpectation,theexpectedupperlimitat95%C.L.andthe1 135

PAGE 136

bandoftheupperlimitat95%C.L.arederivedfromtoys.InFigure 8-9 ,theobservedlikelihoodforwidthiscomparedwiththeexpectedupperlimit(dottedverticalbluelineandthecorresponding1band).Onecanseethattheobservedupperlimitsafelysitswithinthe1bandaroundtheexpectation. Table8-5. Best-tvaluesforthewidthoftheHiggsboson,measuredinthe4`,`=e,nalstates,with1D,2Dand3Dt.Upperlimitsat95%C.L.aregiven. Result1DL(m4`)2DL(m4`,Dkinbkg)3DL(m4`,m4`,Dkinbkg) Bestt(GeV)0.00.00.0Observedupperlimit(GeV)3.83.33.4Expectedupperlimit(GeV)4.23.12.8 136

PAGE 137

A B CFigure8-1. Closuretestofper-eventmassresolutionmodel.Thegureshowstheclosuretestofper-eventmassresolutionmodel.Toydata(dots)obtainedfromsamplingtheper-eventerrorPDFplottedontopofthePDFobtainedbyttingthesignalMonteCarlo(blueline).Theredandgreenlinesrepresent10%variationintheofthebluePDF.The4,4eand2e2channelsareshowninFigureA,FigureBandFigureC,respectively. A B CFigure8-2. Pulldistributionofexpectedmassmeasurements.ThegureshowsthedistributionofthepullsofthettedmassoftheHiggsin1D(L(m4l))(FigureA),2D(L(m4l,m4`))(FigureB),3D(L(m4l,m4`,Dkinbkg))(FigureC). 137

PAGE 138

Figure8-3. DistributionoftheuncertaintyonthettedmassoftheHiggsbosonfortoyMonteCarlosamples.DistributionoftheuncertaintyonthettedmassoftheHiggsbosonfortoyMonteCarlosamplesequivalenttoluminosityof7and8TeVdata,inthecaseofdifferenttcongurations:1D(L(m4l)),2D(L(m4l,m4`)),3D(L(m4l,m4`,Dkinbkg)).Themostprobablevalueisalsoshowninthegureforeachofthethreedistributions. A B CFigure8-4. Observedlikelihoodscanasafunctionofmassforthedifferenttsandfordifferentchannels.Thegureshowsthe1Dlikelihoodscanasafunctionofmassforthedifferenttsfor4(FigureA),4e(FigureB)and2e2(FigureC)nalstates.Solidlinesrepresentsthescanwithfulluncertaintiesincluded,dashedlinesstatisticalerroronly. 138

PAGE 139

A B CFigure8-5. Channelcompatibilityamongdifferentchannels.Thegureshowsa1Dlikelihoodscanasafunctionofmassincludingstatisticalandsystematicuncertaintiesfor1D(FigureA)analysis,2D(FigureB)and3Danalysis(FigureC).Colorsrepresentthedifferentnalstates,blackcurvethecombination.Both7and8TeVdataareconsidered.Solidlinesrepresentsthescanwithfulluncertaintiesincluded,dashedlinesstatisticalerroronly. A B CFigure8-6. Channelcompatibilitywithrespecttothethecombinationofthethreechannels.ThegureshowsthebesttvaluefortheHiggsmassinthedifferentchannels(points)andthecombinationofthethreechannels(line,witherrorbarrepresentingthe1uncertainty)forthedifferenttcongurations:1D(L(m4l))(FigureA),2D(L(m4l,m4l))(FigureB),3D(L(m4l,m4l,Dkinbkg))(FigureC).Theredlineoneachpointrepresentsthetotaluncertainty,andtheblackerrordelimitersrepresentthestatisticalerroronly. 139

PAGE 140

Figure8-7. Observed1Dlikelihoodscanasafunctionofmassfordifferentlikelihoodtmethodsforthecombinationofallnalstates.Thegureshowsthe1Dlikelihoodscanasafunctionofmassfordifferentlikelihoodtsforthecombinationofallnalstates.Solidlinesrepresentsthescanwithfulluncertaintiesincluded,dashedlinesstatisticalerroronly. Figure8-8. Observedwidth.Thegureshowsthe1DlikelihoodscanasafunctionofHiggsdecaywidthwiththe1D(L(m4l)),2D(L(m4l,m4l)),2D(L(m4l,Dkinbkg),3D(L(m4l,m4l,Dkinbkg)t. 140

PAGE 141

Figure8-9. Observedandexpectedwidthupperlimits.Thegureshowsthecomparisonbetweenexpectedupperlimitat95%C.L.withobserved1DlikelihoodscanasafunctionofHiggsdecaywidthusing3D(L(m4l,m4l,Dkinbkg))t. 141

