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Reconstruction of Missing Transverse Energy and Prospect of Searching for Higgs Boson Produced via Vector Boson Fusion i...

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PAGE 4

Firstofall,Iwouldliketoappreciatemywife,Ban,fortheendlessloveandsupportshegaveme.Shetookcareofthefamily,didanexcellentworkinthejob,andneverlosthumorsduringhardtime.Thisthesiswouldhavebeenimpossiblewithouther.Iwouldasloliketoappreciatemyparents,whogavemelifeandalwaysbelievetheirson.Iwouldalsoliketoappreciatemyparentsin-law,sistersandotherfamilymembersinChinafortheirsupport.Iwouldliketoexpressmydeepgratitudetomyadvisor,PaulAvery,forhisinstruction,support,encouragementandmanyinteruptionsonhisworkbecauseofmythesisstudy.Hegavemethepowertoestablishthecollaborationandexploitnewideas,whichexactlymatchedwithmyworkingstyle.IwouldliketosincerelythankJohnYelton,DarinAcosta,AndrewKorytov,RickFieldandGuenakhMitselmakherforthewonderfuldiscussion.John'sadviceswerealwayssouseful.SomtimesIcouldn'thelpknockhisdoor.Darin'ssupportwassocriticalandhelpful.IwouldliketoexpressmydeepgratitudetoJamesRohlfandChristopherTully.TheirsupportonmyworkwaspartofthereasonIcangetthisfar.Iwasluckytogettherighthelpfromtherightpeopleattherighttimeandrightplace.Ialsobenetedalotfromalarge,strongandintelligentgroupbuiltbyPaul.IappreciateJorgeRodriguezforprovidingcomputingresources,CraigPrescottforsuccessfullymanagingtheMonteCarloproduction,RichardCavanaughandDimitriBourilkovforgivingvaluablesuggestionsinphysicsandgridsupport,andYuFuformanyhelpoftuningupthesystem. iv

PAGE 5

page ACKNOWLEDGMENTS ............................. iv LISTOFTABLES ................................. vi LISTOFFIGURES ................................ vii ABSTRACT .................................... viii CHAPTER 1INTRODUCTION .............................. 1 1.1StandardModelandPredictionofHiggsBoson ........... 2 1.2HiggsBosonProductionviaVectorBosonFusion .......... 5 1.3AnalysisGoal .............................. 8 2HIGGSPHYSICSATLARGEHADRONCOLLIDER .......... 10 2.1HiggsBosonProductionandDecay .................. 10 2.2HiggsBosonSearchStrategy ...................... 12 2.3HiggsBosonDiscoveryPotentialatCMS ............... 14 3OVERIEWOFCOMPACTMUONSOLENOIDEXPERIMENT .... 19 3.1TheCMSDetector ........................... 19 3.1.1InnerTrackerandBasicPerformance ............. 20 3.1.2ElectromagneticCalorimeterandBasicPerformance ..... 21 3.1.3HadronicCalorimeterandBasicPerformance ......... 23 3.1.4MuonDetectorandBasicPerformance ............ 24 3.2TriggerandReconstruction ...................... 26 3.2.1DataAcquisitionDesignandLevel-1Trigger ......... 26 3.2.2HighLevelTriggerandReconstruction ............ 30 4JETENERGYDISTRIBUTIONANDCORRECTIONSTUDY ..... 37 4.1DataSamples .............................. 39 4.2DenitionofJetEnergyResolution .................. 41 4.3JetEnergyDistribution ........................ 44 4.3.1CalorimeterResponse ...................... 44 4.3.2ParameterizationofJetEnergyDistribution ......... 45 4.3.3JetEnergyDistributionBasedonEnergyFractionScheme 46 v

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. 53 4.3.5CorrectionPotentialandSensitivity .............. 55 4.4CorrectionMethod ........................... 55 4.4.1JetReconstruction ....................... 55 4.4.2CorrectionFunction ....................... 56 4.4.3FittingoftheCorrectionFunction ............... 62 4.5ResultsandDiscussion ......................... 63 4.5.1JetEnergyResponseinthejj<3.0Region ......... 64 4.5.2JetpTSpectruminthejj<3.0Region ........... 65 4.5.3JetpTResolutioninthejj<3.0Region ........... 67 4.5.4PerformanceofCorrectioninthejj3.0Region ...... 72 4.5.5StabilityoftheCorrectionAlgorithmandJetSelection ... 73 4.6Summary ................................ 76 5STUDYOFMISSGINGTRANSVERSEENERGYINQCDEVENTS 78 5.1MissingTransverseEnergySpectrum ................. 80 5.2MissingTransverseEnergyResolution ................ 87 5.3MissingTransverseEnergyfromJetsandUnclusteredTowers ... 92 5.4CorrelationBetweenJetsandMissingTransverseEnergy ...... 100 5.5EectofTowerEnergyThreshold ................... 107 5.6PossibilityofExcludingUnclusteredRegion ............. 111 5.7Summary ................................ 112 6MISSINGTRANSVERSEENERGYCORRECTIONINLEPTONICEVENTS ................................... 114 6.1DataSamples .............................. 115 6.2CorrectionbyMuon .......................... 117 6.2.1BasicAlgorithm ......................... 118 6.2.2ReconstructionandSystematicEect ............. 118 6.2.3TrackCorrectioninHighRegion ............... 121 6.2.4Results .............................. 124 6.3CorrectionbyElectron ......................... 124 6.3.1BasicAlgorithm ......................... 126 6.3.2SystematicEect ........................ 126 6.4CorrectionAlgorithmBasedonJet .................. 129 6.4.1JetReconstructionandSelection ................ 129 6.4.2BasicAlgorithm ......................... 132 6.4.3JetEnergyResponseScheme .................. 133 6.4.4DevelopmentofJetEnergyCorrection ............ 135 6.5OptimizationofJetCorrection .................... 137 6.5.1OptimizationofJetETThresholdandConeSize ....... 137 6.5.2Channel-DependentTuning ................... 140 6.6CorrectionMethodforPileupandUnderlyingEect ......... 144 6.6.1AverageTransverseEnergyforUnclusteredRegion ...... 145 vi

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............. 147 6.7ImplementationofJetEnergyCorrection ............... 148 6.8ResultsofCorrectedMissingTransverseEnergyinLeptonicEvents 150 6.8.1MissingTransverseEnergyResolution ............. 151 6.8.2MissingTransverseEnergyScaleandResponse ........ 151 6.8.3ClusterandUnclusteredFactor ................ 156 6.9Summary ................................ 158 7FACTORIZATIONMODELOFMISSINGTRANSVERSEENERGY 161 7.1Di-JetMissingTransverseEnergyFactorizationModel ....... 162 7.1.1DenitionoftheBasicModel .................. 163 7.1.2SimplicationunderQCDEvents ............... 164 7.2ImplementationandValidation .................... 166 7.3EectofJetEnergyCalibrationonMissingTransverseEnergy ... 172 7.3.1JetEnergyCalibrationinImbalanceDi-jetSystem ...... 174 7.3.2JetEnergyCalibrationinBalanceDi-jetSystem ....... 177 7.3.3IssuesinMissingTransverseEnergyIdenticationandRe-construction ........................... 180 7.4FactorizationModelinMultipleJetSystem ............. 181 7.4.1ModelDenition ......................... 181 7.4.2EectofJetEnergyCalibration ................ 182 7.5StudyonMissingTransverseEnergyHighLevelTrigger ....... 183 7.5.1MissingTransverseEnergyHLTRatebasedonFactoriza-tionModel ............................ 184 7.5.2SensitivitytoJetEectandSmearingEect ......... 188 7.6Summary ................................ 190 8SEARCHINGFORSTANDARDMODELHIGGSBOSONVIAVEC-TORBOSONFUSIONINH!W+W)]TJ/F2 11.95 Tf 10.82 -4.34 TD[(!`jjWITHmHFROM120TO250GeV/c2 192 8.1SignalandBackground ......................... 194 8.1.1PhysicsChannels ........................ 194 8.1.2OverviewofBackgroundCrossSectionMeasurement .... 197 8.1.3EventGeneration ........................ 201 8.2DetectorSimulationandReconstruction ............... 203 8.3HiggsBosonReconstructionandSelectionStrategy ......... 210 8.3.1OineLeptonSelectionStrategy ............... 210 8.3.2PropertiesofMultipleJetSystem ............... 212 8.3.2.1ForwardJetTagging ................. 212 8.3.2.2HadronicWReconstruction ............. 214 8.3.2.3JetsETSystem .................... 218 8.4BasicEventSelection .......................... 220 8.4.1Level-1andHigh-LevelTriggerforElectronorMuon(Trigger) 221 8.4.2OineLeoptonSelection(L-S) ................. 221 vii

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....... 222 8.4.4ForwardJetTagging(FJT) ................... 222 8.4.5HadronicWReconstruction(H-W) .............. 223 8.4.6LeptonicWReconstruction(L-W) ............... 224 8.4.7SelectionCriterionforHiggsBosonMassbelow160GeV=c2 8.5SummaryofIntermediateResults ................... 224 8.6SelectionOptimization ......................... 228 8.6.1OptimizationofForwardJetSelection(Step-1) ........ 232 8.6.2OptimizationofCentralJetSelection(Step-2) ........ 235 8.6.3OptimizationofqqWWSystem(Step-3) ........... 238 8.7SummaryoftheOptimizationSelectionResults ........... 243 8.7.1DiscoveryPotential ....................... 243 8.7.2SelectionEciency ....................... 243 8.7.3HiggsBosonMassandDistributioninSignalEvents ..... 246 8.7.4BackgroundShapeinHiggsBosonMassDistribution .... 247 8.8ExperimentalIdenticationofVBFHiggsBosonSignature ..... 249 8.8.1SignatureofEmissTinqqWWSystem .............. 251 8.8.2SignatureofLepton-WR ................... 252 8.9EstimationofSelectedSystematicUncertainties ........... 255 8.9.1DetectorSystematicUncertainty ................ 255 8.9.2TheoreticalSystematicUncertainty .............. 257 8.10Summary ................................ 259 9CONCLUSION ................................ 261 REFERENCES ................................... 266 BIOGRAPHICALSKETCH ............................ 270 viii

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Table page 3{1TheCMSLevel-1triggermenuatlowluminosity ............. 27 3{2TheCMSHLTtriggerrateatlowluminosity ............... 31 4{1CrosssectionandnumberofeventsQCDdi-jetdatasampleswithdier-entjetpT 40 4{2ThecongurationofPYTHIAeventgeneration(usedCMSwidein2003-2004) ...................................... 41 4{3Thecongurationofcalorimeterthresholdandnoiselevelindetectorsimulation ................................... 41 4{4Jetenergyresolutioninjj<3.0region .................. 71 4{5Jetenergyresolutioninjj3.0region .................. 73 4{6JetselectionparameterofdierentenergydistributionregionwithjetpTfrom80to120GeV/c .......................... 75 6{1Thecongurationofleptonicdatasamplesincludingttinclusive,ttlep-tonicandW+jets ............................... 116 6{2inthettsamplewithvariousconesizes .......... 141 6{3Fittingresultsofa,bandcofrelativeaccordingtoEg. 6{18 inttevents 151 6{4Fittingresultsofa,bandcofrelativeaccordingtoEq. 6{19 inW+jetssample ..................................... 151 6{5Fittingresultsofa,bandcofRaccordingtoEq. 6{18 usingEmissTandWpT 158 7{1JetandmissingtransverseenergyquantitiesofQCDdi-jetdatasamples 166 7{2METresolutioninDi-jetsystembeforeandafterthejetenergycalibration 177 7{3Fittingresultsofa,bandcaccordingtoEq. 7{24 forvariousMETHLTthresholdfrom60to120GeV ........................ 184 7{4Fittingresultsofbjet eectandbsm eectaccordingtoEq. 7{27 forvariousMETHLTthreshold ............................. 190 ix

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...................... 195 8{2Majorbackgroundcrosssectionandeventgenerated(W+jets,Z+jets,W+tb(tb)+jets,andWW+2jets(EW)includepartonlevelpre-selection) 197 8{3Thecongurationofpartonlevelpre-selectionofmatrixelementeventgenerator(ALPGENandMADGRAPH) .................. 202 8{4ReconstructedWmassresolutioninvariousjetcone.RealWmass(81.2GeV=c2)isusedtoscalethereconstructedWmass(mW),whichleadstoascaleds(mW)=mW=81:2(mW) ................... 216 8{5SelectioneciencyforsignalandbackgroundeventswithscenarioofmH160GeV=c2 228 8{6SelectioneciencyforsignalandbackgroundeventswithscenarioofmH<160GeV=c2 229 8{7Summaryofbasiceventselectioncuts ................... 230 8{8ForwardjettaggingeciencywithvariousjetETthresholdforConser-vative(c)andOptimisticScenario(o) ................... 234 8{9SelectioneciencywithvariousmaximalnumberofextrajetforCon-servative(c)andOptimisticScenario(o) .................. 236 8{10SelectioneciencywithvariousjetETthresholdforConservative(c)andOptimisticScenario(o) ......................... 237 8{11SummaryofoptimizationcutsformH160GeV=c2(mH<160GeV=c2) ........................................ 244 8{12Crosssection(fb)ofthesignalandbackgroundinoptimizedselectionwithmH160GeV=c2forExtraJetVeto(E)andLooseExtraJetVetoScheme(L) .................................. 245 8{13Crosssection(fb)ofsignalandbackgroundinoptimizedselectionwithmH<160GeV=c2forExtraJetVeto(E)andLooseExtraJetVetoScheme(L) ....................................... 246 8{14SummaryofnumberofeventsinregionA,B,C,andDwithrespecttoSignal+BackgroundandBackgroundOnlyscenarios ........... 255 8{15SelectioneciencyofW+3jetswithdierentcongurationscenariotothestandardone ............................... 257 8{16SelectioneciencyofW+4jetswithdierentcongurationscenariotothestandardone ............................... 258 x

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.................................... 258 xi

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Figure page 1{1LoweranduppertheoreticalboundofHiggsbosonmassasafunctionof 4 1{2SMHiggsbosonmassconstraintsbyprecisionmeasurementofelectroweakparametersatLEP,SLC,andTevatron ................... 6 1{3FeynmandiagramsofvariousHiggsbosonproductionprocesses ..... 7 2{1Leadingorder(LO)crosssectionofSMHiggsboson.Thecrosssectionforgg!Hisshowninnexttoleadingorder(NLO) ............ 11 2{2BranchingratioforSMHiggsboson ..................... 11 2{3H!ZZ!`+`)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(`0+`0)]TJ/F1 11.95 Tf 10.98 -4.34 TD[(invariantmasssignal(dark)andbackground(light)formH=130,150,and170GeV=c2withanintegratedluminos-ityof100fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1 14 2{4pTdistributionofsmallerpTleptoninH!WW!`+`)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(signal(white)andtotalbackground(light)formH=140GeV=c2withaninte-gratedluminosityof30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1 15 2{5H!invariantmassdistributionsignal(dark)andbackground(light)formH=130GeV=c2withanintegratedluminosityof100fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1 15 2{6bbinttH!`qqbbbbchannelinvariantmassdistributionsignal(dark)andbackground(light)formH=115GeV=c2withanintegratedlumi-nosityof30fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1 16 2{7SMHiggsbosondiscoverysignicancefor(a)fullmassrangeofmHand(b)lowmassrangeofmHinCMSwithanintegratedluminosityof30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1 2{8The5discoverypotentialofMSSMHiggsbosonfor(a)lighterscalarat30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1,(b)lighterscalarat100fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1,(c)heavyneutralat30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1,and(d)chargedat30fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1 18 3{1TheCMSdetectorlayout .......................... 20 3{2TransverseviewofCMStrackerlayout ................... 21 3{3PionenergyresolutionmeasuredbyTestBeamandMonteCarlosimula-tion ...................................... 24 3{4TheCMSmuonsystem ........................... 25 xii

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.................... 27 3{6IllustrationofLevel-1jetand-jettriggeralgorithm ........... 28 3{7Electronandphotonalgorithm ....................... 29 3{8Level-1muontriggerrateasfunctionofpTthresholdfor(a)lowand(b)highluminosity ................................ 30 3{9JetrejectionversuseciencyobtainedfromLevel-2.5pixelmatchingat(a)lowand(b)highluminosity ....................... 32 3{10Eciencyofthreeisolationalgorithmsonthereferencebackgroundasafunctionofeciencyforthereferencesignalmuonat(a)lowand(b)highluminosity ................................ 33 3{11Principleof-jetidenticationalgorithm .................. 34 3{12Theb-taggingalgorithm ........................... 34 3{13Eciencyofthreeisolationalgorithmsonthereferencebackgroundasafunctionofeciencyforthereferencesignalmuonat(a)lowand(b)highluminosity ................................ 35 4{1AbsoluteJetEnergyResolution(Et)inQCDeventswithpTfrom180to200GeV/c:(a)rawjetwithEt=14.67GeV,(b)correctedjetbyenergydistribution(explainedinlatersection)withEt=13.54GeV,(c)correctedjetbyshiftingthejetenergywithEt=14.97GeV,and(d)correctedjetbyascalingfactorwithEt=15.03GeV ........ 43 4{2RelativeJetEnergyResolution(R)inQCDeventswithpTfrom180to200GeV/c:(a)rawjetwithRof8.42%,(b)correctedjetbyenergydistribution(explainedinlatersection)withRof6.65%,(c)correctedjetbyshiftingthejetenergywithRof7.38%,and(d)correctedjetbyascalingfactorwithRof7.39% ...................... 44 4{3JetenergydistributioninQCDsampleswithvariousjetpT:(a)50-80and(b)80-120GeV/c.Theenergydistributioniscalculatedfromtheratioofenergyineachregiontothetotalenergyin1.0cone.Ineachblockofgures,theupperrowfromlefttorightcorrespondstoratioof0.0-0.2,0.2-0.4,and0.4-0.6respectively,thebottomrowcorrespondsto0.6-0.8and0.8-1.0respectively. ....................... 47 4{4JetenergydistributioninQCDsampleswithvariousjetpT:(a)120-170and(b)170-230GeV/c.Theenergydistributioniscalculatedfromtheratioofenergyineachregiontothetotalenergyin1.0cone.Ineachblockofgures,theupperrowfromlefttorightcorrespondstoratioof0.0-0.2,0.2-0.4,and0.4-0.6respectively,thebottomrowcorrespondsto0.6-0.8and0.8-1.0respectively. ....................... 48 xiii

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....................... 49 4{6JetenergydistributioninQCDsampleswithvariousjetpT:(a)380-470and(b)470-600GeV/c.Theenergydistributioniscalculatedfromtheratioofenergyineachregiontothetotalenergyin1.0cone.Ineachblockofgures,theupperrowfromlefttorightcorrespondstoratioof0.0-0.2,0.2-0.4,and0.4-0.6respectively,thebottomrowcorrespondsto0.6-0.8and0.8-1.0respectively. ....................... 50 4{7SecondMomentinQCDsampleswithvariousjetpT:(a)50-80,(b)80-120,(c)120-170,(d)170-230,(e)230-300,(f)300-380,(g)380-470,and(h)470-600GeV/c.Ineachgure,thecurvesfromlefttorightrepre-sentsthesecondmomentdistributionofconesizeof0.2,0.4,0.6,0.8,and1.0respectively. ............................. 51 4{8Jetenergydistributionbasedonthefractionofeachregion'stransverseenergywithrespecttototaltransverseenergyina1.0coneasafunctionofgeneratorjetpT.Regionsaredenedby0.2cone(square),0.4cone(triangle-up),and0.6cone(triangle-down) ................. 52 4{9PeakpositionofSecondMomentof1.0cone(opensquare),0.8cone(opencircle),0.6(triangle-down),0.4(triangle-up),and0.2(closesquare)asafunctionofgeneratorleveljetpT 54 4{10FWHMofSecondMomentof1.0cone(opensquare),0.8cone(opencir-cle),0.6(triangle-down),0.4(triangle-up),and0.2(closesquare)asafunctionofgeneratorleveljetpT 54 4{11Energyratioofsimpleconejetwithvarioussizetothatofthe0.6itera-tiveconejet.Thesimpleconejetsarebuiltupontheaxisfromiterativeconejet.Variousconesizesinclude(a)0.2,(b)0.4,(c)0.6,(d)0.8,and(e)1.0. ..................................... 57 4{12FittingofFig. 4{11 (c)byusingdoublegaussiandistribution ....... 58 4{13JetenergyresolutionfromvariousBenchmarkparameterizations:(a)rawjetwithEt=10.92GeV,(b)correctedjetsbasedontwoparame-tersBenchmarkEq. 4{7 withEt=10.8GeV,(c)correctedjetsbasedonthreeparametersBenchmarkEq. 4{6 withEt=10.77GeV,and(d)correctedjetsbasedonfourparametersBenchmarkEq. 4{8 .................................. 60 xiv

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................... 65 4{15Jetenergyresponsebefore(triangle-down)andafter(triangle-up)thecorrectionbasedonsecondmoment:(a)0.4cone,(b)0.6cone,(c)0.8cone,and(d)1.0cone ............................ 66 4{16Jetenergyresponsebefore(triangle-down)andafter(triangle-up)thecorrection:(a)basedoncorrectionofenergydistributionand(b)basedonbenchmarkcorrection. .......................... 67 4{17JetpTspectrumbeforeandafterthecorrectioninQCDsamplewithse-lectedrawjetpTrangingfrom170to200GeV/candjj<3:(a)rawjet,(b)generatorleveljet,(c)correctedjetbasedonsecondmoment,(d)correctedjetbasedonenergydensity,and(e)correctedjetspectrumbasedonbenchmarkcorrection ....................... 68 4{18Jetenergyresolutionof0.2cone:(a)absoluteresolutionand(b)relativeresolutionwithrawret(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) ....... 69 4{19Jetenergyresolutionof0.4cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) ....... 69 4{20Jetenergyresolutionof0.6cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) ....... 70 4{21Jetenergyresolutionof0.8cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) ....... 70 4{22Jetenergyresolutionof1.0cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) ....... 71 4{23Jetenergyresponseof0.6conebefore(triangle-down)andafter(triangle-up)thecorrectionbasedonsecondmoment ................ 73 4{24Jetenergyresolutioninforwardregion(jj>3:0)withnocorrection(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up)invariousconesize:(a)0.2,(b)0.4,(c)0.6,(d)0.8,and(e)1.0 ............................ 74 4{25NormalizedSdistributioninQCDsamplewithjetpTrangefrom80to120GeV/c ................................... 75 xv

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................ 81 5{2InclusiveEmissTHLTratecalculatedfromsamplesofjetpTrangesof50-80,80-120,120-170,170-230,230-300,300-380,380-470,470-600,600-800,and800-1000GeV/c.For1kHzrate(Level-1rateforEmissT),thethresholdisroughly50GeV,whichisunderestimatedduetothelowerpTsamples(0-20GeV/c)arenotused;for1Hzrate(HLTrateforEmissT),thethresholdisroughly90GeV,wherethecontributionfromthelowerpTsamplesissmall. ............................. 83 5{3ScalarPETspectrainQCDsamplesin(a)generatorleveland(b)de-tectorlevelthatcorrespondtojetpTranges(fromlefttoright)of20-30,30-50,50-80,80-120,120-170,170-230,230-300,300-380,380-470,470-600,600-800,and800-1000GeV/c. ..................... 84 5{4DetectorPETresponseasafunctionofPEgenT(a)usinggeneratedsig-naleventonlyinORCA-OSCAR(closecircle)andFAMOS(opencircle)and(b)usinggeneratedsignalandgeneratedpileupevents ........ 85 5{5ContributionofpileuptoPEdetTasafunctionofPEgenT 86 5{6Emissxresolutionquantities:(a)EmissxresolutionversusdetectorPET,(b)EmissxresolutionversusgeneratorPET,and(c)Emissxresolutionver-susgeneratorPETusingsignaleventonly ................. 88 5{7quantities:(a)versusdetectorPET,(b)versusgeneratorPET,and(c)versusgeneratorPETusingsignaleventonly ............................... 90 5{8EmissxresolutionquantitiesinlowPETsamples:(a)Emissxresolutionver-susdetectorPETand(b)ttingbasedontheaveragecorrelationofthesesamplesbetweenEmissxresolutionandPET 92 5{9RatioofPETofjetregiontounclusteredregionversusPET. ...... 93 5{10EmissxresolutionofthejetandunclusteredregionsversusPET. ..... 94 5{11EmissTrelatedquantitiesinjetregion:(a)averagedetectorEmissT,(b)de-tectorEmissxresolution,(c)averagedetectorPET,and(d)responseofdetectortogeneratorlevelPETusingsignalevent ............ 95 5{12EmissTrelatedquantitiesintheunclusteredregion:(a)averagedetectorEmissT,(b)detector(Emissx),(c)averagedetectorPETand(d)responseofdetectortogeneratorlevelPETusingsignalevent ........... 96 xvi

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................ 98 5{14Correlationbetweenthejetandunclusteredregions:(a)EmissT;U=EmissT;Jand(b)(EmissT;U)=(EmissT;J)asafunctionofPETusingvariousconesizestodenethejetandunclusteredregions .................... 99 5{15TheangularcorrelationwithQCDsamplesofjet^pTof(a)30-50and(b)50-80GeV/cforfourconesizes:0.2(black),0.4(red),0.6(green),and0.8(blue).ThepeakshowsEmissT;UandEmissT;Jareback-to-back. .... 100 5{16Fractionofeventswithaback-to-backcorrelationjj<1.0betweenthejetandunclusteredregionsasafunctionofPETforfourconesizes:0.2(black),0.4(red),0.6(green),and0.8(blue) ................ 101 5{17quantitiesbetweenthehighestETjetandEmissT:(a)thedistancebe-tweenthehighestETjetandEmissTand(b)thecorrelation(denedas=jet)]TJ/F3 11.95 Tf 12.04 0 TD[(MET+)betweenhighestETjetandEmissT.FiveQCDsam-plesareusedwithjetpTranges:50-80(black),80-120(red),120-170(green),170-230(blue),and230-300(yellow)GeV/c. ........... 103 5{18distancebetween(a)thesecondhighestETjetandEmissTand(b)thethirdhighestETjetandEmissT.FiveQCDsamplesareusedwithjetpTranges:50-80(black),80-120(red),120-170(green),170-230(blue),and230-300(yellow)GeV/c. ........................... 104 5{19Thecorrelation(denedas=1)]TJ/F3 11.95 Tf 12.63 0 TD[(2)ofthetwohighestETjets.FiveQCDsamplesareusedwithjetpTranges:50-80(black),80-120(red),120-170(green),170-230(blue),and230-300(yellow)GeV/c. ... 105 5{20ThecorrelationbetweenEmissT;JandEmissTdenedas=jet)]TJ/F3 11.95 Tf 12.15 0 TD[(EmissT+forveQCDsampleswithjetpTranges:50-80(black),80-120(red),120-170(green),170-230(blue),and230-300(yellow)GeV/c ...... 106 5{21ThecorrelationquantitiesshowninFig. 5{20 asafunctionofPET:(a)theofcorrelationand(b)theaveragePETofthetwojets ... 106 5{22DetctorlevelEmissTresolutionintheorthogonaldirectiontodi-jetasafunctionofPET 107 5{23andofEmissxversustowerenergythresholdinQCDsampleswithjetpT(a)30-50,(b)120-170,(c)300-380,and(d)600-800GeV/c 108 5{24PETspectumunderthreetowerthreshold:0.4(right),1.6(middle),and4.0(left)GeVinsampleofpTrangefrom50-80GeV/c. ....... 109 xvii

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............ 110 5{26Rpt=0asafunctionofPETusingQCDsamplesofjetpTranges:20-30,30-50,50-80,80-120,120-170,170-230,and230-300GeV/c ........ 110 5{27GeneratorlevelEmissxresolutionusingclusterregionasafunctionofPET 6{1ThefractionofeventswithEmissT>30GeVasafunctionofleptonpTthresholdfor(a)ttsamplesand(b)W+jetssamplesrespectively .... 117 6{2EmissTpropertiesasafunctionofMuonCaloFactor:(a)EmissTresolution(dot)andEmissTxresolution(circle)and(b)averageEmissTerrorbetweendetectorandgeneratorlevel ......................... 120 6{3ETofmuonconeisolationcone(a)intheregionofjj<0.8,(b)intheregionof0.810GeV/cand2:4
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...... 138 6{12EmissTquantitieswithrespecttodierentjetconesizesandETthresholdswith90betweenthedetectorandgeneratorlevelinttinclusiveevents 144 6{18RawETdistributionintworegionsasafunctionofEmissTbasedonttinclusiveevents.0.4conesizeisusedforregiondenition:detectorclus-terregion(opentriangle),generatorclusterregion(closesquare),detec-torunclusteredregion(closetriangle),andgeneratorunclusteredregion(opensquare) ................................. 146 6{19EmissTpropertiesafterthePUcorrectionasafunctionofdetectorEmissT:(a)EmissTerror,(b)EmissTresolution,(c)EmissTxresolution,and(d)reso-lution ..................................... 149 6{20EmissTpropertiesaftercorrectionasafunctionofdetectorEmissTinttin-clusiveevents:(a)relativeEmissTresolution,(b)resolution,(c)EmissTresolution,and(d)EmissTxresolution ..................... 152 xix

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....................... 153 6{22EmissTpropertiesaftercorrectionasafunctionofdetectorEmissTinW+jetsevents:(a)relativeEmissTresolution,(b)resolution,(c)EmissTresolution,and(d)EmissTxresolution ........................... 154 6{23EmissTscaleinttinclusiveeventsasfunctionofdetectorrawEmissT:(a)averageEmissTerrorand(b)EmissTresponse ................. 155 6{24EmissTscaleinttleptoniceventsasfunctionofdetectorrawEmissT:(a)av-erageEmissTerrorand(b)EmissTresponse ................... 155 6{25EmissTscaleinW+jetseventsasfunctionofWpT:(a)averageEmissTerrorand(b)EmissTresponse ............................ 156 6{26EmissTpropertiesasafunctionofEmissTinttinclusiveevents:(a)Rand(b)EmissTxresolution .............................. 157 6{27EmissTpropertiesasafunctionofEmissTinttleptonicevents:(a)Rand(b)EmissTxresolution .............................. 157 6{28EmissTpropertiesinW+jetsevents:(a)RasafunctionofETand(b)RasafunctionofEmissT 158 6{29StandaloneEmissTresolutionintheclusterandunclusteredregionrespec-tivelyasafunctionofWpTinW+jetsevents ............... 159 7{1NormalizedMETxdistributionofQCDeventswithleadingjetETbe-tween80and90GeV ............................. 167 7{2METquantitiesindi-jetsystemofQCDeventswithjetETbetween80and90GeV:(a)normalizedMETxdistributionand(b)normalizedcorrelation(=1)]TJ/F3 11.95 Tf 11.95 0 TD[(2)]TJ/F3 11.95 Tf 11.95 0 TD[() ....................... 168 7{3Di-jetangularcorrelationquantities:(a)phiasafunctionofleadingjetETand(b)Ratioofthenarrowcomponenttothewidecomponent 169 7{4METxquantitiesofQCDeventswithjetETbetween80and90GeV:(a)normalizedMETxdistributionand(b)normalizedMETxerrordis-tribution .................................... 169 7{5smasafunctionofleadingjetET 170 7{6NormalizedMETspectrumofQCDevents(opentriangle)andfactoriza-tionmodel(dot)withleadingjetETbetween80and90GeV ....... 170 7{7Resultsof2(a)asafunctionofjet(b)asafunctionofsm 171 xx

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172 7{9NormalizedMETspectrumwithjetET(GeV)of20-25(black),30-35(red),50-55(blue),80-90(green),120-130(black),170-180(red),230-240(blue),300-310(green),380-400(black),470-490(red),600-620(blue),and800-820(green) .............................. 173 7{10JetEnergyResponsewithrespecttogeneratorjetpT 175 7{11QCDjetquantitieswithjetETbetween80and90GeV:(a)distri-butionand(b)Di-jetdistribution .................... 179 7{12FractionofeventswithjetETbetween80and90GeVasafunctionofdi-jetRcut ................................. 180 7{13log10(SHLT)asafunctionofjetETforvariousGeVMETthreshold.Thecurvescorrespondsto60,65,70,75,80,85,90,95,100,105,110,115,and120(GeV)METthresholdfromuptodown. ............. 185 7{14log10(ET)asafunctionofjetET 186 7{15DierentialMETHLTrate(DHLT)asafunctionofjetET.Thecurvescorrespondsto60,65,70,75,80,85,90,95,100,105,110,115,and120(GeV)METthresholdfromuptodown. .................. 187 7{16METHLTrate(Hz)withrespecttogiventhreshold ........... 187 7{17SensitivityofSHLTtojeteectandsmearingeect:(a)SHLTasafunc-tionofjetwithxedsmequaltooptimalvalueofthefactorizationmodeland(b)SHLTasafunctionofsmwithxedjetequaltooptimalvalueofthefactorizationmodel.ThejetETrangeisbetween80and90GeV.VariousMETHLTthreshold(GeV)areused:60(closesquare),65(opensquare),70(closecircle),75(opencircle),and80(tringle) ........ 189 8{1EHcalT=EEcalToftrueelectron(a)andfakedelectron(b)inVBFHiggssam-plewithmH=170GeV=c2 204 8{2E/poftrueelectron(a)andfakedelectron(b)inVBFHiggssamplewithmH=170GeV=c2 205 8{3jE0:2T)]TJ/F1 11.95 Tf 11.17 0 TD[(EeTjoftrueelectron(a)andfakedelectron(b)inVBFHiggssam-plewithmH=170GeV=c2 205 8{4j(E0:2T)]TJ/F1 11.95 Tf 10.42 0 TD[(EeT)=EeTjoftrueelectron(a)andfakedelectron(b)inVBFHiggssamplewithmH=170GeV=c2 206 8{5j(E0:2)]TJ/F4 7.97 Tf 6.59 0 TD[(0:4T=EeTjoftrueelectron(a)andfakedelectron(b)inVBFHiggssamplewithmH=170GeV=c2 206 xxi

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207 8{7j(E0:2T)]TJ/F1 11.95 Tf 13.37 0 TD[(EeT)=EeTjoftruemuon(a)andfakedmuon(b)inVBFHiggssamplewithmH=170GeV=c2 207 8{8j(E0:2)]TJ/F4 7.97 Tf 6.59 0 TD[(0:4T=EeTjoftruemuon(a)andfakedmuon(b)inVBFHiggssam-plewithmH=170GeV=c2 208 8{9OverallReconstructionandSelectionEciencyofElectron(a)andMuonReconstruction(b)inVBFHiggsSample .................. 209 8{10LeptonpTspectrumforthehighestpTlepton(a)andthesecondhigh-estpTlepton(b)intheZ+jetssamplewithZleptonicdecay ....... 211 8{11Quark-jetrelativematchingeciencyasafunctionofjetETthresholdforvalancequark(square)andquarkfromWhadronicdecay(circle)inVBFHiggssamplewithmH=170GeV=c2.Theeciencyisnormalizedto1.0forjetETthresholdof20GeV. .................... 212 8{12Twoforwardquark-jetproperties(a)distribution(b)mqqdistribu-tion ...................................... 213 8{13Therelativerateofsignalevents(mH=170GeV=c2)thatpassforwardjettaggingbyextrajets(butquark-jetfail)tothoseeventsthatquark-jetpassestaggingasafunctionofjetETthreshold.IntensiveISRandFSRlargelyenhancedtheforwardjettaggingeciency,especiallyfortheETthresholdbelow35GeV ....................... 214 8{14TherateofVBFHiggsevents(mH=170GeV=c2)withextrajetthatisoutsideoftherangeoftwojetsmatchedwiththevalancequarkwithdistancebiggerthan3.8asafunctionofjetETthreshold.Theratein-creasessignicantlyasjetETthresholdgoesbelow35GeV,whichin-dicatesastrongenhancementofthesoftjetactivitiesoftheeventsviaISR/FSRanddetectoreects. ........................ 215 8{15ForwardJetTaggingeciencyfordierentthresholdofdistanceinVBFHiggseventswithmH=170GeV=c2 215 8{16mWusingquark-jetthattwoquarksareidentiedfromhadronicWde-cayinVBFHiggseventswithmH=170GeV=c2 216 8{17Numberofextrajetsinthecentralexcludingthequark-jetfromforwardjettaggingandhadronicWreconstructioninVBFHiggseventswithmH=170GeV=c2.AjetETthresholdof20GeVisused. ......... 217 xxii

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.................................. 218 8{19Multiplejetselectioneciency(requiringatleast4jetsinanevent)asafunctionofjetETthreshold.TheeciencyisnormalizedtotheratewithjetETthresholdof16GeVforeachsample.Thephysicschannelsinclude:tt+jets(solidsquare),W+3jets(opencircle),W+4jets(solidtriangle),andVBFHiggswithmH=170GeV/c2(opensquare) 220 8{20NormalizedleptonpTdistribution(a)andnormalizedleptondistribu-tion(b)ofVBFHiggswithmH=170GeV=c2(solid),tt+jets(dash),andW+4jets(dot)respectively ...................... 222 8{21NormalizedEmissTdistribution(a)andnormalizedJetETdistribution(b)ofVBFHiggswithmH=170GeV=c2(solid),tt+jets(dash),andW+4jets(dot)respectively ............................ 223 8{22HadronicWproperties(a)pTerrorand(b)RbetweenthedetectorandgeneratorlevelhadronicW.ThepTerroristtedbyaGaussianwith15.1GeV/c. ............................ 225 8{23LeptonicWproperties(a)pTerrorand(b)RbetweenthedetectorandgeneratorlevelleptonicW.ThepTerroristtedbyaGaussianwith19.5GeV/c. ............................... 225 8{24LeptonicWpropertiesasafunctionofmH(a)averagepTerrorand(b)pTresolutionbetweenthedetectorandgeneratedleptonicWwithun-correctedEmissT(solidsquare)andcorrectedEmissT(opensquare) ..... 227 8{25Di-WRerrorbetweendetectorandgeneratorlevelinVBFHiggseventswithmH=170GeV/c2 227 8{26VBFHiggsmassreconstructedfrombackgroundeventsunderhigh-massscenario.MajorbackgroundincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow). ................. 229 8{27VBFHiggsmassreconstructedfromVBFHiggseventswithmH=170GeV=c2 231 8{28distributionofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).MajorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow). ......... 232 xxiii

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................... 233 8{30mqqdistributionofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).MajorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow). ...... 233 8{31S/BwithrespecttodierentmqqthresholdsforConservative(solidsquare)andOptimisticScenario(opensquare) ................... 234 8{32S/BwithrespecttovariousVBFHiggsmassbyusingtheConservativeScenario .................................... 235 8{33NextraofbackgroundandVBFHiggssignal(mH=170GeV=c2).MajorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow) .................... 236 8{34WMofbackgroundandVBFHiggssignal(mH=170GeV=c2).MajorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow). .................... 237 8{35S/B(a)andsignicance(b)withrespecttovariousVBFHiggsmass.Thehigher(lower)S/BandsignicancecurvescorrespondtoExtraJetVeto(LooseExtraJetVeto)Schemerespectively ............. 239 8{36EmissTinqqWWsystemofbackground(a)andVBFHiggssignal(mH=170GeV=c2)(b) ............................... 240 8{37S/B(a)andsignicance(b)withrespecttoEmissTcutinqqWWsystem.Thehigher(lower)S/Bandsignicancecurvescorrespondtooptimistic(conservative)scenariorespectively ..................... 240 8{38RbetweenleptonicandhadronicWofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).MajorbackgroundincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow).Intheseplots,LooseExtraJetVetoSchemeinStep-2isused. ........ 241 8{39S/B(a)andsignicance(b)withrespecttoRcutandEmissT<40GeVinqqWWsystem.Intheseplots,LooseExtraJetVetoSchemeinStep-2isused.DuetostrongsuppressionoftheW+3jetsbackgroundfromcombiningRandEmissTcuts,thedierencebetweenConservativeandOptimisticScenarioisnegligible. ...................... 241 8{40Rbetweensemi-leptonicandhadronicWofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).MajorbackgroundincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow).Intheseplots,LooseExtraJetVetoSchemeinStep-2isused. ...... 242 xxiv

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................ 243 8{42VBFHiggsmassresolutionusingsignaleventsonlyformH=160(left),190(middle),and220(right)GeV=c2withofHiggsbosonmasswidth:14.1,15.5,and23.9GeV=c2respectively. .................. 247 8{43ResultsofVBFHiggsmassreconstructionbasedonsignal(blue)andprojectedbackground(black) ........................ 248 8{44Thefractionofeventsindierentregionsfortheoverallbackground(a)andVBFHiggssignal(b)asafunctionofEmissTcuts.RegionA(closesquare),RegionB(opensquare),andRegionC(opencircle). ...... 250 8{45TheratioofnumberofeventsasafunctionofR(a)RegionAtoRe-gionB(b)RegionAandRegionC(c)RegionBtoRegionC.Twosce-nariosareillustrated:Signal+Background(opensquare)andBack-groundOnly(solidsquare)respectively. .................. 253 8{46TheratioofSignal+BackgroundScenariotoBackgroundOnlySce-narioasafunctionofRforRegionAtoRegionB(opensquare),Re-gionAtoRegionC(solidsquare),andRegionBtoRegionC(opencircle) 254 8{47Eectsofjetenergysmearing(a)eciencyofbasicselectionnormalizedtonon-smearedratefortt+jetsbackground(square)andVBFHiggssignal(square)asafunctionofjetresolutionfactor(b)Higgsbosonmassresolutionafterbasiclteringasafunctionofjetresolutionfactor .... 256 xxv

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Weperformedfulldetectorsimulationstudiesofmissingtransverseenergy(EmissT)reconstructionandcorrection,andtheprospectsforsearchingforalowmassHiggsBoson(120
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TofullyexploitthecorrelationbetweentheEmissTandvariousphysicsnalstates,wedevelopedaphysicsmodelofEmissTbyfactorizingthejetsystemfromrelateddetectoreectsbasedonQCDdi-jetevents,andthenextendedthismodeltoageneralmultiplejetsystem.WeusedthemodeltoevaluatethejetenergycalibrationonEmissTandtheinuenceofvariousdetectoreectsontheEmissT.Ourstudyprovidedafundamentalframeworktosystematicallyunderstand,analyze,andevaluateEmissTrelatedquantities. WeperformedafeasibilitystudyonadirectHiggsmass(mH)reconstructionforthelowmassregion(120
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In2007theLargeHadronCollider(LHC)attheEuropeanLaboratoryofParticlePhysics(CERN)willusherinaneweraofparticlephysics,providingun-precedentedenergyandsensitivityfornewdiscoveriesandsensitivemeasurements,withascienticprogramthatwillcontinuefordecades.Fourprincipalexperimentswillbeconductedthere:theCompactMuonSolenoid(CMS),AToroidalLHCApparatus(ATLAS),LHCb,andALargeIonColliderExperiment(ALICE).Thersttwoaregeneral-purposedetectorswithabroadphysicsprogram,whilelattertwohavenarrowergoals. TheATLASandCMSdetectorsweredesignedtocarryoutprecisemeasure-mentsatbothlowandhighluminosityconditionswithcoverage(=ln TheLHCbdetectorwasdesignedtostudythephysicsofB-mesonsinvolvingcharge-parity(CP)violationandraredecay.TheALICEdetectorwasdevelopedasadedicatedheavy-iondetectortoinvestigatetheuniquephysicspotentialofnucleus-nucleusinteractions.AkeyaimofALICEistostudythephysicsofstronglyinteractingmatteratextremeenergydensities,whereformationofanewphaseofmatter(thequark-gluonplasma)isexpected. OtherexperimentsincludeTOTEM,anexperimentformeasuringtotalcrosssection,elasticscattering,anddiractiveprocessesatLHC. 1

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1 2 ]providesthecurrenttheoreticalframeworkforexplainingthefundamentalconstituentsofmatterandtheirinteractionsthroughfourtypesofforces:strong,weak,electromagneticandgravitational.Thestrongforceisresponsiblefor\connecting"thequarkstogethertoformprotons,neutronsandrelatedparticles.Theelectromagneticforcebindselectronstoatomicnuclei(clustersofprotonsandneutrons)toformatoms.Theweakforceisresponsibleforseveralformsofradioactivedecaysaswellasforthebasicnuclearreactionsthatpowerthesun.Thegravitationalforceactsbetweenmassiveobjects(althoughitplaysnoroleatthemicroscopiclevel,itisthedominantforceinoureverydaylifeandthroughouttheuniverse). Thestrong,weakandelectromagneticinteractionsaredescribedbygaugesymmetriesmanifestedasSU(3)SU(2)U(1)grouptransformationsinquantumeldtheory.Theinteractionsarecarriedbyparticlescalledgaugebosonswithspin-1.Eachforcehasitsowncharacteristicboson(s): Thefundamentalfermions(spin1 2)thatmakeupmatterareleptonsandquarkshavingnoobservableinternalstructure(pointlike).Theyoccurinthree\generations",whereeachquarkorleptongenerationconsistsofalefthandeddoubletandrighthandedsingletunderSU(2)transformations.Thegenerationsareidenticalexceptformass.SMhassuccessfullypredictedtheexistenceofmanyparticleslaterfoundinhighenergyexperiments.Theweakandelectromagnetic

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interactionswereunitedintoacombinedelectroweakframeworkdescribedbySU(2)U(1)gaugesymmetry.SU(3)isusedtodescribeaquarkhavingthreecolorcharges.However,thispicturesuersfromaproblem:beyondthelowestorderintheperturbation,thetheoryinitsoriginalformdiverges,andthehigh-energybehaviorofmatrixelementsisbad(hierarchyproblem).Mostoftheissuesrelatetothelongitudinal-polarizationcomponentofmassivevectorbosons.Moreover,thelargemassesofWandZbosons,whichbreakSU(2)U(1)symmetry,areinconsistentwiththeoriginalSMframeworkassumingmasslessgaugebosons. ThelaterintroductionofSpontaneousSymmetryBreaking(SSB)[ 3 4 5 ]solvedtheseproblemsandmadecalculationsnitewithinabroadergaugetheoryframework,thoughitrequiredtheintroductionofamassivespinzeroparticleknownastheHiggsboson.Higgsbosoninteractionsgivemasstoallparticlesexceptphotonsandgluonsandregulatethedivergentbehaviorinvectorbosonscattering.TheLagrangianofthegaugeeldthatinvolvestheHiggsbosonis (1{1) whereD=@)]TJ/F3 11.95 Tf 11.95 0 TD[(igA=2)]TJ/F3 11.95 Tf 11.95 0 TD[(g0YB.AandBarethegaugeeldofSU(2)andU(1).gandg0arethecouplingofSU(2)andU(1).isthePaulimatrices.YisthegeneratoroftheU(1)group.istheSU(2)doubletofcomplexscalareld.ThemassofHiggs,WandZcanbeexpressedbyfreeparametersand(Eq. 1{2 ). (1{2) where=q TheHiggsbosonmass(mH)isafreeparameterinSM.However,anupperlimitof1TeV=c2ofmHcanbepredicatedbasedonthestabilityofelectroweak

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vacuumandperturbativevalidityofSM.Ifnewphysicsentersatascalein-dicatingthatSMisembeddedinamoregeneralform,themaximalvalueofmHcanbeestimatedfromthroughthe\triviality"boundmH=p 1{3 1)]TJ/F4 7.97 Tf 17.79 4.71 TD[(3 43logQ2 (1{3) whereQisthemassscaleoftheinteraction.IfissetforPlanckscale(1019GeV),meaningnonewphysicsentersandrequiringtheperturbativevalidity,alowlimitmH<140GeVcanbeset.Givenalower,theupperboundformHwillbelarger.BothandmHwilloverlapattheTeVscale,indicatingthatthediscoveryofeitherHiggsbosonornewphysicsiswithinLHC'sreach(Fig. 1{1 )[ 6 ]. Figure1{1. LoweranduppertheoreticalboundofHiggsbosonmassasafunctionof Supersymmetry(SUSY)hasbeenproposed[ 7 8 ]toalleviatethehierarchyproblemofSMasitsmostplausibleextension.Ifitisprovedviaexperiment,thereexistssupersymmetricpartnersassociatedwithordinaryparticles.Intheminimal

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supersymmetricextensionofSM(MSSM),theHiggsscenarioincludestwoCPeven(handH),oneCPodd(A)andtwochargedHiggsbosons(H).Inthetreelevelcalculation,theHiggsbosonmassesandcouplingsaredeterminedbytwoparameters(mAandtan),andtheMSSMHiggsbosons'massesarewellordered:mh
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Figure1{2. SMHiggsbosonmassconstraintsbyprecisionmeasurementofelec-troweakparametersatLEP,SLC,andTevatron highlysuppressbackgroundsandsignicantlyincreasethesignaltobackgroundratio. Colorcoherencebetweeninitialandnalstategluonbremsstrahlungsup-presseshadronicactivitiesinthecentralregion.Thisisincontrasttomostbackgroundprocesses,whichnormallyhavecolorowinthet-channelandthusleadstocentraljetsinthedetector. Asidefromtheirexperimentalsignature,VBFmediatedprocesseshaveattractedattentionbecauseoftheinsightstheycanprovideonthedynamicsofElectroweakSymmetryBreaking(EWSB).Inparticular,studies[ 12 13 14 ]havedemonstratedthatVBFoersapotenttoolforHiggsbosondiscoveryandformeasurementsofitscoupling.Theseresultsshow,forexample,thatVBFprovideslargediscoverypotentialformHaround170GeV=c2andinthemediateandhighmassregion(mH>300GeV=c2). OncetheHiggsbosonisdiscovered,themeasurementofitscouplingconstantswithfermionandothergaugebosonsmustbeperformedinvariouschannels.AssumingW/Zuniversality,HWWcouplingcanbeseparatelydeterminedinVBF

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Figure1{3. FeynmandiagramsofvariousHiggsbosonproductionprocesses formH>110GeV=c2throughqq!qqH;H!W+W)]TJ/F1 11.95 Tf 7.08 -4.34 TD[(,whileotherHiggschannelsnormallyinvolve2typesofcouplingincludingHgg;H;Hbb;HttandH+)]TJ/F1 11.95 Tf 7.09 -4.33 TD[(.Forexample,gg!ZZinvolvesHggandHZZcoupling.Hggcouplingisdominatedbytop-quarkYukawacouplingwhichcanbeusedtoprobetheHiggscouplingwithup-typefermions. AccordingtodierentrangeofmH,followingHiggsbosondecaychainswithcorrespondingnalstatescanbeexploitedinLHC: qqH!qq+)]TJ/F2 11.95 Tf 10.4 -4.34 TD[(!qq+`+`)]TJ/F1 11.95 Tf 9.73 -4.34 TD[(+EmissT

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qqH!qq+)]TJ/F2 11.95 Tf 10.4 -4.34 TD[(!qq+`+jet+EmissT qqH!qqW+W)]TJ/F2 11.95 Tf 10.4 -4.34 TD[(!qq+`+`)]TJ/F1 11.95 Tf 9.74 -4.34 TD[(+EmissT EmissTisaveryimportantsignatureofnewphysics(e.g.,Higgsboson,SUSY)andplaysabigroleinprecisionmeasurementofSMparameters(e.g.,WmassandTopquarkmass).Itisalsorelatedtooveralldetectorperformance.WestudiedtheEmissTquantitieswithitsreconstructionandcorrectiontechniquestobenetabroadrangeofphysicsstudiesinvolvingtheEmissT. WefocusedonseveralcriticalquestionsaboutEmissTandjetthathavenotbeenwellansweredbefore:

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quantitiescanbeperformed?Whatisthecorrelationbetweenthosequanti-ties?(Chapter5) WeoerinthisthesisseveralsignicantcontributionstotheunderstandingofEmissTandjetreconstruction,includingtherstcomprehensivestudyoftheEmissTquantitiesbeyondthetriggerselection,thedevelopmentofajetcalibrationandcorrectionalgorithmusingjetenergydistributionsthatreducesjetenergymeasurementerrors,therstcomprehensivestudyofcorrectiontechniquesforEmissTbasedonleptonicevents,andthedevelopmentofageneral\factorizationmodel"thatcanbeusedforstudyingEmissTperformanceinCMS. WealsoconductedtherstreconstructionofvectorbosonfusionHiggsthroughH!W+W)]TJ/F2 11.95 Tf 11.08 -4.33 TD[(!`jjchannelinthelowmassregionusingfullysimulateddata.Asdescribedlater,thereconstructiontechniquedevelopedhereshowspromiseforusingthischannelfortheHiggsbosonsearchesinthemostinterestingregionofmHpredictedbyseveralexperiments(120
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Discovery(orexclusion)ofHiggsbosonisoneofthemostimportanttasksofLHC,cruciallyimprovingourunderstandingofnature,especiallyaboutelectroweaksymmetrybreakingmechanism.BecauseSMdoesnotpredicttheexactHiggsbosonmass(mH),LHCmustbeabletoreconstructHiggsbosonsignalandextractitfromlargeSMbackgroundforawiderangeofpossiblemassandchannels. 2{1 )[ 16 ]isdominatedbygluon-gluonfusion(gg!H)overthemHrangebetween100GeV=c2and1TeV=c2.Thecrosssectionisabout10pbaroundmH200GeV=c2.ThecrosssectionofassociatedHiggsbosonproduction,qq!HW,qq!HZ,gg=qq!bbHandgg=qq!ttH,islowerbyafactorof20(1000)atmH100(500)GeV=c2.Vectorbosonfusion(qq!qqH)isanotherlargeprocesswithabout10%ofthecrosssectionforgg!HatmH<200GeV=c2,andrisestosimilarlevelatmH1TeV=c2.Thekfactorofgg!Hisrangingfrom1.5to1.8,1.1forqq!qqHand1.2forotherassociatedprocesses[ 15 ]. ThebranchingratioforSMHiggsbosonisdominatedbybbformH<130GeV=c2andWW=WW,ZZ=ZZforhighermass(Fig. 2{2 )[ 17 ].Inlowmassrange,H!+)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(;arealsosizablewith8%and1:510)]TJ/F4 7.97 Tf 6.58 0 TD[(3(mH<150GeV=c2)respectively. TheMSSMscalarhwillbehavelikeSMHiggsbosonofsimilarcrosssectionanddecaypartialwidth,ifmA>mmaxh.Atlargetan,thecouplingsbetweenheavyneutralHiggsbosonandelectroweakgaugebosonsaresuppressedanddown-typefermionsareenhancedwithtan.gg!H=Aandgg=qq!bbH=Aarethemajor 10

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Figure2{1. Leadingorder(LO)crosssectionofSMHiggsboson.Thecrosssectionforgg!Hisshowninnexttoleadingorder(NLO) Figure2{2. BranchingratioforSMHiggsboson

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productionprocessesforheavyneutralMSSMHiggsboson.Iftan>10andmA>300GeV=c2,thebbH=Adominatesatabout90%ofthetotalrate. ForchargedMSSMHiggsbosonproduction,t!Hbisthedominantprocessviattevents.Otherprocesses,gb!tH,gg!tbH,qq0!H+H)]TJ/F1 11.95 Tf -394.6 -28.24 TD[(andgg!WH,alsocontribute.WithrespecttoMSSMHiggsbosondecay,H;A!bbdominateswithtan>10,andH;A!+)]TJ/F2 11.95 Tf 10.73 -4.34 TD[(10%.ThebranchratioofH!hh;WWand=rmZZandA!hZdependontan,whichisenhancedbysmalltanandreachupto80%and40%ofHandAdecaysrespectively.LightchargedHiggsboson(mH200GeV=c2,Hpm!is10%withmH>400GeV=c2.H!Whmayreach10%atsmalltan.Thebranchingratiotogauginoswillreach10%(30%)forlarge(small)tan. AgoodmassresolutionisparticularlyimportantforH!,duetolargeirreduciblebackgroundpp!+X.Thebackgroundpp!+jet+Xwithajetfragmentingintoaleadingisolated0thatfakescanbereducedbelowthelevelofdi-background. H!canalsobesearchedbyassociatedprocessesWHandttHwithanisolatedleptonfromWleptonicdecaytosuppressthehadronicbackground.

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gg=qq!ttH!ttbbcanalsobeexploited.TheassociatedproductionisnecessarilyusedbecauselargebbbackgroundfromQCDprocessandmodestHiggsbosonmassresolution(11%)inthischannel. FormH<200GeV=c2,H!WW=WW!`+`)]TJ/F3 11.95 Tf 7.08 -4.33 TD[(channelwillbeused.Duetodi-neutrinosinthenalstates,onlythetransverseHiggsbosonmasscanbereconstructed.ThepossibilityofusingH!WW!`jjisoneofthetaskofthisthesisprovidingadirectHiggsbosonmassreconstruction. FormH>200GeV=c2,H!ZZ!`+`)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(`0+`0)]TJ/F1 11.95 Tf 10.99 -4.34 TD[(hasthebestsensitivityuptomH500GeV=c2,whichisverycleanfromQCDbackgroundandirreducibleZZbackgroundbecauseofrelativelysmallHiggsbosonmasswidth.ThebackgroundofttandZbbcanbeecientlysuppressedbyusingleptonisolation,anupperboundontheleptonimpactparametersignicance,anddi-leptoninvariantmass. Thevectorbosonfusionprocessiscomparabletogluon-gluonfusionprocess,andprovideuniqueforwardtaggingjetsignaturetosuppressthebackgroundthatcanbefullyexploited.

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18 19 ]isshowninFig. 2{3 .Fortheisolatedleptonwithjj<2.5,20GeV/cpTthresholdforleadinglepton,15(10)GeV/cthresholdforsecond-largest-pTelectron(muon),10(5)GeV/cfortheresttwoelectrons(muons),andafour-electron(four-muon)acceptanceof33%(41%)formH=130-150GeV=c2isachieved. Figure2{3. H!ZZ!`+`)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(`0+`0)]TJ/F1 11.95 Tf 10.98 -4.34 TD[(invariantmasssignal(dark)andbackground(light)formH=130,150,and170GeV=c2withanintegratedluminos-ityof100fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1 2{4 withmH=140GeV=c2for30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1[ 20 21 ].Thebackgroundfromtt!W+bW)]TJ/F1 11.95 Tf 7.08 -4.33 TD[(bandWWcanbesuppressedfromWWspincorrelationsofthesignalthatmakesmall`+`)]TJ/F1 11.95 Tf 10.98 -4.34 TD[(openingangle.

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Figure2{4. pTdistributionofsmallerpTleptoninH!WW!`+`)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(signal(white)andtotalbackground(light)formH=140GeV=c2withanin-tegratedluminosityof30fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1 2{5 [ 22 ].Thesignaltobackgroundratiois1/10. Figure2{5. H!invariantmassdistributionsignal(dark)andbackground(light)formH=130GeV=c2withanintegratedluminosityof100fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1

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2{6 showstheinvariantmassdistributionofdi-b-jetinttH!`qqbbbbandbackgroundwithmH=115GeV=c2for30fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1[ 23 ]. Figure2{6. bbinttH!`qqbbbbchannelinvariantmassdistributionsignal(dark)andbackground(light)formH=115GeV=c2withanintegratedluminosityof30fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1 24 ]isshowninFig. 2{7 .TheNLOcrosssectionforbothsignalandbackgroundaresuitedforinclusiveH!;H!ZZ=ZZ!`+`)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(`0+`0)]TJ/F1 11.95 Tf 10.99 -4.34 TD[(andH!WW=WW!`+`)]TJ/F3 11.95 Tf 7.09 -4.34 TD[(.PoissonstatisticsareusedtocalculatethestatisticalsignicanceforH!ZZ=ZZ!`+`)]TJ/F3 11.95 Tf 7.08 -4.34 TD[(`0+`0)]TJ/F3 11.95 Tf 7.09 -4.34 TD[(;H!inWH,andH!andH!+)]TJ/F1 11.95 Tf 10.98 -4.34 TD[(inthevectorbosonfusion. MSSMHiggsbosondiscoverypotential[ 24 ]isshowninFig. 2{8 withrespecttolighterscalar,heavyneutral,chargedHiggsboson.

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(a) (b) Figure2{7. SMHiggsbosondiscoverysignicancefor(a)fullmassrangeofmHand(b)lowmassrangeofmHinCMSwithanintegratedluminosityof30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1

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(a)(b) (c)(d) Figure2{8. The5discoverypotentialofMSSMHiggsbosonfor(a)lighterscalarat30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1,(b)lighterscalarat100fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1,(c)heavyneutralat30fb)]TJ/F4 7.97 Tf 6.59 0 TD[(1,and(d)chargedat30fb)]TJ/F4 7.97 Tf 6.58 0 TD[(1

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LHCusestheLargeElectronandPositronCollider(LEP)'s27kilometerlongtunneltocollidetwoprotonbeamswithcenter-of-mass14TeVand40MHzcollisionrate.Itwillberunningatlowluminosityof21033cm)]TJ/F4 7.97 Tf 6.59 0 TD[(1s)]TJ/F4 7.97 Tf 6.58 0 TD[(1intherstthreeyearsstartingfrom2007,thenbeupgradedtoluminosityof1034cm)]TJ/F4 7.97 Tf 6.58 0 TD[(1s)]TJ/F4 7.97 Tf 6.58 0 TD[(1.Itcanalsocollideheavyionswithtotalenergy1150TeV.Inordertoachievebothhighenergyandluminosity,eachofthetworingsinLHCwillbelledwith2835bunchesof1011particleswithlargebeamcurrentmaintainedbyadelicatesuperconductingmagnetsoperatingatcryogenictemperature. TheCMSdetector(Fig. 3{1 )isdesignedtofullyexploitthediscoverypoten-tialofLHCwithafastresponsetomatchthecrossingrateandhighgranularitytohandle20eventsand1000tracksonaverageperbunchcrossing.Itmustalsobeabletorununderaharshradiationenvironmentof3kGyand1013neutron/cm2forthebarrelandupto50kGyand21014neutron/cm2fortheendcaps. 19

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Figure3{1. TheCMSdetectorlayout 3{2 ). Thepixeldetectorishousedinacylindricalvolumeof1mlengthand30cmdiametercenteredaroundtheinteractionpoint.Itconsistsofthreebarrellayersatmeanradiiof4.4,7.3,and10.2cmandtwoendcapdiskoneachside.Thedetectorhasbeendesignedtoprovidetwo-hitcoverageuptojj=2.2,andmaximalthreehitspertrack.Thepixelsizeis150m150mthatmakestheoccupancylow. TheSiliconStripTrackerconsistsof15148siliconstripmoduleswithapitchfrom80-180mdistributedovertenbarrellayers(fourinnerbarrellayersand

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Figure3{2. TransverseviewofCMStrackerlayout sixouterbarrellayers),whichprovideupto14hitspertrack.Theinner(outer)endcapismadeofthree(nine)disksforeachside. Thefundamentalperformanceofinnertrackerissummarizedasfollows:

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compactandputinsidethemagneticcoilcoveringtherapidityrangeuptojj<3.Preciseenergymeasurementforphotonsandelectronscanbeperformeduptojj<2.5exceptfortheregion1.4442
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highvoltage,thelongitudinalleakageoftheshowersduetorestrictedlengthofthecalorimetermedium,andprecisionofinter-calibration. HBandHEaresamplingandconsistof4mmthickplasticscintillatorstilesinsertedbetweenbrassabsorbersplates.DuetoshortinteractionlengthofHB(6.5X0),theHOislocatedinsidethemuonbarrelsystemandoutsideofthesolenoidcoiltomeasuretheHBenergyleakage.HFisplacedatadistanceof11mfromtheinteractionpoint,whichusesquartzbersasanactivematerialembeddedintheironabsorberwedgestobeabletoworkinahighradiationenvironment. Tocompensatefortheradiationdamageinjj>2.0,HEhas3layersoflongitudinalsegmentationtoallowcorrectionforthelossoflightyieldcomparingtoonlyonelayerinHB.HFcovering3.0
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(3{3) Inthedesigngoal,themissingtransverseenergy(EmissT)resolutionasafunctionofthescalarsumofET(ET)inHFis ET=0:55 Figure3{3. PionenergyresolutionmeasuredbyTestBeamandMonteCarlosimu-lation 3{4 ):DriftTubeChambers(DT)inthebarrel(0
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magneticeldandhighrate.Themuonsystemisinsidethemagneticeldreturn,whichallowsastandalonemeasurementofmuonmomentum.Themuonsystemisalignedwithtrackwithin100moferrorwhichisimportantforhighpTmuon. Figure3{4. TheCMSmuonsystem Inthecentralregion,theneutronbackgroundisnegligible,boththemuonrate(<1Hz/cm2)andthemagneticeldarelow.Fourstationsofdetectorsarelocatedincylindersinterleavedwiththeironyoke,ofeachwhichstationcontainsaDTandRPC.Thesegmentationfollowsalongthebeamdirection. Intheendcapregion,themuonrate(<10kHz/cm2)andtheneutronback-groundrate(10kHz/cm2)arehigh,aswellasthemagneticeld.TheCSCsandRPCsinfourdisksareperpendiculartothebeamdirection. IntheinitialrunningofmuonsystemonceLHCstartstotakedata,theouterringofthediskwillbemissingandtheCSCelectronicsfortheLevel1triggerwillbenotbeimplementedintheinnermostchambers,whichlimitsthelevel1muontriggerwithjj<2.1.

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Inthestandalonemuonreconstruction,themuonmomentumresolutionis10%inthebarrel,15%intheoverlapregion(0.8
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Intheallocationofbandwidth,asafetyfactorofthreeistakenforsimulationuncertaintiesbasedonfull(half)capacityforrunningathigh(low)luminosity,whichcorrespondsto33(16)kHz. Figure3{5. OveriewoftheLevel-1triggersystem Table3{1. TheCMSLevel-1triggermenuatlowluminosity Triggerstream ThresholdRateCumulativerate GeV(GeV/c)kHzkHz Inclusiveisolatedelectron/photon 293.33.3Di-electron/di-photon 171.34.3Inclusiveisolatedmuon 142.77.0Di-muon 30.97.9Singlejet 862.210.1Di-jet 591.010.9one,three,fourjet 177,86,703.012.5Jet*EmissT 21*450.815.1Minimumbias(calibration) 0.916.0 Total 16.0 ThecalorimetertriggerisbasedonHCALtower(Fig. 3{6 ).ThetowerenergysumsareformedbyECALandHCAL(includingHF)triggerprimitivegenerator(TPG)circuitsfromtheindividualcellenergies.ForHCAL(ECAL),theenergiesareaccompaniedbyabitindictingthepresenceofminimumionizingenergy

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(electromagneticenergydeposit).TGPinformationistransmittedoverhighspeedcopperlinkstotheregionalcalorimetertrigger(RCT)tondthecandidateelectron,photon,andjet. Figure3{6. IllustrationofLevel-1jetand-jettriggeralgorithm Theultimateoptimizationwillbeperformediterativelyundertherealdata.Initiallyanequalshareofratewillbeallocatedtofourclassesoftrigger:elec-tron/photon,muon,-jet,andjet/missingtransverseenergy.Thentheratemustbesharedwithintheclassesbetweensingleobjectanddouble(multiple)objectstriggers.Thegoalofratesharingandoptimizationistomaintainasucientwideandgeneralsuiteofchannelstomakeasinclusiveaspossibleandopentounexpectedphysics. Theelectromagnetictriggerworksunder33triggertowers(Fig. 3{7 ),applyingathresholdtothesumoftwoadjacenttowers.Thecutsarebasedonisolation,hadronictoelectromagneticfraction,ne-grainlateralshapeinECAL.Theeciencyofturn-oncurvesaretestedfordierentthresholdcuts,forisolatedelectrontriggerasafunctionofelectronmomentum. Thejettriggerisbasedon33windowusing44arraysoftriggertowers(1.0squareregionin-).Severaltypesofjetsaremade:centraljet,forwardjetandjet(usinga-likeshapetoltercentraljet)withadjustablecombined

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Figure3{7. Electronandphotonalgorithm triggercriterionanduptofourjettriggers.Thetopfourcandidatesofeachclassofcalorimetertriggeraresenttoglobaltrigger. TheLevel-1muontriggerusesfastRPCandprecisepositionmeasurementofDTandCSCwithstandalonetriggerlogicineachoftheLevel-1muontriggersystem.RPCstripsareconnectedtopatterncomparatortrigger(PACT),whichisprojectiveinand.CSCformLocalChargedTrack(LCT),whichiscombinedwiththeanodewireinformationforbunchcrossingidenticationonaTriggerMotherboard.DTisequippedwithBunchandTrackIdentier(BTI)electronicsthatndtracksegmentsfromhitsinfourlayersofoneDTsuperlayer. Thebendinginthesuccessivelayersoftheironyokeismeasuredbyrstassemblinglocalvectorsinthemeasurementstationsandassemblingtracksbylinkingthesevectorarecombinedinglobalmuontrigger(GMT).Theghosttrackfromasinglemuonfoundbymorethanonemuonsystemwithnon-matchedsegmentscanbecanceledbyGMT.Thefourbestmuoncandidatesidentiedandsenttotheglobaltrigger.TheresultingmuonLevel-1rateasafunctionofmuonpTisshowninFig. 3{8 [ 28 ].

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(a)(b) Figure3{8. Level-1muontriggerrateasfunctionofpTthresholdfor(a)lowand(b)highluminosity Thefulleventinformationmeansfullgranularityanddesignedresolutionisavailable.TheonlylimitationforHLTistheCPUtimeusageandoutputrate.Forphysicsstudy,theHLTmustbeinclusiveenoughandmustnotrelyonaverypreciseknowledgeofrunconditionandcalibration.TheHLTtriggermenuisincludedinTable 3.2.2 Accordingtothedesignedarchitecture,thehighestlevelofHLTreconstructionsharesalmostthesamealgorithmwithoinereconstruction(andanalysis).Inthe

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Table3{2. TheCMSHLTtriggerrateatlowluminosity Triggerstream ThresholdRateCumulativerate GeV(GeV/c)HzHz Inclusiveelectron 293333Di-electron 17134Inclusivephoton 80438Di-photon 40,25543Inclusivemuon 192568Di-muon 7472Inclusivejet 86375Di-jet 59176one,three,fourjet 657,247984Jet*EmissT 19*45290Inclusivebjet 237595MinimumBias(calibration) 10105 Total 105 following,IbrieydescribesthereconstructionalgorithmformajorobjectsthatisusedforDAQTDR: InLevel-2.5,super-clusterispropagatedbackintheeldfromECALtothepixeldetectorlayers.Thepixellayerisveryclosetothebeampipebeforemostofthetrackermaterials,sothepossibilityofelectronradiationandphotonconversionissmall.Twomatchedhitsallowsgoodelectronidentication.Theunmatchedclustercanbeidentiedasphotoncandidate

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withahigherthreshold.ThejetrejectionversuseciencyisshowninFig. 3{9 [ 26 ]. (a)(b) Figure3{9. JetrejectionversuseciencyobtainedfromLevel-2.5pixelmatchingat(a)lowand(b)highluminosity Thefurtherimprovementofelectron/photonidenticationinvolvesusingfullyreconstructedtracktomatchwithsuper-clusterandproperisolationbasedontracksand/orcalorimeter.Thisresultsinabetterelectron/photontobackgroundratiowithsmallineciency.Thesamestrategycanbeusedinoineanalysisandtobeoptimizedwithgeneralorspecicphysicschannels. AtLevel-2,themuonidenticationisperformedbythemuondetector.Thestatevector(trackposition,momentum,anddirection)associatedwiththesegmentsfoundintheinnermostchambersispropagatedoutwardsthroughironyoke. AtLevel-3,fulltrackisreconstructedintheinterestedregionbasedonKalmanltertechnique,whichisdenedbasedonmuontracksegments.Finallymuontrajectoriesincludingthetrackerhitswithrequiredtracksegmentsareextrapolatedtotheinteractionregionwithinof15mand

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Isolationcutareusedtosuppressthemuondecayfromb,c,Kanddecays.Isolationstrategycanbe:calorimeterisolation,pixeltrackisolation,andfulltrackisolationimplementedinLevel-2,Level-2.5andLevel-3respectively.Theprocedureofisolationoptimizationisthatforanypredenednominaleciencyaconesizeischosenwiththresholddenedinbinsofjj.Thetypicaloptimalconesizesvaryfrom0.2to0.3.TheeciencyofthreeisolationalgorithmsisshowninFig. 3{10 [ 27 ]. (a)(b) Figure3{10. Eciencyofthreeisolationalgorithmsonthereferencebackgroundasafunctionofeciencyforthereferencesignalmuonat(a)lowand(b)highluminosity 3{11 ).Forexample,about90%oftheenergyiscontainedin0.15-0.2coneandabout98%in0.4cone.

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Figure3{11. Principleof-jetidenticationalgorithm AtLevel-2,thecalorimeterbasedselectionisperformedtolookfornarrowjetina0.13coneanddeneanisolationregionof0.4cone.Theselectioncanbefurthertightenedbypixel(track)isolationinLevel2.5(3). 3{12 ). Figure3{12. Theb-taggingalgorithm

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throughtheconstituentofthetowersinthecone.Theprocessterminatesuntilacutocriterionissatised(theiterationreaches100,thechangeofjetdirectionin-issmallenough,orthechangeofjetenergyissmallenough). 3{13 showstheEmissTratewithvariousjetETselectionthresholdatlowandhighluminosity[ 28 29 ]respectively. (a)(b) Figure3{13. Eciencyofthreeisolationalgorithmsonthereferencebackgroundasafunctionofeciencyforthereferencesignalmuonat(a)lowand(b)highluminosity ItisobservedthatthejetselectioncutisredundantforEmissTHLTwithEmissT>120GeVatlowluminosity,becausetheratewithvariousjetthresholdsgivealmostthesameastheinclusiveEmissTratewithoutjetcut.ThisisalsoobservedforEmissTHLTwithEmissT>160GeVinhighluminosity. AftertheDAQTDRwasnishedinlate2002,therewerefurtherdevelopmentofthereconstructionformostofthefundamentalobjects(e.g.,thereconstructionofmissingtransverseenergy,b-tagging...whichwereimplementedlater).Butmostofthefundamentalalgorithmsremainalmostthesame.Forthephysicsanalysis,

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itisgennerallynecessarytobefurtheroptimizedwithrespecttoagivenanalysistopicinordertogetbettereciencyandperformance.

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ThemeasurementofjetisoneofthemajortasksoftheCMScalorimeter[ 30 22 ]toexplorethenewphysicsatLHC.Theconealgorithm(iterativeorsimplecone)iswidelyusedforthejetreconstructionofhadroncollider. Thebasicalgorithmofiterativeconesearchesthemaximumtransverseenergyreconstructionobject(e.g.,thecalorimetertower,tracks,orthegeneratedparticlesthatthejetreconstructionalgorithmisusedagainst)andthrowsan-conearounditsdirection.Anyobjectwithintheconewillbemergedtoformaproto-jet.Theproto-jetdirectioniscalculatedfromtheweightedenergydirectionoftheconstituents,andaconein-isthrownaroundthenewdirectiontoformanewproto-jet.Theprocedureisrepeateduntiltheproto-jetdoesnotchangesignicantlybetweentwoiterations(ET<1%bydefault)and(R<0.01bydefault,whereR=p Thesimpleconealgorithminthisanalysisusesthejetaxisfromtheiterativeconealgorithm(with0.6conesize),theconesizeusedforsimpleconealgorithmischangedaccordingtotheneed.Alltheobjectswithinthepredenedconesizewillbemergedtoformajet.Theconstituentsareremovedfromthelistofobjects,andtheprocedureisrepeateduntilnoobjectsareleftinthelist.ThisprocedureisdierentfromthegenerallydenedthesimpleconealgorithmthatdirectlyusesahighestETtowerinaregionasthejetaxis.ObviouslyusingthehighestETtower 37

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asthejetaxismaycausebiasanddeviationtotheoptimaljetaxisduetothejetenergydistributionmightnotbesymmetricaroundthehighestETtower. ThereareseveralreasonswhytheconealgorithmwillcontinuetoplayanimportantroleinLHCphysicsreconstruction: Thelinearityoftheaveragejetenergyscaleandenergyresolutionaretwocriticalquantitiestoevaluatetheperformanceofthejetreconstructionandcorrection.Thegeneratedjetenergyscaleisrestoredbyusingaveragedetectorresponse,forabetterquality,whichcanbecharacterizedaccordingtodierentreconstructedjetETrangesandcalorimeterranges.SeveralcalibrationmethodsusingthesimilarprinciplehavebeenstudiedinCMS[ 31 32 33 ].Inordertoimprovethejetenergyresolution,weneednotonlyoptimizethejetreconstructionalgorithm,butalsosolvetwocriticalissues:

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parameterizationotherthansolelybasedonthereconstructedjetET.TheETerrorismainlycausedbythestochasticeectofthecalorimeterresponse.ForreconstructedjetsfromagivenET,thevariationtotheircorrespondinggeneratorleveljetpTwillnotbecorrectedbyasimplere-scalingcoecient.SotheresolutionfactorwillbekeptwhereverETisusedandtransformedinhigherlevelreconstructionoranalysis.ThisisthefundamentalreasonwhythecalibrationmethodbasedonETwillnotnaturallyleadtoabetterresolutionofthemeasuredjetenergy.Inlatersection,thiswillbediscussedindetail. 34 35 36 ])requiresthealgorithmtohandlemorecomplicateddetailsofjetconstituentinadditiontoanoveralljetET. Themotivationofthisstudyistodevelopanewevent-basedmethodtocalibrateandcorrectjetenergy,whichisbuiltontheparameterizationofjetenergydistributionusingnegranularityofCMScalorimeterthatallowsthemeasurementofincidentenergydepositaroundthereconstructedjetaxis.Thisapproachcontainsthejetenergydistributionreconstruction,correctionfunctionparameterization,ttingandperformanceanalysis. 4{1 .ThebinningofjetpTisprimarilytoreducethecomputingtimeofdetectorsimulationtocoverawidejetpTrange.SimilarcongurationsofeventsampleswereusedinotherjetandEmissTstudies[ 31 28 ].Thisconguration

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inevitablycausesthedistortionofthespectrumnearthebeginningandendingre-gionofeachbin,becausethedetectorjetETspectrumisaresultoftheconvolutionofthedetectorresponsefunction(aGaussian-likedistributionforagivenmeasuredjetET)withthegeneratorjetpTspectrum.Neareitheredgeofthebin,theimpactofeventsfromcontiguousbinisneglectedduetotheselectioncutinthegeneratorlevel. PYTHIA[ 37 ]implementedinCMKIN[ 38 ]isusedtogeneratetheeventswithp.d.f.(CTEQ7).Theeectsofinitialandnalstateradiation,hadronizationandmultiplepartonscatteringareincluded.MajorcongurationparameterswiththeirvaluesarelistedinTable 4{2 OSCAR.2.4.5[ 39 ](basedonGEANT4)isusedforCMSdetectorsimulation.ORCA.8.6.0[ 40 ]isusedforthereconstructionandanalysis.ThecongurationofcalorimeterthresholdsandnoiselevelsinthesimulationandreconstructionislistedinTable 4{3 .Theeventsarepileupedwithaverage3.5minimumbiaseventswhichcorrespondstothelowluminosity(L=21033cm)]TJ/F4 7.97 Tf 6.58 0 TD[(2s)]TJ/F4 7.97 Tf 6.58 0 TD[(1)atLHC. Table4{1. CrosssectionandnumberofeventsQCDdi-jetdatasampleswithdif-ferentjetpT CrossSection(pb)NumberofEvent 20-30 7.81910850,00030-50 1.84910850,00050-80 2.433107100,00080-120 3.359106100,000120-170 5.654105100,000170-230 1.163105100,000230-300 2.812104100,000300-380 7.848103100,000380-470 2.396103100,000470-600 9.249102100,000600-800 2.038102100,000800-1000 3.56210150,0001000-1400 1.07510150,000

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Table4{2. ThecongurationofPYTHIAeventgeneration(usedCMSwidein2003-2004) Parameterandvalue Explanation Physicsprocess(MSEL=1) qq!qq=gggg!gg=qqqg!qg Fragmentation(MSTJ11=3) Hybridschemewithtreatinglight andheavyavorsseparately RunningalphaS(MSTP2=1) FirstOrder Structurefunction(MSTP51=7) CTEQ7 Structureofmultipleinteraction variousimpactparameterandhadronicmatter(MSTP82=4) overlapindoubleGaussianmatterdistribution Theptcut,matterdistribution Pythiadefaultpowerofenergy-rescalingterm Table4{3. Thecongurationofcalorimeterthresholdandnoiselevelindetectorsimulation Parameter BarrelEndcapVeryforward ECALdigithreshold 90MeV450MeVHCALdigithreshold 300MeV300MeV300MeVNoiselevelinECAL 40MeV150MeVNoiselevelinHCAL 0.610)]TJ/F4 7.97 Tf 6.58 0 TD[(3GeV0.610)]TJ/F4 7.97 Tf 6.59 0 TD[(3GeV0.610)]TJ/F4 7.97 Tf 6.59 0 TD[(3GeV Inordertoeliminatetheambiguityofseveralrepeatedlyusedconceptsinthecontext,wemakefollowingdenitionsofthreetypesofjetenergyresolutionwhichareusedinthecalculationanddiscussion: 1. Absoluteresolution(Et):thestandarddeviationofmeasurementerrorbetweenthedetectorjetandcorrespondinggeneratorjet.Etignorestheeectofaveragedetectorresponseinsteadfocusesonthevariationofenergy

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error,becauseaproperjetcalibrationcanrecoverthelinearityofaveragejetenergyscaleinagoodprecision. Fig. 4{1 illustratesseveralcalibrationmethodsandtheirperformanceonEtusingaselectedjetsample.InasimplemethodthatjetETisshiftedby24.59GeV,avaluecomingfromtheaveragedierencebetweenthegeneratorleveljetpTanddetectorleveljetET,theEtisalmostunchanged.Inanothermethod,aninverseddetectorjetresponse(normallythisvalueisbiggerthanone)ismultipliedtothedetectorjetenergy,whichalsorecoversthelinearityofaveragedetectorresponse,stillnoimprovementofEtisobserved.Byusingthecorrectionmethoddevelopedinthisstudy,theerrorisreducedat10%.AboveexamplesshowthejetcalibrationdoesnotleadtothereductionofEt,thatiswhyweneedtodevelopdedicatedjetenergycorrectionmethod. 2. Idealrelativeresolution(r):thestandarddeviationoftheratioofthedetectorjetenergytotheoriginalgeneratorjetenergy.Similartoabsoluteresolution,itonlyshowstheeectsofvariationofdetectormeasurement,soitisan"ideal"jetresolutionbasedongeneratorjetenergy.Thisquantityisalwaysusedafterjetcalibrationisappliedsothatanunitdetectorresponseisestablished. 3. Relativeresolution(R):thestandarddeviationoftheratioofthejetenergyerrortothedetectorjetenergy.Riswidelyusedinmanydetectorperformancestudies,whichshowstheoveralleectofthecorrection(Fig. 4{2 ). Forevaluatingthejetcorrection,itisveryimportanttoshowtheimprove-mentofRtogetherwithEtandr,andchecktheperformanceonthelinearityofthecorrectedjetenergyresponse(performanceofcalibration).

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(a)(b) (c)(d) Figure4{1. AbsoluteJetEnergyResolution(Et)inQCDeventswithpTfrom180to200GeV/c:(a)rawjetwithEt=14.67GeV,(b)correctedjetbyenergydistribution(explainedinlatersection)withEt=13.54GeV,(c)correctedjetbyshiftingthejetenergywithEt=14.97GeV,and(d)correctedjetbyascalingfactorwithEt=15.03GeV Variousjetcalibrationandcorrectionmethodshavedierentperformanceonthoseresolutionquantities.Inamoregeneraldiscussion,itispossibleforamethodtoachievebetterRwhileworseningEt.Thisnormallyrelatestothecasethatrestoringtheaveragescaleismoreimportantthanreducingthevariationofthemeasurementerror.Inbothcases,therelativeresolutionofcorrectedjetsmightbeimproved,buttheyresultindierentperformanceinhigherlevelreconstruction.Forexample,theEmissTreconstructioninsomephysicsnalstatesgainslittleinjetcalibrationbecausetheEtisnotimproved.Aclearunderstandingofallthe

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(a)(b) (c)(d) Figure4{2. RelativeJetEnergyResolution(R)inQCDeventswithpTfrom180to200GeV/c:(a)rawjetwithRof8.42%,(b)correctedjetbyenergydistribution(explainedinlatersection)withRof6.65%,(c)correctedjetbyshiftingthejetenergywithRof7.38%,and(d)correctedjetbyascalingfactorwithRof7.39% importantaspectsofjetresolutioniscrucialtodevelopandapplyjetcorrectiontoEmissT. 4.3.1CalorimeterResponse 41 ].Thisisthemajorsourceofthenon-linearity.Thestochastic

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detectorresponseisthemajorsourceofthevariationofthemeasurementwhichrelatestothedetectorintrinsicresolution.Otherdetectoreectsalsodeterioratethejetenergyresolution,suchasout-of-conetracksdeectedbymagneticeld,lowpTparticlesstoppedbytrackermaterials,non-uniformityofpileupenergyfromminimumbiaseventsandelectronicnoise.Severalmethodshavebeendevelopedtocorrectspecicfactors[ 32 34 35 36 ].Butthelimitofjetenergycorrectionismainlydeterminedbycalorimeterintrinsicresolution. Twoschemesareusedforparameterizingthejetenergydistribution:

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Fig. 4{4 and 4{6 showthejetenergyfractionfactorwithrespecttovariousjetpTsamples.Asexpected,theinnerregionaroundthejetaxiscontainsmostoftheenergy.AsjetpTgoesup,thefractionofenergyintheinnerregionswillincreases.Theoutertworegions(0.6-0.8and0.8-1.0)showverysimilardistributionacrossawidepTrange. 4{1 .Theregionsforcalculatingsecondmomentisdierentfromthepreviousscheme,thatusesconesof0.0-0.2,0.0-0.4,0.0-0.6,0.0-0.8,and0.0-1.0respectivelyinthe-spacearoundthejetaxis.Secondmomentineachregionshowstheaveragedistanceofallthetowersweightedbyeachtower'stransverseenergy,whichisagoodparameterindescribingthejetshape.Althoughtheenergyisnotexplicitlyshowedinthenalresult,theyareusedforweighting,soitisstillagoodparametertoshowtheenergydistributionassociatedwithajet. whereSandSaredenedas whereETiisthetransverseenergyofatower. Fig. 4{7 showsthesecondmomentdistributionwithrespecttodierentconesizescalculatedinvariousjetpTsamples.Thesecondmomentdistributionisclosetoagaussiandistribution,whichprovidesawaytoevaluatetheuctuationoftheoveralljetenergydistributioninaxedcone.

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(a) (b) Figure4{3. JetenergydistributioninQCDsampleswithvariousjetpT:(a)50-80and(b)80-120GeV/c.Theenergydistributioniscalculatedfromtheratioofenergyineachregiontothetotalenergyin1.0cone.Ineachblockofgures,theupperrowfromlefttorightcorrespondstoratioof0.0-0.2,0.2-0.4,and0.4-0.6respectively,thebottomrowcorrespondsto0.6-0.8and0.8-1.0respectively.

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(a) (b) Figure4{4. JetenergydistributioninQCDsampleswithvariousjetpT:(a)120-170and(b)170-230GeV/c.Theenergydistributioniscalculatedfromtheratioofenergyineachregiontothetotalenergyin1.0cone.Ineachblockofgures,theupperrowfromlefttorightcorrespondstoratioof0.0-0.2,0.2-0.4,and0.4-0.6respectively,thebottomrowcorrespondsto0.6-0.8and0.8-1.0respectively.

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(a) (b) Figure4{5. JetenergydistributioninQCDsampleswithvariousjetpT:(a)230-300and(b)300-380GeV/c.Theenergydistributioniscalculatedfromtheratioofenergyineachregiontothetotalenergyin1.0cone.Ineachblockofgures,theupperrowfromlefttorightcorrespondstoratioof0.0-0.2,0.2-0.4,and0.4-0.6respectively,thebottomrowcorrespondsto0.6-0.8and0.8-1.0respectively.

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(a) (b) Figure4{6. JetenergydistributioninQCDsampleswithvariousjetpT:(a)380-470and(b)470-600GeV/c.Theenergydistributioniscalculatedfromtheratioofenergyineachregiontothetotalenergyin1.0cone.Ineachblockofgures,theupperrowfromlefttorightcorrespondstoratioof0.0-0.2,0.2-0.4,and0.4-0.6respectively,thebottomrowcorrespondsto0.6-0.8and0.8-1.0respectively.

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(a)(b) (c)(d) (e)(f) (g)(h) Figure4{7. SecondMomentinQCDsampleswithvariousjetpT:(a)50-80,(b)80-120,(c)120-170,(d)170-230,(e)230-300,(f)300-380,(g)380-470,and(h)470-600GeV/c.Ineachgure,thecurvesfromlefttorightrepresentsthesecondmomentdistributionofconesizeof0.2,0.4,0.6,0.8,and1.0respectively.

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4{4 and 4{6 ,theaveragefractionofthejetenergyineachregionasafunctionofjetpTisshowedinFig. 4{8 .Theresultscanbeinterpretedasfollowing: Figure4{8. Jetenergydistributionbasedonthefractionofeachregion'stransverseenergywithrespecttototaltransverseenergyina1.0coneasafunc-tionofgeneratorjetpT.Regionsaredenedby0.2cone(square),0.4cone(triangle-up),and0.6cone(triangle-down)

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4{7 ).Thetailsandtheasymmetryofthedistributioncanbeexplainedbycomplicateddetectoreects: ThepeakpositionandFWHM(fullwidthathalfmaximum)ofsecondmomentttedbyaconvolutedGaussianandLandaudistributionareusedtostudy

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theanalyticaldependencyofsecondmomentonthejetpT(Fig. 4{9 and 4{10 ).Tosomeextent,previousdiscussionabouttheenergyfractioncanbeappliedtosecondmomenttoo. Figure4{9. PeakpositionofSecondMomentof1.0cone(opensquare),0.8cone(opencircle),0.6(triangle-down),0.4(triangle-up),and0.2(closesquare)asafunctionofgeneratorleveljetpT 4{8 4{9 ,and 4{10 ).Formeasuredvaluesofthoseparameters,itispossibletopredictjetpTandtobeusedtomakecorrectiononthemeasuredjetET.Thisisthemajormechanismhowtheenergydistributioncanbefactorizedandusedforthejetenergycorrection. Duetotheuctuationofthegeneratedjetshapeandthedetectorresponse,themeasuredjetenergydistributioncontainssignicantuncertainties.AnumberofjetscanbeusedtondthebestcorrelationbetweenthegeneratedjetpTandjetenergydistributionfactor.Thisispartofthettingprocessinordertoderivethejetenergycorrectionfunctions(willbediscussedinthelatersection).

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Figure4{10. FWHMofSecondMomentof1.0cone(opensquare),0.8cone(opencircle),0.6(triangle-down),0.4(triangle-up),and0.2(closesquare)asafunctionofgeneratorleveljetpT Werestrictthisdiscussionfromfurtherquantitativeevaluationofjetenergydistributionfactorssincetheresultsaresensitivetothedetailsofthesimulation(e.g.,settingofelectronicnoiseanddetectorresponse).Otherphysicsaspectsofeventgenerationalsohavebiginuence(e.g.,initialandnalstateradiation,frag-mentationandhadronizationmodel).Ultimatelytheexperimentalmeasurementofjetenergydistributionwillhelpreachabetterunderstandingofthewholeissue.

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4.4.1JetReconstruction ThegeneratoranddetectorjetsarereconstructedrstbyiterativeconealgorithmimplementedinORCAJetssubsystem[ 42 ].Thecongurationofthealgorithmis:0.6ofconesize,1.0GeVofseedETcut,andLorentz4-vectorofrecombinationscheme.Thensimpleconejetswithvariousconesizesarereconstructedbasedonthexedjetaxisfrompreviousstep.Theanalysisofjetcorrectionisdevelopedfrommatchingthegeneratorjetstodetectorjetsbytheiraxisina0.3cone. Thedierenceintheperformancebetweeniterativeconeandsimpleconealgorithmissmall.Fig. 4{11 showstheratioofthejetenergyofvarioussimpleconesizetothatof0.6iterativecone.The0.6simpleconejetalmostcontainsthesameamountoftransverseenergyas0.6iterativecone.AdoublegaussianttingisperformedonFig. 4{11 (c).TheresultisshowedinFig. 4{12 .Theleftpeakwellcenteringon1.0showsthegoodmatchingoftwoconealgorithms.Theeectofiterativeselectionresultsinthewidthofthepeak.Therightpeakisoverlappedwiththeleftonewiththesamewidth,mainlyduetotheeectoftheHCALgranularityontheiterativeselection.Ingeneral,thedierenceinthejetenergyfromtwoalgorithmsarewithinafewpercent.Intherestofthediscussion,simpleconealgorithmisusedtostudytheenergyresolutionandotherrelatedquantities.

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(a)(b) (c)(d) (e) Figure4{11. Energyratioofsimpleconejetwithvarioussizetothatofthe0.6iterativeconejet.Thesimpleconejetsarebuiltupontheaxisfromiterativeconejet.Variousconesizesinclude(a)0.2,(b)0.4,(c)0.6,(d)0.8,and(e)1.0.

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Figure4{12. FittingofFig. 4{11 (c)byusingdoublegaussiandistribution 1. Basedonenergydistributioninsidethe1.0cone(wecall"EnergyDistribu-tionCorrection"or"EDCorrection"). wherethecorrectionsumsoveralltheregionsaroundthejetaxis.Etiisthetotaltransverseenergyinregioni.Et0andEt00aretheuncorrectedandcorrectedjettransverseenergy.ai,bi,andciarethecorrectionparameterstobettedwithdata.Riisthefractionofenergyinregionidenedas 2. Basedonsecondmomentinsidethe1.0cone(wecall"CombinedSecondMomentCorrection"or"CSMCorrection"). (4{5) whereSiisthesecondmomentinregioni.

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3. Basedonoveralljetenergywithlessparameterization(Wecall"BenchmarkCorrection").Itcontainsnoinformationofenergydistribution,soitismainlyusedforcomparisonwithrsttwomethodsthathavemoreparametersanduseenergydistributionfactoraroundthejetaxis. Followingissomeexplanationwhythoseparameterizationisused: 4{7 and 4{8 ). TheresolutionofcorrectedjetsarealmostkeptsameforthosecorrectionfunctionswithdierentorderofEt0(Fig. 4{13 ).Itshowstheoveralllim-itationofthecorrectionfunctionwhichissolelybasedonEt0(withsmallimprovementonresolution)andtheinsensitivityoftheresolutiontotheordersofEt0.ThisfactwillbeclearerinlatersectionthattheBenchmarkCorrectionismainlyacalibrationfunctionandhaslesscapabilityofreducingthevariationofthemeasurementerror(Et).

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(a) (b) (c) (d) Figure4{13. JetenergyresolutionfromvariousBenchmarkparameterizations:(a)rawjetwithEt=10.92GeV,(b)correctedjetsbasedontwopa-rametersBenchmarkEq. 4{7 withEt=10.8GeV,(c)correctedjetsbasedonthreeparametersBenchmarkEq. 4{6 withEt=10.77GeV,and(d)correctedjetsbasedonfourparametersBenchmarkEq. 4{8

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4{3 issimilartoBenchmarkCorrection,whichrepresentstheoveralljetenergycorrectionfactor. 4{3 canbewrittenas (4{9) wheresumEisdenedas Inaboveexpressions,thecorrectionbasedontheenergydistributionisexplicitlymanifestedbyfactorizingtheenergyfractioninvariousregionsassociatedwithajetaxisandmakingcorrectiontojetenergywhichisinsidea1.0cone. InfactthereisnorestrictiononhowEt0iscalculated.Thismethodcanbeappliedtonon-standardorcone-basedjetalgorithms(e.g.,Ktjetalgorithm[ 55 ]).ThephysicscorrelationoftherstsummationtermandsecondoveralljetcorrectionterminEq. 4{3 and 4{9 isthebasisforwhycorrectiontakeeects. 4{5 canberevisedasfollows: (4{11) whichclearlyshowsthattheparameterizationactuallycombinesthefractionofenergyandsecondmomentineachregion.Thisparameterizationcanbegenerallyregardedasacombinationoftheenergydistributionandjetshape.

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Inasummary,acomprehensiveapproachisdevelopedbyfactorizingthejetenergyfractionandsecondmomentintothecorrectionfunctions.Theparameteri-zationisbasedonapredenedconesaroundthejetaxis. Intheimplementationofthealgorithm,thejetenergydistributionismeasuredwithina1.0conearoundthejetaxisbecausewewanttostudyitsperformanceonvariousconesizes.FortheQCDsample,mostofthehighETjetsarewidelyseparated(e.g.,twohighestETjetsinthedetectorlevelareclosetoback-to-backin).Butinsomephysicschannelswithcopiousjetsinthenalstate(e.g.,Toppairevents),itisreasonabletoreducethelargestconesizeoronlyuse3or4coneregionstoparametrizethejetenergydistribution.Thisisfeasiblebecausetheenergydistributioninoutertworegionsisverysimilarwhichmeansthatthesearelessimpactsonthecorrectionresults. Theoverlappingofjetswilldenitelycausetheabnormaldeviationfromnormalenergydistributionandthefailureofthecorrection.Relatedissuesarediscussedinnextsection.Themis-identicationofjetsfromelectron,photonorisolatedhadronwillalsocauseabnormaldeviationintheenergydistribution.Obviouslytheenergydistributioncanbefurtherdevelopedtoapowerfultooltorejectthosefakedjets. 4{12 togettheoptimalvalueoftheparameterization(thephysicscorrelationbetweentheenergydistributionandjetarealsoexpressedbythisparameterizationasattingresult): whereEcisthecorrectedjettransverseenergy,Egisgeneratorleveljettransverseenergy,thesumrunsoveralltheinputevents.ThettingisperformedineverypT

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rangewithrespecttocorrespondingdatasample.Thecorrectionon5dierentconesizesofjet(0.2,0.4,0.6,0.8,and1.0)aretested.Thesameconesizesareusedtoreconstructandmatchthegeneratorjettodetectorjet. Inordertogetbetterperformanceforthecorrectionfunction,itispossibletofurthersplitthemeasuredjetETrangeineachbinintoseveralintervals,becauseasinglesetofparameterswillnotworkwellspanningonalargepTrange,andlowpTandhighpTjetsareverydierentinshape,sizeandenergydistribution.Thecalorimeterresponseindierentenergyregionsisnon-linear,whichalsofavorsmorebinning.Butpracticallyitisverydiculttomaketoosmallandmanybinsbecauseoftheamountofwork.Inthisstudy,thesamepTschemesbasedoneventgenerationofthedatasamplesisusedforcorrectionofdetectorjetET. Jetresponseisdependent,sothecorrectionmustbeperformedinareason-ablecalorimeteracceptancerange.Inthisanalysisvebinsof0-1,1-2,2-3,3-4,and4-5areusedtoclassifyjetaccordingtotheofjetaxis.Smallerbinsizehasbeentestedwithshowinglessimprovementinthecorrection.Thisisbecausea1.0coneisadoptedtofactorizetheenergydistribution,whichmakesthecorrectionalgorithmlesssensitivetotheverysmallbinsfor. Theperformanceofthejetenergycorrectionforthedetectoracceptancerangeofjj<3.0(centralregion)andjj3.0(forwardregion)arediscussedseparately.Althoughagoodimprovementofresolutioninforwardregionisachieved,inthisstudywemainlyfocusoncentralregion,because

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axistoestablishtheparameterizationforenergydistribution.Intheforwardregion,thecoarsegranularitypotentiallyfavorsaschemethatdirectlyusetowergeometryinstead. TheresultsalsoshowtheperformanceofEDCorrectionandCSMCorrectionisveryclose,sowemainlypresenttheresultsbasedonCSMCorrection. 4{14 and 4{15 showcalibrationresultsbasedonQCDsampleswithpTfrom20to300GeV/cand5conesizesofjetsrespectively. TherawjetenergyresponseconcatenatedfromdierentpTrangesisnotcontinuous,becauseofbinnedsamplesandthedistortionofthejetpTspectrum.TheselectioncutofjetpTforeachbincausesthebiasoftheaveragedetectorresponse:toolowintheleftsideandtoohighintherightside.TousebinnedQCDsamplestoestimateacontinuousjetpTspectrumanddetectorresponseisnotthemainfocusofthisstudy.Normallyinthecentralregionofeachbin,thedetectorresponseislessbiased,soitcanbeusedtopredictacontinuousspectrumfromanumberofbinnedsamples.Afterthecorrection,thelinearityofjetenergyresponsewithlessthan1%errorisobtained. UsingacontinuousjetpTsamplecaneliminatetheeectsofdistortedjetspectrum,butthisisabigchallengeintheeventgenerationandfulldetectorsimulation,becausethecrosssectionincreasesquicklyasjetpTgoesdown,soaverylargenumberofQCDeventsneedbeproducedinordertogetareasonablestatisticsforhighpTjets.Inthisstudy,resultsshowthejetenergycorrectionworkswelleveninthebinnedsample.

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Fig. 4{16 showstheperformanceofjetenergycalibrationcalibrationinasingledatasamplewiththegeneratorjetpTfrom170to230GeV/c.Ingeneral,EnergyDensity(ED)CorrectionorCombinedSecondMoment(CSM)CorrectionprovidebetterlinearitythanthatofBenchmarkCorrection. (a)(b) Figure4{14. Jetenergyresponsebefore(triangle-down)andafter(triangle-up)thecorrectionwith0.2cone:(a)basedoncorrectionofenergydistribu-tionand(b)basedonbenchmarkcorrection 4{17 showstheperformanceofthecorrectiononthejetpTspectrum.EDCorrectionandCSMCorrectionrecoverwellthegeneratorjetpTspectrum(Fig. 4{17 (b))fromtherawdetectorspectrum(Fig. 4{17 (a)).BenchmarkCorrectionislackoftheparameterizationtorestorethegeneratedjetpTspectrumandcausesdiscontinuitywhenmergingseveraljetETspectrumfromdierentregions.ThespectrumfromEDandCSMcorrectionshowsgoodconsistencywiththegeneratedone.Thebetterperformancemainlybenetsfromthenon-constantandnon-lineartermsandmoreparameterizationinthecorrectionfunctions.