PAGE 142

CHAPTER9OTHERPROPERTIESOFTHEOBSERVEDHIGGSBOSON 9.1SignalStrengthandConstraintsonProductionModesThesignalstrength=SM,denedasthemeasuredcrosssectionrelativetotheexpectationfortheSMHiggsboson,ismeasuredtobe=0.93+0.30)]TJ /F5 7.97 Tf 6.59 0 Td[(0.24atthebesttmassmH=125.6GeV.ThesignalstrengthmodiercanbefurtherseparatedfordifferentproductionmechanismstoprobetherelativecrosssectionsofthosemechanismscomparedtotheSM.Anaturalseparationoftheproductionmechanismswouldbetodeneacommonsignalstrengthfortheonesthatarefermioninduced(F)andfortheonesthatareWorZinducedV.Assumingthemultidimensionalmodelforeachproductionmodeisgivenbyfi(x)wherexisavectorofthedimensionsusedinthetandtheexpectedyieldfromStandardModelisgivenbyNi,thesignalpartofthelikelihoodismodiedasLH=FNggHfggH(x)+VNqqHfqqH(x)+VNZHfZH(x)+VNWHfWH(x)+FNttHfttH(x) (9)Toextractthevaluesof(V,F)amaximumlikelihoodtisperformedusingthe3Dmodelinthe0/1jetanddijetcategories.Figure 9-1 showsa2Dcontourofthebesttvaluesoftheparametersofinterestandtwocondenceintervalsof68%and95%thathavebeenderivedbyvaryingthelikelihoodbyprolednegativeloglikelihoodNLL=1.15andNLL=2.995respectively.Eachparametercanalsobemeasuredbyprolingtheothergivingaresultof: V=1.4+2.2)]TJ /F5 7.97 Tf 6.59 0 Td[(2.1,F=0.85+0.47)]TJ /F5 7.97 Tf 6.59 0 Td[(0.37, (9) wheretheerrorisgivenbya68%CLinonedimensionderivedbyvaryingthenegativeloglikelihood0.5. 142

PAGE 143

9.2ResultsofSpinandParityHypothesisTestsOnceaStandardModelHiggslikebosonisobservedattheLHC,itiscrucialtodeterminethespinandquantumnumbers.TheseparationoftheSMHiggsbosonmodelandalternativespin/parityhypothesesisstudiedusingMEKD.Asdiscussedearlier,twoobservablescanbecreatedforeachevent,DJPandDbkg.Therstobservableisusedtoseparatedifferentsignalhypothesesandthesecondemphasizessignal-to-backgroundseparation.Fromtheeventdistributionsonthe2Dplanedenedbythetwokinematicdiscriminants,wecancalculateprobabilityofdatatobecompatiblewitheithertheStandardModelHiggsbosonhypothesisoranalternativeJPhypothesis.Besidesthedistributionofkinematicdiscriminants,itisalsocrucialtosetuptheexpectedeventyieldsfordifferentspin/parityhypotheses.TheyieldofexpectedeventsNJPexp(i)inthealternativespin/parityhypothesisJPneedstoincludebothdetectoreffectsandidenticalleptoninterferenceeffect.Inaddition,thefractionof2e2eventsfJP2e2andacceptancechangesfrommodeltomodel.ThenumberofexpectedeventsthathastobecorrectedineachchannelcanbeestimatedasNJPexp(i)=NJPreco NGenf0+2e2 fJP2e2 (9)whereNJPreco(i)isthenumberofeventsselectedusingthecorrespondingspin/parityMCsampleinagivenchanneliassumingthesametotalcross-sectionasaSMHiggs,andNJPGenisthetotalnumberofeventssimulated,NJPGen=PiNJPGen(i).Ontheotherhand,wecanalsochoosetopreservethetotalexpectedyieldafteralldetectoreffects,theyieldforeachmodelcanbescaledbyaconstantfactoroverdifferentnalstatesasNJPnorm(i)=norm(i)N0+exp(i) (9)Wherenorm(i)iscomputedasnorm(i)=NJPexp(i) N0+exp(i)PN0+exp(j) PNJPexp(k) (9) 143