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(a)(b) (c)(d) Figure4{15. Jetenergyresponsebefore(triangle-down)andafter(triangle-up)thecorrectionbasedonsecondmoment:(a)0.4cone,(b)0.6cone,(c)0.8cone,and(d)1.0cone

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(a)(b) Figure4{16. Jetenergyresponsebefore(triangle-down)andafter(triangle-up)thecorrection:(a)basedoncorrectionofenergydistributionand(b)basedonbenchmarkcorrection. 4{18 4{19 4{20 4{21 ,and 4{22 VerysmallimprovementofjetEtisachievedafterBenchmarkCorrection,whichmeansitseectsonRmainlycomefromcalibratingjetpT.CSMCor-rectionreducestheEtatroughly10%acrossthewholepTrangefrom20to600GeV/c,whichcontributetotheimprovementonRinadditiontocalibratingthejetpT.ThehigherthejetpT,themoreimportanteectscanbeseenfromEt,becausejetenergyresponseisclosertounitforhighenergyjetwhichpartiallysuppresstheeectsofcalibration. InlowpTregion(below30GeV/c),gluonjetsfrominitialandnalradiationfromhardscatteringdistortthejetspectrum.AproperanalysisoflowpTjetneedstodierentiatetheconditionofwhetheradditionalhighpTjetispresentedinthesameevent,orwhethersomemethodcanbedevelopedtoroughlyselectthegluonjetandquarkjet.

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(a)(b) (c)(d) (e) Figure4{17. JetpTspectrumbeforeandafterthecorrectioninQCDsamplewithselectedrawjetpTrangingfrom170to200GeV/candjj<3:(a)rawjet,(b)generatorleveljet,(c)correctedjetbasedonsecondmo-ment,(d)correctedjetbasedonenergydensity,and(e)correctedjetspectrumbasedonbenchmarkcorrection

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(a)(b) Figure4{18. Jetenergyresolutionof0.2cone:(a)absoluteresolutionand(b)relativeresolutionwithrawret(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) (a)(b) Figure4{19. Jetenergyresolutionof0.4cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up)

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(a)(b) Figure4{20. Jetenergyresolutionof0.6cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) (a)(b) Figure4{21. Jetenergyresolutionof0.8cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up)

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(a)(b) Figure4{22. Jetenergyresolutionof1.0cone:(a)absoluteresolutionand(b)relativeresolutionwithrawjet(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up) 4{13 .ThettingresultsofrawjetandcorrectedjetbyCSMCorrectionaredisplayedinTable 4{4 ( E)2=a2+(b E)2 Table4{4. Jetenergyresolutioninjj<3.0region Conesize RawjetCorrectedjet 0.2 0:0584L(0:784=p 0:0387L(1:007=p 0:0421L(0:907=p 0:0274L(1:049=p 0:0028L(1:225=p InTable 4{4 ,wefoundsimilarcorrelationbetweenthevalueofeachtermandconesizeforbothrawjetsandcorrectedjets.Therstterm(constantterm)playsanimportantroleinthehighpTregion.Forsmallconejets,thiseectismoreprominent,whileforlargeconejets(0.8and1.0),thersttermalmostvanishes(whichiscompensatedbyincreasingthevalueofthesecondterm).Thephysicsaspectsoftheconstanttermhighlyrelatetothetransversesizeofthehadronic

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shower.Narrowconejetsarelessinuencedbythepileupandelectronicnoise.Alargervalueofconstanttermisprimarilycausedbytheleakingofthehadronicshower.Twooppositeeectsmaintainthebalanceoftherstterm,asjetenergygoesup,thewidthoftheoveralljetsizedecreasesandtheleakingfromparticleshowersincreases. SecondtermdominatesRinthejetpTrangefrom20to600GeV/c,whichmainlyrelatestothestochasticeectofthecalorimeterresponse.Widerconejetscontainalmostallthehadronicshowerofthejet,sothestochasticeectisfullymanifested.Thisleadstoalargervalueofthesecondterm. Theresolutionofthenarrowconejetisgenerallybetterthanthatofthewideconeones,becausemosthighETtowersareclosertothejetaxiswithhigherenergyresponseandhaverelativelysmallerstochasticeectthanlowETtowersfurtherawayfromthecenterofthejet.Sonarrowconejetstakeadvantagefromtheintrinsicfeatureofthedetector.ThefurtheroptimizationoftheconesizeforthejetreconstructionandcorrectionlargelydependsontheanalysisneedandtheinterestedjetpTrange.Normallyitcannotbeonlybasedonthejetenergyresolution. 4{23 showscalibrationofjetenergyof0.6coneinforwardregion(jj>3.0),inwhichtherawjetenergyisalwaysover-measured.Afterthecorrection,thelinearityofjetenergyresponsewithlessthan1.5%errorisobtained. Resultsofabsoluteresolution(Et)isshowedinFig. 4{24 .BecausethecalorimetergranularitygetslargerintheHF,whichmaylimittheaccuracyofthemeasuredjetenergydistribution,butanaverageimprovementofabsoluteresolutionof10%forforwardjetswithvariousconesizeandacrossthepTrangefrom20to300GeV/cisachieved.

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Figure4{23. Jetenergyresponseof0.6conebefore(triangle-down)andafter(triangle-up)thecorrectionbasedonsecondmoment TherelativeresolutionafterthecorrectionisttedbyExp. 4{13 ,theresultsareshowedinTable 4{5 Table4{5. Jetenergyresolutioninjj3.0region Jetconesize Correctedjet 0.2 0:0589L(0:103=p 0:0501L(0:358=p 0:0353L(0:646=p 0:0175L(0:812=p 0:0195L(0:847=p

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(a)(b) (c)(d) (e) Figure4{24. Jetenergyresolutioninforwardregion(jj>3:0)withnocorrection(opencircle),benchmarkcorrection(triangle-down),andcorrectionbasedonsecondmoment(triangle-up)invariousconesize:(a)0.2,(b)0.4,(c)0.6,(d)0.8,and(e)1.0

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Ageneralselectioncriterionbasedonjetenergydistributioncanbecharacter-izedbythesumofsignicance(S)ofthejetenergyineachregion(Eq. 4{14 ). S=5Xi=1Si;Si=Ri)]TJ/F3 11.95 Tf 12.61 0 TD[( i whereRiisdenedinEq.( 4{4 ).istheaverageofRiintheselectedjetpTrange.iisthesigmaofRi.IncasethedistributionsofRihasmuchdeviationfromaGaussian,halfofFWHMisusedinstead.AsmallSgenerallyindicatestheenergydistributioninsidetheobservationregionofthejetisnormal. Fig. 4{25 showstheSdistributioninaselectedjetsample.Table 4{6 showstheandiofthisselectedjetsampleusedforScalculation. Figure4{25. NormalizedSdistributioninQCDsamplewithjetpTrangefrom80to120GeV/c Table4{6. JetselectionparameterofdierentenergydistributionregionwithjetpTfrom80to120GeV/c Coneregion 0.0-0.20.2-0.40.4-0.60.6-0.80.8-1.0 ScanbettedwithaGaussiandistributionwith=1.51,whichshowsitisawell-behavedandappropriateparameterforthejetselectionandeciency

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estimation.ExceptthereasonableuctuationofSofnormaljets,thesystematicdeviationofSofabnormalonescanbe: Thelastcasemainlyrelatestolowenergyjets.Tosuppressthosefakedjetsinthedetectorisachallengebecauseofthehighluminosityenvironment.NormallythosejetscanberejectedbysettingaminimumthresholdofhighestEToftowers(thistoweriscommonlyusedasaseedforjetreconstruction).ButtheeciencyofapplyingthetowerETthresholdwillbelimitedbythefactthathadronicshowercanbesharedbyseveraltowers,solowenergynormaljetshavemorechancetofailtheselection,whichmakestheoptimizationoftowerETthresholddicult.Fortheselectioncriterionthatisbasedontheenergydistributionwhichisnotsensitivetotheenergyofonetowerbutaregion,theissueisavoided. ItisalsopossibletocombiningEq. 4{14 withotherselectionmethods(e.g.,acutonECALtoHCALenergyratiointheinnerconeandsumofchargedtrackenergy)toachievebettereciencyofjetselection.Thecompletetreatmentoftheabnormaljetsrejectionisbeyondthecorrectionmethodweconcentrateon,butenergydistributionisapromisingmethodforoinephysicsanalysisinvolvingtheselectionofjets.

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developed,whichisbuiltontheenergyfractioninthepredenedregionsaroundthejetaxisorthesecondmoment.Anon-trivialcorrelationbetweenthejetenergydistributionandgeneratedjetpTisobserved. Westudiedtheenergydistributionfunctionwithitsparameterization.ThroughacomparisonwithETbasedjetcorrectionalgorithm,thenewschemeshowsgoodperformanceonrestoringtheaveragejetenergyscaleandjetpTspectrum,anddistinctiveimprovementontheabsolutejetresolutionatanaverage8to10%forQCDsampleswithjetpTfrom20to600GeV/c.TheresultalsoshowstheperformanceoftheETbasedjetenergycorrectionalgorithmisinsensitivetothehigherordercorrectionfunctions. Thisstudyshowstheoptimizationofjetreconstructionandreductionofthevariationofrawjetenergyerrorcanbeachievedwithincalorimeterthroughaproperparameterizationofthephysicscorrelationbetweenvariousphysicsobservables.Thejetenergydistributionisanimportantaspectofjetphysics,whichhasnotbeensystematicallystudiedinLHC.Ourresultsshowthisisapromisingdirectiontoimprovethejetenergyresolutionandtounderstandtherelevantdetectoreects. Theframeworkofthejetenergydistributioncanalsobeusedforselectingnormalorabnormaljets.Aprimitiveschemebasedonthesumofsignicanceofthejetenergyinthepredenedregionsistested,whichshowsthestatusofthejetenergydistributioncanbecharacterizedbyaGaussiandistribution. Thejetenergyresolutionofvariousjetconesizesisstudied.Eectsofpileup,electronicnoise,leakingofhadronicshower,out-of-conetrackscausedbymagneticeldarediscussed.ThesefactorslargelycomplicatetherelationshipbetweenthejetenergyresolutionandjetET.

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Itiswellknownthattheunderstandingofthedetectorresponsetostandardmodelphysicsfromquantumchromodynamics(QCD)di-jeteventsisaprerequisitetothesearchfornewphenomenaattheLargeHadronCollider(LHC).Ithasalsobeenlongrealizedthatthemissingtransverseenergy(EmissT)isapowerfultoolfornewphysicsdiscovery[ 43 ].MucheorthasbeenplacedonthedesignofcalorimetersforoperationathadroncolliderstohaveascompletecoverageaspossibleforthepurposeofmakingameaningfulmeasurementofEmissT[ 30 ]. AccuratedeterminationoftheinclusiveEmissTspectrumisanimportantbutdiculttask,becausevariousdetectorfactorscontributeinsubtleways.Thesefactorsinclude: Unlikeregionalreconstructionobjects(e.g.,electronandmuon),EmissTisgloballyreconstructedandpronetoanyabnormalfunctioningofthedetectororunexpectedfactorwhichisnotwellmanifestedinthesimulation.ThepredictionofEmissTspectrumandtriggerthreshold[ 28 ]aresensitivetothecongurationofthesimulation. 78

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QCDeventsprovideanimportantmeanstomeasureandevaluatethereli-abilityandaccuracyofthedetectorsimulationandreconstructionontheEmissT,because: VariousphysicsanalysishasrequiredagoodunderstandingofEmissT.ThestudyshowninthischapterisoneoftheapproachesthatattempttoexploitandoptimizetheEmissTreconstruction.ThetopicsofEmissTcorrectionbasedonleptoniceventsandusingfactorizationmodeltosystematicallystudythecorrelationbetweenEmissTquantitiesanddierentphysicsnalstatescanbefoundinlaterchapters. Thisstudyisperformedonthelatestdataof3millionQCDeventswithfulldetectorsimulationbasedonGEANT4andanaveragepileupof3.5minimumbiaseventsatlowluminosity(L=21033cm)]TJ/F4 7.97 Tf 6.59 0 TD[(2s)]TJ/F4 7.97 Tf 6.59 0 TD[(1).TheeventsaredividedintoanumberofjetpTintervalsfrom20to1000GeV/cinthegeneratorleveltomaximizethereachonhighpTjets.ThelimitationofdatasamplesizeinlowpTeventsisdiscussed,whichisoneofthemainuncertaintiesintheestimationoftriggerthreshold. EventreconstructionandphysicsanalysisisperformedwithORCA[ 40 ].EmissTisreconstructedfromavectorsumofcalorimetertowerswithLevel-3Muoncorrection,whichmuonmainlycomesfromheavyavordecay.Thecrosssectionofthoseeventsisrelativelysmaller,buttheyhasrealcontributiontothedetector

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levelEmissTifthereconstructionalgorithmissolelybasedonthecalorimeter.ThegeneratorlevelEmissTisreconstructedfromallparticleswithinthecoverageofCMSdetectorexceptneutrinos. 5{1 showsthenormalizedEmissTdistributioninthegeneratoranddetectorlevelrespectivelywithdierentjetpTranges: ThedetectorEmissTisacombinedeectofalltheeventsinthesamecrossing(theout-of-timepileupfromothercrossingscanbeapproximatelytreatedasaconstantterm).Usingtheeectivebunchcrossingrate(Rebunch)andknowncrosssectionofeachpTinterval(i),theinclusiveEmissThighleveltrigger(HLT)rateforeachsample(Ri)canbeestimatedbytheweightingmethodprovidedby[ 59 ](Eq. 5{1 ).

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(a) (b) Figure5{1. MissingtransverseenergyspectrainQCDsamplesin(a)generatorleveland(b)detectorlevelthatcorrespondtojetpTranges(fromlefttoright)of20-30,30-50,50-80,80-120,120-170,170-230,230-300,300-380,380-470,470-600,600-800,and800-1000GeV/c. whereRebunch=32MHz,TisthetotalcrosssectionofQCDdi-jets(55mb),andSiisthenormalizedHLTrateofeachsamplewithrespecttoitscrosssectionandHLTthreshold.

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TheoverallEmissTHLTrateandthecontributionfromeachsamplesareshowninFig. 5{2 .ThelowerpTsampleswithpTfrom0to20GeV/careexcludedbecauseoftheirtoolimitedstatisticsandtoosmallselectioneciency(lessthan10)]TJ/F4 7.97 Tf 6.58 0 TD[(4)whichcan'tbeusedtoestimatetheHLTrateabove60GeVlevel.Inothersamples,thelossofstatisticsalsoexists,whichmakesmostofthestatisticaluncertaintyintheestimationbecauseofthelargecrosssectionofthelowpTsamples.Bothourdataandthedatausedforpreviousstudies[ 28 29 ]basedonGEANT3simulationshowthecontributionfromlowerjetpTevents(0-20GeV/c)doesnotsignicantchangetheHLTratewithEmissTabove90GeVthreshold. OurresultsbasedonGEANT4simulationisgenerallyconsistentwithpreviousresults[ 28 29 ],butalowerthreshold(90GeV)correspondingto1HzoutputratefromHLTisindicated.WeplantopursueacompletestudytoupdatetheHLTEmissTtriggerbasedonfastsimulation.Inordertomakepreciseestimationandfullyextractthesystematicandstatisticaluncertainties,averylargenumberoflowETQCDeventsareneeded(108),whichissubstantiallybeyondthecurrentstatisticsoftheavailablefullysimulateddata. WeusedlowpTsampleof0-15GeV/ctoinvestigatetheeectofpileupminimumbiasevents,wherethesignaleventscanbemostlytreatedasminimumbiaseventstoo.Anaverage10GeVintheresolutionofx(y)componentofEmissTisobserved,whichcanbeusedtoestimatetheEmissTvariationfromdetectoreectsinthepureleptonicchannel(e.g.,Z!+)]TJ/F1 11.95 Tf 7.08 -4.34 TD[(,W!),buttheeectofcollinearradiationfromsignaleventsshouldbeconsideredseparately. Thetotalscalartransverseenergy(PET),denedasthescalarsumoftheETofcalorimetertowersinanevent,isaquantityhighlyassociatedwithEmissT[ 44 ].ManyEmissTpropertiescanbeexpressedasafunctionofPETbecauseithasdirectinuenceontheEmissTresolutionviathestochasticeectincalorimetershowersandotherdetectorsignalcollectionprocesses.Fig. 5{3 showsthespectrumofPET.

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Figure5{2. InclusiveEmissTHLTratecalculatedfromsamplesofjetpTrangesof50-80,80-120,120-170,170-230,230-300,300-380,380-470,470-600,600-800,and800-1000GeV/c.For1kHzrate(Level-1rateforEmissT),thethresholdisroughly50GeV,whichisunderestimatedduetothelowerpTsamples(0-20GeV/c)arenotused;for1Hzrate(HLTrateforEmissT),thethresholdisroughly90GeV,wherethecontributionfromthelowerpTsamplesissmall. ThedetectorPETresponseisdenedastheratioofdetectortogeneratorleveltotalscalartransverseenergy(PEdetT/PEgenT).Duetothenon-linearityofcalorimeterresponse,thisratioisnotconstant,butratherafunctionofPET(Fig. 5{4 ).Threetypesofcorrelationsareinvestigated: 1. DetectorPETwithpileupeectversusgeneratorPETusinggeneratedsignaleventonly. (XEdetT=XEgen signalT)=0:9176+242:6 signalT)]TJ/F1 11.95 Tf 11.96 0 TD[(40:44 (5{2) 2. DetectorPETwithoutpileupeectversusgeneratorPETusinggeneratedsignaleventonly(basedonfastsimulation(FAMOS)[ 45 ]). (XEdetT=XEgen signalT)=0:9149+204:2 signalT+463:12 (5{3)

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(a) (b) Figure5{3. ScalarPETspectrainQCDsamplesin(a)generatorleveland(b)detectorlevelthatcorrespondtojetpTranges(fromlefttoright)of20-30,30-50,50-80,80-120,120-170,170-230,230-300,300-380,380-470,470-600,600-800,and800-1000GeV/c.

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(a) (b) Figure5{4. DetectorPETresponseasafunctionofPEgenT(a)usinggeneratedsignaleventonlyinORCA-OSCAR(closecircle)andFAMOS(opencircle)and(b)usinggeneratedsignalandgeneratedpileupevents

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3. DetectorPETwithpileupeectversusgeneratorPETusinggeneratedsignaleventandgeneratedpileupevents. (XEdetT=XEgenT)=0:9192+52:24 (5{4) Comparedtothefullsimulation,themajordierenceinfastsimulation[ 45 ]isthatitdoesnothavein-timepileup(pileupeectfromsamebunchcrossing)andout-of-timepileup(pileupeectfromdierentbunchcrossing)fortheversionweused.ThecomparisonbetweenEq. 5{2 and 5{3 illustratesadetectorlevelpileupeectwithseveralhundredGeVoftransverseenergyintroducedbythisoveralldetectoreect(Fig. 5{5 ).InawidePETrange,thisfactorcanbenearlytreatedasaconstant.ItsvisibledependenceonPETcomesfromvariousandcomplicateddetectoreects:non-linearresponse,electronicnoiseinducedbyincreasingsignalevents'energy,andtheETthresholdinHCALhitreconstruction(500MeV)thatmakeminimumbiasevents'presenceandcontributionpotentiallydependonthesignalevent. Figure5{5. ContributionofpileuptoPEdetTasafunctionofPEgenT

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ThepileupeectiscriticalforPEdetTquantities.ItisstrongerinthelowpTQCDevents.NormallywecanconsiderthatminimumbiaseventscontributearelativelyconstantPETatthegeneratorlevel(200GeVineachcrossingatlowluminosity),whichislesscorrelatedtothePETcomingfromsignalevent(thesameargumentappliestotheEmissT). Inthedetectorlevel,minimumeventsaremainlymeasuredinlowenergytowers.Asweknow,thelowenergycalorimetermeasurementprimarilycomesfromthreesources:minimumbiasevents,lowenergyparticlesfromsignalevents,andelectronicnoise.DuetotheHCALhitthreshold,thesefactorsarepartiallycorrelated.ChangingonefactorwillinuencethepresenceofrestfactorsinPET,whichexplainswhyalargerpileupfactorobservedinthedetectorlevel(400GeV). ThosefactorsareoverlappedandcombinedtogetherinthedetectorPET(wecallthiscombinedeectasanominalpileupeect).Technicallyitisimpossibletomeasurethestandalonedetectorresponseforeachofthosefactors.Inthelatersectionwewillfurtherquantitativelydiscussthiseectfromanotheraspect. 5{6 : 1. EmissTversusdetectorlevelPET.

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(a) (b) (c) Figure5{6. Emissxresolutionquantities:(a)EmissxresolutionversusdetectorPET,(b)EmissxresolutionversusgeneratorPET,and(c)EmissxresolutionversusgeneratorPETusingsignaleventonly

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2. EmissTversusgeneratorlevelPET. 3. EmissTversusgeneratorlevelPETwithsignaleventsonly. signalT)]TJ/F1 11.95 Tf 11.95 0 TD[(378:5)+0:01182(XEgen signalT)]TJ/F1 11.95 Tf 11.95 0 TD[(378:5)2 Fig. 5{7 showstheaverageEmissTversusPET.ThedependencyisinvestigatedinasimilarwayasthatofEmissT: 1. 2. 3. signalT)]TJ/F1 11.95 Tf 11.95 0 TD[(296:8)+0:01792(XEgen signalT)]TJ/F1 11.95 Tf 11.96 0 TD[(296:8)2 ThedependenceofEmissx(y)resolutionandaverageEmissTonPETwillbemea-suredaccuratelyattheLHCbecauseofthelargeproductioncrosssectionofQCDdi-jets,ascomparedtothetheniteMonteCarlosimulationandreconstruction

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(a) (b) (c) Figure5{7.

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samplesusedinthisstudy.Thesesampleswillimproveourunderstandingofvari-ousdetectoreectsanductuationsofjetenergyresponsethatcausefakeEmissTinQCDevents.Apre-scaleddi-jettriggersdowntolowjetET(usingalowerjetETthresholdtotriggertheeventswithascalingfactortocontroltheselectionrate)orusingminimumbiastriggerdataisnecessarytoclearlyunderstandtheEmissTresolutionindetail. ThereisalargeosetofETinthettingfuction,thisisbecause: 5{3 ,sothettingmainlyconsidertheaveragePETresolutioncalculatedfromeachsample. Atowerthresholdcanbeusedtosuppresstheelectronicnoiseandpileupen-ergywhichresultinamuchlowerPET,butthisisquitedierentinphysicsfromthe\true"lowPETinthefronttailofthespectrum,althoughsomecorrelationcanbeexploited(discussedinthelatersection). Inthefollowing,webrieydiscussthecorrelationoftheEmissx(y)resolutionunderthesituationofunder-pileupandthePETbyusingsingleminimumbiaseventandQCDsampleswith^pTof0-15and15-20GeV/c,whichcanbetreatedpileupedminimumbiassamplesbecauseofverylowsignalevents'PET.ThesethreesamplesshowveryconsistentfeaturesinEmissx(y)resolution(Fig. 5{8 (a)).The

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ttingbasedonthesesamples(Fig. 5{8 (b))gives signalT)]TJ/F1 11.95 Tf 11.95 0 TD[(124:3) (5{11) (a)(b) Figure5{8. EmissxresolutionquantitiesinlowPETsamples:(a)EmissxresolutionversusdetectorPETand(b)ttingbasedontheaveragecorrelationofthesesamplesbetweenEmissxresolutionandPET ThevalueofEmissTcanbecalculatedseparatelyforeachregion.Withtworegionsdenedbythereconstructedeventatthedetectorlevel,thegeneratorlevelparticlesareassociatedwithoneoftheregionsbasedontheiryingdirection.Thedenitionofregionsisperformedforeveryevent.Itisimportanttousethedetectorlevelonly(orgeneratorlevelonly)fortheregiondenition,butnotthecombinationofthem,becauseweneedtomaintainaconsistentviewofevent

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geometrybetweenthedetectorlevelandgeneratorlevelofthesameeventtomakecomparisons. Jetsarereconstructedbytheiterativecone(IC)algorithmimplementedinORCAwithconesizeofR=0:5andET>20GeV.Thetowersthatdonotcontributetothejetsarecollectedasunclusteredtowers.Fig. 5{9 showstheratioofPETofjetregiontounclusteredregion.Fig. 5{10 showsseparatelytheEmissxresolutioninjetandtheunclusteredregionsasafunctionofPET,whichindicatesthejetregionplaysamoreimportantroleindeningtheoverallevent'sEmissTquantities. Figure5{9. RatioofPETofjetregiontounclusteredregionversusPET. ThejetconesizewasvariedtoinvestigatetheeectontheregiondenitionandEmissTquantities(Fig. 5{11 andFig. 5{12 ).WeusetheaxisofICjetswithaR=0:5coneasinputtorebuildthejetswithnewconesizesofR=0.2,0.4,0.6,and0.8.

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Figure5{10. EmissxresolutionofthejetandunclusteredregionsversusPET. 0.2coneshowsverydierentbehaviorfromotherconesizesduetothe\leaking"ofthejetenergy(relatedtohadronicshower)toitsproximityregion.ThePETresponseinthejetregion(Fig. 5{11 (d))manifeststhecorrelationbetweenthejetenergyresponseandthejetconesize,whichisconsistentwiththeobservationthatmostofthejetenergylocatedinthenarrowconearoundthejetaxis.ThelargeresponseoflowETeventsisaneectfrompileupenergy.Theinformationofunclusteredregionisusefultojustifytheconesize.Theunclusteredregion'sPETversusoverallPET(Fig. 5{12 (c))showsthat0.4conesizeisverystable.Thisfactindicatesa\optimal"conesizearound0.4. 5{12 (c)and(d))indicatea240GeVtotaltransverseenergyfromminimumbiasandelectronicnoise.ThedierencebetweenthenominalpileupfactorinFig. 5{5 andhereisbecausetherstresultcontainsasystematicbiasduetothe

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(a)(b) (c)(d) Figure5{11. EmissTrelatedquantitiesinjetregion:(a)averagedetectorEmissT,(b)detectorEmissxresolution,(c)averagedetectorPET,and(d)responseofdetectortogeneratorlevelPETusingsignalevent

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(a)(b) (c)(d) Figure5{12. EmissTrelatedquantitiesintheunclusteredregion:(a)averagedetec-torEmissT,(b)detector(Emissx),(c)averagedetectorPETand(d)responseofdetectortogeneratorlevelPETusingsignalevent

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overlappingofallthefactorsintheunclusteredregionandthenon-linearresponseinthejetregionduetothepileupeect.Ingeneral,quantitiesrelatedtothesystematiceectofpileupandelectronicnoisehighlydependonthecongurationofthesimulationandreconstruction.ItsinuenceonEmissTneedtobeclearlyunderstoodespeciallyatthehighluminosity.Intheexistingreconstructionstrategy,theHCALhitETthresholdprovidesapartialcontrolofthesefactors. Wedenethefollowingquantitiestofurtherinvestigatethecorrelationbetweenthejetandunclusteredregions: TherstquantityshowstherelativecontributionofthetworegionstotheoverallEmissTbasedonthemagnitudesofEmissT;UandEmissT;J.ThesecondquantityshowshowtworegionscontributetotheresolutionofEmissT. Fig. 5{13 showsEmissT;U=EmissT;Jand(EmissT;U)=(EmissT;J)asafunctionofPETusingtheR=0:8conesizeforthedenitionoftheregions.Fig. 5{14 showshowvariousconesizesaectEmissT;U=EmissT;Jand(EmissT;U)=(EmissT;J). Fig. 5{15 showstheangularcorrelationbetweenEmissT;UandEmissT;Jdenedbyaback-to-backquantity(=jet)]TJ/F3 11.95 Tf 12.47 0 TD[(uncluster)]TJ/F3 11.95 Tf 12.47 0 TD[().Fig. 5{16 showsthefractionofeventsthatsatisfyjj<1:0withastrongback-to-backcorrelationbetweenthejetandunclusteredregions.Theresultconrms0.4coneisaverystableintheangularcorrelationbetweentwotregions. Theapparentdierencebetweenvariouscones'behaviorinFig. 5{16 showsthatitisaverysensitivewaytoinvestigatetheperformancebasedonthiscorrela-tionwithrespecttovariousjetconesizes.Theoriginofthedierenceshowsboththeintrinsicphysicseectanddetectoreect:

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Figure5{13. EmissT;U=EmissT;Jand(EmissT;U)=(EmissT;J)asafunctionofPETusing0.8conesizetodenethejetandunclusteredregions

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(a) (b) Figure5{14. Correlationbetweenthejetandunclusteredregions:(a)EmissT;U=EmissT;Jand(b)(EmissT;U)=(EmissT;J)asafunctionofPETusingvariousconesizestodenethejetandunclusteredregions

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(a)(b) Figure5{15. TheangularcorrelationwithQCDsamplesofjet^pTof(a)30-50and(b)50-80GeV/cforfourconesizes:0.2(black),0.4(red),0.6(green),and0.8(blue).ThepeakshowsEmissT;UandEmissT;Jareback-to-back.

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Figure5{16. Fractionofeventswithaback-to-backcorrelationjj<1.0betweenthejetandunclusteredregionsasafunctionofPETforfourconesizes:0.2(black),0.4(red),0.6(green),and0.8(blue)

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1. QCDEmissTismainlyadetectoreect.NormallyjetenergycorrectionwillnotrecoverthegeneratorlevelEmissTandpossiblyfurtherbiastheoverallEmissTofthejetsystem. 2. ThesignaleventshavelargetrueEmissTingeneratorlevel(e.g.,SUSY[ 54 ],Top,InvisibleHiggs,andW+jets),thedetectorEmissTisunder-measuredduetothelowcalorimeterresponse.AjetenergycorrectionworksforthistypeofEmissTandcalibratestheaverageEmissTscale. Theeectofnon-uniformityofcalorimeterjetenergyresponsecanbecor-rectedbytheenergyjetcalibration.AsmallfractionofQCDeventswithdi-jethavinglargedierenceandverydierentjetenergyresponsehavethepoten-tialtobenetfromjetenergycorrection,butforthoseeventswithdi-jetshavingsimilar,thejetcalibrationmightdeterioratetheEmissTresolution.Sotheimple-mentationofjetcalibrationforQCDeventsismainlyaselectionofeventsusingdi-jetdistributioninsteadofageneraltechniquethatcanworkforalltypesofphysicsevents.PossiblebiascanbeinducedifitisusedforHLTandmaketheHLTselectionlessinclusive. Chapter7providesadditionalinformationconcerningabovediscussion.AnoptimalstrategyforHLTselectionisunderinvestigation.Foroineselection,usingdi-jetcorrelationismoreeectivetosuppressQCDeventsthanusingjetcorrectionwithrespecttoEmissTquantities.Whichoneisbetterlargelydependsonthespecicneedsoftheanalysis. Inprevioussection,thejetandunclusteredregionsaredenedandusedtostudytheEmissTquantitiesandtheircorrelation.Inthissection,wefurtherexplorethecorrelationbetweenjetsandEmissTinQCDevents.Fig. 5{17 showsthedistancebetweenthehighestETjetandEmissT.Fig. 5{18 showsthedistancebetweenthesecondandthirdhighestETjetsandEmissT.Fig. 5{19 showsthecorrelationbetweentwohighestETjets.

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(a)(b) Figure5{17. EmissTandthehighestETjetarestronglyback-to-backcorrelated.Thisiscausedprimarilybydetectorresolutioneectinducingalargerenergymis-measurementalongthedirectionofdi-jet.ThedirectionoftheEmissTandthesecondhighestETjetalsotendstobecollinearduetotheback-to-backnatureofQCDdi-jetevents.TheEmissTandthethirdhighestETjetarealmostuncorrelated,whichisanticipatedbecausethesoftjetsfromradiation,orjetsfromotherdetectorfactors(e.g.,pileup,underlyingevents,andelectronicnoise)havelesscorrelationwithdi-jetsystem.TheEmissTinQCDeventsdominatedbythejetmeasurements.Fig. 5{20 and 5{21 showthecontributiontoEmissTfromthetwohighestETjets. Fig. 5{22 showsthedetectorlevelEmissTresolutionintheorthogonaldirectiontodi-jet.Thisisaninterestingquantity,becausedi-jetsystemmainlycausesaEmissTinthejetdirection.Intheorthogonaldirection,thecontributionfromdi-jet

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(a) (b) Figure5{18.

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Figure5{19. Thecorrelation(denedas=1)]TJ/F3 11.95 Tf 12.16 0 TD[(2)ofthetwohighestETjets.FiveQCDsamplesareusedwithjetpTranges:50-80(black),80-120(red),120-170(green),170-230(blue),and230-300(yellow)GeV/c.

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Figure5{20. ThecorrelationbetweenEmissT;JandEmissTdenedas=jet)]TJ/F3 11.95 Tf -353.21 -14.44 TD[(EmissT+forveQCDsampleswithjetpTranges:50-80(black),80-120(red),120-170(green),170-230(blue),and230-300(yellow)GeV/c

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(a)(b) Figure5{21. ThecorrelationquantitiesshowninFig. 5{20 asafunctionofPET:(a)theofcorrelationand(b)theaveragePETofthetwojets ismuchsmaller,whichiscausedbyinitialstateradiationandnalstateradiation,magneticelddeectingjetparticles,andtheunderlyingevent. 5{23 inseveralsamples.Ingeneral,highthresholdwilldenitelydeterioratestheresolution.Below0.9GeV,mostofthesamplesshowsinsensitivetothethreshold,thisisbecausethevalueofthresholdisinthesamelevelofthelowenergytower'sresolution(O(1)GeV). AhighthresholdcausesseriousbiasinEmissTmeasurement,becauseitseectisbeyondthesuppressionofelectronicnoiseorpileupevents.TheunclusteredregionisdominatedbythetowerswithET<1GeV,whichisverysensitivetothethreshold,whileinjetregion,thethresholdhaslessinuence.AhighthresholdisequaltoremovingtheunclusteredregionfromEmissTreconstruction,ofwhicheectisdiscussedinnextsection.

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Figure5{22. DetctorlevelEmissTresolutionintheorthogonaldirectiontodi-jetasafunctionofPET 5{24 .AhightowerenergythresholdlargelyreducesthePETlevel.ThecorrelationbetweenthetowerthresholdandPETprovidesawaytomeasure(orpredict)detectorfactorsinthelowenergyregion.AosetofPETwithatowerthresholdtisdenedas (XEtT)=XEtT)]TJ/F7 11.95 Tf 11.95 11.35 TD[(XE0T wherePEtTandPE0TcorrespondtoPETwiththresholdtand0respectively.TheratioofPEtT/PE0T(denedasRt)isillustratedinFig. 5{25 .ThecurvesarettedwithEq. 5{13

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(a)(b) (c)(d) Figure5{23.

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Witht=0GeV,thedetectorRtshouldbeequalto0accordingtothedenition,butprojectedRtatt=0(denedasRpt=0)fromvarioussamplesarealllowerthan0,whichshowsasignicantamountoflowenergytowersareremovedbythe0.4GeVtowerenergythresholdwhichisthelowestoneusedforthetting.ThecorrectionbetweenRpt=0andPETisillustratedinFig. 5{26 Figure5{24. Rpt=0isaninterestingparameterwhichcanbeextracteddirectlyfromex-perimentaldataandiscorrelatedtotheosetinthettingfunctiondiscussedinSection3.Rpt=0isnotaconstantterm,whichreectsthecomplexityofthedependencyofEmissTquantitiesonotherdetectorfactorsandselectioncuts(e.g.,towerenergythreshold).DuetolowpTeventsinfactdominatestheQCDsamples,itisplausibletouse250-300GeVfortheosetforthettingoftheEmissTresolutionversusPET.Anin-depthstudyisneededtocompletelyexploitthecorrelationbetweenRpt=0andosetintheresolutionttingfunctionbyapplyingvariouslevelofelectronicnoiseandpileupcondition.Inthisstudy,wemainlyfocusonlowluminosity,sothecombinedeectofelectronicnoiseandminimumbiasevents

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Figure5{25. Figure5{26. Rpt=0asafunctionofPETusingQCDsamplesofjetpTranges:20-30,30-50,50-80,80-120,120-170,170-230,and230-300GeV/c

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playsanimportantroleinthesensitivenessofEmissTquantitiestothetowerenergythreshold. ThekeyreasonwhyweneedtoconsiderboththejetandtheunclusteredregionsforEmissTisthatthesignaleventsalsodepositlowenergyparticlesintheunclusteredregion.ThegeneratorlevelEmissxresolutionusingjetregionasafunctionofPETisshowninFig. 5{27 .ThedeviationduetotheregionexclusionisgenerallyhigherthestandaloneEmissxresolutioncausedbypileupandotherdetectoreects(10GeV)whichmainlyoccursintheunclusteredregion(discussedinSection2).ThisfactindicatesthatevenvariousdetectoreectscausethedeteriorationofEmissx,butitisstillbettertokeeptheunclusteredregion,whichalsoexplainswhyahightowerenergythresholdmightaecttheEmissTresolution. Inthecaseofhighluminosity,theconclusionmightchange.Ifthestandalonedeviationcausedbyvariousdetectoreectsreaches20GeVlevel,basedonFig. 5{27 ,itcanbeseenthatforlowPETQCDeventswhichroughlycorrespondstotheeventswithjetETbelow150GeV,theexclusionoftheunclusteredregioncanreducetheoveralldeviationofEmissx.ItisexpectedthatusingonlyjetregionhasastrongereectinlowpTsamples.ThusareductionoftheEmissTtriggerratecanbeachievedwithoutaectingthe\inclusiveness"ofthetriggerstrategy,becauseitdoesnotrequireapreciseknowledgeofjetcorrelationlikeotheroptionaltechniqueswhichcanalsosuppressQCDevents(e.g.,jetenergycalibrationfortheeventswithlargedierence,correlationbasedondi-jet).

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Figure5{27. GeneratorlevelEmissxresolutionusingclusterregionasafunctionofPET ThesemeasurementandanalysisprovideacriticalframeworktocharacterizeandevaluatethedetectorperformanceonfundamentaloinePETquantities.SimilarapproachusingexperimentaldatawillbeperformedafterLHCtakesdata.

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TherawEmissTiscalculatedbysumminguptransverseenergyvectorofallcalorimetertowers(Eq. 6{1 ).Thisisapparentlyincompleteforsomephysicschan-nelsthatcontainmuoninthenalstates.Manystudiesofprecisionmeasurementofstandardmodel[ 46 47 ]andsearchingfornewphysics(e.g.,Supersymmetry[ 48 49 50 51 ]andHiggsboson[ 52 53 ])needabetterqualityofEmissTreconstruc-tionandpropertechniquestocorrectthesystematicbiasandineciencyinrawquantitiesduetovariousdetectoreects.Theperformanceandlimitationofthosecorrectiontechniqueswillalsoneedbewellunderstood. Earlierstudies[ 54 29 ]showusingcalibratedjetsforEmissTreconstructioncanrestoretheaverageEmissTscaleinseveralSUSYprocesses,butsimilarmethoddoesnotreducetheEmissTtriggerratedominatedbyQCDevents,inwhichthefakedEmissTmainlycomesfromthestochasticeectofcalorimeterjetenergyresponse.BecauseofverylargecrosssectionoftheQCDprocessathadroncollider,ahightriggerthresholdfortheinclusiveEmissTisnecessarytoreducetheEmissTtriggerratetoareasonableleveltorecordtheeventsfromtheonlinesystem.ThisfactindicatesthatthenormaljetcalibrationmainlyworksoncertainchannelswithlargetruegeneratedEmissT,butineectivetootherchannelsthathavesmallgeneratedbutlargedetectorlevelEmissT.ItraisesasubtlequestionaboutthepossiblebiasofjetenergycorrectiononEmissTfordierentphysicsprocesses,especiallyforthoseanalysisinvolvinghadronicnalstatesorinclusiveEmissTquantities. 114

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OtherthanQCDevents,manyphysicsprocesseswithhadronicnalstates(e.g.,ToppairandW/Z+jetswithW/Zhadronicdecay)maketheEmissTinthedetectorlevel.Thoseeventsaremoreseriousbackgroundtonewphysics.Althoughusingextrasignatures(e.g.tau-tagging,b-tagging,andQCDdi-jetcorrelation)helpsuppressthefakedEmissTandextractthesignalfromthelargebackground,theissuediscussedabovestilllimitstheusageofjetenergycorrectionasanon-selectivetechniquefortheEmissTcorrectioninhadronicnalstates. AmoreappealingnalstatefortheEmissTcorrectionisEmissTpluslepton(calledleptonicevent).ThehigheciencyofleptonidenticationstronglyrejectsQCDandotherhadronicevents.Thesemi-leptonicWbosondecay,resultinginneutrinoandtruegeneratedEmissT,isamajorsourceofleptoniceventswhichdominatesthesingleleptontriggerforleptonpTabove20GeV(detailsin307-308pagesof[ 28 ]).PropertiesofEmissTwiththeircorrectioninleptonicnalstatesisveryimportant,whichhasnotbeensystematicallystudiedinCMSbefore.Someimportanttopics(e.g.WandTopmassreconstruction,searchingforHiggsthatdecaystodi-boson)willsignicantlybenetfromabetterEmissTresolution. ThischapterdescribesastudyofadaptingtherawEmissTreconstructionalgorithmtothepresenceofleptoninleptonicnalstates.Thejetisolationandenergycorrectionisdevelopedandapplied.ThepileupfactorisconsideredinordertofurtherimprovetheEmissTscale.TheoptimizationofthealgorithmandoverallresultsofEmissTresolutionandotherrelatedquantitiesbasedontwomajorleptonicchannels,Toppair(tt)andW+jets,areconducted. 38 39 40 ].ThecongurationofthedatasamplesissummarizedinTable. 6{1

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Table6{1. Thecongurationofleptonicdatasamplesincludingttinclusive,ttleptonicandW+jets Channel CongurationNumberofevent tt inclusive allWdecaymodeswitchedon200,000tt leptonic Wsemileptonicdecaymode200,000W+jets WsemileptonicdecaywithbinnedpT500,000 Inthepre-selection,werequireatleastoneelectronormuonwithpT>6GeV/candjj<3:0inthegeneratorlevelinordertoidentifyaleptonicevent.Thedetectorducialrangeofelectron(jj<3:0)andmuon(jj<2:4)areimplementedinthedetectorreconstructionrespectively.A20GeV=cleptonpTthresholdischosenforanalyzingandevaluatingtheEmissTperformance,whichiscommonlyusedfortheoineelectronandmuonselectionpartiallybecauseabetterisolationcanbeperformedwithhigheridenticationeciencyandbetterenergyresolution. ThecorrelationbetweentheEmissTandtheleptonpTisstudiedbyusingthefractionofeventswithgeneratedEmissT>30GeVasafunctionofleptonpTthreshold(Fig. 6{1 ).ThegeneratorlevelEmissTisreconstructedbyusingalltheparticleswithjj<5.0exceptneutrinos.Asaresultoftheleptonselectionwith20GeV/cpTthreshold,thehadroniceventsinthettinclusivesampleareremovedandeventswithtrueEmissTgetlargersignicance.IntheW+jetssample,thiseectismoreapparentforlowWpTevents,whichactuallydominatetheW+jetscrosssection.ThettleptonicsamplecontainsintrinsicEmissT,whichislessaected.ItcanalsobeseenthatahigherleptonpTthresholdwillnotincreasethesignicanceofeventswithtrueEmissTinttsamples,andwilldramaticallyreducethefractionintheW+jetssampleduetoWmassconstraintontheneutrinoandleptonmomentum. Tauselectionisnotconsideredinthisanalysis,becauseofitsrelativelylowerdetectoridenticationeciencythanthatofmuonandelectronandpossible

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(a)(b) Figure6{1. ThefractionofeventswithEmissT>30GeVasafunctionofleptonpTthresholdfor(a)ttsamplesand(b)W+jetssamplesrespectively EmissTcomingfromcertaindecaymodes.TheoutputofthisstudyultimatelycontributestotheORCAMETsubsystemforthereconstructionandanalysisofEmissT. Thissectiondiscussesthemuoncorrectionalgorithmandthepossibilityofusingtrackerandcalorimeterinformationtomakemuoncorrectionforcertainregionswherenormalmuonidenticationisinecient.Systematiceectsofmuon

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energymeasurementanditscorrelationtothemuonenergydepositincalorimeterarealsoinvestigated. 6{2 ). ~EmissT=)]TJ/F7 11.95 Tf 11.28 11.36 TD[(X~PmuonTvertex AtLHCstartup,thestagedmuondetectorconstructionwilllimitthetriggeracceptancetojj<2:1.Butiftheeventistriggeredbythecentralmuonorotherobjects,themuonintheregionof2:13:0thatisnotcoveredbythetrackerandmuonsystem,muonsignalwillbecompletelylost,whichcauserealfakedEmissTsignature.Intheregionof2:4<<3:0,thereisapossibilityofusingtracksandcalorimeterisolationformuoncorrection(discussedinlatersection). ThemajordierencebetweenthemuonreconstructionforthetriggerpurposeandfortheEmissTcorrectionistheisolationcriterionforlatteronecanbeloose.

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Butthemuonmomentumresolutionlargelydependsonusingtracks,whichissensitivetotheisolationcondition.TheoptimizationofmuonreconstructionforEmissTshouldbefurtherexploited. Inordertounderstandwhetherthemuonenergydepositinthecalorimetermightcausedouble-countingonthecalculationofmuoncorrection,weusetwomethodstostudythepossiblesystematiceects: 6{3 ). ~EmissT=)]TJ/F7 11.95 Tf 11.29 11.36 TD[(X(~PmuonTvertex)]TJ/F3 11.95 Tf 13.76 3.03 TD[(~EmuonTcalo) (6{3) Fig. 6{2 showstheresolutionandaverageerrorofEmissTafterthemuoncorrectionasfunctionofMuonCaloFactor,whereitstransversecomponentEmuonTcaloisusedforthesubtractionofdoublecounting.TheoptimalEmissTresolutionisatEmuoncalo4GeVwitha0.45GeV(2%)ofsystematiceectsintheoverallresolution(thiscanbecalculatedfromthesimplemuoncorrectionthatdoesnotconsiderthedouble-countingeect,whichcorrespondstoEmuoncalo=0). Infact,thisresultalsocontainsthesystematiceectofthemeasuredmuontrackpTcomparingtoitsgeneratorpT,whichexplainswhyalargeoptimalMuonCaloFactorcanbeobservedaccordingtothex(y)componentofEmissT(EmissTx)andaverageEmissTerror(bothquantitiesreachlowestpointatEmuonTcalo8GeV). AlargernegativevalueofaverageEmissTerrorundertheoptimalmuoncorrectionispredictedbecausealowerjetenergyresponsecausestheunder-measurementofEmissT.Itisaninterestingphenomenonthatthedetector

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systematiceectofmuon,ontheotherhand,smearstheunder-measurementbyincreasingtheaverageEmissTscaleandmakesaworseresolution. (a)(b) Figure6{2. EmissTpropertiesasafunctionofMuonCaloFactor:(a)EmissTresolution(dot)andEmissTxresolution(circle)and(b)averageEmissTerrorbetweendetectorandgeneratorlevel Fig. 6{3 showsthedistributionofthetransverseenergy(ET)reconstructedinthemuonisolationconeinthreeregions.Mostoftheconeshavelessthan10GeVofET.SomehaveverylargeET,mainlybecausemuonisoverlappedwithjetorfromtheheavyquarkdecay.SmalldierenceintheEmissTresolutionisfoundbycomparingtheeventswithhighETinisolationconetothosewithnormalETintheisolationcone.

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(a)(b)(c) Figure6{3. ETofmuonconeisolationcone(a)intheregionofjj<0.8,(b)intheregionof0.8
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(a)(b) Figure6{4. EmissTpropertiesasafunctionofMuonIsoConeFactor:(a)EmissTres-olution(dot)andEmissTxresolution(circle)and(b)averageEmissTerrorbetweendetectorandgeneratorlevel isolationtorecoverthemuonsignal.Duetotheavailabilityofthedatawithfullyreconstructedtracks,regionof2:410GeV/cand2:4
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deterioratemuchtheEmissTresolution.Thesamealgorithmistestedfortheeventswithcentralmuonthatanormalmuonidenticationcanbeperformed,resultsshowthatthestandardmuoncorrectionmethodprovidesbetterresolution.Sothistechniqueismainlysuitableinthehighregion. (a)(b) Figure6{5. TheimprovementofEmissTresolutionaftertrackcorrectionforselectedttinclusiveeventswithmuonofpT>10GeV/cand2:4
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Toevaluatetheoverallperformanceofmuoncorrection,twoselectedsamplesoftteventsinthegeneratorlevelareused:themuonsamplewithnoelectronofpT>6GeV/candtheelectronsamplewithnomuonofpT>6GeV/c.Thoseeventscontainingmuonorelectronwithjj>2.4arealsoremovedforaconsistentcomparison. Fig. 6{6 showstheEmissTresolutioninthemuonsampleisimprovedfrom29.99to22.77GeVbythemuoncorrection,andthedierencebetweenthecorrectedmuonsampleandtheelectronsampleiswithin1GeV.Furtherimprovementinmuonidenticationeciencyandtheestimationofitsenergydepositinthecalorimeterwillhelpreducethisdierence,buttheresolutionoftheelectronsamplesetsareasonablelimitofmuoncorrection.

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(a)(b) (c) Figure6{6. TheEmissTresolutionofttinclusiveevents:(a)aftermuoncorrectionfortheselectedmuonsample,(b)fortheselectedelectronsample,and(c)beforemuoncorrectionfortheselectedmuonsample

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energymeasurementonEmissTquantities.Theselectionofelectronisanimportantsteptowardacleanerjetenergycorrectionframeworkduetolargefakedelectronratefromjets,whichisdiscussedtogetherwithjetenergycorrectioninthelatersection. EmissT=)]TJ/F7 11.95 Tf 11.29 11.36 TD[(X(~PelectronTvertex)]TJ/F3 11.95 Tf 13.76 3.02 TD[(~ESCT) (6{5) EmissT=)]TJ/F7 11.95 Tf 11.28 11.36 TD[(X(~PelectronTvertex)]TJ/F3 11.95 Tf 13.77 3.02 TD[(~EconeT) (6{6) Intheanalysis,anelectroncorrectionfactor(Celectron)isintroducedontopofabovemethods(Eq. 6{7 ). EmissT=CelectronEmissT whereCelectronwillbeoptimizedwithrespecttotheEmissTresolution. IntheECALacceptancerangetheEmissTresolutionisstudiedasafunctionofelectroncorrectionfactor:

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6{5 .Theresult(Fig. 6{7 )showsasystematiceectof0.25GeVinEmissTresolution,whichiscalculatedfromtheoptimalCelectron0.25andrawEmissTthatcorrespondstoCelectron=0.WhileacompletereplacementoftheelectronenergyofECALsuperclusterbythetrackmomentumthroughCelectron=1deterioratestheEmissTresolution. (a)(b) Figure6{7. EmissTpropertiesasafunctionofelectroncorrectiontrackfactorusingtrackmomentumandsuper-clusterenergyatECAL:(a)EmissTreso-lution(dot)andEmissTxresolution(circle)and(b)averageEmissTerrorbetweendetectorandgeneratorlevel 6{6 .Asimilarresult(Fig. 6{8 )aspreviousmethodisobserved. 6{8 ),sothefactorconcerningtheelectronenergydepositintheECALcanbeignored.TheresultisinFig. 6{9 EmissT=)]TJ/F3 11.95 Tf 9.3 0 TD[(CelectronX(~PelectronTvertex) (6{8)

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(a)(b) Figure6{8. EmissTpropertiesasafunctionofelectroncorrectionfactorusingtrackmomentumand0.2isolationconeatcalorimeter:(a)EmissTresolution(dot)andEmissTxresolution(circle)and(b)averageEmissTerrorbetweendetectorandgeneratorlevel (a)(b) Figure6{9. EmissTpropertiesasafunctionofelectroncorrectionfactorusingtrackmomentum:(a)EmissTresolution(dot)andEmissTxresolution(circle)and(b)averageEmissTerrorbetweendetectorandgeneratorlevel

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Aboveresultsshowthereisasmallsystematiceect(0.25GeV)inEmissTresolutionconcerningtheelectron.Anoptimizationcanbeachievedbycombiningtheelectrontrackanditscalorimetermeasurement. Intheregionofjj>3.0,theelectronistreatedasjet.TheaverageelectronresponseintheHFis0.9withpTrangefrom30to100GeV/cbasedonthettinclusivesample,whichisconsistentwiththenormaljetenergyresponse[ 55 ].InordertoestimatethesystematiceectsoftheelectronmeasurementintheHF,twoelectronsamplesareselected:eventswithcentralelectronsofpT>6GeV/candjj<2.0,eventswithforwardelectronsofpT>6GeV/candjj>3.0.TheEmissTresolutionbetweentwosamplesarelessthan0.1GeV.TheaverageEmissTerrorbetweenthegeneratoranddetectorlevelarealmostthesame.TheoverallelectronsampleresolutionisshownpreviouslyinFig. 6{6 ThissectionconcentratesonseveralfundamentalaspectsofthejetenergycorrectionalgorithmwithrespecttoEmissTreconstruction.