PAGE 144

Finally,therstchoiceisusedtoseparateStandardModelHiggsandCP-oddboson;fortheothermodels,theexpectedyieldsareestimatedwiththesecondoptions. 9.2.1ResultsforSpinandParityHypothesisTestingThedistributionDbkgisshowninFigure 9-2 .AndinFigure 9-3 theDJPobservablesforalltestedhypothesesincludingtheproductionindependenthypothesesareshown.(TheproductionindependentMEKDisbuiltfromaspecialmatrixelementwhichiscalculatedbyintegratingtheregularmatrix(square)overtheproductionangle.)Thedistributionofteststatistic,denedasq=)]TJ /F8 11.955 Tf 9.3 0 Td[(2ln(LJP=LSM)isderivedbygeneratingtoysconsistofbackgroundandsignaleventsoftwotypes(StandardModelHiggsandJP)formH=126GeVwherethesignalyieldsareallowedtooatindependentlyforeachsignaltypeandthenuisanceparametersfortwohypothesesaretreatedasindependent.ThecompatibilitybetweendataandStandardModelHiggsiscomputedasCLsvaluebycomparingtheobservedteststatisticsanddistributionsofStandardModelHiggs'sandalternativespin/parityhypothesis'steststatistics.ThenalresultsarepresentedinTable 9-1 ,showinganobserveddeviationfromanaverageexpectationforanalternativehypothesisof4especiallyfor2+mqq,1+,and1)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(. 9.2.2ResultsofCPViolationMeasurementInadditiontohypothesisseparationtests,themeasurementoftheCPviolationcontributiontothedecayamplitude,expressedasthefractiontothedecayrateismeasured.Theresultsofthefractionfa3measurementisshowninFigure 9-4 withanobservedupperlimitof0.47at95%C.L.. 144

PAGE 145

Table9-1. Listofmodelsusedinanalysisofspin-parityhypothesescorrespondingtothepurestatesofthetypenoted.Theexpectedseparationisquotedfortwoscenarios,whenthesignalstrengthforeachhypothesisispre-determinedfromthettodataandwheneventsaregeneratedwithSMexpectationforthesignalyield(=1).Theobservedseparationquotesconsistencyoftheobservationwiththe0+modelorJPmodel,andcorrespondstothescenariowhenthesignalstrengthispre-determinedfromthettodata.ThelastcolumnquotesCLsvaluefortheJPmodel. JPmodelJPproductionexpect(=1)obs.0+obs.JPCLs 0)]TJ /F1 11.955 Tf 19.04 -4.34 Td[(any2.4(2.7))]TJ /F1 11.955 Tf 9.3 0 Td[(0.9+3.80.05%0+hany1.7(1.9)0.0+2.14.5%1)]TJ /F4 11.955 Tf 19.04 -4.34 Td[(qq!X2.7(3.3))]TJ /F1 11.955 Tf 9.3 0 Td[(1.4+4.70.002%1)]TJ /F1 11.955 Tf 19.04 -4.34 Td[(any2.5(3.3))]TJ /F1 11.955 Tf 9.3 0 Td[(1.8+4.90.001%1+qq!X2.1(2.7))]TJ /F1 11.955 Tf 9.3 0 Td[(1.5+4.10.02%1+any2.1(2.6)-2.1+4.80.004%2+mgg!X1.9(1.7))]TJ /F1 11.955 Tf 9.3 0 Td[(1.1+3.00.9%2+mqq!X1.7(2.0))]TJ /F1 11.955 Tf 9.3 0 Td[(1.7+3.80.2%2+many1.5(1.6))]TJ /F1 11.955 Tf 9.3 0 Td[(1.6+3.40.7%2+bgg!X1.6(1.9))]TJ /F1 11.955 Tf 9.3 0 Td[(1.4+3.40.5%2+hgg!X3.8(4.1)+1.8+2.02.3%2)]TJ /F7 7.97 Tf 3.32 -8.28 Td[(hgg!X4.0(4.5)+1.0+3.20.09% 145

PAGE 146

Toextractthevaluesof(V,F)amaximumlikelihoodtisperformedusingthe3Dmodelinthe0/1jetanddijetcategories. Figure9-1. Likelihoodcontoursonthesignalstrengthmodiers.Thegureshowsthelikelihoodcontoursonthesignalstrengthmodiersassociatedwithfermions(F)andvectorbosons(V)at68%and95%C.L.. Figure9-2. DistributionofDbkg.ThegureshowsthedistributionofDbkgindataandMCexpectationsforthebackgroundandforasignalresonanceconsistentwithSMHiggsbosonatmH=126GeV. 146

PAGE 147

A B C D E F G H I J K LFigure9-3. DistributionsofDJP.ThegureshowsthedistributionsofDJPwithDbkg>0.5.Distributionsindata(pointswitherrorbars)andexpectationsforbackgroundandsignalareshown.FigureA,BandCcorrespondtoJP=0)]TJ /F8 11.955 Tf 7.08 -4.34 Td[(,1)]TJ /F8 11.955 Tf 7.08 -4.34 Td[(,2+m(gg),FigureD,E,Fcorrespondsto0+h,1+,2+m(qq),FigureG,H,IcorrespondstoJP=2+b,2)]TJ /F7 7.97 Tf 0 -8.28 Td[(h,2+handFigureJ,K,LcorrespondstoproductionindependenttestsofJP=1)]TJ /F8 11.955 Tf 7.08 -4.34 Td[(,1+,2+m,respectively. 147

PAGE 148

Figure9-4. Resultoffa3measurement.Thegureshowsthelikelihoodscanof)]TJ /F8 11.955 Tf 9.3 0 Td[(2lnLin1D(left)asafunctionoffa3,wherefa3isthefractionofobserved0)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(events. 148

PAGE 149

CHAPTER10CONCLUSIONThepropertiesofaHiggsbosoncandidateintheHZZ4Ldecaychannel,withL=e,,arestudiedusingdatafromproton-protoncollisionsattheLHCcorrespondingtoanintegratedluminosityof5.05fb)]TJ /F5 7.97 Tf 6.58 0 Td[(1atcenter-of-massenergyp s=7TeVand19.7fb)]TJ /F5 7.97 Tf 6.59 0 Td[(1atp s=8TeV,recordedwiththeCMSdetector.Thenewbosonisobservedasanarrowresonancewithalocalsignicanceof6.8standarddeviations.Theanalysisusesthematrixelementmethod,whichallowsforenhancingthesearchsensitivitybyabout15%atthelowmassrangeandforestablishingspinandparityquantumnumbersoftheobservedboson,whicharefoundtobeconsistentwiththeexpectationsfortheStandardModelHiggsboson.ThepresenceofanadditionalStandardModellikeHiggsbosonwithamassbetween114.5GeVand119.0GeVor129.5GeVand832.0GeVisruledoutata95%condencelevel.Theproductioncrosssectionofthenewbosontimesthebranchingfractiontofourleptonsismeasuredtobe0.93+0.26)]TJ /F5 7.97 Tf 6.59 0 Td[(0.23(stat.)+0.13)]TJ /F5 7.97 Tf 6.59 0 Td[(0.09(syst.)timesthatpredictedbythestandardmodel.Per-eventfour-leptonmassuncertaintiesareusedinevaluationofthemassandwidthoftheobservedHiggsbosoncandidateandareshowntoimprovetheprecisionofthesemeasurementsbyabout10%.ThemassoftheobservedbosonismeasuredtobemH=125.60.4(stat.)0.2(syst.)GeV,whileitstotalwidthisconstrainedtobelessthan3.4GeVatthe95%condencelevel. 149

PAGE 150

APPENDIXAVALIDATIONONSIGNALMASSSPECTRUMPARAMETERINTERPOLATION A.1ParameterInterpolationofSignalMassSpectrumModelThesixdouble-sidedCrystalBallparameterinterpolationsareshowinFigures A-1 ,Figures A-3 ,Figure A-2 andFigures A-4 forallthesimulatedmassbinsat7and8TeV,respectively. A.2ValidationoftheSignalModelInterpolationWeshowinFigure A-5 andFigure A-6 thevalidationofthePDFsinterpolatedwiththefunctionforsomerepresentativemassesintherangemHfrom120to1000GeVfor8TeVsamples.ThepointsrepresentthedistributionsobtainedfromfullsimulationforthesomeofthediscretemasspointsforwhichwehavetheMonteCarlo,whilethecurvessuperimposedarearetheinterpolatedPDF.AgoodagreementisobservedbetweenthechosenanalyticalPDFandtheactualdistribution.Resultsfor7TeVsamplesareverysimilar.FormassesmH800GeVtheagreementbetweentheinterpolatedPDFandtheMCdistributionisnotverygoodonthetails,duetoanonsmoothbehaviorofthetail.WedidnotintroducedamorecomplicatedparameterizationforthesemassesbecausethedifferencebetweentheinterpolatedPDFandthedistributionissmallerthanthetheoreticalshapeuncertainty. 150

PAGE 151

A B C D E F G H I J K LFigureA-1. Thegureshowsthelinearandconstanttsoftheparametersdescribingf(m4ljmH)asafunctionofmHformH<400GeVat7TeV.FigureA,BandCrepresentmean,FigureD,EandFrepresent,FigureG,HandIrepresent1,andFigureJ,KandLrepresentn1for4,4eand22eevents,respectively. 151

PAGE 152

A B C D E F G H I J K LFigureA-2. Thegureshowsthelinearandconstanttsoftheparametersdescribingf(m4ljmH)asafunctionofmHformH<400GeVat8TeV.FigureA,BandCrepresentmean,FigureD,EandFrepresent,FigureG,HandIrepresent1,andFigureJ,KandLrepresentn1for4,4eand22eevents,respectively. 152