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ThepossiblyfurtherjetreconstructionisperformedaccordingtovariousEmissTcorrectionscenarios: Inthestandalonejetreconstruction,theelectronidenticationisnotcarriedout.Asaresult,electronswillbeidentiedasjets(calledelectron-jetinthefollowing).Thoseelectronsthataremissedbytheelectronidenticationaretreatedasrealjetsduetolimittrackreconstructioneciency,isolationeciency,super-clusterreconstructioneciencyandetc.Ingeneraltheelectron-jetshouldnotbeappliedjetenergycorrection,sinceitscalorimeterenergyresponseiscloseto1.0asshowninFig. 6{10 (a). ThereisapossibilitythatnormaljetsbehavelikeelectronbydepositingmostoftheenergyintheECAL(calledelectron-likejet).Thisphenomenonsimplyreectastatisticeectinlargejetsamples.Itisnecessarytoreducethenumberofmis-identiedelectrons,sincethemis-identicationwillinuencethejetcorrection.Theelectron-likejetenergyresponseiscomparedtothatofthenormaljet,smalldierenceisobservedasshowninFig. 6{10 ForthebetterqualityofEmissTreconstruction,aselectionofelectroncandidatesincludingelectron-jetandelectron-likejetareestablished(Eq. 6{9 ).WeuseenergyfractionbetweentheHCALandECAL(Rh=e)andthejetenergyisolationfactor

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(a)(b) Figure6{10. Electronandjetenergyresponseincalorimeter:(a)theeventsthatpasstheselectioncriterionand(b)theeventsthatfailtheselectioncriterion (RIso0:2andRIso0:4)toparameterizetheselectioncriterionforelectroncandidates. AnoptimizedselectioncriterionwithRh=e<0:05,RIso0:2<0:1andRIso0:4<0.3isusedtolterelectroncandidatesasshown(Fig. 6{10 ):

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EmissT=)]TJ/F7 11.95 Tf 11.29 11.36 TD[(X(~EcT)]TJ/F3 11.95 Tf 13.77 3.03 TD[(~ErT) (6{10) whereEcTandErTarethecorrectedandrawjetETrespectively. Thecompletetreatmentofusingjetenergycorrectionneedsaclearseparationofcluster(jet)andunclusteredtowers,inwhichtwonon-overlappedregionsinthecalorimeter-spacearedened.ThedetailsofregiondenitionbasedonQCDeventsisdescribedinChapter5.Thisprocedureisalsovalidforothertypeofevents. Thepresenceofleptonneedsimplementseveralselectioncriteriondiscussedinprevioussections.ThegeneralformulaofcalculatingEmissTundertheregiondenitionis (6{11) wheretherstsumisovertheclusterregionandsecondovertheunclusteredregion. Allthejetenergycorrectionoccursinclusterregion.Ifrawenergyofunclus-teredtowersareusedforEmissT,theresultsbasedonEq. 6{10 and 6{11 arethesame.Inthisstudy,nocorrectionisappliedonunclusteredtowers,because:

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can'treachcalorimeterordeectedbymagneticeld,theresponsefunctionbetweengeneratorparticlesandcalorimetermeasurementinthesame-regionhasverylargeuctuation.SimplyusingascalingfactorwithoutreducingthevariancewillnotimprovetheEmissTresolution. 54 ]showsthecorrectiononunclusteredtowersdoesnotfurtherimprovetheEmissTresolutionafterapplyingjetcorrection. 56 57 58 ],thejetenergyresponsecanbemeasuredbasedonthephoton-jetbalancingwherethephotonETcanbewell-determined.Thismethodcanbedevelopedtoapurelyexperimentalapproachthatusesexperimentaldataonly.

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Inthefollowing,wefocusonwhatsystematiceectonEmissTfromeachschemecanbeanticipated: FortheEmissTreconstruction,thiscausesdouble-countingiftheconesizeistoosmall,becausemuchout-of-coneenergy(particles)alsocontributetothephoton-jetbalancingduetomanyfactors(e.g.,theuctuationofgeneratedjetconesize,4Tmagneticeldthatdeectschargedparticles,andhadronicshower).Thejetenergycorrectionalreadycompensatestheeectofout-of-coneenergy,whichisthenredundantforEmissTreconstruction. Forlargeconesize,somein-coneenergy(particles)doesnotcontributetothephoton-jetbalancing(e.g.,theenergyfromtheinitialradiation,underlyingeventsandpileupevents),whichcauseothersystematiceectinEmissT.Andthelargerthecone,thestrongerthesystematiceect. Itispossibletolookforanoptimalconesizesothatthecalibratedjetenergyfromaconeisequaltothegeneratedjetenergyofthesamecone,butthisprocessinevitablymakesuseofgeneratorlevelinformationwhichisnotmuchdierentfromthesecondscheme.Inthedetectorlevelreconstruction,thereisalsouncertaintytodecidetheproperconesizeduetotheuctuationofthegeneratedjetshapeandhadronicshowerincalorimeter. Asaresult,wefoundthisschemeimplementedinthestandardreconstructionalgorithmcausedlargeover-correctionofEmissTinleptonicsamples.

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generatedjetshape,whichlargelyreducethesystematiceectsduetotheuctuationofjethadronizationandfragmentationprocess. SomedetectorlevelsystematiceectsonEmissTstillexist(e.g.,theout-of-coneparticlesbecauseof4Tmagneticeldandhadronicshower).Thoseeectsarebettertobestudiedwithbothgeneratoranddetectorleveljets,sothattheoptimizationforEmissTreconstructionneedbeperformedamongvariousconesizes. DespitesomeadvantagesinEmissTreconstruction,ageneralissueassociatedwiththisschemeisthatitdependsmoreontheprecisionofthesimulation. AnoptimalschemeforEmissTwouldbeacombinationofboth.Inthisanalysis,thesecondschemeisused.TheadaptationofrstschemetoEmissTcorrectioniscarriedoutinanindependentstudy.

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Roughly8-10%ofimprovementonabsoluteresolution(ofJetETerrorbetweenthedetectorandgeneratorjetenergy)isobtained,whilenormalETbasedjetcorrectionalgorithmsarelackofabilitytoreducetheandmainlyworkasacalibrationmethod.Therecoveryofunitdetectorjetresponsebasedonenergydistributioncorrectionisalsoperformed,whichshowsextraadvantageinrestoringthegeneratedjetpTspectrumbymoreparameterization. 6{12 ). S=XSi;Si=Ri)]TJ/F3 11.95 Tf 12.61 0 TD[( i whereRiisthefractionofreconstructedenergyinregionifromtotalenergyina1.0conearoundthejetaxis.ByusingtheaverageRi(denotedas)andofRi(denotedasi),thesignicanceofenergydistributionfromeachregionisbuilt.ForQCDandothernormaljets,thedistributionofSiswellttedwithaGaussian,whichallowsastandardselectioncuttobeimplemented.Basedontheresultsofjetenergyenergydistribution,theinner0.2coneplaysaveryimportantroletothejetenergydistribution,extracutsbasedontheratioof0.2coneenergytootherregionareusedtofurtherrejectabnormaljets.

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areappliedwithbenchmarkjetenergycorrectionwhichisnotsensitivetothedetailsofjetconstituentsanditsenergydistributionfactor. Twoimplementationofjetcorrectionstrategyaretested:acombinationofbothcorrectionalgorithmasdescribedaboveandETbasedcorrectionalgorithmonly.WefoundtherstoneprovidesslightlybetterEmissTresolution(1.0%)thanthesecondandtheyhavealmostsameperformanceintheEmissTscale. 6{1 thatagoodsignicanceoftrueEmissTeventscanbeachieved.LowEmissTeventsinmanyphysicschannelshaveamuchlargercrosssectionandmakeseriouscontributiontothehigherdetectorEmissTeventsifnoleptonselectionorgeneratorlevelEmissTselectionisimplemented. TwodetectorEmissTrangesaredened,180>EmissT>90GeVand90>EmissT>30GeV,inordertostudytheresolutionandrelatedperformanceofjetenergycorrection.Theresultsbasedonttinclusiveevents(Fig. 6{11 and 6{12 )show:

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SimilaroptimizationsearchisalsoperformedwithttleptoniceventsthatrequiresbothWbosonleptonicdecay,sincethereismuchchancethattwoisolatedleptonscanbereconstructedwhichmakesaverycleanleptonicsample.SimilarresultsofresolutionofEmissT,EmissTxandquantitiesareobserved.ThemajordierenceisinthequantityasshowninFig. 6{13 Asaresultoftheoptimizationsearch,0.4conesizeisselected,mainlybecauseofitsbettercomprehensiveperformanceintheEmissTresolutionandscale.Thedierencebetween15GeVand20GeVjetETthresholdissmall,butahigherthresholdhelpreducetheeectsoffakedjetsfrompileupandunderlyingevents,ofwhichthejetresponseneedsbebetterunderstood,sothehigherthresholdistaken. 6{13 ,0.4conejetenergycorrectionwith20GeVjetETthresholdmakeunder-measurementofEmissTinthelowrange,butover-measurementinthehighrange,whichischaracterizedbydierenceofbetweentworanges(Eq. 6{13 ). =high)]TJ/F3 11.95 Tf 12.62 0 TD[(low Table 6.5.2 summarizesofvariousconesizeswith20GeVjetETthresholdinthettinclusiveandleptonicsamples.Thelargerbiasinthett

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(a)(b) (c)(d) Figure6{11. EmissTquantitieswithrespecttodierentjetconesizesandETthresh-oldswith30
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(a)(b) (c)(d) Figure6{12. EmissTquantitieswithrespecttodierentjetconesizesandETthresh-oldswith90
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(a)(b) Figure6{13. TheaverageEmissTerrorbetweenthedetectorandgeneratorlevelwithrespecttodierentjetconesizesandETthresholdsinttleptonicevents:(a)30inthettsamplewithvariousconesizes Conesize tt inclusivesamplett leptonicsample 0.2 1.255.60.4 -0.24.90.6 -0.54.60.8 -1.254.2 Ideallyacorrectiontechniquesshouldbelesssensitivetodierenttypesofsamples,butforjetandEmissTquantities,thisissueisnon-trivialduetotheircoarseresolution. Twomajorchannel-dependentfactorsinuencetheEmissTcorrection: 1. ThejetpTspectrumandjettypes.Fig. 6{14 showsthegeneratedjetpTspectruminQCD,ttinclusive,andW+jetsevents.Thecalibrationerror,

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normallyrelatedtocorrectionconstantdevelopedfromonechannelandappliedtoadierentchannel,causessystematicbiasandcan'tbereducedbyincreasingthestatisticsoftheevents.ConsequentlythecorrectedEmissTscalewillbeaected. (a)(b) Figure6{14. Jetpropertitiesinvarioussamples:(a)normalizedinclusivejetpTspectrumand(b)normalizedleadingjetpTspectrum.ThesamplesincludeQCD(solidline),tt(dotline),andW+jetswithWpTbe-tween40and300GeV(dashline) PartofthereasonwedevelopthejetenergycorrectionbasedonQCDeventsistoprovideageneralpurposejetenergycorrectionandtoexploitthepossibilitytomakejetcorrectiontoQCDeventstosuppressthefakedEmissTtriggerrate.Inttevents,alargefractionofjetsoriginatefrombquark,whichshowsdierentresponsefromlightquarkjetorgluonjets.ByapplyingQCDjetscaletoleptonicevents,thesystematicbiasisestimatedas5-10%.Fig. 6{15 showstherawjetresponseofQCD,W+jets,andttsamples. 2. EmissTspectrum.Fig. 6{16 showsthedetectorEmissTandETspectruminttinclusive,ttleptonic,andW+jetsevents.AsimpleapproachtocompensatethebiasduetotheEmissTspectrumistodevelopascalingfactorforeach

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Figure6{15. TherawjetresponseinQCD,W+jets,andttsamples channel,whichissimilartothejetenergyscale.Thefeasibilityofascalingfactorpartiallydependsontheeventidenticationeciencyandwhethertheoineselectionintroducesextrabias. Inordertoinvestigatetheconsequenceofsystematiceectsofjetenergyresponse,atuningofjetenergyresponsefromQCDeventstotteventsistestedbyusingarescalingfactor(Rre)]TJ/F4 7.97 Tf 6.59 0 TD[(scale)denedinEq. 6{14 whereEcorTisthemeasuredjetETcorrectedbyQCDjetenergyscale,EgenTistheoriginalgeneratedjetETfromttevents.ByapplyingRre)]TJ/F4 7.97 Tf 6.59 0 TD[(scaletothecorrectedjetET,theaverageEmissTscaleisshiftingpositivelyby2GeV(Fig. 6{17 )withalmostnochangesinEmissTresolution,whichleadstoaconclusionthatmostofthechannel-dependentsystematiceectsconcerningjetenergyresponseandEmissTspectrumismanifestedinthedetectorEmissTscaleratherthanitsresolution.

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(a)(b) Figure6{16. EmissTandETpropertiesinvarioussamples:(a)NormalizedEmissTspectrumand(b)normalizedETspectrum.Thesamplesincludettinclusive(dashline),ttleptonic(dotline),andW+jetswithWpTbetween40and300GeV(solidline) Figure6{17.

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Intheclusterregion,theperformanceofjetenergycorrectionisinuencedbytheuctuationoftheenergyfromunderlyingeventandminimum-biasevent,whichtogetherintroduceastandalonedeviationinthecorrectedjetenergyresolution,becausethejetcorrectionmethoddoesnotconsiderorestimatethiseectforeachsingleevent,insteadusinganaveragevaluethattreatthePUeectasaconstant.ThissectiondescribesadedicatedcorrectionmethodbyextrapolatingthePUeectbasedonETfromtheunclusteredregiontotheclusterregion,soanevent-basedmeasurementofthePUeectisperformed,whichhelpoptimizetheEmissTcorrectionintheclusterregion. 6{18 where0.4conesizeisusedfortheregiondenition.Intheclusterregion,thereisacleardependencyofitsETonEmissT.SimilarresultsfromQCDeventsareshowninChapter5. InthemeasurementofPUeect,alargeconesizeR=1.0forregiondenitionisusedinordertominimizetheimpactofjetenergyresolution,outof

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Figure6{18. RawETdistributionintworegionsasafunctionofEmissTbasedonttinclusiveevents.0.4conesizeisusedforregiondenition:detectorclusterregion(opentriangle),generatorclusterregion(closesquare),detectorunclusteredregion(closetriangle),andgeneratorunclusteredregion(opensquare)

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coneparticlesdeectedbymagneticeldandleakingofhadronicshower.Thechoiceofconesizeforregiondenitionisnotunique,butalargeconesizemakesthetechniquelessdependentonthespecicsampleandjetETrange. ThequantitativeestimationofPUeectisbasedonfollowingmeasurements: Usingtheseinformation,theenergyofeachtowerofthejetconstituentthatmightcomefromthePUeectcanbeestimated.TheoveralljetETcorrectionfromthePUeect(EPUT)is EPUT=EuT wherethesummationisperformedoveralltheconstituenttowersofajet.

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ConsideringvarioussystematiceectsinthemeasurementofPUeect,weintroducesaparameter(cpileup)toadjustthepileupeectextrapolatedfromtheunclusteredregiontotheclusterregion(Eq. 6{16 ). EjetT=cpileupEPUT whereEjetTisthepileupfactorofagivenjetusedforEmissTcalculation.Inthisstudy,wetakecpileupasageneralconstanttobeoptimizedthroughEmissTresolutionandaveragescale,whichalsopartiallycompensatesthesystematiceectsofjetandEmissTspectrumdiscussedinprevioussection.Itispossibletomakemorecomplicatedparameterizationofcpileup(e.g.,makingitdependingonandjetET),butthismightmakesmoresystematicdependencyonthedatasamplesthatisused. Therefore,anoverallpileupeectsshouldbesubtractedfromEq. 6{10 : EmissT=X~EjetT Fig. 6{19 showstheoverallperformanceofthePUcorrectionontheaverageEmissTscaleandresolutionasafunctionofcpileupinthettinclusivesample: Sameresultsareobservedinotherleptonicsamples.Asaconclusion,thePUcorrectionprovideagoodmeanstoadjusttheEmissTscalewithoutcompromisingtheEmissTresolution,andcanbeperformedatthenalstageofcorrectionasageneraltechniqueoroineanalysistobetunedforspecicchannel.

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(a)(b) (c)(d) Figure6{19. EmissTpropertiesafterthePUcorrectionasafunctionofdetectorEmissT:(a)EmissTerror,(b)EmissTresolution,(c)EmissTxresolution,and(d)resolution

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1. Jetreconstruction.Thisstepuses0.5iterativeconejetasoriginalinput,newconejetwithoptimalconesizeandETthresholdisre-builtonthesameaxis. 2. Electronisolationandjetltering.Thisstepappliesthecalorimeterisolationinthe0.2coneofelectroncandidateswithminimum10GeVET.TheHCALtoECALenergyratioandcalorimeterisolationcriterionareusedfortheselection.The-regioncontainingselectedelectronispreventedfromapplyingjetenergycorrection.Allthejetsmis-identiedfromelectronorwithinthedistanceof0.3in-spacetoanelectronwillbeltered. 3. Independentmuonandelectroncorrection. 4. Unclusteredtowercollection.Thisstepcollectsalltheenergyvectorfromtowers,whichdon'tcontributetojets. 5. Abnormaljetidentication.Usingenergydistributioncriteriontolterabnormaljets.Theselectioniterationis:S<4,energyratioof0.2conetosecondinnercone(0.2-0.4region)>1. 6. Jetenergycorrection.Fornormaljet,energydistributioncorrectionisapplied.Forabnormaljets,ETbasedbenchmarkjetcorrectionisapplied. 7. PileupFactorcorrection.Theevent-basedpileupcorrectionfactorisesti-matedandusedforthosecorrectedjet. ThephysicstuningdiscussedinpreviousSectionisnotincludedinthegeneralEmissTcorrectionchain,becauseitislargelychanneldependent,whichshouldbeappliedunderagivenoineeventselectioncriterion.

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6{20 and 6{21 showtheperformanceofEmissTcorrectionintheresolutionofttinclusiveandttleptoniceventsrespectively.Therelativeresolution(relative)isttedwithEq. 6{18 withresultssummarizedinTable 6{3 : Table6{3. Fittingresultsofa,bandcofrelativeaccordingtoEg. 6{18 inttevents Sample abc ttinclusive(leptoncorrection) -0.77690.36540.0085ttinclusive(allcorrection) -1.13300.42920.0151ttleptonic(leptoncorrection) -1.3410.47790.00745ttleptonic(allcorrection) -1.7630.58480.0100 Fig. 6{22 showstheperformanceofEmissTcorrectioninW+jetsevents.Theab-soluteresolution(EmissTandEmissTx)isttingwithEq. 6{19 withresultssummarizedinTable 6{4

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(a)(b) (c)(d) Figure6{20. EmissTpropertiesaftercorrectionasafunctionofdetectorEmissTinttinclusiveevents:(a)relativeEmissTresolution,(b)resolution,(c)EmissTresolution,and(d)EmissTxresolution

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(a)(b) (c)(d) Figure6{21. EmissTpropertiesaftercorrectionasafunctionofdetectorEmissTinttleptonicevents:(a)relativeEmissTresolution,(b)resolution,(c)EmissTresolution,and(d)EmissTxresolution

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(a)(b) (c)(d) Figure6{22. EmissTpropertiesaftercorrectionasafunctionofdetectorEmissTinW+jetsevents:(a)relativeEmissTresolution,(b)resolution,(c)EmissTresolution,and(d)EmissTxresolution

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Table6{4. Fittingresultsofa,bandcofrelativeaccordingtoEq. 6{19 inW+jetssample Sample abc W+jetsEmissT(leptoncorrection) 11.921.5750.0439W+jetsEmissT(lepton+jetcorrection) 12.571.2360.01689W+jetsEmissTx(leptoncorrection) 12.231.6490.08308W+jetsEmissTx(lepton+jetcorrection) 13.681.180.0 6{23 6{24 ,and 6{25 showtheaverageEmissTscaleandresponseinttleptonic,ttinclusive,andW+jetseventsrespectively (a)(b) Figure6{23. EmissTscaleinttinclusiveeventsasfunctionofdetectorrawEmissT:(a)averageEmissTerrorand(b)EmissTresponse 6{20 )isusedtostudythecorrelationofEmissTinclusterandunclusteredregionandtheirrelativecontributiontotheoverallEmissT.

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(a)(b) Figure6{24. EmissTscaleinttleptoniceventsasfunctionofdetectorrawEmissT:(a)averageEmissTerrorand(b)EmissTresponse (a)(b) Figure6{25. EmissTscaleinW+jetseventsasfunctionofWpT:(a)averageEmissTerrorand(b)EmissTresponse

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whereEmissTuisthestandaloneEmissTintheunclusteredregionandEmissTcisthestandaloneEmissTintheclusterregion.Fig. 6{26 and 6{27 showRandEmissTxasfunctionofEmissTinttinclusiveandttleptonicevents.Fig. 6{28 showsRasfunctionofWpTandETinW+jetsevents.ThedependencyofRonEmissTandWpTisttedwithEq. 6{18 withresultssummarizedinTable 6{5 .TheunclusteredregioningeneralmakeslesscontributiontoEmissTthanclusterregion.ItsresolutiontendstobeaconstantfactorwithstandaloneEmissTuat16GeVlevel. Table6{5. Fittingresultsofa,bandcofRaccordingtoEq. 6{18 usingEmissTandWpT abc ttinclusive(vs.EmissT) 1.0540.00.0427ttleptonic(vs.EmissT) 0.93580.2310.0145W+jets(vs.ET) -12.770.42080.0115W+jets(vs.WpT) 1.6990.00.0225 (a)(b) Figure6{26. EmissTpropertiesasafunctionofEmissTinttinclusiveevents:(a)Rand(b)EmissTxresolution Fig. 6{29 showstheresolutionintheclusterandunclusteredregionofW+jetsevents,inwhichthedependencyofclusterEmissTxonWpT(pWT)isttedwithEq.

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(a)(b) Figure6{27. EmissTpropertiesasafunctionofEmissTinttleptonicevents:(a)Rand(b)EmissTxresolution (a)(b) Figure6{28. EmissTpropertiesinW+jetsevents:(a)RasafunctionofETand(b)RasafunctionofEmissT

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6{19 .Theresultis Figure6{29. StandaloneEmissTresolutionintheclusterandunclusteredregionrespectivelyasafunctionofWpTinW+jetsevents AclearimprovementontheEmissTresolution,resolutionandaveragescale(response)isachievedviaachainofcorrectiontechniquesbasedonttandW+jetsevents: 1. ThemuoncorrectionmakestheEmissTresolutionandscaleofmuoneventsnearthesamelevelofelectronevents.

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2. Theoptimizationbasedonmuonmomentumatvertexandenergydepositinthecalorimeterresultsinextra2%improvementinEmissTresolution.Usingtrackandcalorimeterisolationin2.4<<2.6regionwhichisoutoftheducialrangeofmuondetectorshowspromisingresultformuoncorrection. 3. Theoptimizationbasedonelectronenergyandmomentummeasurementresultsin1%improvementinEmissTresolution.Theselectionofelectrontoreducefakedjetratehasbeendevelopedbasedoncalorimeterisolationstrategy. 4. Thejetenergycorrectionmakeaverage15to20%standaloneimprovementintherelativeEmissTresolution(10%fromreducingtheabsoluteEmissTresolution,5to10%inrestoringtheaverageEmissTscale). 5. CorrectionofPUfactorandchannel-dependenttuninghavebeendevelopedwithimprovingtheEmissTscalewithoutdeterioratingtheEmissTabsoluteresolution.

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Thecomplexityofphysicsnalstateswhichhavesignicantdetectorlevelmissingtransverseenergy(MET)putssevererequirementonunderstandingtheMETresponseandresolutioninthecalorimeter,eitherunderacertainchannel(e.g.,QCD,WorZplusjets)orunderacertainsignature(e.g.,hadronicorleptonicevents)thatcanbeidentiedexperimentally. Earlierresults[ 54 29 ]showthejetenergycorrectionhelprestoretheMETscaleinseveralSUSYchannelsthathavelargegeneratorlevelMET,butnoteectiveinQCDeventswherethegeneratorlevelMETissmall. OneofthemajorpurposesofthisstudyistoprovideananalyticalestimatortoevaluateandunderstandtheeectsofjetenergycorrectionontheMET.ThesophisticationoftheproblemliesonthefactthatphysicschannelswithvariousnalstatesandjetETspectrumcarrydierentdependencyonthejetenergycorrectionandrelateddetectoreects. ThischapteraimstoprovideaframeworktosystematicallyfactorizethecorrelationbetweentheMETanddierentphysicsnalstates,andillustratehowitinuencestheperformanceoftheMETreconstruction.Normallyaphysicsnalstatecanbecharacterizedbyajetsystemwithpossiblepresenceofleptons.Thehadronicsignaturescanbeclassiedas: 1. Containingabalancejet(hadronic)systeminthegeneratorlevel,whiletheMETismainlyadetectoreect. 2. Containinganimbalancejet(hadronic)systeminthegeneratorlevel.TheMETisacombinationofthegeneratoranddetectoreects. 161

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AthirdtypeofthesignaturewithrespecttotheMETisaboutleptonicevents,whichcanbetreatedasanimbalancehadronicsystempluslepton.Somostfeaturesofleptoniceventsarehighlysimilartothesecondtypeofhadronicsignature. Thischapterdescribesthedevelopmentofafactorizationmodelasacompre-hensiveapproachtostudytheMETfromthenewprospectofunderstanding,whichincludesadi-jetMETfactorizationmodel,theimplementationandvalidationofthemodelwithrespecttoQCDevents,theeectofjetenergycorrectiononMETbasedontwohadronicsignatures,theextensionofthemodeltomultiplejetsystem,andtheanalysisoftheQCDMETtriggerquantities. Afactorizationmodelisdevelopedusingdi-jetsystemasaframeworktostudythebasicMETquantities: ThefurtherextensionofthemodeltomultiplejetandimbalancejetsystemsmakesitapowerfultooltoanalyzethecorrelationbetweentheMETandvari-oushadronicnalstates.Somecrucialquestionscanbeaddressedthroughthe

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comparisonbetweentheresultsfromthefactorizationmodelandthedetectormeasurement(basedonsimulationatpresent),suchaswhetherthehighMETtriggerthresholdisreasonable,whyjetenergycalibrationmainlyworksforphysicschannelswithtrueMET. jet=jEgenT1)]TJ/F3 11.95 Tf 11.95 0 TD[(EgenT2j (7{2) (7{3) jet)is jet=jEdetT1)]TJ/F3 11.95 Tf 11.95 0 TD[(EdetT2j

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whereEdetT1andEdetT2aretwojets'energymeasurement,Gisarandomgeneratorfunctionbasedongaussiandistribution,usedtosimulatethestochasticeectofcalorimeterjetenergyresponse. InadditiontotheMETofdi-jetsystemwhereitsoccupancy-spaceiscalledcluster(jet)region,theMETintherestofthecalorimeter-space(calledunclusteredregion)canalsobereconstructed.VariousdetectoreectscontributetotheunclusteredMET:pileupevents,trackermaterials,magneticeld,andlimitedcoverageofcalorimeter.Intheclusterregion,theinuenceofthosedetectoreectsalsoexists,butitismuchlessthanthejetactivitiesfromQCDhardscatteringprocessanddetectorleveljeteect. Theoveralldetectoreectintheunclusteredregion(calledsmearingeect)canbecharacterizedbyastandalonedetectorlevelMETinxandydirectionrespectively,andexpressedbyagaussiandistributionwithsm. (7{5) Basedonabovedenition,theoveralldetectorMETis jetcos(di jet) (7{6) jetsin(di jet) wheredi jetisthetransversedirectionofthedi-jetsystemandgeneratedbyarandomfunction.

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1. QCDeventsalwayshavemorethantwojets.TheextralowETjetscomefromsignalQCDprocessviainitialstateradiation(ISR)andnalstateradiation(FSR),pileupminimumbiasevents,orotherdetectoreects.Ingeneral,thosejetshavemuchworseenergyresolution,andtheircontributiontoMETcanbetreatedaspartofthesmearingeect.IfextrajetshavehighETandwidelyseparatefromtheprimarydi-jets,theycanbehandledbyanextensionofdi-jettomulti-jetmodeldiscussedinSection5,whichshowsthesimilarconclusionsasthatofdi-jetmodel. Duetoextrajetactivities,thedi-jetarenotexactlyback-to-backin,thisfactorisaddressedintheimplementationofthefactorizationmodel. Thedependentjetenergyresponseisnotfactorized.Insteadanaverageresponseinthecentralregion(jj<3.0)isused. 2. TheMETofclusterandunclusteredregionarenottotallyindependent,whichismanifestedbythecorrelationbetweentheangleofthestandaloneMETofeachregiondueto: Thedetectorlevelcorrelationispartiallyreducedbythejetenergycorrectionintheclusterregion.Realizingthepileupeventsandvariousdetectoreectarelesscorrelatedwiththesignalevent,forthesimplicityofthefactorizationmodel,itispracticaltousejeteecttoabsorbthecorrelationfactorandassumethattheMETfromtheunclusteredregionislesscorrelatedwiththeMETfromtheclusterregionintheangle.

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Inasummary,jeteectismainlyusedtodescribethejetrelatedactivitiesandmostofthecorrelationfactorbetweentheclusterandtheunclusteredregion.TheconsequenceofjeteectisthatthedirectionandmagnitudeoftheMETwillbehighlybiasedwithrespecttotheenergyowofthedi-jetsystem. Smearingeectisusedtodescribetherandomeectinthedetector,whichislesscorrelatedwiththedirectionofsignal'sQCDprocess.Themagnitudeofsmearingeectwillstillbeaectedbysignal'sQCDprocess. 7{1 .Thedetectorsimulationisunderlowluminosity(L=21033cm)]TJ/F4 7.97 Tf 6.58 0 TD[(2s)]TJ/F4 7.97 Tf 6.58 0 TD[(1)withaverage3.5pileupevents.Inthissection,wemainlyusetheeventswithjetETbetween80and90GeVtoillustratetheprocedureandtheperformance. Table7{1. JetandmissingtransverseenergyquantitiesofQCDdi-jetdatasamples JetET(GeV) AverageJetET(GeV)(ET)(GeV)ofMETx(GeV) 20-25 22.614.5110.9630-35 32.476.0612.2550-55 52.467.9114.1580-90 84.7810.5016.91120-130 124.8213.2319.32170-180 174.8315.7022.20230-240 234.8918.0125.29300-310 304.8419.9528.11380-400 389.5322.5632.45470-490 479.6726.4635.79600-620 609.7830.7239.63800-820 809.7935.0745.82 Inadditiontothedenition,theimplementationaddressesgeneratorlevelMETandcorrelationofdi-jets:

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selectedQCDsampleisshowninFig. 7{1 ,whichisttedwithasumoftwogaussiandistributionfunctions.SamplesofvariousjetETshowalmostthesameresults:anarrowgaussianpartwith2.3GeV,awidegaussianpartwith5.6GeV. Figure7{1. NormalizedMETxdistributionofQCDeventswithleadingjetETbetween80and90GeV 7{2 (a)).TheeectofISRandFSRwithradiationofextrajetscausesnon-trivialcorrelationofthedi-jetsysteminQCDeventsasshowninFig. 7{2 (b). Thecongurationofcriticalparametersofjeteectandsmearingeectinthefactorizationisperformedviafollowingsteps:

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(a)(b) Figure7{2. METquantitiesindi-jetsystemofQCDeventswithjetETbetween80and90GeV:(a)normalizedMETxdistributionand(b)normalizedcorrelation(=1)]TJ/F3 11.95 Tf 11.96 0 TD[(2)]TJ/F3 11.95 Tf 11.95 0 TD[() 7{3 7{4 ). 7{7 basedontheresultsofjeteectandMETx(y)resolutionobtainedfromprevioussteps.smisttedasafunctionofleadingjetETasshowninFig. 7{5 Inasummary,thevaluesoftheparametersofthefactorizationmodelareob-tainedfromeitherthedirectmeasurementorthederivativeofdetectorquantities. Thevalidationusesthe2testbetweentheMETspectrumofthesimulationdataandpredictionofthefactorizationmodel(Fig. 7{6 ).

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(a)(b) Figure7{3. Di-jetangularcorrelationquantities:(a)phiasafunctionoflead-ingjetETand(b)Ratioofthenarrowcomponenttothewidecomponent (a)(b) Figure7{4. METxquantitiesofQCDeventswithjetETbetween80and90GeV:(a)normalizedMETxdistributionand(b)normalizedMETxerrordistribution

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Figure7{5. NormalizedMETspectrumofQCDevents(opentriangle)andfactor-izationmodel(dot)withleadingjetETbetween80and90GeV

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ResultshowninFig. 7{7 conrmstheleastvalueof2=n:d:fis1.0(n.d.f=45),whichisconsistentwiththeresultsfromcongurationandindicatesagoodtofthesimulationdatatothepredictionoffactorizationmodel. (a)(b) Figure7{7. Resultsof2(a)asafunctionofjet(b)asafunctionofsm

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WealsotestsimplyusingagaussiandistributiontorepresenttheoverallMETx(y)error,hencenocorrelationbetweenMETxandMETyismanifestedviajeteect.Similar2testsareperformedwithvariousvaluesofMETx(y)resolution(Fig. 7{8 ).Theleast2=n:d:fisequalto2.0,indicatingapoorermatchingbetweenthedataandtheprediction. Figure7{8. 7{9 7{8 ).

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Figure7{9. NormalizedMETspectrumwithjetET(GeV)of20-25(black),30-35(red),50-55(blue),80-90(green),120-130(black),170-180(red),230-240(blue),300-310(green),380-400(black),470-490(red),600-620(blue),and800-820(green)

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ThissectionstudieshowtheMETresolutionandscaledependsonIgenandIdetwhenthejetenergycalibrationisapplied.ForasimplicationofEq. 7{2 and 7{3 ,thejetenergyresponse(Rjet)andresolution(jet)withrespecttodetectorjetEdetTtaketheformasshowninEq. 7{9 Thediscussionfocusesonjeteect,becausethejetenergycorrectionoccursintheclusterregionandthesmearingeectislessaected. 7{9 ,therawdetectorlevelMET(METrawdi jet)is jet=jR1EgenT1)]TJ/F3 11.95 Tf 11.96 0 TD[(R2EgenT2j(ET1)(ET2) (7{10) ThersttermshowsthereisasystematicbiasbetweenthedetectorandgeneratorlevelMET(denedbyEq. 7{1 ).IfweconsideraspectrumofjetETindetectorlevel,itisclearthatthersttermnotonlyinuencesthescalebutalsotheresolutionoftheMET.Whiletherestofthetermsmainlyinuencetheresolutiononly. ForawidejetETrange,therealjetresponsefunctioncanbetreatedasalinear-likefunctionwithrespecttojetETasdenedinEq. 7{9 .TheaverageQCDjetenergyresponsewith0.6conesizeisshowninFig. 7{10 .SothersttermofEq. 7{10 is whereanominalMETresponse(RMET)isobtained

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Ifb2EgenT1EgenT2isnegligible,RMETismainlydeterminedbya=(1:0)]TJ/F1 11.95 Tf 12.05 0 TD[(b(EgenT1+EgenT2),wherea+b(EgenT1+EgenT2)=1:0providesacriticalconditionwiththeMETresponseRMETequalto1.SothesumoftwojetET(=EgenT1+EgenT2)canbeusedtoestimatetheoverallMETresponse.Theaveragejetenergyresponsewithjj<5.0inFig. 7{10 indicatesthattherewillbetheunder-measurementoftheMETforadi-jetsystemwithjetETuptoTeVlevel.Butthisestimationisonlyvalidforimbalancedi-jetsystem,ifET1andET2areclose(e.g.QCDevents),theMETresponseislargelydeterminedbytheresttermsinEq. 7{10 Theconesizehasnon-trivialinuenceonthejetenergyresponse.Foraverylargeconesize,therealjetenergyresponseisdistortedbythedetectoreectfromunderlyingandpileupevents,whichweputthosefactorsintosmearingeectinsteadofjeteect.TheresultinChapter5indicatesthataconesizefrom0.4to0.6isoptimalforawidejetETrange,whichisconsistentwithabovediscussion. Figure7{10. JetEnergyResponsewithrespecttogeneratorjetpT

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Inthefollowing,thejetenergycalibrationisperformedonthedi-jetsystem(Eq. 7{13 ). jet=jEcorT1)]TJ/F3 11.95 Tf 11.95 0 TD[(EcorT2jEcorT1=EdetT1 jetisthedetectordi-jetMETaftercorrection,EcorT1andEcorT2arethedetectorjetETaftercorrection,EdetT1andEdetT2aredenedbyEq. 7{5 .InordertocompareMETcordi jettoMETgendi jet(generatorlevelMETdenedbyEq. 7{1 )andMETrawdi jet(rawdetectorMETdenedbyEq. 7{10 ),Eq. 7{13 needbeexpressedasafunctionofgeneratorjetEgenT.AgeneralformofEcorTwithrespecttoEgenTundersecondorderTaylorexpansionis: (7{14) whereRisthejetenergyresponseandsatisesEq. 7{9 andR=a+b(EgenTR).SoMETcordi jetbasedonEq. 7{14 canbeexpressedas jet=(EgenT1)]TJ/F3 11.95 Tf 11.95 0 TD[(EgenT2)| {z }1+(G(1) {z }2)]TJ/F3 11.95 Tf 11.29 0 TD[(b(G(1) {z }3)]TJ/F3 11.95 Tf 11.29 0 TD[(b(G(1)2 {z }4+b2(G(1)2 {z }5+b2(G(1)3 {z }6 wherethethecontributionof(3),(4),(5),and(6)termsaresmallduetocoecientb,whichisattheorderof10)]TJ/F4 7.97 Tf 6.58 0 TD[(2)]TJ/F1 11.95 Tf 11.95 0 TD[(10)]TJ/F4 7.97 Tf 6.59 0 TD[(3.Thersttermshowsthejetenergy

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correctionrecoverthegeneratorlevelMETscale,whichalsoimprovesMETresolution.ThesecondtermonlyinuencetheMETresolution,whichisthesumofstochasticeectbasedongaussiandistributionfromdi-jet(p jet>p jet


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Intheimbalancedi-jetsystemdiscussedintheprevioussection,thesecondtermisalsoworsenbythejetcalibration,butthiseectislargelyovercomebytheimprovementrstterm,whichresultsinabetteroverallMETscaleandresolution.Forsomejetcorrectionalgorithmsthatareabletoreducetheofjetresolution,thesecondtermcanbepossiblyimproved.Herewedeneanewparameter,jetcorrectionfactor(R),tostudythelimitofawellperformedjetenergycorrectiononMETresolution(Eq. 7{16 ). wherecorandrawarecorrectedandrawjetenergyresolutionrespectively.Jetenergyresponse(Rjet)andjetcorrectionfactor(R)canbeusedtoconstructanestimatorfortheperformanceofthejetenergycorrection:ifRRjet>1.0,thedi-jetMETresolutionwillbeimproved. AccordingtotheknownperformanceofthejetenergycorrectiondiscussedinChapter4,Ris1.1forthecentraljetETfrom30to600GeVwith<3.0,sotherawjetenergyresponseneedbeabove0.90inordertobenetthedi-jetMETresolution,whichcorrespondsto300-400GeVofthecentraljetETasshowninFig. 7{10 ,whereweusetheaveragejetenergyresponse.Ifconsideringthedependenceofjetenergyresponsethatforwardjetshavehigherresponsethanthatofcentralones,theETthresholdforthecentraljetwillbeevenhigher(whileitwillbelowerfortheforwardjet). AsmentionedinSection2,thefactorizationmodelmainlyconsidersthestochasticjetenergyresponseandneglectsitsdependence.ObviouslythesecondfactorintherawMETquantitiescanbelargelycorrectedbyjetcalibration,whichwillpartiallyimproveMETresolution.Inthefollowing,weuseeventswithjetETbetween80and90GeVtostudythiseect.Thedi-jetdistributionanddistance()areshowninFig. 7{11 ,whereweseethecanbettedby

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agaussiandistributionwith2.0.partiallydependsonjetET(e.g.,forjetETbetween300GeVand320GeV,theis1.8).Thedierenceofdi-jetresponse(R)canbeestimatedfromandjetenergyresponsewithrespectto,whichcanbefoundinFig.14of[ 55 ].Weuse(ET)=ETtocharacterizetheRthreshold,whichcorrespondstoRistheatthesamelevelofjetresolution. 7{12 ). 7{12 too. (a)(b) Figure7{11. QCDjetquantitieswithjetETbetween80and90GeV:(a)dis-tributionand(b)Di-jetdistribution

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Figure7{12. FractionofeventswithjetETbetween80and90GeVasafunctionofdi-jetRcut Asaconclusion,basedonthefactorizationmodel,forbalancedjetsystem,itischallengingtoachievebetterMETresolutionbyusingjetenergycorrectionforlowandmediumETjets,whichexplainwhyitishardtoseetheimprovementofMETresolutionandtriggerrateinQCDevents.Onepossiblewaytopursuejetcalibrationistoselectdi-jetwithlarge,thisworkisunderseparatestudythroughsimulateddataanalysis. 7{15 byaectingthersttermfortheimbalancedi-jetsystem,andthesecondtermforthebalancedi-jetsystem.ThejetenergycalibrationisnormallybasedonthemeasuredjetETandjetenergyresponse.Ingeneral,thejetenergyresolutionsetsanultimatelimitofMETquantitiesinthedi-jetsystem,provideddependentjetenergyresponsefeaturescanbewellhandled.Itisaninterestingworktolookforbetterjetcorrectionalgorithmthatcanfurtherreduce

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the(ET),whichwilldenitelyhelptheMETresolution,especiallyforthebalancejetsystem. Fortheimbalancedi-jetsystem,jetenergycalibrationismoreeective.ThemajorquestionleaveswhetheritisreliabletouseIdet>1.0(orMETdetdi jet>p Toavoidthisissue,extrasignatureisneededtoincreasethesignicanceoftrueMETeventsandreducethefakedMETevents.Forexample,leptonselectionhelpextractWdecayeventswhichcarriestrueMET.UsinganglecorrelationbetweentwohighestETjetscansuppressQCDevents.AstrictercriterionbasedonIdetcanhelpreducethefakedMETevents,whichalsodependsonthekinematicsofthesignalevents(e.g.,averagejetETandaverageMETscale).

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jet=jnXi=1EgenTicos(i)jMETygenmulti jet=jnXi=1EgenTisin(i)j 7{2 and 7{3 jet=jnXi=1EdetTicos(i)jMETydetmulti jet=jnXi=1EdetTisin(i)j whereEdetTiisdenedas (7{19) Smearingeectisthesameasthatofdi-jetmodel(Eq. 7{5 ),sotheMETofmultiplejetsystemis jet+METxsmMETydet=METydetmulti jet+METysm 7{14 )isstillvalid.TheresultsofcorrectedMETbasedonthesimilarformofEq. 7{15 is jet=nXi=1(EgenTi+G(i) jet=nXi=1(EgenTi+G(i) (7{21)

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whichcanbeexpressedas jet=nXi=1^ni(EgenTi+G(i) (7{22) where^niistheunitvectorofithjetmomentum. Afterthejetenergycalibration,thegeneratorlevelMETscaleisrecovered.Buttheresolutiontermareaected.Theoverallresolutionofjeteectisp jet jet Weseemostoftheconclusionbasedonthedi-jetsystemappliestothemultiplejetsystem. Inthissection,thedi-jetfactorizationmodelisusedtostudytheQCDMETtriggerrateanditssensitivitytovariousdetectoreects(e.g.,stochasticjetenergyresponse,smearingeect).

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7{1 ,108eventsaregeneratedbyfactorizationmodeltostudytheMETHLTquantities.TheMETHLTthresholdfrom60to120GeVwith5GeVastepareused,ofwhichtwoboundaryisdenedbythelevel-1threshold(60GeV)andHLTthreshold(120GeV)respectivelyinDAQTDR[ 28 ]underlowluminosityofLHC. SincethefactorizationmodelisoptimizedwithdiscretejetETrangesofthedatasamples,attingfunction(Eq. 7{24 )isusedtoestablishacontinuousHLTselectioneciency(SHLT)withrespecttothejetET.Fig. 7{13 showsthelog10(SHLT)withvariousMETthreshold.ThettingresultsofgivenMETthresholdsaresummarizedinTable 7{3 Table7{3. Fittingresultsofa,bandcaccordingtoEq. 7{24 forvariousMETHLTthresholdfrom60to120GeV HLTthreshold(GeV) abc 60 0.42510.023920.591965 0.38160.018260.626970 0.44390.015840.627575 0.58320.014920.608580 0.11810.0072040.767785 0.22830.0073290.736190 0.62850.0099370.635495 0.083250.0043490.809100 -0.1030.0026340.8955105 0.021660.0029610.8506110 -0.012630.002490.8689115 0.012130.002310.8666120 -0.1330.0015520.9311 ThedierentialjetcrosssectionasafunctionoftheleadingjetETisshowninFig. 7{14 ,whichisalsoestablishedfromthejetcrosssectionineachdiscreteET

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Figure7{13. log10(SHLT)asafunctionofjetETforvariousGeVMETthreshold.Thecurvescorrespondsto60,65,70,75,80,85,90,95,100,105,110,115,and120(GeV)METthresholdfromuptodown. rangefromthedatasamplesandthenttedwithacontinuouscurve. ThedierentialMETHLTrate(DHLT)canbecalculatedforaHLTthresholdandagivenjetETrangeofthedatasampletoo(Eq. 7{26 ).TheoverallresultsareshowninFig. 7{15 whereiisthecrosssectionoftheQCDeventsestimatedbytheleadingjetETwitha1GeVbin,RebunchisthefullLHCcrossingrateof32MHzoutoftotalcrossingrateof40MHz,TisthetotalQCDcrosssectionof55mb(T).ThecalculationisbasedontheprinciplethattheinclusiveMETistreatedasacombinationofmultipleevents'contributioninabunchcrossing[ 59 ].

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Figure7{14. log10(ET)asafunctionofjetET 7{16 showstheHLTrateusingjetETrangefrom20to1000GeV.FromFig. 7{15 ,weseeeventsofveryloworhighjetETwillnotmakesignicantcontributionstotheMETHLTratebecauseofthedroppingofDHLTinbothsides. Wefoundathresholdof80GeVwith1HzHLTrateispredictedbythefactorizationmodelwhichisalmost40GeVlowerthanthatfromDAQTDRbyusingthesimulateddatasamplebutwithmuchcoarsestatistics.ThisdiscrepancyindicatesextrafactorsotherthanjeteectandsmearingeectthatareusedforfactorizationmodelmakeanextraordinaryhigherrateinthetailofMETdistribution.Althoughintherelativelylow-mediumMETrangeforeachjetETsample,thefactorizationmodeldescribeswelltheMETspectrum. Oneofthepossiblesourcesthatcausehightailisminimumbiasevents.Ingeneral,minimumbiaseventshavemuchlessjetactivitieswithlowerETthanthesignalevents.ButforlowjetETsignalevents,thepossibilityforapileupevent

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Figure7{15. DierentialMETHLTrate(DHLT)asafunctionofjetET.Thecurvescorrespondsto60,65,70,75,80,85,90,95,100,105,110,115,and120(GeV)METthresholdfromuptodown. Figure7{16. METHLTrate(Hz)withrespecttogiventhreshold

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containinghigherETjetincreases,whichcausesunexpectedhightail,ThiseectisfurtherenhancedbyverylargecrosssectionoflowjetETevents.DuetoverylessstatisticsintheexistingdatatofurtherfactorizethiseectorstudythesystematicissueinthepileupmechanismanditsinuenceontheestimationoftheMETtriggerrate,weconcludethat: Fig. 7{17 showstheMETHLTselectioneciency(SHLT)injetETbetween80and90GeVrangeasafunctionofjetandsmrespectively. Aclosetolinearrelationshipbetweenlog10SHLTandjet(orsm)indicatestheslopeofthisdependencyprovidesaquantitativemeasurementofthesensitivityoftheHLTratetojetandsmearingeect(Eq. 7{27 ).Theresultsaresummarizedin

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(a)(b) Figure7{17. SensitivityofSHLTtojeteectandsmearingeect:(a)SHLTasafunctionofjetwithxedsmequaltooptimalvalueofthefactoriza-tionmodeland(b)SHLTasafunctionofsmwithxedjetequaltooptimalvalueofthefactorizationmodel.ThejetETrangeisbetween80and90GeV.VariousMETHLTthreshold(GeV)areused:60(closesquare),65(opensquare),70(closecircle),75(opencircle),and80(tringle)

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Table 7{4 ,whichshowsjeteectplaysabiggerrole. Table7{4. Fittingresultsofbjet eectandbsm eectaccordingtoEq. 7{27 forvariousMETHLTthreshold HLTThreshold(GeV) bjet eectbsm eect 0.0900.07865 0.1140.08970 0.1360.10275 0.1550.11380 0.1850.137 Ingeneral,mostofthedetectorfactorsthatcontributetosmearingeectareverydiculttoberecovered,becausetheydirectlycorrespondtothelimitationandineciencyoftheinstruments.Forthecorrectionofjeteect,severaltech-niquesbasedonjetenergycorrection,pileupenergysubtraction,possibleuseoftracksandvertexaredeveloped. Resultsillustratenormaljetcalibrationcan'timprovetheMETresolutioninQCDevents(orbalancedjetsystem),insteaditworksmoreeectivelyfortheimbalancejetsystem.Thethresholdoftheimbalance(orbalance)ofjetsystemcanbeestimatedfromthejetenergyresolution.

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Underthejeteectandsmearingeectdenedbythefactorizationmodel,METHLTthresholdfor1Hzrateisabout80GeVindicatingalargestatisticandsystematicbiasintheestimationbasedonsimulatedQCDdatasamples.