PAGE 153

A B C D E F G H I J K LFigureA-3. Thegureshowsthelinearandconstanttsoftheparametersdescribingf(m4ljmH)asafunctionofmHformH400GeVat7TeV.FigureA,BandCrepresentmean,FigureD,EandFrepresent,FigureG,HandIrepresent1,andFigureJ,KandLrepresentn1for4,4eand22eevents,respectively. 153

PAGE 154

A B C D E F G H I J K LFigureA-4. Thegureshowsthelinearandconstanttsoftheparametersdescribingf(m4ljmH)asafunctionofmHformH400GeVat8TeV.FigureA,BandCrepresentmean,FigureD,EandFrepresent,FigureG,HandIrepresent1,andFigureJ,KandLrepresentn1for4,4eand22eevents,respectively. 154

PAGE 155

A B C D E F G H I J K LFigureA-5. Thegureshowstheprobabilitydensityfunctionsf(m4ljmH)fortheHiggsbosonmassatthereconstructionlevelafterthefullleptonandeventselectionsareapplied.Thedistributionsobtainedfrom8TeV,massrangemHbetween115and400GeVMCsamplesaresuperimposedwiththeinterpolatedmodel.FromFigureA,BandCusemH=120GeVMCsample.FigureD,EandFusemH=126GeVMCsample.FigureG,H,IusemH=160GeVMCsample.FigureJ,K,LusemH=300GeVMCsample. 155

PAGE 156

A B C D E F G H I J K LFigureA-6. Thegureshowstheprobabilitydensityfunctionsf(m4ljmH)fortheHiggsbosonmassatthereconstructionlevelafterthefullleptonandeventselectionsareapplied.Thedistributionsobtainedfrom8TeV,massrangemHbetween115and400GeVMCsamplesaresuperimposedwiththeinterpolatedmodel.FromFigureA,BandCusemH=450GeVMCsample.FigureD,EandFusemH=500GeVMCsample.FigureG,H,IusemH=800GeVMCsample.FigureJ,K,LusemH=1000GeVMCsample. 156

PAGE 157

APPENDIXBANALYTICALAPPROXIMATIONFORTHEDOUBLE-SIDEDCRYSTALBALLANDBREIT-WIGNERCONVOLUTIONTheCrystalBallfunctioncanberewrittenasaGaussianextendingoverthefullrangeofxplusafunctionthatdescribesthetailstructureasfCB(x;,n,s,)=G(x;s,)+Tx;,n,s, (B)G(x;s,)=e)]TJ /F13 5.978 Tf 7.78 3.86 Td[((x)]TJ /F10 5.978 Tf 5.75 0 Td[(s)2 22for)-222(1<>:A(B)]TJ /F7 7.97 Tf 13.15 4.7 Td[(x)]TJ /F7 7.97 Tf 6.59 0 Td[(s )]TJ /F7 7.97 Tf 6.59 0 Td[(n))]TJ /F4 11.955 Tf 11.96 0 Td[(e)]TJ /F13 5.978 Tf 7.79 3.86 Td[((x)]TJ /F10 5.978 Tf 5.76 0 Td[(s)2 22ifx)]TJ /F7 7.97 Tf 6.59 0 Td[(s )]TJ /F3 11.955 Tf 21.92 0 Td[(0otherwise9>=>; (B)TheCrystalBallfunctiondecomposedintotheGaussianandtailcanbeseeninFigure B-1 .TheBreit-Wignerfunctionisdenedasfollows fBW(x;m,!)=! [(x)]TJ /F4 11.955 Tf 11.96 0 Td[(m)2+!2](B)TheconvolutionoftheCrystalBallfunctionandBreit-WignerfunctionscanbewrittenintermsoftheGaussianandtailfunctionsas: fCBBW(x)=Z1G(x)]TJ /F4 11.955 Tf 11.95 0 Td[(y)fBW(y)dy+Z1T(x)]TJ /F4 11.955 Tf 11.95 0 Td[(y)fBW(y)dy(B)TheconvolutionoftheGaussandBreit-WignerfunctionsiscalledtheVoigtianfunctioninRooFitpackage[ 74 ]ofwhichthenormalizationcanbedoneinananalyticalway.However,theconvolutionintegralofthetailfunctioninEquation B andBreit-Wignercannotbeevaluatedanalyticallyintermsofanyknownfunctionalforms.Therefore,werecastthetailfunctionusinganapproximationofitsactualshapeandusetheapproximationtoevaluatetheconvolutionintegralanalytically.Thisapproximateformof 157

PAGE 158

thetailfunctionisasT(x;,n,s,)=8>>>><>>>>:A(B)]TJ /F7 7.97 Tf 13.15 4.7 Td[(x)]TJ /F7 7.97 Tf 6.59 0 Td[(s )]TJ /F7 7.97 Tf 6.59 0 Td[(n)ifx)]TJ /F7 7.97 Tf 6.59 0 Td[(s )]TJ /F3 11.955 Tf 21.91 0 Td[()]TJ /F3 11.955 Tf 11.96 0 Td[(c1(x)]TJ /F7 7.97 Tf 6.59 0 Td[(s +)2+c2(x)]TJ /F7 7.97 Tf 6.59 0 Td[(s +)if)]TJ /F3 11.955 Tf 11.95 0 Td[()]TJ /F3 11.955 Tf 11.96 0 Td[(>>>=>>>>; (B)Themotivationforthisformisthefollowing.Whenxisfarfromthepeak,thevalueofT(x)isdominatedthepowerlawsincetheGaussianexponentialdiesoffmorequickly.Hence,inthisregionthevalueofT(x)canbeapproximatedfromthepowerlawalone.TherangeofxinwhichthepowerlawisagoodapproximationforT(x)isdeterminedbytheparameterinEquation( B ).Intherange)]TJ /F3 11.955 Tf 9.29 0 Td[()]TJ /F3 11.955 Tf 12.4 0 Td[(
PAGE 159

T2(x)=Z)]TJ /F6 7.97 Tf 6.59 0 Td[()]TJ /F6 7.97 Tf 6.58 0 Td[()]TJ /F6 7.97 Tf 6.59 0 Td[((c1(x)]TJ /F7 7.97 Tf 6.59 0 Td[(s +)2+c2(x)]TJ /F7 7.97 Tf 6.58 0 Td[(s +))!dy [(y)]TJ /F4 11.955 Tf 11.95 0 Td[(m)2+!2] (B)TheintegralT2(x)canbeexpressedinaclosedformwhileT1(x)canonlybeexpressedinarecursiveformforintegervaluesofnusingtherecurssionrelation.Theproceduredescribedsofarhasbeensetupforasingle-sidedCrystalBallfunctionwhichcanbeextendedfortheHiggsanalysis,wherethesignallineshapeistheconvolutionofadouble-sidedCrystalBallfunctionconvolvedwithaBreit-Wignerfunction.Figure B-3 showsthecomparisonbetweenfCBBWshapesobtainedusingantheanalyticalapproximationforaCrystalBallfunctionwiths=0,=1,L=R=1,nL=nR=2andBreit-Wignerfunctionwithm=0,!=1. 159

PAGE 160

FigureB-1. DecompostionofaCrystal-Ballfunction.ThegureshowsthattheCrystalBallfunction(blackcurve)canbewrittenasasumoftheGaussiancore(bluecurve)andthetail(redcurve). FigureB-2. ApproximateCrystalBallfunction.Thegureshowsthatthetailfunction(redcurve)oftheCrystalBallfunction(blackcurve)canbeapproximatedasthegreencurveandthecorrespondingCBshapeobtainedonaddingthegreencurvewiththecoreGaussian(bluecurve)isshownbytheorangecurve.=2.3isusedforobtainingthegreenandorangecurves. 160

PAGE 161

FigureB-3. ComparisonbetweenapproximateandexactCrystalBallfunction.Thegureshowsthecomparisonbetweenthelineshapesobtainedbyperformingtheconvolutionofadouble-sidedCrystalBallfunctionwiththeBreit-WignerfunctionusingFFT(redcurve)andusingtheanalyticalapproximation(bluecurve). 161

PAGE 162

REFERENCES [1] P.W.Higgs,Phys.Lett.12,132(1964). [2] F.EnglertandR.Brout,Phys.Rev.Lett.13,321(1964). [3] P.W.Higgs,Phys.Rev.Lett.13,508(1964). [4] G.Bhattacharyya,Rept.Prog.Phys.74,026201(2011). [5] LHCHiggsCrossSectionWorkingGroup,CERNReportNo.CERN-2011-002,2011.[ http://cdsweb.cern.ch/record/1318996 ]. [6] T.Plehn,arXiv:0910.4182. [7] ALEPHCollaboration,DELPHICollaboration,L3Collaboration,OPALCollaboration,andTheLEPWorkingGroupforHiggsBosonSearches,Phys.Lett.B565,61(2003). [8] TevatronNewPhenomenaandHiggsWorkingGroupfortheCDFandD0Collaborations,arXiv:0903.4001. [9] H.Flacher,M.Goebel,J.Haller,A.Hoecker,K.Monig,andJ.Stelzer,Eur.Phys.J.C60,543(2003). [10] J.Ellisa,J.R.Espinosaa,G.F.Giudicea,A.Hoeckera,andA.Riotto,Phys.Lett.B79,369(2009). [11] O.S.Bruning,P.Collier,P.Lebrun,S.Myers,R.Ostojic,J.Poole,andP.Proudlock,ReportNo.CERN-2004-003-V-1,2004.[ http://cdsweb.cern.ch/record/782076 ]. [12] CMSCollaboration,JINST3,S08004(2008). [13] G.Bolla,D.Bortoletto,C.Rott,A.Roy,S.Kwan,C.Y.Chien,H.Cho,B.Gobbi,R.Horisberger,andR.Kaufmann,Nucl.Instrum.Meth.A461,182(2001). [14] K.Arndt,G.Bolla,D.Bortoletto,K.Giolo,R.Horisberger,A.Roy,T.Rohe,andS.Son,Nucl.Instrum.Meth.A511,106(2003). [15] L.Borrello,A.Messineo,E.Focardi,andA.Macchiolo,CMSNoteReportNo.CMS-NOTE-2003-020,2003.[ http://cdsweb.cern.ch/record/687861 ]. [16] J.L.Agrametal.,Nucl.Instrum.Meth.A517,77(2004). [17] A.A.Annenkov,M.V.KorzhikandP.Lecoq,Nucl.Instrum.Meth.A490,30(2002). [18] R.Loosetal.,ConferenceReportNo.CMS-2000-054-MEETING,CERN-ECAL-EDR-4,2000.[ http://cdsweb.cern.ch/record/539819 ]. [19] G.CharpakandF.Sauli,Nucl.Instrum.Meth.113,381(1973). 162