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ForSMHiggsbosonsdecayingviaH!W+W)]TJ/F2 11.95 Tf 12.31 -4.34 TD[(!``wheretheHiggsbosonisproducedviaeithergluon-gluonfusionorVBF,alargediscoverypotential[ 60 61 ]ispossibleoveralargemHmassrangebecausethedi-leptonsignaturecanbeobservedovertheSMbackground.However,thepresenceoftwo(unobservable)neutrinosinthenalstatespreventsadirectmeasurementoftheHiggsbosonmass.ApreciseestimationofthebackgroundisextremelyimportanttoidentifytheleptonexcessifitisoriginatedfromtheHiggsbosonsignal. Inthemedium-highmassrange(mH>300GeV=c2),HiggsbosonsproducedviaVBFanddecayingasH!W+W)]TJ/F2 11.95 Tf 10.5 -4.34 TD[(!`jjfromVBF,provideanotherpotentialroutetodiscovery.ThenalstatesarecharacterizedbytwohighETforwardjets,twohighETcentraljetsfromWhadronicdecay,andonehighpTleptonandlargemissingtransverseenergy(EmissT)fromtheWleptonicdecay.Ahighjet 192

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ETthresholdisfeasibleforbothforwardandcentraljetsofthesignalevents,soastorejectSMbackgroundwithmuchlowerjetETspectra.ThischannelturnsouttohavethebestdiscoverypotentialwithmH>600GeV=c2,becauseoftheincreaseofHiggsbosonmasswidthasmHgoesupandtoosmallcrosssectionofH!ZZ!4`. Thepossibilityofextendingtheuseofthischanneltothelowmassrange(mH<300GeV=c2)isintriguing.Forexample,inthe160
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Tomeetthesechallenges,weproposearobustreconstructionandselectionstrategyforHiggsbosonsproducedbyVBFanddecayingviaH!W+W)]TJ/F2 11.95 Tf 10.88 -4.33 TD[(!`jjthatminimizessystematicuncertainties.Therestofthechapterisorganizedasfollowing:thesignalandbackgroundarediscussedin 8.1 .Section 8.2 containsdetailsofthebasicparticleandjetreconstructionalgorithms.Section 8.3 describestheHiggsbosonreconstructionstrategy.In 8.4 ,ageneralselectioncutsareintro-duced.In 8.5 ,theintermediateresultsofgeneralselectioncutsaresummarized.In 8.6 ,theoptimizationofselectioncutswithnalresultsispresented.In 8.7 ,theresultofVBFHiggsdiscoverypotentialandmassdistributionaresummarizedanddiscussed.In 8.8 ,experimentaldataanalysisapproachesaredescribed.In 8.9 ,thesystematicuncertaintiesofthischannelwithrespecttoreconstructionbiasandtheoreticaluncertaintyarediscussed.Thesummaryisin 8.10 8.1.1PhysicsChannels 8{1 .Thesignatureofthesignalis: Thosephysicschannelsthathavesimilarnalstatesindetectorlevelareconsideredasbackgroundprocesses:

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Table8{1. VBFHiggsbranchingratiowithWleptonicdecay,crosssection,andeventsimulatedin`jjnalstates mH 120 0.1220.178910734465.8%130 0.2790.362321738230.0%140 0.4800.552033120150.9%150 0.6850.703742222118.4%160 0.9180.85305118097.70%170 0.9670.84895093498.17%180 0.9290.763945834109.1%190 0.7780.599535970139.0%200 0.7350.528731704157.7%210 0.7270.489529370170.2%220 0.7190.453927234183.6%250 0.7000.370122206225.2% Thereisapotentialover-estimationofthebackgroundduetothehigherordercorrectionofW+3jets(basedonISRandFSR)partiallyoverlappingwithW+4jets.Acompletetreatmentofcorrelatedbackgroundprocessesislargelybeyondthescopeofthisanalysisandunderaseparatestudy.ButitshouldbeemphasizedthattheHiggsdiscoverypotentialinthepresenceofbothW+3jetsandW+4jetsbackgroundsismoreconservativethanthatofusingonlyW+4jets.

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can'tbeidentied,oroneleptonofrelativelylowpTcan'tbewellrecon-structed).Especiallytheelectronintheforwardregionismis-reconstructedasaforwardjet. Inthisanalysis,Z+Njets(N=3,4)areconsideredasthemainbackgroundprocesses.ThecrosssectionofZ+jetsthatgiveslepton+jetsnalstateistwoordersofmagnitudelowerthanthatofW+jets,butitscrosssectioncanbemeasuredpreciselyandisalmostfreefromthebackground,whichcanbeusedtoestimateW+jetscrosssectionexperimentally. W+tb(tb)hasthesamenalstatesoftt.IntheeventgenerationofW+tb(tb),theFeynmandiagramsthatcontainttareexcluded.Thegluon-gluonfusiondominatesthecrosssectionofW+tb(tb),whichisabout60pbintheleadingorderofmatrixelements.ThefusionofuuandddforW+tb(tb)

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isnegligible.ButtheinterferencebetweenW+tb(tb)processesandttproductionprocessesmustbeconsideredsincetheyarenotinthecalculationofttproduction,whichisattheorderof10pbforgluon-gluonfusionandeachofquark-quarkfusion.TheoverallcrosssectionofW+tb(tb)isestimatedas100pb,whichisstillmuchsmallerthanthatoftt+jetsandW+jets. ThecrosssectionofabovebackgroundprocessesarelistedinTable 8{2 .W+jets,Z+jets,W+tb(tb)+jetsandWW+2jets(EW)havepartonlevelpre-selection,whichisexplainedinsection2.3. Table8{2. Majorbackgroundcrosssectionandeventgenerated(W+jets,Z+jets,W+tb(tb)+jets,andWW+2jets(EW)includepartonlevelpre-selection) Channels tt+jets 84050.4million6.9%W+tb(tb) 1006.0million57.6%WW+jets(QCD) 73.14.39million3.95%WW+2jets(EW) 1.2675600113.0%WZ+jets 27.21.63million15%ZZ+jets 10.70.642million68.1%W+4jets 255.9(e=+)15.4million5.16%W+3jets 360.6(e=+)21.6million4.86%Z+4jets 1.7(ee=)102613292.84%Z+3jets 4.35(ee=)2611572229.7%

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boson.Manysystematicuncertaintiesrelatedtonext-to-leadingorder(NLO)pre-dictionanddetectoreciencywillberesolvedexperimentally.Measuringthecrosssectionofthosebackgroundprocessesisanon-trivialtask.Twocommonissuesneedtobehandled: 1. Multiplebackgroundprocesseshavesimilarnalstates(e.g.,tt+jetsandW+jetscontributetolepton+jetssignaturewithlargecrosssection).Inordertohighlysuppresscertainbackgroundprocesses,somehardcutsareinevitable,whichintroducesystematicuncertaintyinthereconstructionandselection.Itispossibletomeasuretheoverallcrosssectionofseveralbackgroundprocessestogetherandcomparetothetheoreticalprediction.Thefeasibilityneedsbeinvestigated. 2. TheimpactoftheuctuationoftheenergydepositofminimumbiaseventsonjetenergyscaleisverystrongforthelowETjet.Clearlyidentifyingsoftjetsfromthephysicseventsandfakedjetsfromvariousdetectoreectsisanotherreconstructionchallenge. AreasonablejetETthresholdisnecessarytoreducethosesystematiceects,butthisneedsamorecarefultreatmentintheanalysis.Forexample,experimentalZ+onehardjeteventmightcomefromZ+1jeteventorZ+multiplejetseventinwhichsoftjetisexcludedbytheselection.Thetheoreticalpredictionforthesetwotypesofprocessesarefundamentallydierent,althoughtheylooksthesame\experimentally". Inthefollowing,IprovideanoverviewabouttheexpectationofbackgroundmeasurementofVBFHiggsandpossibleissuesinthereconstructionandselection: Z+jetscanbemeasuredbythedi-electronanddi-muonresonancethatgivesaZmass.TheinclusiveZpTspectrumprovidesagoodwaytotunethetheoreticalestimationofZ+jets,sincethereconstructioncanbeperformed

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byleptononly.Z+jetscanalsobeextractedfromtheexclusiveZ+Njets(N>0)withasignicantjetETthreshold(e.g.,ET>50GeV),sothattheeectoffakedjetsfromdetectorarenegligible. W+jetscanbemeasuredfromWeventswithlepton+EmissTnalstate.Inordertoreducetheinuenceofsoftleptonfromheavyavordecay,aleptonpTthresholdisnecessaryaccompaniedwithproperisolationcuts.TheW+jetsratecanalsobeextractedfromexclusiveonelepton+Njets(N>0)eventswithasignicantleptonpTandjetETthreshold.ButttandQCDmultiplejetseventsthatpasstheleptonselectioncauseseriousproblemsinidentifyingtheoriginofexperimentalonelepton+Njets(N>0)nalstates,becausenoeectiveselectioncutscanbeappliedtoW+jets.Ifthemaximalnumberofassociatedjetsisrequiredtobelessthantwo,theeectofttandQCDislargelysuppressed,thatleadstothegoodprecisioninthemeasurementofW+1jet.ThefeasibilityofmeasuringW+Njets(N>1)directlyneedsacarefulstudy. FortheinterestofVBFHiggsbackgroundmeasurement,therateofonelepton+Njets(N4)comingfromW+jets,tt+jetsandotherprocesses,canbemeasuredtogetherexperimentally.Iftherelativecontributionfromtt,QCDandotherbackgroundprocessesarewellunderstood,theW+Njets(N>1)canbecalculated.Buttheresultcontainsallthesystematicsofotherbackgroundprocesses. ItispracticaltousemeasuredZ+Njets(N>0)andW+1jetcrosssectiontoprojecttheW+Njetscrosssection,whichmayhavelesssystematicuncertainties.

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ForZZ+jetsandZW+jets,thenarrowZmasspeakcanbereconstructedfromZsemi-leptonicdecaychannelswithlittlebackground.Theassociativejetrateinthesechannelscanbereconstructedaswell. ForWW+jets,di-leptonfrombothWsemi-leptonicdecayprovidearelativelycleansignature.Di-leptonmasswillbeusedtoexcludetheZevents.Thesuitablenalstatesforcrosssectionmeasurementwillbedi-leptononlyanddi-lepton+1jet,becauseitisanticipatedtt+jetseventsdominatetherateofdi-lepton+Njet(N>1). Inadditiontothedirectreconstructionofthetopquarkmassandusingitsselectioneciencytoestimatethecrosssectiontt+jets,di-lepton+Njets(N>1)providesthepromisingnalstatestomeasurethesetwobackgroundtogether,sinceW+tb(tb)isanirreduciblebackgroundtott. Intheleading-order(LO),tt+1jetcrosssectionisevenbiggerthantt.DuetoajetETthresholdinthereconstructionthatignoreslowETjets,acarefulcomparisonstudyontherateofdi-lepton+2jets,di-lepton+3jetsandetc.isimportanttoidentifyandunderstandthecrosssectionoftt+Njets(N=0,1,2..). Inthereconstructionofmostofabovechannels,anisolationcriteriononleptonreconstructionisnecessaryinordertoidentifythesignatureofWorZleptonicdecay,whichalsoleadstoasignicantsuppressingfactorontheleptonfromheavyavordecay. Mostofthesephysicsprocessescanbeidentiedwithasimpleandrobustselectionstrategyforlepton+possibleassociatedjet(s)nalstates.Therelatedbackgroundcanbecontrolledtobeatleastoneortwoorderslower,whichleadstotheuncertaintyofcrosssectioninseveralpercentorlessandlargelyreducethesystematicuncertaintyintheMonteCarloprediction.

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Theaccuracycanbefurtherimprovedbycross-checkingphysicsrelatedchan-nels(e.g.,Z+jetsandW+jets),extractingthesignaturefromthebackgroundandttingthethedistributionbasedoncombinedbackgroundduetorelativelargenumberofeventsinvolved. Theeventgenerationforthisanalysisissummarizedasfollows: 37 ].AlldecaymodeofWandZbosoninbackgroundwereswitchedonexceptthesignaleventswithonlysemi-leptonicmodeswitchedon.ThenumberofeventsforeachprocessislistedinTable 8{1 and 8{2 .Thecongurationofgeneratorincludes:ISR,FSR,hadronization,multiplepartoninteractionandunderlyingevent.CTEQ5mPartonDistributionFunction(PDF)setwaschosen. 62 ].Duetoverylargecrosssectionofthoseprocesses,thepartonlevelpre-selectioncutsareimplementedbasedonjetpTthreshold(pjT),jetrange

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(j)andminimumjet-jetdistance(Rjj).DuetoW+4jetsisthemajorbackground,alowerpjTisused.Renormalizationandfactorizationscaleweresetto0=mWandCTEQ5lPDFsetwaschosen. WW+2jets(EW)wasgeneratedbyMadGraph[ 63 ]withsamepartonlevelpre-selectioncutsandcongurationasALPGEN. W+tb(tb)+jetswasgeneratedbyCOMPHEP[ 64 ],noselectioncutisappliedtotquark,minimumbquarkpTissetto15GeV/cwithjj<5. EventsgeneratedbyALPGEN,MADGRAPH,andCOMPHEP(calledMatrixElementEventGenerator,orMEgenerator)werethenprocessedbyPYTHIAforpartonshoweringwiththesamesettingsdescribedaboveexceptthePDFsetwaschangedtobecompatiblewiththeMEgenerator. ThecongurationofALPGENandMADGRAPHisillustratedinTable 8{3 Table8{3. Thecongurationofpartonlevelpre-selectionofmatrixelementeventgenerator(ALPGENandMADGRAPH) GeneratorChannel pjT(GeV/c)jRjj 255.00.5ALPGENZ+4jets 255.00.5ALPGENW+3jets 255.00.5ALPGENW+4jets 205.00.5MADGRAPHWW+2jets 205.00.5 ThePDFcontributesnon-trivialuncertainties.TheimpactofPDFisdierentforvariousphysicschannels.AsummaryofPDFcanbefoundin[ 65 ]. TheeectsofNLO(nexttoleadingorder)correctionarenotgenerallyconsideredinthisanalysisbecauseNLOcalculationsofsomebackgroundarenotavailable,e.g.,W+Njets(N3),Z+Njet(N3)WW/ZZ/WZ+Njets(N2).TheNLO(leadingorder)crosssectionforsingleW,ZorWW/ZZ/WZproductionisavailable,buttheylargelyoverlapwithleadingordercalculationofvectorboson+associatedjets.Forttprocess,theNLOisincludedbasedonwidelyusedvalue[ 66 ].Thek-factorforVBFHiggsis1.1[ 15 ],whichisgenerally

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smallerthanthatofgluon-gluonfusionHiggs(1.5-1.8)[ 15 ]andsomebackgroundprocesses. AcompleteinclusionofNLOofsignalandbackgroundwillreducethediscoverypotentialofVBFHiggs.DuetorelativelysmallNLOcorrectionofsignalevents,thesystematicuncertaintiesoftheresultsinthisanalysiswithrespecttoNLOmainlycomefrombackground,W+Njets(N3)andtt+jets. 39 ]isperformedforthesignalandbackgroundprocessesincludingVBFHiggs,tt+jets,WW+jets(QCD),WZ+jetsandZZ+jets.FastCMSdetectorsimulationbasedonFAMOSisperformedforbackgroundprocessesincluding:W+Njets(N=3,4),Z+Njets(N=3,4),WW+2jets(EW),W+tb(tb)+jets.Thepile-upconditionissetforlowluminosityofLHC(L=21033cm)]TJ/F4 7.97 Tf 6.58 0 TD[(2s)]TJ/F4 7.97 Tf 6.58 0 TD[(1).ThedigitizationandreconstructionarebasedonstandardCMSsoftwareORCA[ 40 ]andFAMOS[ 45 ]. JetsarereconstructedwithaniterativeconealgorithmwithconesizeofR=0:6.Nooinethresholdontowerconstituentisused.ThejetenergycorrectionisappliedaccordingtothejetenergyresponsebasedonQCDjets. EmissTisreconstructedfromallthecalorimetertowerswithamuonmomentumcorrectionappliedifamuonispresentintheevent.JetenergycorrectionforEmissTistested.BecauseofthelowHiggsbosonmassusedinthisstudy,thecorrectedEmissTscaleislargelyinuencedbylowETcentraljets,whichismorechallengingthanthatofotherbackgroundprocesses(e.g.,tt+jets)thathaveharderjetETspectrumandpotentiallybenetmorefromthejetenergycorrection. Electronsandmuonsarereconstructedusingstandardoinealgorithms.Becauseofthepresenceofmultiplejetsinsignalandbackgroundnalstates,astrongcalorimeterbasedisolationisusedtoidentifytheleptonsfromWorZdecay.

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Theisolationcriteriaforreconstructedoineelectronobjectincludesthefollowingcomponents: 8{1 ). 8{2 ). jE0:2T)]TJ/F1 11.95 Tf 12.12 0 TD[(EeTj<5.0GeVandj(E0:2T)]TJ/F1 11.95 Tf 12.12 0 TD[(EeT)=EeTj<0.3,whereE0:2TisthetotalETinthe0.2isolationconeandEeTistheelectronsuper-clusterET(Fig. 8{3 and 8{4 ). 8{5 ). (a)(b) Figure8{1. EHcalT=EEcalToftrueelectron(a)andfakedelectron(b)inVBFHiggssamplewithmH=170GeV=c2 jE0:2T)]TJ/F1 11.95 Tf 11.49 0 TD[(pTj<9.0GeVandj(E0:2T)]TJ/F1 11.95 Tf 11.49 0 TD[(peT)=pTj<0.3,whereE0:2TisthetotalETinthe0.2isolationconeandpTisthemuontransversemomentummeasuredinTracker(Fig. 8{6 and 8{7 ).

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(a)(b) Figure8{2. E/poftrueelectron(a)andfakedelectron(b)inVBFHiggssamplewithmH=170GeV=c2 Figure8{3.

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(a)(b) Figure8{4. Figure8{5.

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8{8 ). (a)(b) Figure8{6. Figure8{7. 8{9 .Itcanbeseenthatintensivejetactivitiescause

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(a)(b) Figure8{8. tt+jetseventswereusedtochecktheperformanceoftheisolation.ThepurityoftheisolatedleptonswithpT>30GeV/cis99.73%and99.88%forelectronandmuonrespectively. Itmightbearguedthattheleptonisolationeciencycanbefurtheroptimizedbyusingtrackbasedisolationmethods(e.g.,countingnumberoftracksaroundtheleptontrackinanisolationcone,settingathresholdforthesumoftransversemomentumfromtracksnearby,andusingvertexinformationtofurthersuppressleptonsfromb-quarkdecays).However,furtheroptimizationoftheisolationeciencyprobablywillnotincreasetheratioofsignaltobackground.Thetrack-basedisolationcriteriondoesnotnecessarilyleadtotheloosecalorimeter-basedisolationcriterionbecauseofthepresenceofmultiplejetsandsignicantneutralenergynotaccountedforinthetrackermeasurement.

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(a) (b) Figure8{9. OverallReconstructionandSelectionEciencyofElectron(a)andMuonReconstruction(b)inVBFHiggsSample

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Fromthepointviewofresultsandtheirsensitivitytothereconstructiontechniques,thebasicobjects(forwardjets,centraljets,lepton,EmissT)canbeclassiedintworatherindependentgroups:lepton+EmissTsystemandjetsystem.Inthefollowing,thediscussionfocusesonleptonandjetselection. TechnicallytheisolationcriterionishardtoapplytothelowpTleptonduetothesignicantreconstructedcalorimeterenergyfromjetactivities,pileupandunderlyingevents,inwhichtheperformanceofisolationismoresensitivetothosefactorsandhaslargesystematicuncertaintyevenitisfeasiblebasedonexistingdetectorsimulationandreconstruction.

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theprobabilityforpassingthemultiplejetselectioncriteriaismuchlowerthaneventswithoneofthevectorbosonsdecayingintotwojets. 8{10 (a)(b) Figure8{10. LeptonpTspectrumforthehighestpTlepton(a)andthesecondhighestpTlepton(b)intheZ+jetssamplewithZleptonicdecay Asdiscussedabove,thepresenceofoneormorelowpTleptoninadditiontoanisolatedhighpTdoesnotjeopardizethereconstruction.Arobustleptonselectionstrategyisusedinthisanalysis,whichislessinuencedfromvariousphysicsanddetectorsystematiceects:

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8{11 Figure8{11. Quark-jetrelativematchingeciencyasafunctionofjetETthresh-oldforvalancequark(square)andquarkfromWhadronicdecay(circle)inVBFHiggssamplewithmH=170GeV=c2.Theeciencyisnormalizedto1.0forjetETthresholdof20GeV.

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quarksinthesignalevents(mH=170GeV=c2)areshowninFig. 8{12 .Thereisapeakaround5.0indistribution,sotheplausiblerangeforminimumisbelow5.0,otherwisethesignaleciencywilldecreasesquickly.Theminimummqqcanbesetabove1000GeV=c2,whichneedbeoptimizedwiththesignalandbackgroundeciencytogether. (a)(b) Figure8{12. Twoforwardquark-jetproperties(a)distribution(b)mqqdistri-bution ExtradetectorjetfromISRandFSRordetectoreectsthathashigherjjmightcausemis-identicationinforwardjettagging.Forexample,inthosesignaleventsthattwovalancequarkdoesnothavewideenoughdistance,extrajetscansignicantlyenhancethechanceofthoseeventsthatpassforwardjettagging,butthiseectislargelyreducedbyahigherjetETthresholdasshowninFig. 8{13 .Althoughthiseectdoesnotinuencetheforwardjettaggingeciency,itincreasesthechanceofmis-identicationofcentraljetsforhadronicWreconstruction. AhighjetETthresholdcanbeusedtoremovethoseextrajetswhichareoutsidethequark-jetasshowninFig. 8{14 .ForajetETthresholdbelow35GeV,thereisamuchstrongerdependencyofforwardjettaggingeciencyonthejetET

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Figure8{13. Therelativerateofsignalevents(mH=170GeV=c2)thatpassfor-wardjettaggingbyextrajets(butquark-jetfail)tothoseeventsthatquark-jetpassestaggingasafunctionofjetETthreshold.IntensiveISRandFSRlargelyenhancedtheforwardjettaggingeciency,especiallyfortheETthresholdbelow35GeV threshold,whichcanbeexplainedbytheintensivesoftjetactivities.Duetothisfact,thesystematicuncertaintyofjetenergyscalewillbesignicantlyenhancedinforwardjettaggingforETthresholdbelow35GeV,whichshouldbeconsideredintheoptimizationoftheselectioncuts. TheincreaseofjetETthresholdanddistancethresholdcausesthereductionoftaggingeciencyasshowninFig. 8{11 .Withthexedquark-jetETthreshold,theincreaseofdistancewillreducethemid-identicationrate,butitalsoresultsinthereductionofoveralltaggingeciency,asshowninFig. 8{15 8{16 ,whichprovidesabasichadronicWmassresolutionof14.8GeV/c2.ThereconstructioneciencyisverysensitivetojetETthresholdasshowninFig. 8{11 .Athreshold

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Figure8{14. TherateofVBFHiggsevents(mH=170GeV=c2)withextrajetthatisoutsideoftherangeoftwojetsmatchedwiththevalancequarkwithdistancebiggerthan3.8asafunctionofjetETthreshold.TherateincreasessignicantlyasjetETthresholdgoesbelow35GeV,whichindicatesastrongenhancementofthesoftjetactivitiesoftheeventsviaISR/FSRanddetectoreects. Figure8{15. ForwardJetTaggingeciencyfordierentthresholdofdistanceinVBFHiggseventswithmH=170GeV=c2

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higherthan30GeVwillhaveseriousimpactonthesignalselectioneciencyduetothelowmassofHiggsbosonstudiedinthisanalysis. Figure8{16. mWusingquark-jetthattwoquarksareidentiedfromhadronicWdecayinVBFHiggseventswithmH=170GeV=c2 8{4 .Itshows0.6conejetprovidesabetterWmassscaleandresolution,whichallowsasymmetricdi-jetmassselectionwindowwithrespecttothetrueWmassinthereconstruction. Table8{4. ReconstructedWmassresolutioninvariousjetcone.RealWmass(81.2GeV=c2)isusedtoscalethereconstructedWmass(mW),whichleadstoascaleds(mW)=mW=81:2(mW) ConeSize 55.111.5216.80.6 82.314.7514.40.8 90.2717.2515.4

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MultiplecentraljetscausecombinatorialproblemifthehadronicWcanbereconstructedfrommorethanonepair.Inthefollowing,anoverviewofseveralpossibleselectionstrategiesareprovided: 8{17 shows60%oftheVBFHiggseventshaveextrajetswithET>20GeVindetectorlevel. Figure8{17. Numberofextrajetsinthecentralexcludingthequark-jetfromfor-wardjettaggingandhadronicWreconstructioninVBFHiggseventswithmH=170GeV=c2.AjetETthresholdof20GeVisused.

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8{18 Figure8{18. TheIDofextrajet,whichisnumberedbasedonjetETfromhighesttolowestinVBFHiggseventswithmH=170GeV=c2.Thequark-jetfromforwardjettaggingareexcluded.IftwohighestETcentraljetsarerequiredforWreconstruction,themis-identicationrateishigh,becauseextrajetsare17%(19%)ofthehighest(secondhighest)ETjetsinthecentral. Theoptimizedcentraljetselectionstrategyusedinthisstudycombinestherstandsecondmethodsintoamodiedcentraljetvetoschemebylookingforadi-jetmasswithleasterrortothetrueWmassandcontrollingthemaximumnumberofcentraljetsinanevent,sothatthecombinatorialeectisreducedandphysicsnatureoftherealjetfromWdecaycanbemanifested.

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andhadronicWreconstruction.Theprimaryinterestsaboutextrajetsrelatetothejetsthatwithintherangeoftwotaggedforwardjets,sotheextrajetsarecountedonlyinthisrange. InthereconstructionofforwardjetandhadronicW,weavoidtousehighestjetETselectioncriterion(e.g.,usingtwohighestETjetsfortheforwardjettaggingand/ortheresttwohighestETjetsforthehadronicW),whichlargelyreducethesystematiceectsofjetenergyresponseandcalibrationbiasbetweendierentregionofthecalorimeter.Forexample,jetenergyresponseisquitedierentbetweenthecentralandforwardregion.ThejetenergyscaleissensitivetothejetETspectrum,whichinevitablycausessystematicbias.TheapproachbasedonhighestETselectionalsoshowssignicantmis-identicationrate(aspreviouslyshowninFig. 8{18 )andlossofthetrueeciency. Fortheforwardjettagging,anrobuststrategyisusedforthisanalysisthatisbasedonthethresholdsofjetET,di-jetanddi-jetmass.ThejetcanbemeasuredingoodprecisionduetothenegranularityofCMSHCAL.AsimilarstrategyisusedforhadronicWasdiscussedinprevioussection. TherearedetectorreconstructionconstraintsonoptimizingjetETduetoalargenumberoflowETdetectorjetswhichpurelycomefromthedetectoreects(e.g.,electronicnoise,pileupandunderlyingevents).A25GeVthresholdonjetETisused,sothatthosejetsbelowthisthresholdwillnotbecounted,whichlargelypreventtheanalysisandresultsfromvariousdetectoreectsandsystematicuncertainties.Thisthresholdisalsoconsistentwiththepartonlevelpre-selectionfortheW+4jets,oneofthemainbackgroundprocesses,whichhas20GeV/cforminimumquarkpT.ItisanticipatedthattheaveragedetectorjetsETwillbelowerthanthequarkbecauseofISRandFSR,butalowthresholdwillstillbeinuencedbythepartonlevelpre-selectioncuts.

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Fig. 8{19 showsthemultiplejetselectioneciency(requiringatleast4jetsinanevent)forvarioussamplesasafunctionofjetETthreshold.ThecurveofW+3jetsismoresensitivetothethreshold(asthethresholdgoesdown,thepassingrateofW+jetsincreasessignicantly),sincesoftjetsfromISRandFSRplaysastrongerroleinmakingW+3jetspassthe4jetselectioncriterionthanothersamples.Forthethresholdaround25GeV,theeciencycurvesofvarioussampleshavealmostthesameslope,whichindicatestheratioofsignaltobackgroundwillbelessaectedbythesystematiceectsofjetenergyscaleandintrinsicfeaturesofvariousphysicsprocesses. Figure8{19. Multiplejetselectioneciency(requiringatleast4jetsinanevent)asafunctionofjetETthreshold.TheeciencyisnormalizedtotheratewithjetETthresholdof16GeVforeachsample.Thephysicschannelsinclude:tt+jets(solidsquare),W+3jets(opencircle),W+4jets(solidtriangle),andVBFHiggswithmH=170GeV/c2(opensquare)

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VBFHiggssignatureandreducetheinuenceofsystematiceectinthedetectorreconstruction.Theselectioncutsareintroducedaccordingtheirsequenceusedinthereconstructionchain. TheanalysismainlytargetsatbothWfromtheHiggsbosondecayareon-shell,especiallyfor160
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(a)(b) Figure8{20. NormalizedleptonpTdistribution(a)andnormalizedleptondis-tribution(b)ofVBFHiggswithmH=170GeV=c2(solid),tt+jets(dash),andW+4jets(dot)respectively TheEmissTisrequiredtobeabove30GeV.IfjetenergycorrectionisappliedforEmissT,non-trivialsystematiceectswillbecausedbythesignicantdierenceinthegeneratorlevelEmissTspectrumanddetectorjetETspectrumbetweenVBFHiggsandseveralmainbackgroundprocessesasshowninFig. 8{21 .SonojetenergycorrectionisusedforEmissT.Thiswillbefurtherdiscussedinthesummary.

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(a)(b) Figure8{21. NormalizedEmissTdistribution(a)andnormalizedJetETdistribution(b)ofVBFHiggswithmH=170GeV=c2(solid),tt+jets(dash),andW+4jets(dot)respectively j1)]TJ/F3 11.95 Tf 11.96 0 TD[(2j>3.8

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SincetheHiggsbosonmassisveryclosetodi-Wmass(160.8GeV=c2),itisanticipatedthattwoWshaveverysmallmomentumintheHiggsbosonrestframe,andintheexperimentalframe(undertheboostofHiggsmomentum)twoWsarecloseintheyingdirection.Thisfeaturecanbeusedtoresolvetheambiguityofneutrino'smomentuminzdirection.TheRbetweeneachoftwoleptonicWcandidatesandthehadronicWiscalculated.TheonewithsmallerRisselectedasleptonicW. 8{22 and 8{23 ).ThelimitedEmissTresolutioncausestheworsequalityoftheleptonicWthanthatofthehadronicW.

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(a)(b) Figure8{22. HadronicWproperties(a)pTerrorand(b)RbetweenthedetectorandgeneratorlevelhadronicW.ThepTerroristtedbyaGaussianwith15.1GeV/c. (a)(b) Figure8{23. LeptonicWproperties(a)pTerrorand(b)RbetweenthedetectorandgeneratorlevelleptonicW.ThepTerroristtedbyaGaussianwith19.5GeV/c.

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ThereconstructedleptonicWpThasbeenusedtoevaluatethepossibilityofapplyingthejetenergycorrectionforEmissT(Fig. 8{24 ).AsHiggsbosonmassgoesup,WpTerrorshiftfrompositivetonegative.ApositiveshiftofpTcorrespondstoover-measuredEmissT,whichisthecommonfeatureofintrinsiclowEmissTevents(e.g.,QCDevents),thatvariousdetectoreectsrandomlyenhancetheEmissTspectrum.Inthiscase,jetenergycorrectionwillnotworkwellforEmissT.Asaresult,duetothelowHiggsbosonmassandinducedlowEmissTspectrumstudiedinthisanalysis,jetenergycorrectionisnotappliedforEmissT. FormH>200GeV=c2,theWpTerrorturnsnegative,whichshowstheeectoflowjetenergyresponseinthedetectorthatcausestheunder-measurementofEmissT.ThisisthecommonfeatureofhighEmissTevents.Inthiscase,therandomdetectoreectswillonlydeterioratetheEmissTresolutionbutnotchangesthescaleofEmissT.TherestorationofEmissTscalewillneedjetenergycorrection.RoughlyatmH=250GeV=c2,averageWpTerroris0afterapplyingjetenergycorrection. Forbothcases,nosignicantdierenceinWpTresolutionbetweenthecorrectedandun-correctedEmissTisobserved. ThedistancebetweenthehadronicandleptonicW(RDi)]TJ/F4 7.97 Tf 6.59 0 TD[(W)denedinEq. 8{2 playsanimportantroleinthereconstructedHiggsbosonmass.TheerrorofthedistancebetweenthedetectorandgeneratorlevelcanttedbyaGaussiandistributionwithaof0.25(Fig. 8{25 ).Thisleadsto20GeVresolutioninreconstructedHiggsmass.ThelongtailattributestothewrongidenticationofjetsinthehadronicWreconstructionandlimitedEmissTresolutionintheleptonicWreconstruction. RDi)]TJ/F8 7.97 Tf 6.59 0 TD[(W=q TheselectioneciencyforthesignalandbackgroundwithrespecttotworeconstructionscenariosofmH160GeV=c2andmH<160GeV=c2areincluded

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(a)(b) Figure8{24. LeptonicWpropertiesasafunctionofmH(a)averagepTerrorand(b)pTresolutionbetweenthedetectorandgeneratedleptonicWwithun-correctedEmissT(solidsquare)andcorrectedEmissT(opensquare) Figure8{25. Di-WRerrorbetweendetectorandgeneratorlevelinVBFHiggseventswithmH=170GeV/c2

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inTable 8{5 and 8{6 respectively.ThesummaryoftheselectioncutsisincludedinTable 8{7 Table8{5. SelectioneciencyforsignalandbackgroundeventswithscenarioofmH160GeV=c2 TriggerL-SE-SFJTH-WL-W(fb) VBFHiggs(mH=160) 0.5940.5190.3460.3470.7980.64216.15VBFHiggs(mH=170) 0.6070.5390.3720.3530.7950.55215.99VBFHiggs(mH=180) 0.6180.5710.3830.3480.8100.55916.28VBFHiggs(mH=190) 0.6290.5860.4000.3660.8090.54214.16VBFHiggs(mH=200) 0.6440.5960.4130.3740.8210.53513.78VBFHiggs(mH=210) 0.6520.6030.4240.3700.8100.54913.43VBFHiggs(mH=220) 0.6640.6080.4430.3830.8140.52813.35VBFHiggs(mH=250) 0.6820.6100.4110.3830.8350.54210.71tt+jets 0.4220.3100.4650.0630.8160.5681494.2WW+jets(QCD) 0.2270.5390.0780.0480.7180.3939.27WW+jets(EW) 0.2520.5300.4170.3190.7680.4587.88ZZ+jets 0.1470.2890.0970.0510.7580.5941.00ZW+jets 0.1770.4640.0980.0570.7770.6317.23W+tb(tb) 0.4220.1230.4280.0560.7060.45292.8W+4j(W!e=+) 0.5560.5580.4640.0780.6240.5931194.8W+3j(W!e=+) 0.5450.5730.2540.0600.5630.563541.8Z+4j(Z!ee=) 0.7620.4100.5030.0830.6120.4266.97Z+3j(Z!ee=) 0.7430.3980.2790.0610.5720.4134.82 ThereconstructedHiggsbosonmassfromoverallbackgroundeventsundermH160GeV=c2scenarioisshowninFig. 8{26 andthesignalofVBFHiggs(mH=170GeV=c2)isshowninFig. 8{27 Themajorbackgroundistt+jets,W+jetsandW+tb(tb)+jets.Asdiscussedinprevioussection,W+3jetseventscanyieldthedetectorsignatureoflepton+Njets(N4),whichispartiallyoverlappedwithW+4jetsevents.This

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Table8{6. SelectioneciencyforsignalandbackgroundeventswithscenarioofmH<160GeV=c2 TriggerL-SE-SFJTH-WL-W(fb) VBFHiggs(mH=120) 0.4600.4650.2060.3110.7410.7051.28VBFHiggs(mH=130) 0.4920.4850.2300.3550.7670.7474.03VBFHiggs(mH=140) 0.5230.4960.2560.3470.7870.7137.12VBFHiggs(mH=150) 0.5610.5100.2880.3430.8020.65911.01tt+jets 0.4220.3100.4650.0630.8070.5701483.0WW+jets(QCD) 0.2270.1220.0780.0480.7440.3979.70WW+jets(EW) 0.2520.5300.4170.3190.7810.4547.94ZZ+jets 0.1470.2890.0970.0510.7580.5650.954ZW+jets 0.1770.4640.0980.0570.8040.7457.45W+tb(tb) 0.1230.4280.0560.7410.471101.5W+4j(W!e=+) 0.55600.5580.4640.0780.6540.6161323.0W+3j(W!e=+) 0.54500.5730.2540.0600.6130.598637.5Z+4j(Z!ee=) 0.76190.4100.4930.0830.6330.4467.59Z+3j(Z!ee=) 0.74270.3980.2890.0610.6100.4465.56 Figure8{26. VBFHiggsmassreconstructedfrombackgroundeventsunderhigh-massscenario.MajorbackgroundincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow).

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Table8{7. Summaryofbasiceventselectioncuts Selection Conguration Electron:EHcalT=EEcalT<0.05 0.90.5 Eventselection Njet>4jetswithET>25GeV(E-S) EmissT>30GeV ET>30GeVForwardjettagging mqq>800GeV=c2 wM<25GeV=c2(mH160GeV=c2)(H-W) 30
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Figure8{27. VBFHiggsmassreconstructedfromVBFHiggseventswithmH=170GeV=c2 Inthisanalysistwoscenarios,Conservative(c)andOptimistic(o),areusedtoestimatetheW+jetsbackground:

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Theoptimizationoftheselectionstrategyisdoneinthreestepswithmultipleparametersconsideredforeachstep.Duetonitesizeofbackgroundsamplesandlargesuppressionfactorfromseveraleectivekinematiccuts,averylowstatisticsdoesnotallowagoodestimationofHiggsbosonmassdistributionfromthebackgroundevents,althoughaHiggsbosonmasspeakfromthesignaleventscanbereconstructed. Fig. 8{28 showsthedistributionofthebackgroundandVBFHiggssignal(mH=170GeV=c2).Fig. 8{29 showstheS/Bwithrespecttodierentthresholds(minimumcut). (a)(b) Figure8{28. distributionofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).MajorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow).

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Figure8{29. S/BwithrespecttodierentthresholdforConservative(solidsquare)andOptimisticScenario(opensquare) Fig. 8{30 showsthemqqdistributionofthebackgroundandVBFHiggssignal(mH=170GeV=c2)withathresholdof4.3.Fig. 8{31 showstheS/Bwithrespecttodierentmqqthresholds(minimummqqcut). (a)(b) Figure8{30. mqqdistributionofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).MajorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow).

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Figure8{31. S/BwithrespecttodierentmqqthresholdsforConservative(solidsquare)andOptimisticScenario(opensquare) SeveralETthresholdfortaggedjetsaretestedwithmqq>1200GeV=c2and>4.3(Table 8{8 ),thatshowstheS/BgetsomeincreasewithhigherthresholdofEFHTbutincreasingEFLTsignicantlyreducesthesignalselectioneciency. Table8{8. ForwardjettaggingeciencywithvariousjetETthresholdforConser-vative(c)andOptimisticScenario(o) EFHTEFLT 3530 0.00640.00730.6124030 0.00650.00740.6034530 0.00670.00770.6014035 0.00700.00800.6004535 0.00720.00820.5064540 0.00780.00900.504 Inthisstep,theoverallbackgroundisstillseveralhundredtimesbiggerthanthesignal.ThelossofsignaleciencyissignicantwithmodestincreaseofS/B.Butahigherthresholdispreferredtoreducethesystematicissuesofvariousdetectoreectsaspartoftheoptimization.Followingcongurationofthecutsisusedfortheeventselection:

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FormH<160GeV=c2,theselectioncutsaremodiedwithslightlylowerjetETthreshold: Afterthisstepoftheselectioncuts,theoverallS/BratiowithrespecttovariousVBFHiggsbosonmassisshowninFig. 8{32 Figure8{32. S/BwithrespecttovariousVBFHiggsmassbyusingtheConserva-tiveScenario TheNextraofthebackgroundandVBFHiggssignal(mH=170GeV=c2)isshowninFig. 8{33 .TheresultsofS/BwithrespecttodierentselectioncutsonthemaximalnumberofNextraissummarizedinTable 8{9 ,thatshowsalargeincreaseofS/Bwithrequiringlessnumberofextracentraljets. ThehadronicWmass(wM)ofthebackgroundandVBFHiggssignal(mH=170GeV=c2)isshowninFig. 8{34 .UsingNextra<2,theresultsofS/Bwithrespect

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(a)(b) Figure8{33. NextraofbackgroundandVBFHiggssignal(mH=170GeV=c2).Ma-jorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow) Table8{9. SelectioneciencywithvariousmaximalnumberofextrajetforCon-servative(c)andOptimisticScenario(o) MAX(Nextra) S/B(c)S/B(o)Signaleciency 4 0.00740.00850.8893 0.00790.00910.8712 0.00920.01100.8281 0.01330.01670.7320 0.03370.05170.517

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todierentselectioncutsonECHTandECLTaresummarizedinTable 8{10 ,thatshowsaninsensitivenessofS/BwithrespecttojetETthreshold. (a)(b) Figure8{34. WMofbackgroundandVBFHiggssignal(mH=170GeV=c2).MajorbackgroundprocessesincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow). Table8{10. SelectioneciencywithvariousjetETthresholdforConservative(c)andOptimisticScenario(o) EFHTEFLT 3025 0.01310.01640.7073030 0.01270.01560.4983525 0.01250.01550.6493530 0.01250.01530.4803535 0.01110.01330.310 Inthisstep,theoverallbackgroundisreducedtoabout80timesofthesignal.ThelossofsignaleciencyismodestwithincreaseofS/B.AsignicantlossthesignaleciencywithhighercentraljetETthresholdforhadronicWreconstructionisobservedbecausetheVBFHiggseventshavelowerjetsETthanthatofthebackground.ThecontrolofNextraprovidesalargeincreaseofS/B.TwoschemesaredenedwithrespecttoNextra:

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Duetolimitedstatisticsofbackgroundevents,alooseforwardjettaggingcutisused:mqq>1000GeV=c2. FormH<160GeV=c2,theselectioncutsofWmassselectionismodied: Alooseforwardjettaggingcutisused:mqq>1000GeV=c2. Usingoptimizedselectioncuts,theoverallS/BandsignicancewithrespecttovariousVBFHiggsbosonmassisshowninFig. 8{35 qqWWsystemiskeypartofthesignalevents.ItisanticipatedqqWWsystemshouldcontainsmallEmissT.Whilefortheotherbackgroundevents,theexistenceofextrajets,extraleptonsthataremissedinthedetectorreconstruction,lowpTleptonsorlowETjetsthatarenotcountedwillmakemoresignicantEmissTinqqWWsystem.

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(a)(b) Figure8{35. S/B(a)andsignicance(b)withrespecttovariousVBFHiggsmass.Thehigher(lower)S/BandsignicancecurvescorrespondtoExtraJetVeto(LooseExtraJetVeto)Schemerespectively TheEmissTinqqWWsystemofthebackgroundandVBFHiggssignal(mH=170GeV=c2)isshowninFig. 8{36 .TheS/BandsignicancewithrespecttothemaximumEmissTcutinqqWWsystemisshowninFig. 8{37 .AlargeincreaseofS/BandsignicanceisachievedduetofundamentaldierenceintheEmissTdistributionbetweenthesignalandbackground. AsignicantdierenceinRdistributionbetweenvariousbackgroundprocessesandVBFHiggsbosonsignal(mH=170GeV=c2)isshowninFig. 8{38 .TheS/BandsignicanceasafunctionofRcutcombinedwithEmissT<40GeVisshowninFig. 8{39 .AlargeincreaseofS/BandsignicanceisachievedwithlowthresholdofR(maximumRcut). Inthereconstructionofsemi-leptonicW,asmallerRwiththehadronicWisselectedinordertoremovetheambiguitycausedbyneutrinomomentuminz-direction.ForlowmassHiggsboson,thisparametercanalsoprovidea

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(a)(b) Figure8{36. EmissTinqqWWsystemofbackground(a)andVBFHiggssignal(mH=170GeV=c2)(b) (a)(b) Figure8{37. S/B(a)andsignicance(b)withrespecttoEmissTcutinqqWWsys-tem.Thehigher(lower)S/Bandsignicancecurvescorrespondtooptimistic(conservative)scenariorespectively

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(a)(b) Figure8{38. RbetweenleptonicandhadronicWofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).MajorbackgroundincludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow).Intheseplots,LooseExtraJetVetoSchemeinStep-2isused. (a)(b) Figure8{39. S/B(a)andsignicance(b)withrespecttoRcutandEmissT<40GeVinqqWWsystem.Intheseplots,LooseExtraJetVetoSchemeinStep-2isused.DuetostrongsuppressionoftheW+3jetsback-groundfromcombiningRandEmissTcuts,thedierencebetweenConservativeandOptimisticScenarioisnegligible.

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strongsuppressionofbackgroundeventsasillustratedinFig. 8{40 .MostofthesignaleventslocatesinR<1.0,whilebackgroundhasamuchlongertail.Soathresholdof1.0forRisimplementedwithlittlelossofHiggsbosoneciency.ButforhighmassHiggsboson,theRisnotsmall, (a)(b) Figure8{40. Rbetweensemi-leptonicandhadronicWofbackground(a)andVBFHiggssignalwithmH=170GeV=c2(b).Majorbackgroundin-cludeW+4jets(red),W+3jets(green),tt+jets(blue),andW+tb(tb)(yellow).Intheseplots,LooseExtraJetVetoSchemeinStep-2isused. Afterthisstepoftheselection,theoverallbackgroundisreducedtoaboutthesimilarlevelofthesignalwithmH=170GeV=c2.SeveraleectiveselectionsmakeasignicantincreaseofsignicanceandS/B.ThiseectismoreapparentcombinedwithExtraJetVetoScheme(Nextra<1).Duetothebackgroundisreducedtoaverylowstatistics,thatresultsinalargestatisticuncertainty.Twoschemesofselectioncutsaccordingtheextrajetselectionschemesareadopted: 1. ForLooseExtraJetVeto,EmissT(qqWW)<40GeV,R(lepton-W)<1.6,andR(Di-W)<1.0. 2. ForExtraJetVeto,EmissT(qqWW)<40GeV,R(lepton-W)<2.0,andR(Di-W)<1.0.

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InthisScheme,astrongersuppressionofbackgroundandimprovementofthesignicanceandS/Bcanbeachieved.InordertogetenoughstatisticstoestimatethesignicanceandS/B,severalcutsareloosened. FormH<160GeV=c2,theselectioncutsarethesameinthisstep. Itisanticipated,thebestselectioneciencyandsignicancewillbeachievedbycombiningtheLooseExtraJetVetoandExtraJetVetowithmqq<1200GeV=c2inStep-1,Nextra<1inStep-2,andR(lepton-W)<1.6inStep-3. 8.7.1DiscoveryPotential 8{41 (a)(b) Figure8{41. S/BandsignicancewithrespecttovariousHiggsbosonmasses.Thehigh(low)curvesofS/BandsignicancecorrespondtoExtraJetVeto(LooseExtraJetVeto)Schemerespectively

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includedinTable 8{12 and 8{13 respectively.TheoptimizedselectioncutsaresummarizedinTable 8{11 Table8{11. SummaryofoptimizationcutsformH160GeV=c2(mH<160GeV=c2) Selection LooseExtraJetVeto ExtraJetVeto EFHT>45(40)GeV EFHT>45(40)GeVStep-1 EFLT>35(30)GeV EFLT>35(30)GeV(L-S) >4.2 >4.2 mqq>1200GeV=c2 ECHT>30GeVStep-2 EFLT>25GeV EFLT>25GeV(E-S) 30
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Table8{12. Crosssection(fb)ofthesignalandbackgroundinoptimizedselectionwithmH160GeV=c2forExtraJetVeto(E)andLooseExtraJetVetoScheme(L) Channels S-1(L)S-2(L)S-3(L) S-1(E)S-2(E)S-3(E) VBFHiggs(mH=160) 7.6395.4822.564 9.5314.5802.989VBFHiggs(mH=170) 8.0995.7302.600 9.8144.8283.006VBFHiggs(mH=180) 8.0065.6352.165 9.9164.7112.738VBFHiggs(mH=190) 7.3655.2561.498 9.3634.2942.010VBFHiggs(mH=200) 6.9635.1451.520 8.6264.3411.983VBFHiggs(mH=210) 6.4674.7941.122 8.2114.0801.571VBFHiggs(mH=220) 6.6554.8470.824 8.2274.1281.259VBFHiggs(mH=250) 5.4633.9820.463 6.9003.4260.810 tt+jets 413.167.4961.478 626.516.7511.232WW+jets(QCD) 0.8430.843<0:008 1.2650.422<0:008WW+jets(EW) 7.7476.1700.0277 9.6834.454<0:0277ZZ+jets 0.1710.098<0:001 0.2690.0245<0:001ZW+jets 1.6680.667<0:001 2.3350.223<0:001W+tb(tb) 20.74510.8210.05787 35.214.427<0:05787W+4j(W!e=+) 388.5176.80.6463 583.072.0660.323W+3j(W!e=+) 142.886.1<0:3147 228.268.633<0:3147Z+4j(Z!ee=) 2.8040.7050.0104 3.7130.1410.0104Z+3j(Z!ee=) 1.6070.620<0:0067 2.3130.233<0:0067 SumofBackground 979.7350.322.220 1492.5167.381.565

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Table8{13. Crosssection(fb)ofsignalandbackgroundinoptimizedselectionwithmH<160GeV=c2forExtraJetVeto(E)andLooseExtraJetVetoScheme(L) Channels S-1(L)S-2(L)S-3(L) S-1(E)S-2(E)S-3(E) VBFHiggs(mH=120) 0.7110.4470.184 0.9510.3630.231VBFHiggs(mH=130) 2.2801.3060.536 3.0041.1250.664VBFHiggs(mH=140) 4.4052.8981.380 5.5202.3691.656VBFHiggs(mH=150) 6.5564.2241.965 8.3453.5052.317 tt+jets 555.284.490.739 859.520.940.493WW+jets(QCD) 2.9510.422<0:004 4.2150.422<0:004WW+jets(EW) 8.7707.1100.0277 11.215.395<0:0277ZZ+jets 0.2940.0979<0:001 0.4650.0979<0:001ZW+jets 2.5570.900<0:01 3.7810.334<0:01W+tb(tb) 33.18716.030.0868 54.376.799<0:0289W+4j(W!e=+) 520.0264.70.6463 778.5118.90.323W+3j(W!e=+) 218.6146.5<0:343 346.6113.90.343Z+4j(Z!ee=) 3.4570.8410.01044 4.7000.1520.00522Z+3j(Z!ee=) 2.2131.0670.01333 3.1600.353<0:01333 SumofBackground 1347.2522.21.524 2066.5267.21.164 8{42 .Usingprojectedbackground,theoverallreconstructionresultsareillustratedinFig. 8{43 UsingtheConservativeScenarioandLooseExtraJetVetoScheme,theoverallnumberofbackgroundeventsisestimatedat133afteralltheselectioncuts,whichleadstoaverylowstatisticsinthenalresultsforthebackgroundchannels,sinceonlyasmallfractionofbackgroundeventsweregeneratedandsimulatedforthosechannelsthathavelargecrosssection. AnestimationofthebackgrounddistributionisperformedbyusingalooseEmissTcutofqqWWsystem(EmissT<125GeV)inthethirdstepofoptimization,soastogetmorestatisticsfromthebackground.Therestselectioncutsarestillthesame.