PAGE 163

[20] J.Beringeretal.(ParticleDataGroup),Phys.Rev.D86,010001(2012). [21] S.Bafoni,C.Charlot,F.Ferri,D.Futyan,P.Meridiani,I.Puljak,Ivica,C.Rovelli,R.Salerno,Y.Sirois,CMSNoteReportNo.CMS-NOTE-2006-040,2006.[ http://cdsweb.cern.ch/record/934070 ]. [22] CMSCollaboration,CMSPhysicsAnalysisSummaryReportNo.CMS-PAS-EGM-10-004,2010.[ http://cdsweb.cern.ch/record/1299116 ]. [23] CMSCollaboration,CMSDetectorPerformanceSummaryReportNo.CMS-DP-2011-003,2011.[ http://cdsweb.cern.ch/record/1360227 ]. [24] CMSCollaboration,ReportNo.CMS-HIG-13-002,CERN-PH-EP-2013-220,2013.[ http://cdsweb.cern.ch/record/1637951 ]. [25] M.CacciariandG.P.Salam,Phys.Lett.B/bf659,119(2008). [26] M.Cacciari,G.P.Salam,andG.Soyez,J.HighEnergyPhys.04(2008)005. [27] M.S.MauroDonega,DavidFutyan,CMSPhysicsAnalysisSummaryReportNo.CMS-PAS-HIG-13-001,2013.[ http://cdsweb.cern.ch/record/1530524 ]. [28] CMSCollaboration,JINST7,10002(2012). [29] R.Fruhwirth,Nucl.Instrum.Meth.A.262,444(1987). [30] CMSCollaboration,CMSPhysicsAnalysisSummaryReportNo.CMS-PAS-PFT-10-003,2010.[ http://cdsweb.cern.ch/record/1279347 ]. [31] CMSCollaboration,CMSPhysicsAnalysisSummaryReportNo.CMS-PAS-PFT-09-001,2009.[ http://cdsweb.cern.ch/record/1194487 ]. [32] CMSCollaboration,CMSPhysicsAnalysisSummaryReportNo.CMS-PAS-PFT-10-002,2010.[ http://cdsweb.cern.ch/record/1279341 ]. [33] M.Cacciari,G.P.Salam,andG.Soyez,J.HighEnergyPhys./bf4(2008)63. [34] M.CacciariandG.P.Salam,Phys.Lett.B659,119(2008). [35] CMSCollaboration,CMSPhysicsAnalysisSummaryReportNo.CMS-PAS-JME-10-010,2010.[ http://cdsweb.cern.ch/record/1308178 ]. [36] CMSCollaboration,CMSPhysicsAnalysisSummaryReportNo.CMS-PAS-LUM-13-001,2013.[ http://cdsweb.cern.ch/record/1598864 ]. [37] S.Frixione,P.Nason,andC.Oleari,arXiv:0709.2092. [38] D.deFlorian,G.Ferrera,M.Grazzini,andD.Tommasini,J.HighEnergyPhys.1206(2012)132. 163