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Figure8{42. VBFHiggsmassresolutionusingsignaleventsonlyformH=160(left),190(middle),and220(right)GeV=c2withofHiggsbosonmasswidth:14.1,15.5,and23.9GeV=c2respectively. ThereasonweusealooseEmissTcutinsteadofothercuts(e.g.RbetweenleptonandhadronicWandRbetweenhadronicandleptonicW)isbecausethefeaturethatEmissThighlyrelatestoextrajetactivitieswhichhaslessinuenceonthereconstructeddi-Wsystem,sothereconstructedHiggsbosonmassdistributionanditsshapefrombackgroundcanbebetterreserved.Forwardjettaggingcriterion(e.g.,di-jetmassanddi-jetdistance)alsoprovidesawaytogetmorestatisticswithoutheavilyinuencingthedi-Wsystem. Duetothechangesoftheselectioncriterion,theprojectionshouldbetakenasarst-orderapproximationofthebackgrounddistribution.Asignal-likepeakinthebackgroundcanbeobserved.

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(a)(b) (c)(d) (e) Figure8{43. ResultsofVBFHiggsmassreconstructionbasedonsignal(blue)andprojectedbackground(black)

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8{44 ): WithtighteningtheEmissTcut,therelativecontributionfromRegionCincreasesandrelativecontributionfromRegionAdecreases.BetweenRegionAandC,RegionBwithwidthof17GeV(Higgsbosonmassresolutionofthesignalevents)getsverylittleinuencefromtheEmissTcut.Soweconcludethatthebackgroundeventsaremorewidelydistributedindierentregions.Amuchlowerbumpfromthebackgroundthanthesignaleventsisexpected,whichmainlyliesonthetailofthesignal'speakdistribution. ThemajorresultsofthereconstructioninthisVBFHiggschannelisbasedontheHiggsmassdistribution,towhichbothVBFHiggsandbackgroundprocesses

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(a)(b) Figure8{44. Thefractionofeventsindierentregionsfortheoverallbackground(a)andVBFHiggssignal(b)asafunctionofEmissTcuts.RegionA(closesquare),RegionB(opensquare),andRegionC(opencircle). (mainlytt+jetsandW+jets)contribute.Onceapeakisfound,itisnon-trivialtoconrmthatthepeakcomesfromthesignalandnotfromtheuctuationofthebackgroundselectioneciencyorunder-estimationoftheircrosssection.Ingeneral,thebackgroundcrosssectioncanbemeasuredingoodprecision(discussedinSection2),sotheformerfactorhasbiggerimpactontheanalysisresults,especiallyforVBFHiggsthatalongselectionchainandhardcutscontainspotentiallargesystematicuncertainties.ItisanticipatedthatintensivelyusingdetectorsimulationtoestimatethereconstructionandselectioneciencywillplayanimportantroleforVBFHiggsstudy. Inadditionaltoanaccurateeventgenerationanddetectorsimulation,someextrasignatureoftheexistenceofHiggseventscanbeextractedfromdata,whichisthemajortaskoftheexperimentalapproachtoconrmtheexistenceofVBFHiggssignalwithoutrequiringanaccurateknowledgeofeventselectioneciency.TwotypeofsignaturesofVBFHiggsarediscussedinthefollowing,whichcanbe

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helpexperimentallyresolvetheambiguityoftheoriginofthereconstructedHiggsmasspeak. Inthefollowing,amethodofidentifyingexcessofeventswiththepresenceofVBFHiggsbosonsignalisdescribed,whichusesthephasespacedenedbyEmissTofqqWWsystem.ThreeregionswithrespecttoEmissTaredenedas: ThenumberofeventsineachregionasdenedasNA,NBandNCrespectively.AlooseselectioncutsbasedonRbetweentheleptonandhadronicWisapplied: Usingthephasespacedenedabove,wecaninvestigatethecorrelationofthenumberofeventsineachregionwithrespecttovariousvalueofRcuts.ThiscorrelationismainlyaectedbywhetherthereistheexistenceofVBFHiggssignal(calledScenarioofSignal+Background)orjustthebackground(calledScenarioofBackgroundOnly).Theselectioneciencywillplaysalessroleinthecorrelation.ItisexpectedthatRegionAwillbeinuencedbyVBFHiggssignal,whiletheresttworegionsgetmuchlessinuence. Fig. 8{45 showstheratioofthenumberofeventsbetweeneachoftworegions(RAB=NA=NB,RAC=NA=NC,andRBC=NB=NC).ItcanbeseenthatRABand

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RACarehighlyaectedbytheexistenceofVBFHiggsbetweentwoscenarios,whilethereisalmostnochangeinRBC. ThedierencebetweentwoscenariosprovidesavaluablewaytoidentifytheexistenceofVBFHiggsinadditiontotheHiggsbosonmasspeak.EspeciallyusingRACasshownFig. 8{45 (b),thevaluefromBackgroundOnlyScenarioisabout0.8,buttheSignal+BackgroundScenariocangiveamuchlargerratiowhichcanbeidentiedeasily. Thescaleoftheratios(denedasRs+b=Rb,whereRs+bistheratioofSignal+BackgroundScenario,RbistheratioofBackgroundOnlyScenario)betweentwoscenariosareillustratedinFig. 8{46 ,whichshowstheexcessinthelowEmissT(RegionA)causessignicantincreaseofthescaleasRgoeslower.Ingeneral,theratiosbetweendierentregionsdenedbyEmissTprovideagoodprobeofVBFHiggssignature. TheexperimentalmeasurementofthesequantitiescombinedwithHiggsbosonmasspeakcanalsobecomparedtothepredictionofMonteCarlosimulationandreconstruction. TheangularcorrelationbetweenleptonandhadronicWprovidesthepossi-bilityofdeningaphasespacethatwecanuseasecondun-correlatedparameter(oraselectioncut)todividethephasespaceintoseverallattices,andprojectthenumberofeventsintheregionwherewebelievesignaleventswillexistandmakeexcessfromtherestregionsthatbackgrounddominates.Thebackgroundnormal-izationmethodcanbeheavilyexploited,sincedetectorreconstructionandselectioneciencycanbeindirectlydeterminedinbackgroundregionandextrapolatedtothesignalregion.AsignicantexcessofeventsintheregionthatsignalexistsprovideanexperimentalsignatureoftheexistenceofVBFHiggs.

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(a) (b) (c) Figure8{45. TheratioofnumberofeventsasafunctionofR(a)RegionAtoRegionB(b)RegionAandRegionC(c)RegionBtoRegionC.Twoscenariosareillustrated:Signal+Background(opensquare)andBackgroundOnly(solidsquare)respectively.

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Figure8{46. TheratioofSignal+BackgroundScenariotoBackgroundOnlySce-narioasafunctionofRforRegionAtoRegionB(opensquare),RegionAtoRegionC(solidsquare),andRegionBtoRegionC(opencircle) Twoparameters(selectioncuts):RbetweenleptonandhadronicWanddi-jetmass(mqq)intheforwardjettaggingselection,areusedtodenethetwo-dimensionalphasespace.TherestoftheselectioncutsarethesameasthoseofoptimizedoneswithLooseExtraJetVetoScheme. 8{14

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Table8{14. SummaryofnumberofeventsinregionA,B,C,andDwithrespecttoSignal+BackgroundandBackgroundOnlyscenarios Region Ns+bNbNumberofsignalevents A 55148269B 387213174C 64461925D 35330449 UsingNA,NCandNDwithSignal+BackgroundScenario,weprojectNBwillbe302eventsandobserve387events,whichmakesanexcessof85eventswithsignicanceof85=p 8.9.1DetectorSystematicUncertainty Thesmearedjetenergyresolutionareusedtostudythesensitivityofrecon-structionandselectioneciencybyworsening(ET)with5%,10%,20%,30%,

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and40%.TheEmissTisre-calculatedeventbyeventaccordingly.TheimpactofthesmearingisillustratedinFig. 8{47 .Thett+jetsprocesssignicantlybenetfromaworsejetenergyresolution,becauselowETjetsintteventscanbemis-measuredandincreasetheselectioneciencybasedonaxedjetETthreshold.Insignalevents,thejetactivitiesaresuppressed,sotheinuenceofjetenergyresolutionismuchsmaller.Usingextrajetveto,itisexpectedthattheeciencyinttcanbelargelysuppressed,butitstillshowsalargeunexpecteduncertaintiescanbeintroducedbyjetenergyresolution. CurrentdetectorsimulationisconsistentwiththeresultsfromTestBeam,itisanticipatedthattheultimatedetectorjetenergyresolutionlargelydeterminedbystochasticeectofhadronresponseintheHCAL,willbeclosetothatofthesimulation(<10%),whichintroduce5-10%systematicuncertaintiesintheS/B. (a)(b) Figure8{47. Eectsofjetenergysmearing(a)eciencyofbasicselectionnor-malizedtonon-smearedratefortt+jetsbackground(square)andVBFHiggssignal(square)asafunctionofjetresolutionfactor(b)Higgsbosonmassresolutionafterbasiclteringasafunctionofjetresolutionfactor

PAGE 284

Thissectionsummarizesseveraloutstandingsystematicissuesinthethe-oreticalside(generatorlevel):theeectofISRandFSR,eectofunderlyingevent(UE)model.W+3jetsandW+4jetsaremainlyusedforthisstudyasbenchmarkprocesses. Followingscenariosintheeventgenerationotherthanthestandardoneareconsidered: Otherun-speciedparametersintheeventgenerationarethesameasstan-dardones.Dierentcongurationscenarioscausessignicantchangesintherateofeventspassingvariousselectioncutsinthebasicltering:E-S,FJTandH-W.Basedontheresultsfromstandardsamples,thenumberofeventsforthosescenar-iosarecomparedwithitsratiotothestandardonesummarizedinTable 8{15 and 8{16 Table8{15. SelectioneciencyofW+3jetswithdierentcongurationscenariotothestandardone SelectionCut UENoISRNoFSRNoISRandFSR E-S 0.8470.8400.4250.187FJT 0.7550.6590.5990.216H-W 0.8080.7590.3670.208

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Table8{16. SelectioneciencyofW+4jetswithdierentcongurationscenariotothestandardone SelectionCut UENoISRNoFSRNoISRandFSR E-S 0.9650.9801.0651.021FJT 0.9170.8861.4701.254H-W 0.8900.9220.6510.544 SomeinterestingeectsarefoundinW+4jetswhentheISRand/orFSRareswitchedo:theeventselectionrateinsomestepevengetenhanced,buttheoveralleciencyafterhadronicWreconstructionreceivesasignicantreduction.ThiseectisbecauseFSRnormallysmearsthejetETspectrumandmakelesseventspassthethreshold.IfFSRisswitchedo,aharderjetETspectrumcausemoreeventspassthethreshold.ButswitchingoFSRalsoresultsinlowerprobabilityofgettingapairofjetswithinvariantmasswithintheWmassselectionwindow,whichturnsouttomakeastrongereect. Thescalarsumoftotaltransverseenergy(ET)isanotherdetectorobservablehighlyrelatedtotheUE,ISR/FSRconguration,whichalsodirectlyinuencetheleptonisolationcuteciencyandjetenergyscale.AverageETforW+3jetsandW+4jetswithdierentcongurationsareincludedinTable 8{17 Table8{17. AverageETofW+3jetsandW+4jetswithdierentcongurationscenarios Channel UENoISRNoFSRNoISRandFSRStandard W+3jets 399.3483.1482.5465.4498.4W+4jets 537.9620.4608.9595.4634.5 Amongdierentcongurations,thevarianceinETis100GeV,whichroughlycorrespondsto0.2-0.5(0.5-1.0)GeVoftotaltransverseenergyina0.2(0.2-0.4)isolationregion,theinuenceontheisolationeciencyof30GeV/cleptonislessthan3%.Forjetenergyscale,theuctuationofjetETwith0.6conesize1-2GeV,whichis5-10%systematiceectsinthejetenergyscale.AfterLHCtakesdata,allthiseectwillbewellmeasuredandwillnothavesignicant

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impactontheselectioneciencyaftertuningtheselectioncutswithexperimentaldata. Wecarriedoutacomprehensivestudyofcalorimeter-basedleptonisolationandjetselectionstrategies.ThereconstructionandselectionchainwasoptimizedtoreducethedetectorsystematiceectsandenhancetheHiggsbosonsignal. TheestimationofbackgroundincludescorrelatedprocessesofW+jetsandZ+jets,makingthediscoverypotentialconservative.Bettersignicancecanbeachievedwithmorestatisticsofthemajorbackgroundchannels(tt+jetsandW+jets),sothattheoptimizedselectioncutscanbeappliedmoreeectivelywithfewersystematicuncertainties. Wefoundthatseveralselectionscriteriawerehighlyeectiveinsuppressingbackgrounds:forwardjettagging,extrajetveto,EmissTinqqWWsystem,RbetweenleptonandhadronicW,andRbetweendi-W.ThedetectorEmissTresolutionandjetenergyresolutionweredeterminedtobecriticaltothequalityofreconstructedHiggsboson.BecausethelowvalueofmHusedinthisanalysisreducestheexpectedaverageEmissTandaveragejetenergy,eectivebackgroundsuppressionreliesonheavyexploitationofthesignalsignature. WealsocarriedoutadataanalysisapproachusingEmissTinqqWWsystemandRbetweenleptonandhadronicW.InadditiontoHiggsbosonmassasthemajorsignature,extrasignatures(EmissTinqqWWsystemandRbetweenleptonandhadronicW)canbeeectivelyextracted,whichcanbeusedtoresolvethe

PAGE 287

ambiguityofHiggsbosonmasspeakwithoutrequiringmuchaccurateknowledgeofselectioneciency. Mostofthesystematicuncertaintiesofthisstudyrelatedtothejetenergyresolutionandcongurationofeventgenerationdescribingthevariousphysicsfactors.However,sinceS/B>1wasachievedforthemostinterestingHiggsbosonmassrange,theestimatedvaluesofthesystematiceectsstudiedherewillnotsignicantlyinuencethediscoverypotential.

PAGE 288

Thisthesisdescribesthestudyofmissingtransverseenergy(EmissT)recon-structionandcorrection,andprospectsfordiscoveringlowmassHiggsboson(120
PAGE 289

themeasuredEmissTresolutioninbothhighandlowpTQCDsamplestoafunctionofPET,thesumofthetransverseenergiesintheevent.Ageneralpileupeectwasquantitativelyextracted. ToenhancesearchesfornewphysicsprocessesrelyingcriticallyonaEmissTsignature,webuiltacomprehensiveEmissTcorrectionstrategyforleptonicevents.ApplyingthiscorrectiontottandW+jetseventsshowedthattheEmissTresolution,resolutionandaverageEmissTscalewereallimproved.Additionalcorrectionsbasedonjet,lepton,calorimeterisolation,pileupandunderlyingeventeectsandchannel-dependenttuningweredevelopedandoptimized.Wefound

PAGE 290

calorimeterisolationinthe2.4<<2.6region(outsidetheducialmuondetectionrange)showspromiseasanadditionalmuoncorrection.Furthermore,wedevelopedacalorimeterisolationstrategythatenhanceselectronidenticationandthusreducesfakeratesduetojets. InordertobetterutilizetheEmissTsignatureinphysicsnalstates,wede-velopedaphysicsmodelofEmissTbasedonfullyreconstructedQCDdi-jeteventsandextendedittomultiplejetsystems.This\factoredjet"modelwasusedtoevaluatetheperformanceofjetenergycalibrationonEmissT,aswellastheinuenceofvariousdetectoreectsandhigh-leveltriggerquantities.Wemadethefollowingndings

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ThesensitivityofQCDtriggerratesonjeteectandsmearingeectissignicant. ThediscoveryoftheHiggsbosonandaccuratemeasurementsofitspropertiesrankamongthemostimportantgoalsoftheLHCexperiments.TheVectorbosonfusionprocesshadpreviouslybeenknowntooergoodprospectsforthediscoveryofHiggsbosoninalargemassregionattheLHC.Accordingly,weinvestigatedthefeasibilityofmeasuringHiggsbosonsproducedinVBFprocessesdecayingviaH!W+W)]TJ/F2 11.95 Tf 10.98 -4.34 TD[(!`jjnalstates,wherethejetsandchargedleptonwereexplicitlyreconstructedandEmissTwasusedtotracktheneutrinoandthuspermitHiggsbosonmassreconstruction.Auniquepartofthisstudywasthelargenumber(20millionevents)ofbackgroundprocessesthatwerefullysimulatedandanalyzedusingGEANT4,oneofthelargestscalefulldetectorsimulationsforphysicsstudiesperformedinCMSsofar.Thisstudyledtothefollowingconclusions

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ThemajorcontributionsmadeinthisthesisincludetherstcomprehensivestudyofEmissTbeyondthetriggerselection;thedevelopmentofajetcalibrationandcorrectionalgorithmbasedonthejetenergydistributionthatreducesthevarianceofjetenergyerrorbetweenthegeneratoranddetectorlevel;therstcomprehensivestudyofcorrectiontechniquesforEmissTinleptonicevents;thedevelopmentofafactorizationmodelforunderstandingEmissTperformanceinCMS;andthecreationofanalysisproceduresthatextendsthediscoverypotentialofvectorbosonfusionHiggsusingH!W+W)]TJ/F2 11.95 Tf 10.73 -4.34 TD[(!`jjnalstatestothemassregionof160
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HaifengPiwasborninWuHan,acentralcityofChinaandnearYangZiRiver.HeenrolledintheDepartmentofAppliedPhysicsofTsingHuaUniversityin1990.HeobtainedtheBachlorandMaterofSciencedegreein1995and1998respectively.HebeganstudyingatUniversityofFloridain1999.Hehasconductedexperimentalhighenergyphysicsanalysissince2000.GoGators! 270


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Title: Reconstruction of Missing Transverse Energy and Prospect of Searching for Higgs Boson Produced via Vector Boson Fusion in Compact Muon Solenoid Experiment
Physical Description: Mixed Material
Copyright Date: 2008

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Holding Location: University of Florida
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Title: Reconstruction of Missing Transverse Energy and Prospect of Searching for Higgs Boson Produced via Vector Boson Fusion in Compact Muon Solenoid Experiment
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
Holding Location: University of Florida
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RECONSTRUCTION OF MISSING TRANSVERSE ENERGY AND PROSPECT
OF SEARCHING FOR HIGGS BOSON PRODUCED VIA VECTOR BOSON
FUSION IN COMPACT MUON SOLENOID EXPERIMENT
















By

HAIFENG PI


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Haifeng Pi
















To my wife, Ban, and our daughter, Nicole















ACKNOWLEDGMENTS

First of all, I would like to appreciate my wife, Ban, for the endless love and

support she gave me. She took care of the family, did an excellent work in the job,

and never lost humors during hard time. This thesis would have been impossible

without her. I would aslo like to appreciate my parents, who gave me life and

ah--, i- believe their son. I would also like to appreciate my parents in-law, sisters

and other family members in ('Ci i for their support.

I would like to express my deep gratitude to my advisor, Paul Avery, for his

instruction, support, encouragement and many interruptions on his work because of

my thesis study. He gave me the power to establish the collaboration and exploit

new ideas, which exactly matched with my working style. I would like to sincerely

thank John Yelton, Darin Acosta, Andrew Korytov, Rick Field and Guenakh

Mitselmakher for the wonderful discussion. John's advices were ahv-- so useful.

Sometimes I couldn't help knock his door. Darin's support was so critical and

helpful.

I would like to express my deep gratitude to James Rohlf and ('!in -1I ..! r

Tully. Their support on my work was part of the reason I can get this far. I was

lucky to get the right help from the right people at the right time and right place.

I also benefited a lot from a large, strong and intelligent group built by Paul.

I appreciate Jorge Rodriguez for providing computing resources, Craig Prescott

for successfully managing the Monte Carlo production, Richard Cavanaugh and

Dimitri Bourilkov for giving valuable -ii.:. -1. ~.i.- in physics and grid support, and

Yu Fu for many help of tuning up the system.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ...... iv

LIST OF TABLES ...................... ......... vi

LIST OF FIGURES ................... ......... vii

ABSTRACT . . . . . . . . viii

CHAPTER

1 INTRODUCTION .................... ....... 1

1.1 Standard Model and Prediction of Higgs Boson ........... 2
1.2 Higgs Boson Production via Vector Boson Fusion .......... 5
1.3 Analysis Goal . . . . . . . 8

2 HIGGS PHYSICS AT LARGE HADRON COLLIDER .......... 10

2.1 Higgs Boson Production and Decay ......... ........ 10
2.2 Higgs Boson Search Strategy ........... ...... .... 12
2.3 Higgs Boson Discovery Potential at CS . . ...... 14

3 OVERIEW OF COMPACT MUON SOLENOID EXPERIMENT .... 19

3.1 The C'\!S Detector .......... . . ... 19
3.1.1 Inner Tracker and Basic Performance . . 20
3.1.2 Electromagnetic Calorimeter and Basic Performance ..... 21
3.1.3 Hadronic Calorimeter and Basic Performance . . 23
3.1.4 Muon Detector and Basic Performance . . 24
3.2 Ti1.-.-- i and Reconstruction ..... ........ ... . 26
3.2.1 Data Acquisition Design and Level-1 Ti1-. .- ....... 26
3.2.2 High Level Ti1.-.-- r and Reconstruction . . 30

4 JET ENERGY DISTRIBUTION AND CORRECTION STUDY ..... 37

4.1 Data Samples .... ........... .......... .. 39
4.2 Definition of Jet Energy Resolution ............. .. 41
4.3 Jet Energy Distribution ............... . .. 44
4.3.1 Calorimeter Response . . .... ...... 44
4.3.2 Parameterization of Jet Energy Distribution . ... 45
4.3.3 Jet Energy Distribution Based on Energy Fraction Scheme .46









4.3.4 Jet Energy Distribution Based on Second Moment Scheme .53
4.3.5 Correction Potential and Sensitivity . . 55
4.4 Correction Method ............... ....... .. 55
4.4.1 Jet Reconstruction ............ ... ... .. 55
4.4.2 Correction Function ............... .... 56
4.4.3 Fitting of the Correction Function . . 62
4.5 Results and Discussion ..... . . ...... 63
4.5.1 Jet Energy Response in the I T 1< 3.0 Region . ... 64
4.5.2 Jet PT Spectrum in the I ] 1< 3.0 Region .......... ..65
4.5.3 Jet PT Resolution in the I \ 1< 3.0 Region . .... 67
4.5.4 Performance of Correction in the I T 1> 3.0 Region . 72
4.5.5 Stability of the Correction Algorithm and Jet Selection .. 73
4.6 Summary .................. ............. .. 76

5 STUDY OF MISSING TRANSVERSE ENERGY IN QCD EVENTS 78

5.1 Missing Transverse Energy Spectrum ................ .. 80
5.2 Missing Transverse Energy Resolution . . ..... 87
5.3 Missing Transverse Energy from Jets and Unclustered Towers .. 92
5.4 Correlation Between Jets and Missing Transverse Energy ..... ..100
5.5 Effect of Tower Energy Threshold .... . ... 107
5.6 Possibility of Excluding Unclustered Region . . 111
5.7 Summary ............... .......... .. .. 112

6 MISSING TRANSVERSE ENERGY CORRECTION IN LEPTONIC
EVENTS .. .. .. ... .... .. .. .. .. .. .... .. 114

6.1 Data Samples ............... .......... .. 115
6.2 Correction by Muon ............... .... .. 117
6.2.1 Basic Algorithm . . ....... .... 118
6.2.2 Reconstruction and Systematic Effect . . 118
6.2.3 Track Correction in High TI Region . . . 121
6.2.4 R results . . . . . . .. .. 124
6.3 Correction by Electron .................. .... 124
6.3.1 Basic Algorithm .................. .... 126
6.3.2 Systematic Effect ................ .. 126
6.4 Correction Algorithm Based on Jet ............. 129
6.4.1 Jet Reconstruction and Selection . . 129
6.4.2 Basic Algorithm .................. .... 132
6.4.3 Jet Energy Response Scheme ..... . . 133
6.4.4 Development of Jet Energy Correction . . ... 135
6.5 Optimization of Jet Correction ..... . . .. 137
6.5.1 Optimization of Jet ET Threshold and Cone Size ....... 137
6.5.2 C('!i i ., 1-Dependent Tuning . . . 140
6.6 Correction Method for Pileup and Underlying Effect ......... 144
6.6.1 Average Transverse Energy for Unclustered Region ..... ..145









6.6.2 Pileup Adjustment Parameter for Jet . . 147
6.7 Implementation of Jet Energy Correction . . . ... 148
6.8 Results of Corrected Missing Transverse Energy in Leptonic Events 150
6.8.1 Missing Transverse Energy Resolution . . .. 151
6.8.2 Missing Transverse Energy Scale and Response . ... 151
6.8.3 Cluster and Unclustered Factor . . .... 156
6.9 Summary ............... .......... 158

7 FACTORIZATION MODEL OF MISSING TRANSVERSE ENERGY 161

7.1 Di-Jet Missing Transverse Energy Factorization Model ...... 162
7.1.1 Definition of the Basic Model ...... . ..... 163
7.1.2 Simplification under QCD Events . . .... 164
7.2 Implementation and Validation ..... . . .. 166
7.3 Effect of Jet Energy Calibration on Missing Transverse Energy 172
7.3.1 Jet Energy Calibration in Imbalance Di-jet System ..... .174
7.3.2 Jet Energy Calibration in Balance Di-jet System ....... 177
7.3.3 Issues in Missing Transverse Energy Identification and Re-
construction ......... . . . .... 180
7.4 Factorization Model in Multiple Jet System . . 181
7.4.1 M odel Definition .................. ...... .. 181
7.4.2 Effect of Jet Energy Calibration . . . 182
7.5 Study on Missing Transverse Energy High Level Tii. r ..... . 183
7.5.1 Missing Transverse Energy HLT Rate based on Factoriza-
tion Model ................. .. ........ 184
7.5.2 Sensitivity to Jet Effect and Smearing Effect ........ 188
7.6 Summary ............... .......... 190

8 SEARCHING FOR STANDARD MODEL HIGGS BOSON VIA VEC-
TOR BOSON FUSION IN H -- W+W- -+ jj WITH mH FROM 120
TO 250 GeV/c2 ................. . ... 192

8.1 Signal and Background ............... ... .. 194
8.1.1 Physics C(' .i,., ..... ... . .... 194
8.1.2 Overview of Background Cross Section Measurement . 197
8.1.3 Event Generation .................. ... 201
8.2 Detector Simulation and Reconstruction . . 203
8.3 Higgs Boson Reconstruction and Selection Strategy . ... 210
8.3.1 Offline Lepton Selection Strategy . . 210
8.3.2 Properties of Multiple Jet System . . 212
8.3.2.1 Forward Jet T,.;ii:.; ... . . 212
8.3.2.2 Hadronic W Reconstruction . . 214
8.3.2.3 Jets ET System .............. .. .. 218
8.4 Basic Event Selection ......... . . ..... 220
8.4.1 Level-1 and High-Level Til-.-. i for Electron or Muon (Til -.-. ) 221
8.4.2 Offline Leopton Selection (L-S) .... . . 221









8.4.3 Event Selection of Jet Counting and E'iSs (E-S) ...... ..222
8.4.4 Forward Jet T,.--ii-; (FJT) .... . .... 222
8.4.5 Hadronic W Reconstruction (H-W) ............. ..223
8.4.6 Leptonic W Reconstruction (L-W) . . 224
8.4.7 Selection Criterion for Higgs Boson Mass below 160 GeV/c2 224
8.5 Summary of Intermediate Results .... . ... 224
8.6 Selection Optimization .... . . ...... 228
8.6.1 Optimization of Forward Jet Selection (Step-) . ... 232
8.6.2 Optimization of Central Jet Selection (Step-2) . ... 235
8.6.3 Optimization of qqWW System (Step-3) . .... 238
8.7 Summary of the Optimization Selection Results . .... 243
8.7.1 Discovery Potential ..... .......... .... 243
8.7.2 Selection Efficiency .... . . .... 243
8.7.3 Higgs Boson Mass and Distribution in Signal Events . 246
8.7.4 Background Shape in Higgs Boson Mass Distribution . 247
8.8 Experimental Identification of VBF Higgs Boson Signature . 249
8.8.1 Signature of E'iss in qqWW System . . ..... 251
8.8.2 Signature of Lepton-W AR .... . ... 252
8.9 Estimation of Selected Systematic Uncertainties . .... 255
8.9.1 Detector Systematic Uncertainty . . 255
8.9.2 Theoretical Systematic Uncertainty ........... .257
8.10 Summary ............... .......... .. .. 259

9 CONCLUSION ............... ............ .. 261

REFERENCES ............... ............ .. .. 266

BIOGRAPHICAL SKETCH .................. ......... .. 270















LIST OF TABLES
Table page

3-1 The C'\!S Level-1 trigger menu at low luminosity . 27

3-2 The C' \S HLT tri -.. r rate at low luminosity .............. .31

4-1 Cross section and number of events QCD di-jet data samples with differ-
ent jet PT ................... .............. .. 40

4-2 The configuration of PYTHIA event generation (used C'\!S wide in 2003-
2004) . . . . . . . . .. .. 4 1

4-3 The configuration of calorimeter threshold and noise level in detector
simulation .................. ................ .. 41

4-4 Jet energy resolution in Tr1 < 3.0 region ................. .. 71

4-5 Jet energy resolution in Tr1 > 3.0 region ................. .. 73

4-6 Jet selection parameter of different energy distribution region with jet
PT from 80 to 120 GeV/c .................. ....... .. 75

6-1 The configuration of leptonic data samples including tt inclusive, tt lep-
tonic and W +jets .................. ............ .. 116

6-2 A < AE'iss > in the tt sample with various cone sizes . ... 141

6-3 Fitting results of a, b and c of -relative according to Eg. 6-18 in tt events 151

6-4 Fitting results of a, b and c of relative according to Eq. 6-19 in W+jets
sample ................... ..... .... ....... 151

6-5 Fitting results of a, b and c of R according to Eq. 6-18 using E'iss and
W P T . . . . . . . . 158

7-1 Jet and missing transverse energy quantities of QCD di-jet data samples 166

7-2 MET resolution in Di-jet system before and after the jet energy calibration 177

7-3 Fitting results of a, b and c according to Eq. 7-24 for various MET HLT
threshold from 60 to 120 GeV .................. ..... 184

7-4 Fitting results of bjet_effect and bsmeffect according to Eq. 7-27 for various
MET HLT threshold .................. ........ .. .. 190









8-1 VBF Higgs branching ratio with W leptonic decay, cross section, and
event simulated in vjj final states .................. ..... 195

8-2 A1, i wr background cross section and event generated (W + jets, Z + jets,
W + tb(tb) + jets, and WW + 21i 1i (EW) include parton level pre-selection)197

8-3 The configuration of parton level pre-selection of matrix element event
generator (ALPGEN and MADGRAPH) . . ....... 202

8-4 Reconstructed W mass resolution in various jet cone. Real W mass (81.2
GeV/c2) is used to scale the reconstructed W mass (mw), which leads
to a scaled os(mw) = mw/81.2 o(mw) ................ 216

8-5 Selection efficiency for signal and background events with scenario of
mH > 160 GeV/c2 .................. ........... .. 228

8-6 Selection efficiency for signal and background events with scenario of
mH < 160 GeV/c2 .................. ........... .. 229

8-7 Summary of basic event selection cuts .................. .. 230

8-8 Forward jet ,.-I-iii,-; efficiency with various jet ET threshold for Conser-
vative (c) and Optimistic Scenario (o) .................. .. 234

8-9 Selection efficiency with various maximal number of extra jet for Con-
servative (c) and Optimistic Scenario (o) ................. .. 236

8-10 Selection efficiency with various jet ET threshold for Conservative (c)
and Optimistic Scenario (o) .................. ... 237

8-11 Summary of optimization cuts for mH > 160 GeV/c2 ( mH < 160 GeV/c2
) . . . . . . . . . .. 244

8-12 Cross section (fb) of the signal and background in optimized selection
with mH > 160 GeV/c2 for Extra Jet Veto (E) and Loose Extra Jet Veto
Schem e (L) .. .. .. ... .. .. .. ... .. .. .. .. ..... .. 245

8-13 Cross section (fb) of signal and background in optimized selection with
mH < 160 GeV/c2 for Extra Jet Veto (E) and Loose Extra Jet Veto Scheme
(L) ................... ............ ...... 246

8-14 Summary of number of events in region A, B, C, and D with respect to
Signal + Background and Background Only scenarios . . ... 255

8-15 Selection efficiency of W + 3jets with different configuration scenario to
the standard one .................. ............ .. 257

8-16 Selection efficiency of W + 4jets with different configuration scenario to
the standard one .................. ............ .. 258









8-17 Average EET of W + 3jets and W + 4jets with different configuration
scenarios .................. ................. .. 258















LIST OF FIGURES
Figure page

1-1 Lower and upper theoretical bound of Higgs boson mass as a function of A 4

1-2 SM Higgs boson mass constraints by precision measurement of electroweak
parameters at LEP, SLC, and Tevatron ..... . ... 6

1-3 Feynman diagrams of various Higgs boson production processes . 7

2-1 Leading order (LO) cross section of SM Higgs boson. The cross section
for gg -+ H is shown in next to leading order (NLO) . . .... 11

2-2 Branching ratio for SM Higgs boson ................ .... 11

2-3 H -+ ZZ* --i f+f -t+'- invariant mass signal (dark) and background
(light) for mH 130, 150, and 170 GeV/c2 with an integrated luminos-
ity of 100 fb-1 ............... .............. .. 14

2-4 PT distribution of smaller PT lepton in H -+ WW* -+ ftvi-v signal
(white) and total background (light) for mH 140 GeV/c2 with an inte-
grated luminosity of 30 fb-1 ............... ... .. 15

2-5 H -- 7y invariant mass distribution signal (dark) and background (light)
for mH 130 GeV/c2 with an integrated luminosity of 100 fb-1 ..... 15

2-6 bb in ttH -+ qqbbbb channel invariant mass distribution signal (dark)
and background (light) for mH 115 GeV/c2 with an integrated lumi-
nosity of 30 fb-1 .................. ............ .. 16

2-7 SM Higgs boson discovery significance for (a) full mass range of mH and
(b) low mass range of mH in C'\IS with an integrated luminosity of 30 fb-1 17

2-8 The 5 a discovery potential of MSSM Higgs boson for (a) lighter scalar
at 30 fb-1, (b) lighter scalar at 100 fb-1, (c) heavy neutral at 30 fb-1,
and (d) charged at 30 fb-1 .................. .... 18

3-1 The C'\!S detector layout .................. ....... .. 20

3-2 Transverse view of C \! S tracker layout .................. .. 21

3-3 Pion energy resolution measured by Test Beam and Monte Carlo simula-
tion ..... .............. .................. .. 24

3-4 The C'\!S muon system ............... ........ .. 25









3-5 Overiew of the Level-1 tri -. .--r system ................ 27

3-6 Illustration of Level-1 jet and T-jet trigger algorithm . ... 28

3-7 Electron and photon algorithm .................. .. 29

3-8 Level-1 muon tri.-.--r rate as function of PT threshold for (a) low and (b)
high luminosity .................. ............. .. 30

3-9 Jet rejection versus efficiency obtained from Level-2.5 pixel matching at
(a) low and (b) high luminosity .................. .. 32

3-10 Efficiency of three isolation algorithms on the reference background as
a function of efficiency for the reference signal muon at (a) low and (b)
high luminosity .................. ............. .. 33

3-11 Principle of T-jet identification algorithm ................. .. 34

3-12 The b-' .--:1i -; algorithm .................. ...... .. .. 34

3-13 Efficiency of three isolation algorithms on the reference background as
a function of efficiency for the reference signal muon at (a) low and (b)
high luminosity .................. ............. .. 35

4-1 Absolute Jet Energy Resolution (aEt) in QCD events with PT from 180
to 200 GeV/c: (a) raw jet with aEt = 14.67 GeV, (b) corrected jet by
energy distribution (explained in later section) with cEt = 13.54 GeV,
(c) corrected jet by shifting the jet energy with JEt = 14.97 GeV, and
(d) corrected jet by a scaling factor with JEt = 15.03 GeV . ... 43

4-2 Relative Jet Energy Resolution (CR) in QCD events with PT from 180
to 200 GeV/c: (a) raw jet with aR of 8. 1-' (b) corrected jet by energy
distribution (explained in later section) with aR of 6.1-'.'-. (c) corrected
jet by shifting the jet energy with aR of 7. ;'. and (d) corrected jet by
a scaling factor with JR of 7.3:I' .............. ...... 44

4-3 Jet energy distribution in QCD samples with various jet PT: (a) 50-80
and (b) 80-120 GeV/c. The energy distribution is calculated from the
ratio of energy in each region to the total energy in 1.0 cone. In each
block of figures, the upper row from left to right corresponds to ratio of
0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row corresponds to
0.6-0.8 and 0.8-1.0 respectively. ............. ... 47

4-4 Jet energy distribution in QCD samples with various jet pr: (a) 120-170
and (b) 170-230 GeV/c. The energy distribution is calculated from the
ratio of energy in each region to the total energy in 1.0 cone. In each
block of figures, the upper row from left to right corresponds to ratio of
0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row corresponds to
0.6-0.8 and 0.8-1.0 respectively. ............. ... 48









4-5 Jet energy distribution in QCD samples with various jet PT: (a) 230-300
and (b) 300-380 GeV/c. The energy distribution is calculated from the
ratio of energy in each region to the total energy in 1.0 cone. In each
block of figures, the upper row from left to right corresponds to ratio of
0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row corresponds to
0.6-0.8 and 0.8-1.0 respectively ............. ..... 49

4-6 Jet energy distribution in QCD samples with various jet PT: (a) 380-470
and (b) 470-600 GeV/c. The energy distribution is calculated from the
ratio of energy in each region to the total energy in 1.0 cone. In each
block of figures, the upper row from left to right corresponds to ratio of
0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row corresponds to
0.6-0.8 and 0.8-1.0 respectively. .................. .... 50

4-7 Second Moment in QCD samples with various jet PT: (a) 50-80, (b) 80-
120, (c) 120-170, (d) 170-230, (e) 230-300, (f) 300-380, (g) 380-470, and
(h) 470-600 GeV/c. In each figure, the curves from left to right repre-
sents the second moment distribution of cone size of 0.2, 0.4, 0.6, 0.8,
and 1.0 respectively ........ ........... . ... 51

4-8 Jet energy distribution based on the fraction of each region's transverse
energy with respect to total transverse energy in a 1.0 cone as a function
of generator jet PT. Regions are defined by 0.2 cone (square), 0.4 cone
(triangle-up), and 0.6 cone (triangle-down) ................ ..52

4-9 Peak position of Second Moment of 1.0 cone (open square), 0.8 cone (open
circle), 0.6 (triangle-down), 0.4 (triangle-up), and 0.2 (close square) as a
function of generator level jet PT .................. ..... 54

4-10 FWHM of Second Moment of 1.0 cone (open square), 0.8 cone (open cir-
cle), 0.6 (triangle-down), 0.4 (triangle-up), and 0.2 (close square) as a
function of generator level jet PT .................. ..... 54

4-11 Energy ratio of simple cone jet with various size to that of the 0.6 itera-
tive cone jet. The simple cone jets are built upon the axis from iterative
cone jet. Various cone sizes include (a) 0.2, (b) 0.4, (c) 0.6, (d) 0.8, and
(e) 1.0 ...... ............. ................. .. 57

4-12 Fitting of Fig. 4-11(c) by using double gaussian distribution ...... ..58

4-13 Jet energy resolution from various Benchmark parameterizations: (a)
raw jet with cEt = 10.92 GeV, (b) corrected jets based on two parame-
ters Benchmark Eq. 4-7 with JEt = 10.8 GeV, (c) corrected jets based
on three parameters Benchmark Eq. 4-6 with JEt = 10.77 GeV, and (d)
corrected jets based on four parameters Benchmark Eq. 4-8 JEt = 10.77
GeV. The results are based on jet sample with PT ranging from 80 to
120 GeV/c ............... ............. .. 60









4-14 Jet energy response before (triangle-down) and after (triangle-up) the
correction with 0.2 cone: (a) based on correction of energy distribution
and (b) based on benchmark correction .................. .. 65

4-15 Jet energy response before (triangle-down) and after (triangle-up) the
correction based on second moment: (a) 0.4 cone, (b) 0.6 cone, (c) 0.8
cone, and (d) 1.0 cone .................. ......... .. 66

4-16 Jet energy response before (triangle-down) and after (triangle-up) the
correction: (a) based on correction of energy distribution and (b) based
on benchmark correction. .................. ....... .. 67

4-17 Jet PT spectrum before and after the correction in QCD sample with se-
lected raw jet pT ranging from 170 to 200 GeV/c and qIr < 3: (a) raw
jet, (b) generator level jet, (c) corrected jet based on second moment,
(d) corrected jet based on energy density, and (e) corrected jet spectrum
based on benchmark correction .................. .. 68

4-18 Jet energy resolution of 0.2 cone: (a) absolute resolution and (b) relative
resolution with raw ret (open circle), benchmark correction (triangle-
down), and correction based on second moment (triangle-up) ...... ..69

4-19 Jet energy resolution of 0.4 cone: (a) absolute resolution and (b) relative
resolution with raw jet (open circle), benchmark correction (triangle-
down), and correction based on second moment (triangle-up) ...... ..69

4-20 Jet energy resolution of 0.6 cone: (a) absolute resolution and (b) relative
resolution with raw jet (open circle), benchmark correction (triangle-
down), and correction based on second moment (triangle-up) ...... ..70

4-21 Jet energy resolution of 0.8 cone: (a) absolute resolution and (b) relative
resolution with raw jet (open circle), benchmark correction (triangle-
down), and correction based on second moment (triangle-up) ...... ..70

4-22 Jet energy resolution of 1.0 cone: (a) absolute resolution and (b) relative
resolution with raw jet (open circle), benchmark correction (triangle-
down), and correction based on second moment (triangle-up) . 71

4-23 Jet energy response of 0.6 cone before (triangle-down) and after (triangle-
up) the correction based on second moment ............... 73

4-24 Jet energy resolution in forward region (I r > 3.0) with no correction
(open circle), benchmark correction (triangle-down), and correction based
on second moment (triangle-up) in various cone size: (a) 0.2, (b) 0.4, (c)
0.6, (d) 0.8, and (e) 1.0 . . . . . ..... 74

4-25 N, ii Ji.i. E S distribution in QCD sample with jet PT range from 80 to
120 GeV/c ...... ............. .............. .. 75









5-1 Missing transverse energy spectra in QCD samples in (a) generator level
and (b) detector level that correspond to jet PT ranges (from left to right)
of 20-30, 30-50, 50-80, 80-120, 120-170, 170-230, 230-300, 300-380, 380-
470, 470-600, 600-800, and 800-1000 GeV/c. .............. 81

5-2 Inclusive Episs HLT rate calculated from samples of jet PT ranges of 50-
80, 80-120, 120-170, 170-230, 230-300, 300-380, 380-470, 470-600, 600-
800, and 800-1000 GeV/c. For 1kHz rate (Level-1 rate for Episs), the
threshold is roughly 50 GeV, which is underestimated due to the lower
PT samples (0-20 GeV/c) are not used; for 1 Hz rate (HLT rate for Episs),
the threshold is roughly 90 GeV, where the contribution from the lower
PT samples is small. .................. .......... .83
5-3 Scalar L ET spectra in QCD samples in (a) generator level and (b) de-
tector level that correspond to jet PT ranges (from left to right) of 20-30,
30-50, 50-80, 80-120, 120-170, 170-230, 230-300, 300-380, 380-470, 470-
600, 600-800, and 800-1000 GeV/c. ............. . 84

5-4 Detector L ET response as a function of L E1" (a) using generated sig-
nal event only in ORCA-OSCAR (close circle) and FAMOS (open circle)
and (b) using generated signal and generated pileup events . ... 85

5-5 Contribution of pileup to L Ef4t as a function of E" . . 86

5-6 Exiss resolution quantities: (a) Exiss resolution versus detector ET,
(b) Exiss resolution versus generator ET, and (c) Emiss resolution ver-
sus generator L ET using signal event only ................ .. 88

5-7 < E~"ss > quantities: (a) < E"ss > versus detector ET, (b) < Eis >
versus generator E ET, and (c) < E'iss > versus generator E ET using
signal event only .................. ............ .. 90

5-8 Eiss resolution quantities in low L ET samples: (a) E"iss resolution ver-
sus detector L ET and (b) fitting based on the average correlation of
these samples between Eiss resolution and L ET . . ..... 92

5-9 Ratio of L ET of jet region to unclustered region versus ET....... 93

5-10 E"iss resolution of the jet and unclustered regions versus L ET . .. 94

5-11 E"iss related quantities in jet region: (a) average detector ETiss, (b) de-
tector Eiss resolution, (c) average detector ET, and (d) response of
detector to generator level L ET using signal event . . 95

5-12 Episs related quantities in the unclustered region: (a) average detector
Efiss, (b) detector a(ExiSs), (c) average detector ET and (d) response
of detector to generator level L ET using signal event . .... 96









5-13 E T,/ETs and (E, )/a(Ef's) as a function of E ET using 0.8 cone
size to define the jet and unclustered regions . . ..... 98

5-14 Correlation between the jet and unclustered regions: (a) Emss/Elmss and
(b) a(E(m')/a(E's) as a function of EET using various cone sizes to
define the jet and unclustered regions ................ .. 99

5-15 The Q angular correlation with QCD samples of jet p^T of (a) 30-50 and
(b) 50-80 GeV/c for four cone sizes: 0.2 (black), 0.4 (red), 0.6 (green),
and 0.8 (blue). The peak shows E', and E'Ts are back-to-back. .... 100

5-16 Fraction of events with a back-to-back correlation 16|1< 1.0 between the
jet and unclustered regions as a function of E ET for four cone sizes: 0.2
(black), 0.4 (red), 0.6 (green), and 0.8 (blue) . . ..... 101

5-17 Q quantities between the highest ET jet and EpiSS: (a) the Q distance be-
tween the highest ET jet and E'iSs and (b) the Q correlation (defined as
6 = jet QMET + 7T) between highest ET jet and E'iss. Five QCD sam-
ples are used with jet PT ranges: 50-80 (black), 80-120 (red), 120-170
(green), 170-230 (blue), and 230-300 (yellow) GeV/c. . .... 103

5-18 Q distance between (a) the second highest ET jet and E'iss and (b) the
third highest ET jet and ETiSS. Five QCD samples are used with jet PT
ranges: 50-80 (black), 80-120 (red), 120-170 (green), 170-230 (blue), and
230-300 (yellow) GeV/c. .................. ....... 104

5-19 The Q correlation (defined as 6 Q = 1 Q2) of the two highest ET jets.
Five QCD samples are used with jet PT ranges: 50-80 (black), 80-120
(red), 120-170 (green), 170-230 (blue), and 230-300 (yellow) GeV/c. .. 105
5-20 The Q correlation between E' ~ and E'iSS defined as 6 Qjet ,. +
7 for five QCD samples with jet PT ranges: 50-80 (black), 80-120 (red),
120-170 (green), 170-230 (blue), and 230-300 (yellow) GeV/c ..... ..106

5-21 The Q correlation quantities shown in Fig. 5-20 as a function of Y ET:
(a) the a of Q correlation and (b) the average E ET of the two jets 106

5-22 Detctor level E'iSS resolution in the orthogonal direction to di-jet as a
function of Y ET .................. ............ 107

5-23 < E'is" > and a of Ex's versus tower energy threshold in QCD samples
with jet PT (a) 30-50, (b) 120-170, (c) 300-380, and (d) 600-800 GeV/c 108

5-24 ET spectum under three tower threshold: 0.4 (right), 1.6 (middle),
and 4.0 (left) GeV in sample of PT range from 50-80 GeV/c. ...... 109


xvii









5-25 E E /E E} as a function of tower energy threshold with samples of jet
PT ranges: 20-30, 30-50, 50-80, 80-120, 120-170, 170-230, and 230-300
GeV/c (from top to bottom). The tested tower thresholds include 0.4,
0.8, 1.2, 1.6, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0 GeV . . ... 110

5-26 R P as a function of Y ET using QCD samples of jet PT ranges: 20-30,
30-50, 50-80, 80-120, 120-170, 170-230, and 230-300 GeV/c . ... 110

5-27 Generator level E'iss resolution using cluster region as a function of ET 112

6-1 The fraction of events with Episs > 30 GeV as a function of lepton PT
threshold for (a) tt samples and (b) W+jets samples respectively . 117

6-2 Eiss properties as a function of Muon Calo Factor: (a) Emiss resolution
(dot) and Ess resolution (circle) and (b) average Efiss error between
detector and generator level .................. .... 120

6-3 ET of muon cone isolation cone (a) in the region of I|T\ < 0.8, (b) in the
region of 0.8 < Iry < 1.6, and (c) in the region of 1.6 < ITry < 2.4 ..... .121

6-4 Eiss properties as a function of Muon IsoCone Factor: (a) E iss reso-
lution (dot) and ETss resolution (circle) and (b) average E'iss error be-
tween detector and generator level .................. .. 122

6-5 The improvement of E'iss resolution after track correction for selected tt
inclusive events with muon of PT > 10 GeV/c and 2.4 < Irll < 2.6: (a)
raw E'iss and (b) corrected E'iSS . 123

6-6 The E"iss resolution of tt inclusive events: (a) after muon correction for
the selected muon sample, (b) for the selected electron sample, and (c)
before muon correction for the selected muon sample . .... 125

6-7 E"is properties as a function of electron correction track factor using
track momentum and super-cluster energy at ECAL: (a) Ei"ss resolution
(dot) and Ess resolution (circle) and (b) average E'iss error between
detector and generator level .................. .... 127

6-8 Eis" properties as a function of electron correction factor using track
momentum and 0.2 isolation cone at calorimeter: (a) E'iss resolution
(dot) and ETss resolution (circle) and (b) average E'piss error between
detector and generator level .................. .... 128

6-9 ETis properties as a function of electron correction factor using track
momentum: (a) E'iss resolution (dot) and ETss resolution (circle) and
(b) average Episs error between detector and generator level ...... ..128

6-10 Electron and jet energy response in calorimeter: (a) the events that pass
the selection criterion and (b) the events that fail the selection criterion 131


xviii









6-11 E"iss quantities with respect to different jet cone sizes and ET thresholds
with 30 < ETiss < 90 GeV in tt inclusive events: (a) E"iss resolution, (b)
Emiss resolution, (c) average Eiss error between detector and generator
level, and (d) y resolution. The different cone sizes include 0.2 (open cir-
cle), 0.4 (close circle), 0.6 (open square), and 0.8 (close square) ..... .138

6-12 E"iss quantities with respect to different jet cone sizes and ET thresholds
with 90 < Emiss < 180 GeV in tt inclusive events: (a) ETiSS resolution,
(b) Ess resolution, (c) average ETiss error between detector and genera-
tor level, and (d) ( resolution. Different cone sizes include 0.2 (open cir-
cle), 0.4 (close circle), 0.6 (open square), and 0.8 (close square) ..... .139

6-13 The average Emiss error between the detector and generator level with
respect to different jet cone sizes and ET thresholds in tt leptonic events:
(a) 30 < Eiss" < 90 GeV and (b) 90 < ETiSS < 180 GeV. Different cone
sizes include 0.2 (open circle), 0.4 (close circle), 0.6 (open square), and
0.8 (close square) ............... ......... .. 140

6-14 Jet propertities in various samples: (a) normalized inclusive jet PT spec-
trum and (b) normalized leading jet PT spectrum. The samples include
QCD (solid line), tt (dot line), and W+jets with W pT between 40 and
300 GeV (dash line) ............... ........ 142

6-15 The raw jet response in QCD, W+jets, and tt samples . ... 143

6-16 ETiss and EET properties in various samples: (a) N. iii ii. .1 ETiss spec-
trum and (b) normalized EET spectrum. The samples include tt inclu-
sive (dash line), tt leptonic (dot line), and W+jets with W pT between
40 and 300 GeV (solid line) ................ ... .. 143