PAGE 164

[39] H.L.Lai,J.Huston,Z.Li,P.Nadolsky,J.Pumplin,etal.,Phys.Rev.D82,054021(2010). [40] J.Gao,M.Guzzi,J.Huston,H.-L.Lai,Z.Li,etal.,arXiv:1302.6246 [41] T.Sjostrand,S.Mrenna,andP.Skands,J.HighEnergyPhys.0605(2006)026. [42] S.Bolognesi,Y.Gao,A.V.Gritsan,K.Melnikov,M.Schulze,N.V.Tran,andA.Whitbeck,Phys.Rev.D86,095031(2012). [43] T.Binoth,N.Kauer,andP.Mertsch,arXiv:0807.0024. [44] J.Alwall,M.Herquet,F.Maltoni,O.Mattelaer,andT.Stelzer,J.HighEnergyPhys.06(2011)128. [45] Campbell,JohnM.andEllis,R.K.,Nucl.Phys.Proc.Suppl.205,10(2010). [46] S.Alekhinetal.,arXiv:1101.0536. [47] A.D.Martin,W.J.Stirling,R.S.ThorneandG.Watt,Eur.Phys.J.C63,189(2009). [48] R.D.Ball,L.DelDebbio,S.Forte,A.Guffanti,J.I.Latorre,J.RojoandM.Ubiali,Nucl.Phys.B838,136(2010). [49] S.Goria,G.Passarino,andD.Rosco,Nucl.Phys.B864,530(2012). [50] G.Passarino,J.HighEnergyPhys.08(2012)146. [51] A.V.ManoharandW.J.Waalewijn,arXiv:1202.5034. [52] B.Humpert,R.Odorico,Phys.Lett.B154,211(1985). [53] L.Ametller,N.Paver,andD.Treleani,Phys.Lett.B169,289(1986). [54] TheATLASCollaboration,ATLASNoteReportNo.ATLAS-CONF-2011-160,2011.[ http://cdsweb.cern.ch/record/1404953 ]. [55] T.Sjostrand,S.Mrenna,andP.Skands,arXiv:0710.3820. [56] A.SoniandR.Xu,Phys.Rev.D48,5259(1993). [57] V.D.Bargeretal.,Phys.Rev.D49,79(1994). [58] S.Choietal.,Phys.Lett.B553,6(2003). [59] B.Allanachetal.,J.HighEnergyPhys.0212(2002)039. [60] C.Buszelloetal.,Eur.Phys.J.C32,209(2004). [61] R.M.Godbole,D.J.Miller,andM.M.Muhlleitner,J.HighEnergyPhys.12(2007)031. 164

PAGE 165

[62] W.-Y.Keung,I.Low,andJ.Shu,Phys.Rev.Lett.101,091802(2008). [63] O.AntipinandA.Soni,J.HighEnergyPhys.102008018. [64] K.Hagiwara,Q.Li,andK.Mawatari,J.HighEnergyPhys.07(2009)101. [65] Y.Gao,A.V.Gritsan,Z.Guo,K.Melnikov,M.Schulze,andN.V.Tran,Phys.Rev.D81,075022(2010). [66] J.S.Gainer,K.Kumar,I.Low,andR.Vega-Morales,J.HighEnergyPhys.11(2011)027. [67] Y.Chen,N.Tran,andR.Vega-Morales,J.HighEnergyPhys.01(2013)182. [68] P.Avery,D.Bourilkov,M.Chen,T.Cheng,A.Drozdetskiy,J.S.Gainer,A.Korytov,K.T.Matchev,P.Milenovic,G.Mitselmakher,M.Park,andA.Rinkevicius,Phys.Rev.D87,055006(2012). [69] CMSCollaboration,Phys.Lett.B716,30(2012). [70] CMSCollaboration,Phys.Rev.Lett.110,081803(2013). [71] TheATLASandCMSCollaborationsandtheLHCHiggsCombinationGroup,ReportNo.ATL-PHYS-PUB-2011-11,CMSNOTE-2011/005,2011.[ http://cdsweb.cern.ch/record/1379837 ]. [72] A.L.Read,J.Phys.G28,2693(2002). [73] CMSCollaboration,J.HighEnergyPhys.12(2012)034. [74] W.VerkerkeandD.Kirkby,arXiv:0306116. 165

PAGE 166

BIOGRAPHICALSKETCH TongguangChengwasborninSeptember1984,inBeijing,China.Heattendedlocalpublicschoolstherethroughhighschool.InSeptember2002,heenrolledatthePhysicsDepartmentofTsinghuaUniversity.InJune2006,hegraduatedandobtainedhisBachelorofSciencedegree.InSeptember2006,hejoinedthegroupofProfessorYongGuoatthesamedepartmenttostudycondensedmatterphysicsandinJune2008,hewasawardedhisMasterofSciencedegree.InAugust2008,heewtoGainesvilletostartgraduateschoolattheDepartmentofPhysicsattheUniversityofFlorida.Inthespringof2011,hejoinedCMSgroupattheUniversityofFloridatostudyHiggsphysicsattheLHC.HereceivedhisPh.D.fromtheUniversityofFloridainthespringof2014. 166