6-17 < AE iss > between the detector and generator level in tt inclusive events 144

6-18 Raw EET distribution in two regions as a function of E"is" based on tt
inclusive events. 0.4 cone size is used for region definition: detector clus-
ter region (open triangle), generator cluster region (close square), detec-
tor unclustered region (close triangle), and generator unclustered region
(open square) ............... ........... 146

619 ET"i properties after the PU correction as a function of detector ET"ss
(a) E'ss error, (b) Eiss resolution, (c) ETss resolution, and (d) ( reso-
lution . . . . . . . . ..... 149

6-20 ET"" properties after correction as a function of detector ETmi in tt in-
clusive events: (a) relative ETs resolution, (b) 0 resolution, (c) E'is
resolution, and (d) ETss resolution .................. .. 152









6-21 ETss properties after correction as a function of detector Ep'iss in tt lep-
tonic events: (a) relative Efiss resolution, (b) 0 resolution, (c) Efiss reso-
lution, and (d) Emss resolution .................. ...... 153

6-22 E iss properties after correction as a function of detector Emiss in W+jets
events: (a) relative Efiss resolution, (b) 0 resolution, (c) Efiss resolution,
and (d) ETmis resolution .. .... .......... ....... 154

6-23 E'iss scale in tt inclusive events as function of detector raw EPiss: (a)
average E'5is error and (b) EDi's response ...... . . 155

6-24 Episs scale in tt leptonic events as function of detector raw EJiss: (a) av-
erage Emiss error and (b) Emiss response .................. 155

6-25 E"iss scale in W+jets events as function of W PT: (a) average E iss error
and (b) E 'iss response .................. ......... 156

6-26 E~7'5 properties as a function of Efiss in tt inclusive events: (a) R and
(b) E si resolution . . . . . . .. .. 157
6-27 ETiss properties as a function of E1iss in tt leptonic events: (a) R and
(b) E si resolution . . . . . . .. .. 157
6-28 ETiss properties in W+jets events: (a) R as a function of EET and (b) R
as a function of Episs .................. ...... .. 158

6-29 Standalone ETiss resolution in the cluster and unclustered region respec-
tively as a function of W PT in W+jets events . . ..... 159

7-1 Normalized METx distribution of QCD events with leading jet ET be-
tween 80 and 90 GeV ............... ......... 167

7-2 MET quantities in di-jet system of QCD events with jet ET between 80
and 90 GeV: (a) normalized METx distribution and (b) normalized Q
correlation (A0 = 1 2 7) ............ ... ...... 168

7-3 Di-jet Q angular correlation quantities: (a) crphi as a function of leading
jet ET and (b) Ratio of the narrow a component to the wide a component 169

7-4 METx quantities of QCD events with jet ET between 80 and 90 GeV:
(a) normalized METx distribution and (b) normalized METx error dis-
tribution .. .. .. .. ... .. .. .. ... .. .. .. ....... 169

7-5 ,,sm as a function of leading jet ET .................. .. 170

7-6 Normalized MET spectrum of QCD events (open triangle) and factoriza-
tion model (dot) with leading jet ET between 80 and 90 GeV ...... .170

7-7 Results of X2 (a) as a function of cjet (b) as a function of as.m ....... .171









7-8 X2 test as a function of METx a .................. ...... 172

7-9 Normalized MET spectrum with jet ET (GeV) of 20-25 (black), 30-35
(red), 50-55 (blue), 80-90 (green), 120-130 (black), 170-180 (red), 230-
240 (blue), 300-310 (green), 380-400 (black), 470-490 (red), 600-620 (blue),
and 800-820 (green) ............... .......... 173

7-10 Jet Energy Response with respect to generator jet PT . .... 175

7-11 QCD jet T] quantities with jet ET between 80 and 90 GeV: (a) T] distri-
bution and (b) Di-jet AT/ distribution ................ 179

7-12 Fraction of events with jet ET between 80 and 90 GeV as a function of
di-jet A R cut .................. .............. 180

7-13 loglo(SHLT) as a function of jet ET for various GeV MET threshold. The
curves corresponds to 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115,
and 120 (GeV) MET threshold from up to down. . . 185

7-14 loglo(aET) as a function of jet ET .................. ..... 186

7-15 Differential MET HLT rate (DHLT) as a function of jet ET. The curves
corresponds to 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, and 120
(GeV) MET threshold from up to down. ................ 187

7-16 MET HLT rate (Hz) with respect to given threshold . .... 187

7-17 Sensitivity of SHLT to jet effect and smearing effect: (a) SHLT as a func-
tion of cjet with fixed asm equal to optimal value of the factorization model
and (b) SHLT as a function of ,sm with fixed cjet equal to optimal value
of the factorization model. The jet ET range is between 80 and 90 GeV.
Various MET HLT threshold (GeV) are used: 60 (close square), 65 (open
square), 70 (close circle), 75 (open circle), and 80 triangle ) . ... 189

8-1 ETHal/EEcal of true electron (a) and faked electron (b) in VBF Higgs sam-
ple with mH 170 GeV/c2 .................. ..... 204

8-2 E/p of true electron (a) and faked electron (b) in VBF Higgs sample with
mH 170 GeV/c2 .................. ........... .. 205

8-3 |E.2 E| of true electron (a) and faked electron (b) in VBF Higgs sam-
ple with mH 170 GeV/c2 .................. ..... 205

8-4 1(E-2 E)/E I of true electron (a) and faked electron (b) in VBF Higgs
sample with mH 170 GeV/c2 .................. ...... 206

8-5 I(E2-0.4/EtI of true electron (a) and faked electron (b) in VBF Higgs
sample with mH 170 GeV/c2 .................. ...... 206









8-6 |E.2 ETI of true muon (a) and faked muon (b) in VBF Higgs sample
with mH 170 GeV/c2 ............... ......... .. 207

8-7 |(E 2 Et)/Et of true muon (a) and faked muon (b) in VBF Higgs
sample with mH 170 GeV/c2 ................ .... 207

8-8 8 (E2-0.4/E of true muon (a) and faked muon (b) in VBF Higgs sam-
ple with mH 170 GeV/c2 ............... .... .. 208

8-9 Overall Reconstruction and Selection Efficiency of Electron (a) and Muon
Reconstruction (b) in VBF Higgs Sample . . ...... 209

8-10 Lepton PT spectrum for the highest PT lepton (a) and the second high-
est PT lepton (b) in the Z+jets sample with Z leptonic decay ...... .211

8-11 Quark-jet relative matching efficiency as a function of jet ET threshold
for valance quark (square) and quark from W hadronic decay (circle) in
VBF Higgs sample with mH 170 GeV/c2. The efficiency is normalized
to 1.0 for jet ET threshold of 20 GeV. ................ . 212

8-12 Two forward quark-jet properties (a) AT/ distribution (b) mqq distribu-
tion ................... ..... .... ....... 213

8-13 The relative rate of signal events (mH = 170 GeV/c2) that pass forward
jet --:ii:-; by extra jets (but quark-jet fail) to those events that quark-
jet passes : r.'iil-; as a function of jet ET threshold. Intensive ISR and
FSR largely enhanced the forward jet -ii.-; efficiency, especially for
the ET threshold below 35 GeV ................ .... 214

8-14 The rate of VBF Higgs events (mH = 170 GeV/c2) with extra jet that is
outside of the range of two jets matched with the valance quark with T]
distance bigger than 3.8 as a function of jet ET threshold. The rate in-
creases significantly as jet ET threshold goes below 35 GeV, which in-
dicates a strong enhancement of the soft jet activities of the events via
ISR/FSR and detector effects. ............... .... 215

8-15 Forward Jet T -'-;ii:-; efficiency for different threshold of r distance in
VBF Higgs events with mH 170 GeV/c2 ............. .. 215

8-16 mw using quark-jet that two quarks are identified from hadronic W de-
cay in VBF Higgs events with mH 170 GeV/c2 . . 216

8-17 Number of extra jets in the central excluding the quark-jet from forward
jet ,-'-ii.-; and hadronic W reconstruction in VBF Higgs events with
mH 170 GeV/c2. A jet ET threshold of 20 GeV is used . .... 217


xxii









8-18 The ID of extra jet, which is numbered based on jet ET from highest to
lowest in VBF Higgs events with mH 170 GeV/c2. The quark-jet from
forward jet .--::ii-; are excluded. If two highest ET central jets are re-
quired for W reconstruction, the mis-identification rate is high, because
extra jets are ~ 17' (19 .) of the highest (second highest) ET jets in
the central. .................. ............... .. 218

8-19 Multiple jet selection efficiency (requiring at least 4 jets in an event) as
a function of jet ET threshold. The efficiency is normalized to the rate
with jet ET threshold of 16 GeV for each sample. The physics channels
include: tt + jets (solid square), W + 3jets (open circle), W + 4 jets
(solid triangle), and VBF Higgs with mH 170 GeV/c2 (open square) 220
8-20 N i i, 1i.. .1 lepton PT distribution (a) and normalized lepton ty distribu-
tion (b) of VBF Higgs with mH 170 GeV/c2 (solid), tt + jets (dash),
and W + 4jets (dot) respectively ................ ....... 222

8-21 N iii 1i. Eriss distribution (a) and normalized Jet ET distribution (b)
of VBF Higgs with mH 170 GeV/c2 (solid), tt + jets (dash), and W +
4jets (dot) respectively ............... ......... .. 223

8-22 Hadronic W properties (a) PT error and (b) AR between the detector
and generator level hadronic W. The PT error is fitted by a Gaussian
with a ~ 15.1 GeV/c. .................. ......... .. 225

8-23 Leptonic W properties (a) PT error and (b) AR between the detector
and generator level leptonic W. The PT error is fitted by a Gaussian with
a 19.5 GeV/c. ................. .... ....... 225

8-24 Leptonic W properties as a function of mH (a) average PT error and (b)
PT resolution between the detector and generated leptonic W with un-
corrected E'isS (solid square) and corrected E'iSS (open square) . 227

8-25 Di-W AR error between detector and generator level in VBF Higgs events
with mH = 170 GeV/c2 ............... ......... .. 227

8-26 VBF Higgs mass reconstructed from background events under high-mass
scenario. Major background include W + 4jets (red), W + 3jets (green),
tt + jets (blue), and W + tb (tb)(yellow). ............... 229

8-27 VBF Higgs mass reconstructed from VBF Higgs events with mH 170
GeV/c2 ............... ............. 231

8-28 ATl distribution of background (a) and VBF Higgs signal with mH 170
GeV/c2 (b). Major background processes include W + 4jets (red), W +
3jets (green), tt + jets (blue), and W + tb (tb) (yellow). . . 232


xxiii









8-29 S/B with respect to different Aq threshold for Conservative (solid square)
and Optimistic Scenario (open square) .................. .. 233

8-30 mqq distribution of background (a) and VBF Higgs signal with mH
170 GeV/c2 (b). A\I iiP background processes include W + 4jets (red),
W + 3jets (green), tt + jets (blue), and W + tb (tb)(yellow). . 233

8-31 S/B with respect to different mqq thresholds for Conservative (solid square)
and Optimistic Scenario (open square) .................. .. 234

8-32 S/B with respect to various VBF Higgs mass by using the Conservative
Scenario ............... ............... .. 235

8-33 Nextra of background and VBF Higgs signal (mH =170 GeV/c2). Major
background processes include W + 4jets (red), W + 3jets (green), tt +
jets (blue), and W + tb (tb)(yellow) ................ 236

8-34 WM of background and VBF Higgs signal (mH = 170 GeV/c2). M ii.
background processes include W + 4jets (red), W + 3jets (green), tt +
jets (blue), and W + tb (tb)(yellow). .................. 237

8-35 S/B (a) and significance (b) with respect to various VBF Higgs mass.
The higher (lower) S/B and significance curves correspond to Extra Jet
Veto (Loose Extra Jet Veto) Scheme respectively . . 239

8-36 Eiss in qqWW system of background (a) and VBF Higgs signal (mH
170 GeV/c2) (b) ............... ........... .. 240

8-37 S/B (a) and significance (b) with respect to E'iss cut in qqWW system.
The higher (lower) S/B and significance curves correspond to optimistic
(conservative) scenario respectively .................. .. 240
8-38 AR between leptonic and hadronic W of background (a) and VBF Higgs
signal with mH 170 GeV/c2 (b). A, i i. background include W + 4jets
(red), W + 3jets (green), tt + jets (blue), and W + tb (tb)(yellow). In
these plots, Loose Extra Jet Veto Scheme in Step-2 is used ........ 241

8-39 S/B (a) and significance (b) with respect to AR cut and Em~ss < 40 GeV
in qqWW system. In these plots, Loose Extra Jet Veto Scheme in Step-
2 is used. Due to strong suppression of the W + 3jets background from
combining AR and Emiss cuts, the difference between Conservative and
Optimistic Scenario is negligible. . . . 241

8-40 AR between semi-leptonic and hadronic W of background (a) and VBF
Higgs signal with mH 170 GeV/c2 (b). Major background include W
+ 4jets (red), W + 3jets (green), tt + jets (blue), and W + tb (tb)(yellow).
In these plots, Loose Extra Jet Veto Scheme in Step-2 is used. . 242


xxiv









8-41 S/B and significance with respect to various Higgs boson masses. The
high (low) curves of S/B and significance correspond to Extra Jet Veto
(Loose Extra Jet Veto) Scheme respectively ............... ..243

8-42 VBF Higgs mass resolution using signal events only for mH 160 (left),
190 (middle), and 220 (right) GeV/c2 with a of Higgs boson mass width:
14.1, 15.5, and 23.9 GeV/c2 respectively. ................ 247

8-43 Results of VBF Higgs mass reconstruction based on signal (blue) and
projected background (black) .................. .... 248

8-44 The fraction of events in different regions for the overall background (a)
and VBF Higgs signal (b) as a function of E'iss cuts. Region A (close
square), Region B (open square), and Region C (open circle). . 250

8-45 The ratio of number of events as a function of AR (a) Region A to Re-
gion B (b) Region A and Region C (c) Region B to Region C. Two sce-
narios are illustrated: Signal + Background (open square) and Back-
ground Only (solid square) respectively. ................. 253

8-46 The ratio of Signal + Background Scenario to Background Only Sce-
nario as a function of AR for Region A to Region B (open square), Re-
gion A to Region C (solid square), and Region B to Region C (open circle) 254

8-47 Effects of jet energy smearing (a) efficiency of basic selection normalized
to non-smeared rate for tt + jets background (square) and VBF Higgs
signal (square) as a function of jet resolution factor (b) Higgs boson mass
resolution after basic filtering as a function of jet resolution factor . 256


XXV















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

RECONSTRUCTION OF MISSING TRANSVERSE ENERGY AND PROSPECT
OF SEARCHING FOR HIGGS BOSON PRODUCED VIA VECTOR BOSON
FUSION IN COMPACT MUON SOLENOID EXPERIMENT

By

Haifeng Pi

December 2005

C('! i: Paul Avery
Major Department: Physics

We performed full detector simulation studies of missing transverse energy

(Episs) reconstruction and correction, and the prospects for searching for a low

mass Higgs Boson (120 < mH < 250 GeV/c2) produced via the vector boson

fusion (VBF) process through the decay of H -- W+W- vjj at Compact Muon

Solenoid (C'\ S) experiment in Large Hadron Collider (LHC).

We developed a new jet energy correction algorithm by parameterizing the jet

energy distribution around the jet axis. The jet energy resolution is improved by

calibrating the jet energy scale and by reducing the variance of the measurement

error. Correction functions showed good performance in restoring the jet transverse

momentum (PT) spectrum. The methods provide a good framework to study jet

quantities and optimize jet reconstruction and correction techniques.

We evaluated the performance of the C \! S detector for measuring the Episs

using QCD events. We also studied the contributions from detector resolution,

minimum bias pileup, event topology, tower energy thresholds and the exclusion of

the unclustered region in the calorimeter.


xxvi









We built a comprehensive strategy for the E'iss correction for leptonic events.

The performance as applied to tt and W+jets events showed improved the Episs

resolution, the azimuthal (Q) resolution and average EpiSs scale. Correction

techniques based on jet, lepton, calorimeter isolation, pileup, underlying effect, and

tunings based on specific physics channels were developed and optimized.

To fully exploit the correlation between the E'iss and various physics final

states, we developed a physics model of E iS by factorizing the jet system from

related detector effects based on QCD di-jet events, and then extended this model

to a general multiple jet system. We used the model to evaluate the jet energy

calibration on Episs and the influence of various detector effects on the ET'is. Our

study provided a fundamental framework to systematically understand, analyze,

and evaluate E'iSs related quantities.

We performed a feasibility study on a direct Higgs mass (mH) reconstruction

for the low mass region (120 < mH < 250 GeV/c2) by explicitly reconstructing

hadronic and leptonic W from the Higgs boson decay using vjj final states.

A large number of background processes were simulated and studied. Various

techniques were developed (lepton isolation, forward jet ,.- -i i- central jet

selection, hadronic and leptonic W reconstruction, and E'iss selection) to increase

the significance of the signal events.

For an integrated luminosity of 30 fb-1, a 5a discovery for 160 < mH < 180

GeV/c2 can be achieved. We developed experimental data analysis methods to

identify the existence of Higgs boson without needing accurate knowledge of the

selection efficiency. Two main systematic issues were discussed: jet energy scale

and initial (final) state radiation. The feasibility of the reconstruction paves the

way of the H -- W+W- vjj as an effective channel for the Higgs boson search

via VBF in the most interested region of 120 < mH < 220 GeV/c2, while this

channel was mainly considered for high mass Higgs boson search before.


xxvii















CHAPTER 1
INTRODUCTION

In 2007 the Large Hadron Collider (LHC) at the European Laboratory of

Particle Physics (CERN) will usher in a new era of particle physics, providing un-

precedented energy and sensitivity for new discoveries and sensitive measurements,

with a scientific program that will continue for decades. Four principal experiments

will be conducted there: the Compact Muon Solenoid (C'\lS), A Toroidal LHC

Apparatus (ATLAS), LHCb, and A Large Ion Collider Experiment (ALICE). The

first two are general-purpose detectors with a broad physics program, while latter

two have narrower goals.

The ATLAS and C S detectors were designed to carry out precise measure-

ments at both low and high luminosity conditions with Ti coverage (If ln, where

0 is the polar angle) of Irll < 5. Both detectors were optimized for precise mea-

surements of leptons, photons, jets, and missing transverse energy (Eiss), allowing

exploration of the fundamental nature of matter and the basic forces that shape

our universe.

The LHCb detector was designed to study the physics of B-mesons involving

charge-parity (CP) violation and rare decay. The ALICE detector was developed

as a dedicated heavy-ion detector to investigate the unique physics potential

of nucleus-nucleus interactions. A key aim of ALICE is to study the physics of

strongly interacting matter at extreme energy densities, where formation of a new

phase of matter (the quark-gluon plasma) is expected.

Other experiments include TOTEM, an experiment for measuring total cross

section, elastic .i I Iiir- and diffractive processes at LHC.









1.1 Standard Model and Prediction of Higgs Boson

The Standard Model (SM) [1, 2] provides the current theoretical framework for

explaining the fundamental constituents of matter and their interactions through

four types of forces: strong, weak, electromagnetic and gravitational. The strong

force is responsible for "connecting" the quarks together to form protons, neutrons

and related particles. The electromagnetic force binds electrons to atomic nuclei

(clusters of protons and neutrons) to form atoms. The weak force is responsible for

several forms of radioactive decays as well as for the basic nuclear reactions that

power the sun. The gravitational force acts between massive objects (although it

pl -v. no role at the microscopic level, it is the dominant force in our every iv life

and throughout the universe).

The ir, .- weak and electromagnetic interactions are described by gauge

symmetries manifested as SU(3)xSU(2)xU(1) group transformations in quantum

field theory. The interactions are carried by particles called gauge bosons with

spin-1. Each force has its own characteristic boson(s):

Gluons mediate the strong force that "glues" quarks together.

Photons carry the electromagnetic force.

W and Z bosons mediate the weak force.

Gravitons transmit the gravitational force, which is many orders of magnitude

weaker than other three elementary forces, and remains a hypothetical

particle due to the extreme difficulty of observing it at the subatomic level.

The fundamental fermions (spin 1) that make up matter are leptons and

quarks having no observable internal structure (point like). They occur in three

,. I ii i-:", where each quark or lepton generation consists of a left handed

doublet and right handed singlet under SU(2) transformations. The generations

are identical except for mass. SM has successfully predicted the existence of many

particles later found in high energy experiments. The weak and electromagnetic









interactions were united into a combined electroweak framework described by

SU(2)xU(1) gauge symmetry. SU(3) is used to describe a quark having three color

charges. However, this picture suffers from a problem: beyond the lowest order

in the perturbation, the theory in its original form diverges, and the high-energy

behavior of matrix elements is bad (hierarchy problem). Most of the issues relate

to the longitudinal-polarization component of massive vector bosons. Moreover,

the large masses of W and Z bosons, which break SU(2)xU(1) symmetry, are

inconsistent with the original SM framework assuming massless gauge bosons.

The later introduction of Spontaneous Symmetry Breaking (SSB) [3, 4, 5]

solved these problems and made calculations finite within a broader gauge theory

framework, though it required the introduction of a massive spin zero particle

known as the Higgs boson. Higgs boson interactions give mass to all particles

except photons and gluons and regulate the divergent behavior in vector boson

scattering. The Lagrangian of the gauge field that involves the Higgs boson is


L = (D,)+(DK) [/12{+ + A(i+4)2] (1 1)


where D = O, igApo/2 g'YB,. A. and B. are the gauge field of SU(2) and

U(1). g and g' are the coupling of SU(2) and U(1). a is the Pauli matrices. Y is

the generator of the U(1) group. K is the SU(2) doublet of complex scalar field.

The mass of Higgs, W and Z can be expressed by free parameters A and p

(Eq. 1-2).


/ 2 V V
mH = m = 9 m2 1+g12 (1-2)
2 A W 2

where v .

The Higgs boson mass (mH) is a free parameter in SM. However, an upper

limit of ~ 1 TeV/c2 of mH can be predicated based on the stability of electroweak









vacuum and perturbative validity of SM. If new physics enters at a scale A in-

dicating that SM is embedded in a more general form, the maximal value of mH

can be estimated from A through the I i liiv ,ly" bound mH = P2a (p) and

a(A) < 1, where p is the vacuum expectation value (= 246 GeV) and a is the

running coupling shown in Eq. 1-3.


a(Q) = 3 -3)
1 5 4b '(

where Q is the mass scale of the interaction. If A is set for Planck scale (~ 1019

GeV), meaning no new physics enters and requiring the perturbative validity, a low

limit mH < 140 GeV can be set. Given a lower A, the upper bound for mH will be

larger. Both A and mH will overlap at the TeV scale, indicating that the discovery

of either Higgs boson or new physics is within LHC's reach (Fig. 1-1)[6].


600

.600


400


200



103 106 109 1012 1015 1018
A (GeV)

Figure 1-1. Lower and upper theoretical bound of Higgs boson mass as a function
of A


Supersymmetry (SUSY) has been proposed [7, 8] to alleviate the hierarchy

problem of SM as its most plausible extension. If it is proved via experiment, there

exists supersymmetric partners associated with ordinary particles. In the minimal






5


supersymmetric extension of SM (\ SSM), the Higgs scenario includes two CP

even (h and H), one CP odd (A) and two charged Higgs bosons (H'). In the tree

level calculation, the Higgs boson masses and couplings are determined by two

parameters (mA and tan3), and the MSSM Higgs bosons' masses are well ordered:

mh < mz, mh < mA < mH, mA < mH, mZ < mH and 1 < tan3 < mlh/mb. Due to

the radiative correction, which is proportional to m4op (mtop is the top quark mass),

the upper bounds of Higgs masses are very large in MSSM.

The Higgs boson in SM or MSSM however has not yet been found. Within

SM, Higgs boson mass can be constrained by precise measurement of particles'

masses and their interactions (couplings), because in SM prediction, as mH in-

creases, the Higgs self couplings and its coupling to vector boson (W or Z) increases

as well. The precision measurement of W and Z mass can be used to estimate the

valid Higgs boson mass range.

Results from the Large Electron and Positron Collider (LEP) experiment

showed that mH is between 114.4 and 219 GeV/c2 at 95'. confidence level [9].

In MSSM, a lower bound of 91.0(91.9) GeV/c2 for mh (mA) [10] is also set. The

excluded tan3 regions are 0.5 < tan/3 < 2.4 for maximal mh scenario and 0.7

< tan/3 < 10.5 for No Stop Mixing Scenario. Fits based on precision measurements

of several experiments (LEP, SLC and Tevatron) predict the SM Higgs boson mass

to have the value mH "".'' GeV/c2 (Fig. 12)[11].

1.2 Higgs Boson Production via Vector Boson Fusion

At LHC energies, the Higgs boson can be produced via several processes:

gluon-gluon fusion, vector boson fusion (VBF), and associated production with

tt or W boson (Fig. 1-3). In the VBF process, the Higgs boson is radiated off

t-channel W or Z, and leaves two highly scattered original quarks in the forward

region, providing a unique signature that can be exploited (forward jet ,.--i i--) to
























cinurI! Ilai rlinm r w.ru "

10 1:" *0'


Figure 1-2. SM Higgs boson mass constraints by precision measurement of elec-
troweak parameters at LEP, SLC, and Tevatron


highly suppress backgrounds and significantly increase the signal to background

ratio.

Color coherence between initial and final state gluon bremsstrahlung sup-

presses hadronic activities in the central region. This is in contrast to most

background processes, which normally have color flow in the t-channel and thus

leads to central jets in the detector.

Aside from their experimental signature, VBF mediated processes have

attracted attention because of the insights they can provide on the dynamics of

Electroweak Symmetry Breaking (EWSB). In particular, studies [12, 13, 14] have

demonstrated that VBF offers a potent tool for Higgs boson discovery and for

measurements of its coupling. These results show, for example, that VBF provides

large discovery potential for mH around 170 GeV/c2 and in the mediate and high

mass region (mH > 300 GeV/c2).

Once the Higgs boson is discovered, the measurement of its coupling constants

with fermion and other gauge bosons must be performed in various channels.

Assuming W/Z universality, HWW coupling can be separately determined in VBF














g g fusion


00 0 ---> ---
9 HO






q
t fusion


q9 WZ W'Z w

HO
W, Z bremsstrahlung




Ho
q W ,Z

WW, ZZ fusion' q

Figure 1-3. Feynman diagrams of various Higgs boson production processes


for mH > 110 GeV/c2 through qq qqH, H W+W-, while other Higgs channels

normally involve 2 types of coupling including Hgg, H77, Hbb, Htt and HTr+r-. For

example, gg ZZ involves Hgg and HZZ coupling. Hgg coupling is dominated by

top-quark Yukawa coupling which can be used to probe the Higgs coupling with

up-type fermions.

According to different range of mH, following Higgs boson decay chains with

corresponding final states can be exploited in LHC:

In low mass region (mH < 140 GeV/c2)

qqH qqr+-r -4 qq + +.- + ETiss









qqH qqr+T- qq + + jet + E'iss

qqH qq77

In intermediate and high mass region (mH > 140 GeV/c2)

qqH qqW+W- qq + .+.- + E'iss

qqH qqW+W- qq + + 2jet + E'iss

In the intermediate and high mass regions, all final states have one or two

high pT lepton, ETiSS, two jets in the forward regions and possible extra jet(s)

in the central region.

1.3 Analysis Goal

This study mainly concerns the detector reconstruction and physics analysis of

missing transverse energy and the prospects for searching for Higgs boson produced

via vector boson fusion process with H -- W+W- -- vjj at C'\ S. Because of high

identification efficiency and excellent PT resolution for leptons in C \ S detector, the

primary challenge of VBF Higgs reconstruction is the reliable reconstruction of jet

and Epmiss
E~iss is a very important signature of new physics (e.g., Higgs boson, SUSY)

and p1 i',i- a big role in precision measurement of SM parameters (e.g., W mass and

Top quark mass). It is also related to overall detector performance. We studied the

E'iss quantities with its reconstruction and correction techniques to benefit a broad

range of physics studies involving the E'iss.

We focused on several critical questions about EDiss and jet that have not been

well answered before:

What is the limit of calorimeter based jet energy corrections? Can other

approaches improve the jet energy resolution further, for example, by

including the information contained in jet energy distributions? (C'!i Ilter 4)

What is the basic performance of the C' \S detector on the E'iss? What

1n i ri quantities are involved? What experimental measurement of those









quantities can be performed? What is the correlation between those quanti-

ties? (C'! plter 5)

What issues must be addressed when applying jet energy correction for

Episs? What final states can the jet energy correction can be applied to?

What systematic issues are expected in carrying out Efiss corrections? What

detector factors are the most reliable? (C'!i pter 6)

Should jet energy corrections reduce the E'iss tri --r rate? What is the

correlation between the jet system and EDisS? How do we quantitatively

predict and evaluate the performance of the Episs reconstruction and correc-

tion? What is the sensitivity of Efiss tri ._--r rate to 1i .iji detector factors?

(C'!i Ipter 7)

We offer in this thesis several significant contributions to the understanding

of E'iss and jet reconstruction, including the first comprehensive study of the

E'iss quantities beyond the tri'i -r selection, the development of a jet calibration

and correction algorithm using jet energy distributions that reduces jet energy

measurement errors, the first comprehensive study of correction techniques for E'isS

based on leptonic events, and the development of a general I I i i. II 11i model"

that can be used for studying EpiSs performance in C'\!S.

We also conducted the first reconstruction of vector boson fusion Higgs

through H -- W+W- -+ vjj channel in the low mass region using fully simulated

data. As described later, the reconstruction technique developed here shows

promise for using this channel for the Higgs boson searches in the most interesting

region of mH predicted by several experiments (120 < mH < 220 GeV/c2), whereas

before it had been mainly considered for high mass Higgs boson searches.














CHAPTER 2
HIGGS PHYSICS AT LARGE HADRON COLLIDER

Discovery (or exclusion) of Higgs boson is one of the most important tasks of

LHC, crucially improving our understanding of nature, especially about electroweak

symmetry breaking mechanism. Because SM does not predict the exact Higgs

boson mass (mH), LHC must be able to reconstruct Higgs boson signal and extract

it from large SM background for a wide range of possible mass and channels.

2.1 Higgs Boson Production and Decay

The production of Higgs boson (Fig. 2-1)[16] is dominated by gluon-gluon

fusion (gg -+ H) over the mH range between 100 GeV/c2 and 1 TeV/c2. The cross

section is about 10 pb around mH ~ 200 GeV/c2. The cross section of associated

Higgs boson production, qq -i HW, qq -i HZ, gg/qq -+ bbH and gg/qq -+ ttH,

is lower by a factor of ~ 20 (1000) at mH 100 (500) GeV/c2. Vector boson

fusion (qq -+ qqH) is another large process with about 10'1. of the cross section for

gg -+ H at mH < 200 GeV/c2, and rises to similar level at mH ~ 1 TeV/c2. The

k factor of gg H is ranging from 1.5 to 1.8, ~ 1.1 for qq -i qqH and ~ 1.2 for

other associated processes [15].

The branching ratio for SM Higgs boson is dominated by bb for mH < 130

GeV/c2 and WW*/WW, ZZ*/ZZ for higher mass (Fig. 2-2)[17]. In low mass range,

H -+ -T+--,77 are also sizable with ~ '-, and 1.5 x 10-3 (mH < 150 GeV/c2)

respectively.

The MSSM scalar h will behave like SM Higgs boson of similar cross section

and decay partial width, if mA > mjax. At large tan3, the couplings between heavy

neutral Higgs boson and electroweak gauge bosons are suppressed and down-type

fermions are enhanced with tan3. gg -i H/A and gg/qq -+ bbH/A are the 1i i i' r























0-

1 010


0 200 400 600 800

MH (GeV)


Figure 2-1. Leading order (LO) cross section of SM Higgs boson.
for gg H is shown in next to leading order (NLO)










S .......................................... W W




1 10 ..* ..****............ bb




10- '.... .............. **......... "
c c
-





105







10100 110 120 130 140 150 160 170 180 19(
105


100 110 126 i-'6 i-4 0, 19(


107


1 06
I
-o
105 C


104

3
103


.... 102



1000




The cross section


Figure 2-2. Branching ratio for SM Higgs boson









production processes for heavy neutral MSSM Higgs boson. If tan3 > 10 and mA >

300 GeV/c2, the bbH/A dominates at about 9ii''. of the total rate.

For charged MSSM Higgs boson production, t -+ H'b is the dominant

process via tt events. Other processes, gb -i tH', gg -i tbH', qq' -i H+H-

and gg -- W'H', also contribute. With respect to MSSM Higgs boson decay,

H, A bb dominates with tan3 > 10, and H, A -+ -7-+7 1 0'. The branch ratio

of H hh, WW and /rmZZ and A -+ hZ depend on tan3, which is enhanced by

small tan3 and reach up to ~ I and 40'U. of H and A decays respectively. Light

charged Higgs boson (mH < mtop) almost exclusively decays to T-,. For large

tan3, Hpm -i tb dominates with mH > 200 GeV/c2, Hpm -+ -v, is ~ 10'A, with

mH > 400 GeV/c2. H -+ Wh may reach 10C'. at small tan3. The branching ratio

to gauginos will reach ~ 10'. (3C:' .) for large(small) tan3.

2.2 Higgs Boson Search Strategy

With respect to different range of mH, following decay modes will provide the

discovery potential of Higgs boson:

For mH < 130 GeV/c2, H 77, H -- ZZ* -- f+f-'+'- and H -- r+r- can

be exploited, where the first one need suppress a large jet faked 7 background

and second mode provides a clean signature. The mass reconstruction can be

optimized to benefit from a very narrow Higgs boson mass width (FH < 1

GeV/c2).

A good mass resolution is particularly important for H y77, due to large

irreducible background pp y77 + X. The background pp -- 7 + jet + X with

a jet fragmenting into a leading isolated 7r that fakes 7 can be reduced below

the level of di-7 background.

H y77 can also be searched by associated processes WH and ttH with an

isolated lepton from W leptonic decay to suppress the hadronic background.









gg/qq ttH -+ ttbb can also be exploited. The associated production is

necessarily used because large bb background from QCD process and modest

Higgs boson mass resolution (~ 11 .) in this channel.

* For mH between 130 and 500 GeV/c2, H -- WW*/WW and H -- ZZ*/ZZ

can be exploited via both gluon-gluon fusion or vector boson fusion. Around

mH = 170 GeV/c2, the branch fraction of H -- ZZ* is highly suppressed,

which makes H -- WW as the primary discovery channel. Because of

the prediction of mH from other existing experiment is between 114 and

219 GeV/c2, that is largely within this range, it is extremely important to

optimize the Higgs boson reconstruction especially in this mass region.

For mH < 200 GeV/c2, H -- WW*/WW -- +v-v channel will be used. Due

to di-neutrinos in the final states, only the transverse Higgs boson mass can

be reconstructed. The possibility of using H -- WW -- 0vjj is one of the

task of this thesis providing a direct Higgs boson mass reconstruction.

For mH > 200 GeV/c2, H -- ZZ E+-'+{'- has the best sensitivity

up to mH ~ 500 GeV/c2, which is very clean from QCD background and

irreducible ZZ background because of relatively small Higgs boson mass

width. The background of tt and Zbb can be efficiently suppressed by using

lepton isolation, an upper bound on the lepton impact parameter significance,

and di-lepton invariant mass.

* For mH > 500 GeV/c2, H -- ZZ/WW with one W or Z hadronic decay can

be exploited to get larger branch fraction, and the jet and missing transverse

energy resolution benefiting from high mH is much better than that of low

mH.

The vector boson fusion process is comparable to gluon-gluon fusion process,

and provide unique forward :: I--,- jet signature to suppress the background

that can be fully exploited.









2.3 Higgs Boson Discovery Potential at CMS

The status up to 2003 about Higgs boson discovery potential at C'\!S are

summarized in this section. Several important channels exist:

The result of four lepton invariant mass distribution of H -+ ZZ* -

St+-f'+'- and background with mH 130, 150, and 170 GeV/c2 in a

luminosity of 100 fb-1 [18, 19] is shown in Fig. 2-3. For the isolated lepton

with I|r| < 2.5, 20 GeV/c PT threshold for leading lepton, 15 (10) GeV/c

threshold for second-largest-PT electron (muon), 10 (5) GeV/c for the rest

two electrons muonss), and a four-electron (four-muon) acceptance of 3 :'.

(41 ,) for mH 130-150 GeV/c2 is achieved.


H ZZ*- 4-- '-
100 fb-1
CMS





tt +Zbb +ZZ*




120 140 160 180 200
M (4 t) [GeV / c2]

Figure 2-3. H ZZ* (+-'+i'- invariant mass signal (dark) and background
(light) for mH = 130, 150, and 170 GeV/c2 with an integrated luminos-
ity of 100 fb-1


The result of H WW*/WW i+v--v is shown in Fig. 2-4 with mH = 140

GeV/c2 for 30 fb-1 [20, 21]. The background from tt -- W+bW-b and WW

can be suppressed from WW spin correlations of the signal that make small

+- opening angle.












MHiggs= 140 GeV

Pt (max) events for 30 fb-1
c Higgs W*W- tt Wtb
= 3540 events
liW'W -i- tt -i Wtb
= 2679 events
W'W-
= 1883 events


0 25 50 75 100 125 150 175 200
Pt(max) [ GeV ]


225 250


0 20 40 60 80 100
Pt(min) [ GeV ]


PT distribution of smaller PT lepton in H -
(white) and total background (light) for mH
tegrated luminosity of 30 fb-1


120 140


WW* -- +viv signal
= 140 GeV/c2 with an in-


* The result of di-photon invariant mass distribution of H --


ground with mH = 130 GeV/c2 for 100 fb-1 is shown Fig. 2-5 [22]. The signal

to background ratio is ~1/10.


600


o
0
400



oD



w
200



W


.......... I ...... ... I ......
) 120 130 14
mr (GeV)


110
b)


120 130
mr (GeV)


Figure 2-5. H 77 invariant mass distribution signal (dark) and background
(light) for mH = 130 GeV/c2 with an integrated luminosity of 100 fb-1


102



10


pt (max) 30-46 GeV
Higgs +- WW- -+ tt Wtb
= 1949 events
SW'W + tt +- Wtb
= 1403 events
W'W-
= 1029 events


Figure 2-4.


8000



7000



6000



5000



4000


77 and back-









Fig. 2-6 shows the invariant mass distribution of di-b-jet in ttH

'vqqbbbb and background with mH 115 GeV/c2 for 30 fb-1 [23].


o 25
SCMS ttH, H -> bb
S20 -
S 20 \ mH: 115GeV/c2

15-


10

5


0 50 100 150 200 250 300
minv(,j) [GeV/c2]

Figure 2-6. bb in ttH -+ vqqbbbb channel invariant mass distribution signal
(dark) and background (light) for mH 115 GeV/c2 with an integrated
luminosity of 30 fb-1


The significance for the SM Higgs boson with 30 fb-1 [24] is shown in Fig. 2-7.

The NLO cross section for both signal and background are suited for inclusive

H -+ 77, H -- ZZ*/ZZ -- E+-4'+'- and H -+ WW*/WW -- f+v-v. Poisson

statistics are used to calculate the statistical significance for H -+ ZZ*/ZZ -

4+. '+ '-, H -- 77 in WH, and H -- 77 and H -- T+T- in the vector boson fusion.

MSSM Higgs boson discovery potential [24] is shown in Fig. 2-8 with respect

to lighter scalar, heavy neutral, charged Higgs boson.


















CMS, 30 fb-1


40 I-


M qqH. H--\AN->Iv~jj
O qqH, H-*ZZ-*1v,v,
V H--VWNItV\-Aiv,v,, NLO
~77"*I77 1l1 1t1 Nil rn


S qqH, H--.yy,'t
o H->yy inclusive, NLO
tTH,WH,H -bE
S-- Total significance
S5(at 2 fb-









5' '-,5Cat30fb


.. .


40

C9


20


C,,

ib 10


53
6


100


200


300 400 500 800
mH(GeV/c 2)


100 110 120 130 140 150
mH(GeV/c 2)


Figure 2-7. SM Higgs boson discovery significance for (a) full mass range of mH
and (b) low mass range of mH in CMS\ with an integrated luminosity of
30 fb-1


20





























100 150 200 250 300 350 400 450 500 100 150 200 250 300 350 400 450 500
mA(GeV/c2) m (GeV/c2)
(a) (b)


C C
CMS, 30 fb-
S= 300 GeV/c2, M =200 GeV/c2
40 A =F TeV/c2m,MsY 1 TeV/c2 40


30 .. 0 30


20 ..... 20 CMS, 30 fb1

H,A HA -- 2 jets + X, 60 fb1 = -200 GeVlc2, M = 200 GeVIc2

10 H,A 2 leptons+X 10 At = 2450 GeVlc2, Msus= 1 TeVI/c
H,A -ut7- lepton +jet + X

100 200 300 400 500 600 700 800 100 150 200 250 300 350 400 450 500 550
mA(GeV/c2) mA(GeV/c2)

(c) (d)

Figure 2-8. The 5 a discovery potential of MSSM Higgs boson for (a) lighter scalar
at 30 fb-1, (b) lighter scalar at 100 fb-1, (c) heavy neutral at 30 fb-1,
and (d) charged at 30 fb-1















CHAPTER 3
OVERIEW OF COMPACT MUON SOLENOID EXPERIMENT

LHC uses the Large Electron and Positron Collider (LEP)'s 27 kilometer

long tunnel to collide two proton beams with center-of-mass 14 TeV and 40 MHz

collision rate. It will be running at low luminosity of 2 x 1033 cm-s-1 in the first

three years starting from 2007, then be upgraded to luminosity of 1034 cm s-1S.

It can also collide heavy ions with total energy 1150 TeV. In order to achieve

both high energy and luminosity, each of the two rings in LHC will be filled with

2835 bunches of 1011 particles with large beam current maintained by a delicate

superconducting magnets operating at cryogenic temperature.

The C'\IS detector (Fig. 3-1) is designed to fully exploit the discovery poten-

tial of LHC with a fast response to match the crossing rate and high granularity to

handle ~ 20 events and ~ 1000 tracks on average per bunch crossing. It must also

be able to run under a harsh radiation environment of 3 kGy and 1013 neutron/cm2

for the barrel and up to 50 kGy and 2 x 1014 neutron/cm2 for the endcaps.

3.1 The CMS Detector

The detector design combines a compact superconducting solenoid generating

a 4T magnetic field with a muon system, which provides high efficiency and high

precision muon measurement. The best possible electromagnetic calorimeter and

high quality tracker are also in the design goal which allow critical measurement

of electron, photon and charged particle tracks. The hadronic calorimeter will

perform the reconstruction of jet and missing transverse energy. In the following,

the components of the C\ IS detector with their basic performance will be briefly

described from inner to outer.











Very-forward Pi:l Deector
Calorimeter
Preshower

1'/-111. b I I








Hadronic
Calorimeter
Calorimeter Muon
Detectors
Compact Muon Solenoid

Figure 3-1. The C \IS detector layout


3.1.1 Inner Tracker and Basic Performance

C'\ S tracker system is under all-silicon layout and inside the 4T magnetic

field, which allows to precisely measure the transverse momentum of tracks. The

tracker is divided into four silicon strip subdetectors and two pixel subdetectors.

Silicon strip subdetectors include Track Outer Barrel (TOB), Tracker Inner Barrel

(TIB), Track Inner Disk (TID), and Tracker Endcap (TEC). Pixel subdetectors

include pixel barrel and pixel disk. All active components are built in a cylindrical

volume with a length of 5.4 m and a diameter of 2.4 m (Fig. 3-2).

The pixel detector is housed in a cylindrical volume of 1 m length and 30 cm

diameter centered around the interaction point. It consists of three barrel livrs at

mean radii of 4.4, 7.3, and 10.2 cm and two endcap disk on each side. The detector

has been designed to provide two-hit coverage up to Irl = 2.2, and maximal three

hits per track. The pixel size is 150pmx 150pm that makes the occupancy low.

The Silicon Strip Tracker consists of 15148 silicon strip modules with a pitch

from ~ 80-180 pm distributed over ten barrel li-,-%rs (four inner barrel lmvrs and









,0,0 pt1 .02 .03 ,0.4 .0.5 Q.6 0.7 0,8 ,0.9 1,0 1,1 ,12 .1.3 .1,4
I ,,
I -

I I i ,' '
I I



-.,I,



,,,,--r ;'.. ..'-;-, &- i 1 __ -' r- 41 -- ----'
^W^ ^^11""


,1.5 -16

.1.7


-2i
--''" 1,9



I. --"-B'.--LB
r;---"-.2,5


Figure 3-2. Transverse view of C'\ I- tracker 1-,-out


six outer barrel 1-v. rs), which provide up to 14 hits per track. The inner (outer)

endcap is made of three (nine) disks for each side.

The fundamental performance of inner tracker is summarized as follows:

For qrJ < 1.25 and pT < 100 GeV/c, the momentum resolution is better than



For q r between 1.7 and 2.2, the momentum resolution degrades to 5'. (i'.)

for 100(10) GeV/c tracks.

The impact parameter resolution is better than 30 pm in rQ and better than

100 pm in z.

Track reconstruction efficiencies (for Ir, < 2) for single muons are larger than

95' 85'. for single pions, and ~ 80'_ for pions in jets.

3.1.2 Electromagnetic Calorimeter and Basic Performance

C'\ !S electromagnetic calorimeter (ECAL) is located between the tracker and

hadronic calorimeter, composed of about 75848 lead tungstate (PbWO4) ( i',-1 i-!

because of its high energy resolution, high density (8.28 g/cm3), short decay

scintillation time constant and short radiation length (Xo = 0.89 cm). The small

Moliere radius (2.2 cm) allows a very fine granularity of ECAL. The calorimeter is









compact and put inside the magnetic coil covering the rapidity range up to Irll <

3. Precise energy measurement for photons and electrons can be performed up to

Irl < 2.5 except for the region 1.4442 < Irl < 1.5660.

The <( i --I 1I have a cross section of 22x22mm2 and length of 23 cm (= 25.8

Xo) in the barrel and 22 cm (= 24.7 Xo) in the endcap. They are arranged in

barrel (covering the central rapidity region of Irl < 1.48 and transverse granularity

of 0.0174x0.0174 in yl-)), two endcaps (covering 1.48 < Irl < 3 with coarse

granularity), and grouped in mechanical unties of 5x5 <( i v-i I- (super-crystals).

In the barrel, crystals are tilted with an angle of 3 with a line from the nominal

vertex point. In the endcap, the < i --I I- and super-crystals are arranged in a

rectangular x-y grid with axes off-pointing from the nominal vertex with an angle

of 20 and 5.

A preshower detector consisting two lead radiators (3 Xo) and silicon strip

detector l zv-is, is used before the < i-- l I endcap (1.65 < KIl < 2.61) in order to

provide 7r-7 separation, which is needed in the forward region.

The physics goal of ECAL is the precise energy and position measurement of

electrons and photons with energy resolution described by Eq. 3-1.

a(E) a b
7 (De-DC (3-1)
EE E

where

a is the stochastic term of ~ 2.7'.- (5.7'.) GeV1/2 for barrel (edncap), which

is limited by the photoelectron statistics.

b is the noise term of ~ 155 (210) and 770 (915) MeV for barrel and endcap

at low (high) luminosity, which relates to the photodetector dark current,

electronic noise, and event pileup effect.

c is the constant term of ~ 0.55' which depends on the longitudinal non-

uniformities of the light collection, the fluctuations due to temperature and









high voltage, the longitudinal leakage of the showers due to restricted length

of the calorimeter medium, and precision of inter-calibration.

3.1.3 Hadronic Calorimeter and Basic Performance

C'\!S hadronic calorimer (HCAL) covering Irll up to 5.191 is composed of

barrel (HB) and endcaps (HE) inside the magnetic coil, forward calorimeter (HF),

and outer calorimeter (HO). The granularity is 0.087x0.087 in rl-Q for HB and HE

(except near |ry| = 3 where the size is doubled) and 0.17x0.17 for HF.

HB and HE are sampling and consist of 4 mm thick plastic scintillators tiles

inserted between brass absorbers plates. Due to short interaction length of HB

(~ 6.5 Xo), the HO is located inside the muon barrel system and outside of the

solenoid coil to measure the HB energy leakage. HF is placed at a distance of 11 m

from the interaction point, which uses quartz fibers as an active material embedded

in the iron absorber wedges to be able to work in a high radiation environment.

To compensate for the radiation damage in |Tq\ > 2.0, HE has 3 lv.,- r- of

longitudinal segmentation to allow correction for the loss of light yield comparing

to only one lv,- r in HB. HF covering 3.0 < ITrl < 5.0 is designed to increase

the calorimeter acceptance and reduce the dead region, which is important for

measuring forward jet and missing transverse energy.

The calorimeter readout has a dynamic range from 5 MeV to 3 TeV. The

energy resolution for single hadrons at rf = 0 can be roughly parametrized as

aE 11',
-( 5: (32)


where JE and E are measured by GeV. The correlation between JE and E is

confirmed by the Monte Carlo (M\C) studies and test beam (Fig. 3-3)[25]. For HF,

the expected energy resolution of singal pion and jets is













a (3 + 1)

aE (128 ( 10)1
S (28 ) (2 1). (3-3)


In the design goal, the missing transverse energy (E"PiSS) resolution as a

function of the scalar sum of ET (EET) in HF is

a(ET 88) 0.55 (3
(3-4)


S40

35 a OSCAR245-GEANT452 (TB02)
b QGSP-2.7
30- OSCAR245-GEANT452 (TB02)
LHEP-3.6
25 TBO2 Data

20

15

10

5s Includes Electronic Noise

0 50 100DO 150 200 250 300DD
Pion Beam Energy (GeV)

Figure 3-3. Pion energy resolution measured by Test Beam and Monte Carlo simu-
lation


3.1.4 Muon Detector and Basic Performance

C'\ S muon system is composed of three types of gaseous detector with

excellent time resolution (Fig. 3-4): Drift Tube C'! iinhers (DT) in the barrel (0

< Ir|l < 1.1), Cathode Strip C(!, i~.ers (CSC) in the endcap (0.9 < Ir|l < 2.4) and

Resistive Plate C(! iiiihers (RPC) in both barrel and endcap, which is dedicated for

trigger. DT uses the time-t ,.-.-ii_-; to identify the bunch crossings. CSC is capable

of precisely measuring space and time of the interaction in the presence of strong









magnetic field and high rate. The muon system is inside the magnetic field return,

which allows a standalone measurement of muon momentum. The muon system is

aligned with track within ~ 100 pm of error which is important for high PT muon.

o DT
Seta=.08 RPC 1,04 ...-1 .2
700

Soo







U 2.4
100 2. .1






0 I .... -



Figure 3-4. The C \S muon system


In the central region, the neutron background is negligible, both the muon rate

(< 1 Hz/cm2) and the magnetic field are low. Four stations of detectors are located

in cylinders interleaved with the iron yoke, of each which station contains a DT and

RPC. The segmentation follows along the beam direction.

In the endcap region, the muon rate (< 10 kHz/cm2) and the neutron back-

ground rate (~ 10 kHz/cm2) are high, as well as the magnetic field. The CSCs and

RPCs in four disks are perpendicular to the beam direction.

In the initial running of muon system once LHC starts to take data, the outer

ring of the disk will be missing and the CSC electronics for the Level 1 trigger will

be not be implemented in the innermost chambers, which limits the level 1 muon

tri j'ir with |r] < 2.1.









In the standalone muon reconstruction, the muon momentum resolution is

~ 10' in the barrel, 15'. in the overlap region (0.8 < I|T < 1.2) and 1'.t. in the

endcaps (1.2 < TI1 < 2.1). Combining muon system and inner tracker, a best muon

momentum measurement can be achieved with 1.0'. in the barrel, 1.!' in the

overlap region and 1.7'. in the endcaps.

3.2 Trigger and Reconstruction

3.2.1 Data Acquisition Design and Level-1 Trigger

C'\!S data acquisition system (DAQ) is designed to operate at 100 kHz rate

with 1 MB size per event. A customer Level-1 processor is used to perform the

event selection with a reduction factor of ~ 4000 based on 40 MHz bunch crossing

rate. The event will be stored in frontend pipeline with an average 3 ps latency (~

120 bunch crossing).

The high level trigger is performed by a farm built on standard commercial

processors. This architecture achieves the largest flexibility to be capable of

adapting the system to latest computing technology without built-in design

limitations. In the high level selection, a sophisticated algorithm which is not

much different from that of offline reconstruction can be used online and handle

any unforeseen issues. Thus the hardware construction is minimized to reduce the

maintenance and cost.

C' \S Level-1 trigger (Fig. 3-5) is based on calorimeter and muon to perform

the electron/photon, jet and energy sum, and muon trigger using local data.

The rejection factor and Level-1 acceptance rate are mainly determined by the

bandwidth of switch network that handles the data flow. The trigger hardware

is organized in calorimeter and muon system respectively, and the results will be

combined in a global trigger, where the final decision is made and return to the

frontend. The transmission delay in whole process is about 2 ps. The Level-1

ti --.- -r menu is included in Table 3.2.1.









In the allocation of bandwidth, a safety factor of three is taken for simulation

uncertainties based on full (half) capacity for running at high (low) luminosity,

which corresponds to 33 (16) kHz.


Figure 3-5. Overiew of the Level-1 trigger system


Table 3-1. The C\! S Level-1 trigger menu at low luminosity


Ti i -r stream Threshold Rate Cumulative rate
GeV (GeV/c) kHz kHz
Inclusive isolated electron/photon 29 3.3 3.3
Di-electron/di-photon 17 1.3 4.3
Inclusive isolated muon 14 2.7 7.0
Di-muon 3 0.9 7.9
Single jet 86 2.2 10.1
Di-T jet 59 1.0 10.9
one, three, four jet 177, 86, 70 3.0 12.5
Jet E "ss 88 46 2.3 14.3
Electron jet 21 45 0.8 15.1
Minimum bias (calibration) 0.9 16.0
Total 16.0


The calorimeter trigger is based on HCAL tower (Fig. 3-6). The tower energy

sums are formed by ECAL and HCAL (including HF) tri -. ir primitive generator

(TPG) circuits from the individual cell energies. For HCAL (ECAL), the energies

are accompanied by a bit indicting the presence of minimum ionizing energy









(electromagnetic energy deposit). TGP information is transmitted over high

speed copper links to the regional calorimeter trigger (RCT) to find the candidate

electron, photon, r and jet.

T riggee-r,


I

r rI .



HCAL
ECAL
PbWO4 Crystal Ai,A =0348
ATi,A$= a

Figure 3-6. Illustration of Level-i jet and T-jet tri-'-i-r algorithm


The ultimate optimization will be performed iteratively under the real data.

Initially an equal share of rate will be allocated to four classes of trigger: elec-

tron/photon, muon, r-jet, and jet/missing transverse energy. Then the rate must

be shared within the classes between single object and double (multiple) objects

triggers. The goal of rate sharing and optimization is to maintain a sufficient

wide and general suite of channels to make as inclusive as possible and open to

unexpected p1 ],i -

The electromagnetic trigger works under 3x3 trigger towers (Fig. 3-7),

applying a threshold to the sum of two .,.i] i'ent towers. The cuts are based on

isolation, hadronic to electromagnetic fraction, fine-grain lateral shape in ECAL.

The efficiency of turn-on curves are tested for different threshold cuts, for isolated

electron trigger as a function of electron momentum.

The jet trigger is based on 3x3 window using 4x4 arrays of tri.'_.,r towers

(~ 1.0 square region in q-0). Several types of jets are made: central jet, forward

jet and 7 jet (using a r-like shape to filter central jet) with adjustable combined










0.01711 Sliding window centered on all
SECAL/HCAL trigger tower pairs

0a Candidate Energy:

M Max E of
Neighbors
Hit + Max
E > Threshold

o087

0. 08os7

Figure 3-7. Electron and photon algorithm


trigger criterion and up to four jet triggers. The top four candidates of each class of

calorimeter trigger are sent to global trigger.

The Level-1 muon trigger uses fast RPC and precise position measurement

of DT and CSC with standalone trigger logic in each of the Level-1 muon trigger

system. RPC strips are connected to pattern comparator trigger (PACT), which is

projective in rT and Q. CSC form Local C(!i ged Track (LCT), which is combined

with the anode wire information for bunch crossing identification on a Trigger

Motherboard. DT is equipped with Bunch and Track Identifier (BTI) electronics

that find track segments from hits in four 1'-, rs of one DT superlayer.

The bending in the successive 1-.i ris of the iron yoke is measured by first

assembling local vectors in the measurement stations and assembling tracks by

linking these vector are combined in global muon trigger (GMT). The ghost track

from a single muon found by more than one muon system with non-matched

segments can be canceled by GMT. The four best muon candidates identified and

sent to the global trigger. The resulting muon Level-1 rate as a function of muon

PT is shown in Fig. 3-8[28].













C 4 P C n o ... R s n-.. .. ..


........ "...... ..... .. .... 10 ---.----- -..--i--------. .- .. ..--- -

L1 trigger rate (GMT) i L1 trigger rate (GMT)
--DT/CSC standalone ...DT/CSC standalone

generated rate generated rate
1 10 102 1 10 102
pTthreshold [GeV/c] pTthreshold [GeV/c]
(a) (b)

Figure 3-8. Level-1 muon trigger rate as function of pT threshold for (a) low and
(b) high luminosity


3.2.2 High Level Trigger and Reconstruction

The final output rate of high level trigger (HLT) is as 0(102 Hz) with the

total reduction factor for rate at 0(102) from Level-1. Several "virtual" trigger

levels are implemented to synchronize the reconstruction process and availability of

information:

At Level-2, calorimeter and muon trigger information is used.

At Level-2.5, tracker pixel information is used.

At Level-3, full event information (especially fully reconstructed tracks) can

be used.

The full event information means full granularity and designed resolution is

available. The only limitation for HLT is the CPU time usage and output rate.

For phr..-i. study, the HLT must be inclusive enough and must not rely on a very

precise knowledge of run condition and calibration. The HLT trigger menu is

included in Table 3.2.2.

According to the designed architecture, the highest level of HLT reconstruction

shares almost the same algorithm with offline reconstruction (and analysis). In the









Table 3-2. The CMS HLT t.-i ---- rate at low luminosity


Ti, .. stream Threshold Rate Cumulative rate
GeV (GeV/c) Hz Hz
Inclusive electron 29 33 33
Di-electron 17 1 34
Inclusive photon 80 4 38
Di-photon 40, 25 5 43
Inclusive muon 19 25 68
Di-muon 7 4 72
Inclusive 7 jet 86 3 75
Di-r jet 59 1 76
one, three, four jet 657, 247 9 84
Jet I 1 I 5
Electron i. 19 45 2 90
Inclusive b i. i 237 5 95
Minimum Bias (calibration) 10 105
Total 105


following, I briefly describes the reconstruction algorithm for 1 ii wr objects that is

used for DAQ TDR:

Electron reconstruction starts from the cluster using full ECAL granularity.

The electron bremsstrahlung radiation in tracker causes spray of energy in

Q beyond the boundary of a single electron shower due to 4T magnetic field

(e.g. for electron with PT = 35 GeV/c and q| < 1.5, and mean energy loss is

43.1 '. between the interaction point and ECAL, which corresponds to 0.57 Xo

of material). A region (super-cluster) to collect all these energy (electron and

radiated quasi-collinear low energy photon) is defined to recover the radiation

effect.

In Level-2.5, super-cluster is propagated back in the field from ECAL to

the pixel detector l V rs. The pixel 1.i.-r is very close to the beam pipe

before most of the tracker materials, so the possibility of electron radiation

and photon conversion is small. Two matched hits allows good electron

identification. The unmatched cluster can be identified as photon candidate









with a higher threshold. The jet rejection versus efficiency is shown in

Fig. 3-9[26].

100 I 100 I
^, b W 2x1033 m2/s 1034 2/
C L 95 a) 95
a+ a)






S 10 15 20 25 10 15 20 25
Jet rejection Jet rejection
(a) (b)

Figure 3-9. Jet rejection versus efficiency obtained from Level-2.5 pixel matching at
(a) low and (b) high luminosity


The further improvement of electron/photon identification involves using fully

reconstructed track to match with super-cluster and proper isolation based

on tracks and/or calorimeter. This results in a better electron/photon to

background ratio with small inefficiency. The same strategy can be used in

offline ,ii i. -~i and to be optimized with general or specific physics channels.

The muon track reconstruction used in HLT is seeded by the muon candidate

found by Level-1 GMT.

At Level-2, the muon identification is performed by the muon detector. The

state vector (track position, momentum, and direction) associated with the

segments found in the innermost chambers is propagated outwards through

iron yoke.

At Level-3, full track is reconstructed in the interested region based on

Kalman filter technique, which is defined based on muon track segments.

Finally muon ti ii i 1l i including the tracker hits with required track

segments are extrapolated to the interaction region within a of 15 pm and










a of 5.3 cm of beam spot. The track reconstruction algorithm contains:

trajectory building, trajectory (1. ,ii and trajectory smoothing.

Isolation cut are used to suppress the muon decay from b, c, K and 7 decays.

Isolation strategy can be: calorimeter isolation, pixel track isolation, and full

track isolation implemented in Level-2, Level-2.5 and Level-3 respectively.

The procedure of isolation optimization is that for any predefined nominal

efficiency a cone size is chosen with threshold defined in bins of irl. The

typical optimal cone sizes vary from 0.2 to 0.3. The efficiency of three

isolation algorithms is shown in Fig. 310 [27].

Low Lumi, p, (m'") > 16 GeV, I hi < 2.4 High Lumi, pT (mon) > 22 GeV, I hi < 2.4
m 0.5 ii m 0.5 ii

S0.4- 0.4-
lUI L2 Calorimeter Isolation W L2 Calorimeter Isolation
0.3 L3 Pixel Isolation 0.3- L3 Plxel Isolation
L3 Tracker Isolation L3 Tracker Isolation
0.2 0.2 -

0.1 0.1
(a) (b)
0.75 0.8 0.85 0.9 0.95 1 0.75 0.8 0.85 0.9 0.95 1
EfficiencyW EfficiencyW

(a) (b)

Figure 3-10. Efficiency of three isolation algorithms on the reference background
as a function of efficiency for the reference signal muon at (a) low and
(b) high luminosity


The 7 reconstruction in HLT is optimized with SUSY channels (e.g. A/H -

r+r- and H -- rv). In hadronic decay mode of 7, a narrow jet containing

relatively small number of charged or neutral hadrons can be used for

its identification (Fig. 3-11). For example, about 91,-. of the 7 energy is

contained in 0.15-0.2 cone and about 'I-' in 0.4 cone.









LvI-2 -C-jet axis
signal cone F
signal cone R.t t


P p

Figure 3-11. Principle of T-jet identification algorithm


At Level-2, the calorimeter based selection is performed to look for narrow jet

in a 0.13 cone and define an isolation region of 0.4 cone. The selection can be

further tightened by pixel (track) isolation in Level 2.5 (3).

* b-jet identification relies on track impact parameter. The impact parameter

is signed as positive if Q is upstream of V in the jet direction and negative

otherwise. The tag makes use of the track impact parameter significance,

which is defined as the ratio between the value of the impact parameter and

its error. The b- .--i:.-: criterion normally is: minimum number of tracks

exceeding a given threshold on the impact parameter significance (Fig. 3-12).

track


linearised S
track
minimum
"i.p. \distance jet

V Q

Figure 3-12. The b-j ._._--i.i algorithm


* Jet reconstruction is primarily based on an iterative cone algorithm starting

from a seed which corresponds to the tower with the highest ET in the list.

Then a "proto-jet" is established and an iterative process is used to add

more tower to the jet and continuously update the direction of "proto-jet"










through the constituent of the towers in the cone. The process terminates

until a cutoff criterion is satisfied (the iteration reaches 100, the change of jet

direction in qr-Q is small enough, or the change of jet energy is small enough).

SThe missing transverse energy (Epmiss) is reconstructed by a simple vector

sum of all calorimeter towers with a 500 MeV threshold. The HLT Episs is

combined with one jet selection. Fig. 3-13 shows the Ep'is rate with various

jet ET selection threshold at low and high 1-iiiiiii; -;i [28, 29] respectively.

105 105
104 10 A
A : : : : : : A

S103- A 103 000 A
SA no jet cut A no jet cut
102 A ^ O 1 jet > 50 GeV g 2 o O 1 jet > 50 GeV
O0 A 1 jet > 80 GeV A O 1 jet > 80 GeV
10 0o I jet 140Ge\ 10 6 0 I jet 140e\
0o A ['*
1 *-o 1 i i .
1 ,^ -1 6
10 DOAA 10
-12 0 -2
1 10 OO
103 10
10 1-40 n 1-4
10 i i I i
1-5 10
0 50 100 150 200 250 300 0 50 100 150 200 250 300
missing E, (GeV) missing E, (GeV)
(a) (b)

Figure 3-13. Efficiency of three isolation algorithms on the reference background
as a function of efficiency for the reference signal muon at (a) low and
(b) high luminosity


It is observed that the jet selection cut is redundant for EpTss HLT with

E"pss > 120 GeV at low luminosity, because the rate with various jet

thresholds give almost the same as the inclusive ETiss rate without jet cut.

This is also observed for ETiss HLT with ETiss > 160 GeV in high luminosity.

After the DAQ TDR was finished in late 2002, there were further development

of the reconstruction for most of the fundamental objects (e.g., the reconstruction

of missing transverse energy, b-t ,-.-ii:- ... which were implemented later). But most

of the fundamental algorithms remain almost the same. For the physics analysis,






36


it is generally necessary to be further optimized with respect to a given analysis

topic in order to get better efficiency and performance.















CHAPTER 4
JET ENERGY DISTRIBUTION AND CORRECTION STUDY

The measurement of jet is one of the i ii' ,r tasks of the C \!S calorimeter

[30, 22] to explore the new physics at LHC. The cone algorithm iterativee or simple

cone) is widely used for the jet reconstruction of hadron collider.

The basic algorithm of iterative cone searches the maximum transverse energy

reconstruction object (e.g., the calorimeter tower, tracks, or the generated particles

that the jet reconstruction algorithm is used against) and throws an rl-Q cone

around its direction. Any object within the cone will be merged to form a proto-

jet. The proto-jet direction is calculated from the weighted energy direction of

the constituents, and a cone in rT-Q is thrown around the new direction to form

a new proto-jet. The procedure is repeated until the proto-jet does not change

significantly between two iterations (AET < 1 by default) and (AR < 0.01 by

default, where AR = /AL2 + A2). The constituents are removed from the list of

objects and the same algorithm will be used to search for new jets. For the detector

reconstruction, normally this process starts from the highest ET tower from the

calorimeter.

The simple cone algorithm in this analysis uses the jet axis from the iterative

cone algorithm (with 0.6 cone size), the cone size used for simple cone algorithm is

changed according to the need. All the objects within the predefined cone size will

be merged to form a jet. The constituents are removed from the list of objects,and

the procedure is repeated until no objects are left in the list. This procedure is

different from the generally defined the simple cone algorithm that directly uses a

highest ET tower in a region as the jet axis. Obviously using the highest ET tower









as the jet axis may cause bias and deviation to the optimal jet axis due to the jet

energy distribution might not be symmetric around the highest ET tower.

There are several reasons why the cone algorithm will continue to p1 i an

important role in LHC physics reconstruction:

Cone jets have a standard shape, which is clearly defined by its axis and

cone size. The cone size is a sensitive and easily tunable parameter for

reconstruction and analysis purpose. The reconstruction and selection

criterion in the algorithm is simple and robust.

Cone jets provide a consistent view in T]-Q space between different reconstruc-

tion scenarios. Various detector objects (e.g., track, tower, and lepton) or

generator objects (e.g., parton and final state particle) can be associated to

the same jet by their direction. This is a non-trivial factor when developing

the jet correction for the missing transverse energy (Ess) or other high level

offlinee) reconstruction and correction techniques.

Some abstract and advanced jet quantities can be easily built from cone jets

(e.g., energy distribution and second moment based on the distance of jet

constituent to axis).

The linearity of the average jet energy scale and energy resolution are two

critical quantities to evaluate the performance of the jet reconstruction and

correction. The generated jet energy scale is restored by using average detector

response, for a better quality, which can be characterized according to different

reconstructed jet ET ranges and calorimeter Tr ranges. Several calibration methods

using the similar principle have been studied in C'\!S [31, 32, 33]. In order to

improve the jet energy resolution, we need not only optimize the jet reconstruction

algorithm, but also solve two critical issues:

A correction algorithm need manifest the physics correlation between

generator particles and their detector response through more complicated









parameterization other than solely based on the reconstructed jet ET. The

ET error is mainly caused by the stochastic effect of the calorimeter response.

For reconstructed jets from a given ET, the variation to their corresponding

generator level jet PT will not be corrected by a simple re-scaling coefficient.

So the resolution factor will be kept wherever ET is used and transformed

in higher level reconstruction or analysis. This is the fundamental reason

why the calibration method based on ET will not naturally lead to a better

resolution of the measured jet energy. In later section, this will be discussed

in detail.

The detector jet constituents (e.g., track, tower, vertex, and readout from

several calorimeter l1.Vr-i) provide important information of how to correct

jet energy from each single event. An event-based jet correction (e.g.,

track correction of jet [34, 35, 36]) requires the algorithm to handle more

complicated details of jet constituent in addition to an overall jet ET.

The motivation of this study is to develop a new event-based method to

calibrate and correct jet energy, which is built on the parameterization of jet

energy distribution using fine granularity of C'\ IS calorimeter that allows the

measurement of incident energy deposit around the reconstructed jet axis. This

approach contains the jet energy distribution reconstruction, correction function

parameterization, fitting and performance analysis.

4.1 Data Samples

The analysis is performed under the full detector simulation and reconstruc-

tion. QCD di-jet events are used to study the jet energy correction with PT ranging

from 20 to 600 GeV/c. The datasets with number of events used for this analysis

are listed in Table 4-1. The inning of jet PT is primarily to reduce the computing

time of detector simulation to cover a wide jet PT range. Similar configurations of

event samples were used in other jet and E'iss studies [31, 28]. This configuration









inevitably causes the distortion of the spectrum near the beginning and ending re-

gion of each bin, because the detector jet ET spectrum is a result of the convolution

of the detector response function (a Gaussian-like distribution for a given measured

jet ET) with the generator jet PT spectrum. Near either edge of the bin, the impact

of events from contiguous bin is neglected due to the selection cut in the generator

level.

PYTHIA [37] implemented in C \ I 1IN [38] is used to generate the events with

p.d.f.(CTEQ7). The effects of initial and final state radiation, hadronization and

multiple parton scattering are included. Major configuration parameters with their

values are listed in Table 4-2.

OSCAR.2.4.5 [39] (based on GEANT4) is used for C\ detector simulation.

ORCA.8.6.0 [40] is used for the reconstruction and analysis. The configuration of

calorimeter thresholds and noise levels in the simulation and reconstruction is listed

in Table 4-3. The events are pileuped with average 3.5 minimum bias events which

corresponds to the low luminosity (L = 2 x 1033cm-2s-1) at LHC.

Table 4-1. Cross section and number of events QCD di-jet data samples with dif-
ferent jet PT

Jet Pt Range Cross Section (pb) Number of Event
20-30 7.819 x l0 50,000
30-50 1.849 x l0 50,000
50-80 2.433 x107 100,000
80-120 3.359 x106 100,000
120-170 5.654 x105 100,000
170-230 1.163 x105 100,000
230-300 2.812 x104 100,000
300-380 7.848 x 103 100,000
380-470 2.396 x 103 100,000
470-600 9.249 x102 100,000
600-800 2.038 x102 100,000
800-1000 3.562 x101 50,000
1000-1400 1.075 x101 50,000









Table 4-2. The configuration of PYTHIA event generation (used ( ". i. wide in
-, :-2004)


Parameter and value Explanation
Physics process (' IEL = 1) -qq/ /qq i
Fragmentation (MSTJ 11 = 3) Hybrid scheme with treating light
and heavy flavors .- ..: Iely
Running alphaS (MSTP 2= 1) First Order
Structure function (. S'TP 51 = 7) CTEQ7
Structure of multiple interaction various impact parameter and hadronic matter
( :STP 82 = 4) overlap in double Gaussian matter distribution
Tl.. pt cut, matter distribution Pythia default
power of energy-rescaling term

Table 4-3. The configuration of calorimeter threshold and noise level in detector
simulation

Parameter Barrel F:1. i Very forward
ECAL digi threshold 90MeV 450MeV
ICAL digi threshold '*V :, i. -V V'. ,V
"..;-. level in ECAL 40MeV 150MeV
.,: .. level in IICAL 0.6 10-3 GeV 0.6 10-3 GeV 0.6 10-3 GeV


4.2 Definition of Jet Energy Resolution

The jet energy calibration means using a scaling factor to adjust the measured

jet ET. The outcome is to make the average detector jet ET consistent with the

generator jet PT, so as to achieve the unit detector response. The jet energy

correction concentrates on reducing the variation of energy measurement error

between the generator and detector level, so it mainly aims at resolution factors.

In order to eliminate the ambiguity of several repeatedly used concepts in the

context, we make following definitions of three types of jet energy resolution which

are used in the calculation and discussion:

1. Absolute resolution (rEt): the standard deviation of measurement error

between the detector jet and corresponding generator jet. rEt ignores the

effect of average detector response instead focuses on the variation of energy









error, because a proper jet calibration can recover the linearity of average jet

energy scale in a good precision.

Fig. 4-1 illustrates several calibration methods and their performance on

JEt using a selected jet sample. In a simple method that jet ET is shifted

by 24.59 GeV, a value coming from the average difference between the

generator level jet PT and detector level jet ET, the JEt is almost unchanged.

In another method, an inversed detector jet response (normally this value is

'i.-._--r than one) is multiplied to the detector jet energy, which also recovers

the linearity of average detector response, still no improvement of JEt is

observed. By using the correction method developed in this study, the error

is reduced at ~ 10'1. Above examples show the jet calibration does not lead

to the reduction of GEt, that is why we need to develop dedicated jet energy

correction method.

2. Ideal relative resolution (ar): the standard deviation of the ratio of the

detector jet energy to the original generator jet energy. Similar to absolute

resolution, it only shows the effects of variation of detector measurement, so

it is an "ideal" jet resolution based on generator jet energy. This quantity is

ah--,i-i used after jet calibration is applied so that an unit detector response is

established.

3. Relative resolution (uR): the standard deviation of the ratio of the jet

energy error to the detector jet energy. JR is widely used in many detector

performance studies, which shows the overall effect of the correction (Fig. 4

2).

For evaluating the jet correction, it is very important to show the improve-

ment of JR together with JEt and Jr, and check the performance on the

linearity of the corrected jet energy response (performance of calibration).





















(a) (b)


AE (GeV) AET (GeV)
(c) (d)
Figure 4-1. Absolute Jet Energy Resolution (-Et) in QCD events with PT from 180
to 200 GeV/c: (a) raw jet with oEt = 14.67 GeV, (b) corrected jet by
energy distribution (explained in later section) with oEt = 13.54 GeV,
(c) corrected jet by shifting the jet energy with oEt = 14.97 GeV, and
(d) corrected jet by a scaling factor with oEt = 15.03 GeV

Various jet calibration and correction methods have different performance on

those resolution quantities. In a more general discussion, it is possible for a method

to achieve better TR while worsening aEt. This normally relates to the case that

restoring the average scale is more important than reducing the variation of the

measurement error. In both cases, the relative resolution of corrected jets might be

improved, but '1 -.- result in different performance in higher level reconstruction.

For example, the E'p1ss reconstruction in some ]p!. -i final states gains little in

jet calibration because the oEt is not improved. A clear understanding of all the






















(a) (b)


Figure 4-2.


AET/E, AE/ET
(c) (d)
Relative Jet Energy Resolution (aR) in QCD events with PT from
180 to 200 GeV/c: (a) raw jet with OR of 8. ", (b) corrected jet
by energy distribution (explained in later section) with aR of 6.1 '.,
(c) corrected jet by shifting the jet energy with aR of 7. '", and (d)
corrected jet by a scaling factor with aR of 7.3 1'


important aspects of jet resolution is crucial to develop and apply jet correction to
Emiss

4.3 Jet Energy Distribution

4.3.1 Calorimeter Response

The (' !S calorimeter geometry and granularity is described in ('!i li' r 3.

The jet energy calibration and correction need to cope with two major systematic

detector effects: the detector response non-linearity and the rl dependency of jet ET

resolution. The ECAL and HCAL have different responses on electrons, photons,

and hadrons [41]. This is the major source of the non-linearity. The stochastic









detector response is the i i, ji" source of the variation of the measurement which

relates to the detector intrinsic resolution. Other detector effects also deteriorate

the jet energy resolution, such as out-of-cone tracks deflected by magnetic field,

low PT particles stopped by tracker materials, non-uniformity of pileup energy from

minimum bias events and electronic noise. Several methods have been developed

to correct specific factors [32, 34, 35, 36]. But the limit of jet energy correction is

mainly determined by calorimeter intrinsic resolution.

4.3.2 Parameterization of Jet Energy Distribution

Quantitatively measuring and evaluating the jet energy distribution is a key

factor of the correction algorithm. A framework of dividing t]-Q space that circles

around the jet axis into several rings is developed. The radius of the rings are set

for 0.2, 0.4, 0.6, 0.8, and 1.0 respectively. Each pair of two .,1i i,.ent rings covers

a region, so as to calculate the energy quantities. Jet constituents are calorimeter

towers of a size which is the same as that of HCAL tower. The energy of ECAL

- i -1 i- is added to corresponding tower according to its T] and Q. The distance

from the center of the tower to jet axis, defined as AR = /AVy2 + A2, is used to

assign the tower within jet 1.0 cone to a specific region.

Two schemes are used for parameterizing the jet energy distribution:

SUsing the fraction of the sum of transverse energy in a region to the total

transverse energy in the 1.0 cone. In each circular region of radius 0.0-0.2,

0.2-0.4, 0.4-0.6, 0.6-0.8, and 0.8-1.0 around the jet axis, the sum of the

transverse energy in the calorimeter is calculated. From inner most to outer

most, the regions cover the area of 0.1257, 0.3770, 0.6283, 0.8796, and 1.1309

respectively in T]-Q space. Due to the calorimeter granularity, the actual area

of each region in the reconstruction has a small fluctuation with respect to

above ideal values. In the forward region, the granularity gets bigger, which

further influences the accuracy of the measurement.









Fig. 4-4 and 4-6 show the jet energy fraction factor with respect to various

jet PT samples. As expected, the inner region around the jet axis contains

most of the energy. As jet PT goes up, the fraction of energy in the inner

regions will increases. The outer two regions (0.6-0.8 and 0.8-1.0) show very

similar distribution across a wide PT range.

SUsing Second Moment defined by Eq. 4-1. The regions for calculating second

moment is different from the previous scheme, that uses cones of 0.0-0.2,

0.0-0.4, 0.0-0.6, 0.0-0.8, and 0.0-1.0 respectively in the Tl-p space around the

jet axis. Second moment in each region shows the average distance of all the

towers weighted by each tower's transverse energy, which is a good parameter

in describing the jet shape. Although the energy is not explicitly showed in

the final result, they are used for weighting, so it is still a good parameter to

show the energy distribution associated with a jet.


S = S + S (4-1)

where S, and S66 are defined as



S AE A E A.2 (4-2)
2 ETi 2 ETi

where ETi is the transverse energy of a tower.

Fig. 4-7 shows the second moment distribution with respect to different cone

sizes calculated in various jet PT samples. The second moment distribution

is close to a gaussian distribution, which provides a way to evaluate the

fluctuation of the overall jet energy distribution in a fixed cone.
























Energy Fraction


Energy Fraction


Energy Fracton


Energy Fracton


Energy Fraction


Figure 4-3.


Jet energy distribution in QCD samples with various jet PT: (a) 50-80

and (b) 80-120 GeV/c. The energy distribution is calculated from the

ratio of energy in each region to the total energy in 1.0 cone. In each
block of figures, the upper row from left to right corresponds to ratio of

0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row corresponds to

0.6-0.8 and 0.8-1.0 respectively.


Energy Fraction


Energy Fraction


Energy Fraction


Energy Fraction


























E1 n 4 F t E n r FIaco
Energy Fraction


Energy Fraction


Energy Fracton


Energy Fraction


Energy Fracton


Energy Fraction


Energy Fraction


Figure 4-4.


Jet energy distribution in QCD samples with various jet PT: (a) 120-

170 and (b) 170-230 GeV/c. The energy distribution is calculated

from the ratio of energy in each region to the total energy in 1.0 cone.

In each block of figures, the upper row from left to right corresponds

to ratio of 0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row

corresponds to 0.6-0.8 and 0.8-1.0 respectively.


Energy Fraction


Energy Fraction


z 1






o l 02 o3 o o I or l or l
Energy Fraction

























Energy Fraction


Energy Fraction


Energy Fracbon


Energy Fracbon


Energy Fraction


Figure 4-5.


Jet energy distribution in QCD samples with various jet PT: (a) 230-

300 and (b) 300-380 GeV/c. The energy distribution is calculated
from the ratio of energy in each region to the total energy in 1.0 cone.

In each block of figures, the upper row from left to right corresponds

to ratio of 0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row

corresponds to 0.6-0.8 and 0.8-1.0 respectively.


Energy Fraction


Energy Fraction


Energy Fraction


Energy Fraction

























Energy Fraction


Energy Fraction


Energy Fracon


Energy Fraction


Energy Fracton


Energy Fraction


Energy Fraction


Figure 4-6.


Jet energy distribution in QCD samples with various jet PT: (a) 380-

470 and (b) 470-600 GeV/c. The energy distribution is calculated

from the ratio of energy in each region to the total energy in 1.0 cone.

In each block of figures, the upper row from left to right corresponds

to ratio of 0.0-0.2, 0.2-0.4, and 0.4-0.6 respectively, the bottom row

corresponds to 0.6-0.8 and 0.8-1.0 respectively.


Energy Fraction


Energy Fraction


Energy Fracton

















S..(-



/eodMmn


Second Moment

(b)











Second Moment


Second Moment

(C)


01 0 03 04 0 06
Second Moment

(e)










Second Moment


Second Moment

(f)










Second Moment


Figure 4-7. Second Moment in QCD samples with various jet PT: (a) 50-80, (b)
80-120, (c) 120-170, (d) 170-230, (e) 230-300, (f) 300-380, (g) 380-470,
and (h) 470-600 GeV/c. In each figure, the curves from left to right
represents the second moment distribution of cone size of 0.2, 0.4, 0.6,
0.8, and 1.0 respectively.










4.3.3 Jet Energy Distribution Based on Energy Fraction Scheme

Based on Fig. 4-4 and 4-6, the average fraction of the jet energy in each

region as a function of jet PT is showed in Fig. 4-8. The results can be interpreted

as following:









0 .7 .I.......... ................ .............................................................................
0. -


0.7
0 -





S.. ............ ..................... ................... ........... ... ............ ..... ...............


0 100 200 300 400 600 600 700
Jet Pt

Figure 4-8. Jet energy distribution based on the fraction of each region's transverse
energy with respect to total transverse energy in a 1.0 cone as a func-
tion of generator jet PT. Regions are defined by 0.2 cone (square), 0.4
cone (triangle-up), and 0.6 cone (triangle-down)


There is an apparent non-trivial dependency of the average energy fraction in

each region on the generated jet PT. For each jet, its generated PT is not only

manifested in the measured jet ET, but also in the energy fraction.

The smallest radius ring contains most of the energy, so it 1pl ,i- a crucial role

on the overall jet energy resolution. While the further away the region from

the center, the larger the rl-Q area it covers with less energy density. In the

outer region, the energy deposit is more coming from detector effects (e.g.,

pileup and electronic noise) instead of the generated jet. As a result, the

energy fraction contains critical information of how various detector effects

influence the jet.









For those generated jets of a given pT, there is fluctuation in the energy

fraction in fact, which is mainly associated with the stochastic jet energy

response and traverse size of the hadronic shower. Other detector effects and

several generator level physics factors (e.g., jet fragmentation, initial and final

state radiation) contribute to the fluctuation too.

4.3.4 Jet Energy Distribution Based on Second Moment Scheme

The second moment distribution is not a Gaussian (Fig. 4-7). The tails and

the .,-vmmetry of the distribution can be explained by complicated detector effects:

One factor is the energy deposit of pileup and underlying events, which is

approximately equally distributed inside the jet cone so as to enlarge the

second moment. This effect is more apparent in large size cone, since the jet

energy from fragmentation and hadronization is more centralized. (We should

note that the average pileup energy is a function of T] across the full detector

coverage, but this effect is small in a relative small region.)

The magnetic field distorts the second moment as well, because low PT

charged tracks are deflected away from the center to the vicinity region (or

become loopers for very low PT charged particles). This effect can be seen in

the low PT jet, the loss of the low PT charged particle from the reconstructed

jet cone causes a low side tail. But on the contrary, for high PT jets with

large cone size, the deflected tracks are still in the reconstruction cone, so its

second moment are enhanced by this effect.

The non-compensation calorimeter response is the third reason of the

distortion of the second moment distribution, because the detector response

is characterized by the energy of hadrons instead of their transverse energy

which leads to different responses between the central and forward region.

The peak position and FWHM (full width at half maximum) of second

moment fitted by a convoluted Gaussian and Landau distribution are used to study










the analytical dependency of second moment on the jet PT (Fig. 4-9 and 4-10). To

some extent, previous discussion about the energy fraction can be applied to second

moment too.


0.6


0 40.4 4 ... .. .. .. ..
|035 -
0
2 0.3
0.26
S0.2
0
0.16 ..


0.05
0 .0 6 ................... ....................... ......................... ................................................. .......................

0 100 200 300 400 500 600
Jet Pt

Figure 4-9. Peak position of Second Moment of 1.0 cone (open square), 0.8 cone
(open circle), 0.6 (triangle-down), 0.4 (triangle-up), and 0.2 (close
square) as a function of generator level jet PT



4.3.5 Correction Potential and Sensitivity

As mentioned earlier, non-trivial correlations between parameters of both

schemes and jet PT are observed (Fig. 4-8, 4-9, and 4-10). For measured values of

those parameters, it is possible to predict jet PT and to be used to make correction

on the measured jet ET. This is the 1 i i' mechanism how the energy distribution

can be factorized and used for the jet energy correction.

Due to the fluctuation of the generated jet shape and the detector response,

the measured jet energy distribution contains significant uncertainties. A number of

jets can be used to find the best correlation between the generated jet PT and jet

energy distribution factor. This is part of the fitting process in order to derive the

jet energy correction functions (will be discussed in the later section).



























Figure 4-10. FWHM of Second Moment of 1.0 cone (open square), 0.8 cone (open
circle), 0.6 (triangle-down), 0.4 (triangle-up), and 0.2 (close square) as
a function of generator level jet PT


A similar sensitivity of the parameters from both schemes to the jet PT is

observed (the changes of the values of the parameters are in a similar range as jet

PT changes from 20 to 600 GeV/c), indicating the similar performance in the jet

energy correction of both schemes. Results in the later section are consistent with

this finding. The further improvement of the correction algorithm partially depends

on whether other more sensitive parameters (schemes) can be invented.

We restrict this discussion from further quantitative evaluation of jet energy

distribution factors since the results are sensitive to the details of the simulation

(e.g., setting of electronic noise and detector response). Other physics aspects of
event generation also have big influence (e.g., initial and final state radiation, frag-

mentation and hadronization model). Ultimately the experimental measurement of

jet energy distribution will help reach a better understanding of the whole issue.









4.4 Correction Method

4.4.1 Jet Reconstruction

The correction algorithm is designed based on the comparison between the

generator and detector level jet energy. But the same algorithm can be built

on purely experimental data (e.g., using Z plus one jet or photon plus one jet

events). In those channels, Z or photon PT can be accurately reconstructed which

is balanced by jet PT in generator level. This approach will be quite useful in the

realistic jet calibration and correction without using the Monte Carlo after LHC

taking data. The relevant analysis is under a separate study.

The generator and detector jets are reconstructed first by iterative cone

algorithm implemented in ORCA Jets subsystem [42]. The configuration of the

algorithm is: 0.6 of cone size, 1.0 GeV of seed ET cut, and Lorentz 4-vector

of recombination scheme. Then simple cone jets with various cone sizes are

reconstructed based on the fixed jet axis from previous step. The analysis of jet

correction is developed from matching the generator jets to detector jets by their

axis in a 0.3 cone.

The difference in the performance between iterative cone and simple cone

algorithm is small. Fig. 4-11 shows the ratio of the jet energy of various simple

cone size to that of 0.6 iterative cone. The 0.6 simple cone jet almost contains the

same amount of transverse energy as 0.6 iterative cone. A double gaussian fitting

is performed on Fig. 4-11(c). The result is showed in Fig. 4-12. The left peak well

centering on 1.0 shows the good matching of two cone algorithms. The effect of

iterative selection results in the width of the peak. The right peak is overlapped

with the left one with the same width, mainly due to the effect of the HCAL

granularity on the iterative selection. In general, the difference in the jet energy

from two algorithms are within a few percent. In the rest of the discussion, simple

cone algorithm is used to study the energy resolution and other related quantities.






























1200 1


k I


Figure 4-11.


3500

3000 -

2500 -

2000 -

1500 -

1000 -

500
I


Energy ratio of simple cone jet with various size to that of the 0.6

iterative cone jet. The simple cone jets are built upon the axis from

iterative cone jet. Various cone sizes include (a) 0.2, (b) 0.4, (c) 0.6,

(d) 0.8, and (e) 1.0.


6000

5000

4000

3000 -

2000 -

1000

o o o


1 12 4 atio
Ratio


Ratio


Ratio
























Ratio


Figure 4-12. Fitting of Fig. 4-11(c) by using double gaussian distribution


4.4.2 Correction Function

In this study jet energy correction functions take following forms:

1. Based on energy distribution inside the 1.0 cone (we call "Energy Distribu-

tion Correction" or "ED Correction").

5
Et'o = Eti(a, + bAR, + cRR2) + (ao + boEto + coEt) (4-3)
i=1

where the correction sums over all the regions around the jet axis. Eti is the

total transverse energy in region i. Eto and Et' are the uncorrected and

corrected jet transverse energy. ai, bi, and ci are the correction parameters to

be fitted with data. Ri is the fraction of energy in region i defined as


Et,
Ri t (4 4)
Y: Eti

2. Based on second moment inside the 1.0 cone (we call "Combined Second

Moment Correction" or "CSM Correction").

5
Et'o = Et(ai + biSi + ci S) + (ao + boEto + coEt) (4-5)
i=1


where Si is the second moment in region i.









3. Based on overall jet energy with less parameterization (We call "Benchmark

Correction"). It contains no information of energy distribution, so it is mainly

used for comparison with first two methods that have more parameters and

use energy distribution factor around the jet axis.


Et' = ao + boEto + coEt0 (4-6)


Following is some explanation why those parameterization is used

Benchmark Correction is the basic parameterization taking into account the

detector response with respect to the overall jet energy, which is mainly the

first order correction via quadratic term for the non-compensation detector

effect. Other types of Benchmark correction with different orders of correction

are tested (Eq. 4-7 and 4-8).


Et' = ao + boEto (4-7)


Et'o = ao + boEto + coEt + doEt3 (4-8)


The resolution of corrected jets are almost kept same for those correction

functions with different order of Eto (Fig. 4 13). It shows the overall lim-

itation of the correction function which is solely based on Eto (with small

improvement on resolution) and the insensitivity of the resolution to the

orders of Eto. This fact will be clearer in later section that the Benchmark

Correction is mainly a calibration function and has less capability of reducing

the variation of the measurement error (aEt).

The introduction of new parameters in Energy Distribution Correction and

Combined Second Moment Correction takes the similar form as Benchmark

Correction in order to maintain the correction in the same (or higher) order.























































Figure 4-13.


AE,(GeV)


Jet energy resolution from various Benchmark parameterizations: (a)
raw jet with (Et = 10.92 GeV, (b) corrected jets based on two pa-
rameters Benchmark Eq. 4-7 with (Et = 10.8 GeV, (c) corrected jets
based on three parameters Benchmark Eq. 4-6 with (Et = 10.77 GeV,
and (d) corrected jets based on four parameters Benchmark Eq. 4-8
(Et = 10.77 GeV. The results are based on jet sample with PT ranging
from 80 to 120 GeV/c.









* The parameterization of Energy Distribution Correction in each region is

built on the fraction of transverse energy to the total transverse energy

of 1.0 cone. The second bracket term in Eq. 4-3 is similar to Benchmark

Correction, which represents the overall jet energy correction factor.

* Eq. 4-3 can be written as
5
Et' sumE(aiRi + biR2 + cR3) + (ao + boEto + coEt) (4-9)
i= 1

where sumE is defined as




sumE = Et (4-10)


In above expressions, the correction based on the energy distribution is

explicitly manifested by factorizing the energy fraction in various regions

associated with a jet axis and making correction to jet energy which is inside

a 1.0 cone.

In fact there is no restriction on how Eto is calculated. This method can be

applied to non-standard or cone-based jet algorithms (e.g., Kt jet algorithm

[55]). The physics correlation of the first summation term and second overall

jet correction term in Eq. 4-3 and 4-9 is the basis for why correction take

effects.

* The parameterization of Combined Second Moment Correction in Eq. 4-5

can be revised as follows:
5
Et'o sumE(aiRi + biRiSi + cRS) + (ao + boEto + coEt ) (4-11)
i= 1

which clearly shows that the parameterization actually combines the fraction

of energy and second moment in each region. This parameterization can be

generally regarded as a combination of the energy distribution and jet shape.









In a summary, a comprehensive approach is developed by factorizing the jet

energy fraction and second moment into the correction functions. The parameteri-

zation is based on a predefined cones around the jet axis.

In the implementation of the algorithm, the jet energy distribution is measured

within a 1.0 cone around the jet axis because we want to study its performance

on various cone sizes. For the QCD sample, most of the high ET jets are widely

separated (e.g., two highest ET jets in the detector level are close to back-to-back

in p). But in some physics channels with copious jets in the final state (e.g., Top

pair events), it is reasonable to reduce the largest cone size or only use 3 or 4 cone

regions to parametrize the jet energy distribution. This is feasible because the

energy distribution in outer two regions is very similar which means that these are

less impacts on the correction results.

The overlapping of jets will definitely cause the abnormal deviation from

normal energy distribution and the failure of the correction. Related issues are

discussed in next section. The mis-identification of jets from electron, photon

or isolated hadron will also cause abnormal deviation in the energy distribution.

Obviously the energy distribution can be further developed to a powerful tool to

reject those faked jets.

4.4.3 Fitting of the Correction Function

Least square fitting method is used to minimize the quantity defined by

Eq. 4-12 to get the optimal value of the parameterization (the physics correlation

between the energy distribution and jet are also expressed by this parameterization

as a fitting result):


(E E)2 (4-12)

where Ec is the corrected jet transverse energy, Eg is generator level jet transverse

energy, the sum runs over all the input events. The fitting is performed in every PT









range with respect to corresponding data sample. The correction on 5 different

cone sizes of jet (0.2, 0.4, 0.6, 0.8, and 1.0) are tested. The same cone sizes are used

to reconstruct and match the generator jet to detector jet.

In order to get better performance for the correction function, it is possible to

further split the measured jet ET range in each bin into several intervals, because

a single set of parameters will not work well spanning on a large PT range, and

low PT and high PT jets are very different in shape, size and energy distribution.

The calorimeter response in different energy regions is non-linear, which also favors

more inning. But practically it is very difficult to make too small and many bins

because of the amount of work. In this study, the same PT schemes based on event

generation of the data samples is used for correction of detector jet ET.

Jet response is rT dependent, so the correction must be performed in a reason-

able calorimeter acceptance range. In this analysis five Tr bins of 0-1, 1-2, 2-3, 3-4,

and 4-5 are used to classify jet according to the TI of jet axis. Smaller bin size has

been tested with showing less improvement in the correction. This is because a 1.0

cone is adopted to factorize the energy distribution, which makes the correction

algorithm less sensitive to the very small bins for r1.

4.5 Results and Discussion

The correction is first performed on each data sample and then concatenated

together to build a full spectrum from 20 to 600 GeV/c, because of the nature of

event data samples.

The performance of the jet energy correction for the detector acceptance

range ofI r 1< 3.0 (central region) and | 1 |> 3.0 (forward region) are discussed

separately. Although a good improvement of resolution in forward region is

achieved, in this study we mainly focus on central region, because

The granularity of calorimeter tower is smaller in the central region. It is

appropriate to use current scheme based on various cones around the jet









axis to establish the parameterization for energy distribution. In the forward

region, the coarse granularity potentially favors a scheme that directly use

tower geometry instead.

A 1.0 cone is used to reconstruct the jet energy distribution. For jet Ir,] >

4.0, a complete energy distribution factor can't be built. So the comparison

between the central and forward region is less instructive.

The results also show the performance of ED Correction and CSM Correction

is very close, so we mainly present the results based on CSM Correction.

4.5.1 Jet Energy Response in the I| ] < 3.0 Region

The linearity of the jet energy response is recovered after the correction.

Fig. 4-14 and 4-15 show calibration results based on QCD samples with PT from

20 to 300 GeV/c and 5 cone sizes of jets respectively.

The raw jet energy response concatenated from different PT ranges is not

continuous, because of binned samples and the distortion of the jet PT spectrum.

The selection cut of jet PT for each bin causes the bias of the average detector

response: too low in the left side and too high in the right side. To use binned

QCD samples to estimate a continuous jet PT spectrum and detector response is

not the main focus of this study. Normally in the central region of each bin, the

detector response is less biased, so it can be used to predict a continuous spectrum

from a number of binned samples. After the correction, the linearity of jet energy

response with less than 1 error is obtained.

Using a continuous jet PT sample can eliminate the effects of distorted jet

spectrum, but this is a big challenge in the event generation and full detector

simulation, because the cross section increases quickly as jet PT goes down, so a

very large number of QCD events need be produced in order to get a reasonable

statistics for high PT jets. In this study, results show the jet energy correction

works well even in the binned sample.










Fig. 4-16 shows the performance of jet energy calibration calibration in a

single data sample with the generator jet PT from 170 to 230 GeV/c. In general,

Energy Density (ED) Correction or Combined Second Moment (CSM) Correction

provide better linearity than that of Benchmark Correction.



%.A------------------------------ ~ ~ k~kaIM t* I ---------------I


0 . .. . .09 .. .5. .. .


05 1 : : I :
1 0D .. ..... ... ...... ..... ................... . ...................... ...................................... ......................... ...................................................
SI I I | If .



50 100 150 200 250 300 5 100 150 200 250 300
Jet Pt JetPt

(a) (b)

Figure 414. Jet energy response before (triangle-down) and after (triangle-up) the
correction with 0.2 cone: (a) based on correction of energy distribu-
tion and (b) based on benchmark correction


4.5.2 Jet PT Spectrum in the I| 1< 3.0 Region

Fig. 4-17 shows the performance of the correction on the jet pr spectrum. ED

Correction and CSM Correction recover well the generator jet pr spectrum (Fig. 4

17(b)) from the raw detector spectrum (Fig. 4-17(a)). Benchmark Correction is

lack of the parameterization to restore the generated jet pr spectrum and causes

discontinuity when merging several jet ET spectrum from different r regions. The

spectrum from ED and CSM correction shows good consistency with the generated

one. The better performance mainly benefits from the non-constant and non-linear

terms and more parameterization in the correction functions.





















































50 100 150 200 250 300
Jet Pt


(a)




115 -- --------










0ii








Jet Pt
50 1D0 150 200 250 3DD
JetPt


(b)


12

115 -
1 1 -......T ........... .... ......................... ...................... ....................... ....................... .................

10 ... .. ..... ............... ............. .................. ......................................................................



08
- : I : I











50 100 150 200 250 300
Jet Pt


Figure 4-15. Jet energy response before (triangle-down) and after (triangle-up) the

correction based on second moment: (a) 0.4 cone, (b) 0.6 cone, (c) 0.8

cone, and (d) 1.0 cone


i i*


v T V V TvV
S . .. . .


i. ----- - -. ..- - .- ....


. ....




08 y





S .- .. 0. .. .. .. .. ..

50 1o 1i 200 250 3A


0
C
0
Q1
0
U
Q!














0 .. .. ... ... .. ... ... ... .... . .... ... . . .. . 1. ...... .......... .. ........................ .. ................... ................... ..................


0 9 ... .. ...........................................................09... . .. ...... ... ......... ..... ... ... ........ .. ..
A0 . 0
01 : : w T : : T

0 ...... ... ............_.. .... .... ....... ..
: T i i i i i T : I i i
160 180 200 220 240 260 280 io3 10 110 200 220 20 260 280 300
JetPt JetPt

(a) (b)

Figure 416. Jet energy response before (triangle-down) and after (triangle-up)
the correction: (a) based on correction of energy distribution and (b)
based on benchmark correction.


4.5.3 Jet pT Resolution in the I rl < 3.0 Region

Results of the absolute resolution (aEt) and relative resolution (uR) for

different cone sizes as a function of the generated jet pr are showed in Fig. 4 18,

4-19, 4-20, 4-21, and 4-22.

Very small improvement of jet (Et is achieved after Benchmark Correction,

which means its effects on (R mainly come from calibrating jet pr. CSM Cor-

rection reduces the uEt at roughly 10'. across the whole pr range from 20 to 600

GeV/c, which contribute to the improvement on (R in addition to calibrating the

jet PT. The higher the jet PT, the more important effects can be seen from uEt,

because jet energy response is closer to unit for high energy jet which partially

suppress the effects of calibration.

In low PT region (below 30 GeV/c), gluon jets from initial and final radiation

from hard scattering distort the jet spectrum. A proper ii Jl.-i.- of low PT jet needs

to differentiate the condition of whether additional high pr jet is presented in the

same event, or whether some method can be developed to roughly select the gluon

jet and quark jet.
























Jet Pt (GeV) Jet Pt (GeV)
(a) (b)


Jet Pt (GeV)


Jet Pt (GeV)
(d)


Figure 4-17.


Jet Pt (GeV)
(e)

Jet PT spectrum before and after the correction in QCD sample with
selected raw jet PT ranging from 170 to 200 GeV/c and Irll < 3: (a)
raw jet, (b) generator level jet, (c) corrected jet based on second mo-
ment, (d) corrected jet based on energy density, and (e) corrected jet
spectrum based on benchmark correction








































0 100 200 300
Jet Pt (GeV/c)


100 200 300
Jet Pt (GeV/c)


Figure 4-18. Jet energy resolution of 0.2 cone: (a) absolute resolution and (b)

relative resolution with raw ret (open circle), benchmark correction

(triangle-down), and correction based on second moment (triangle-up)


100 200 300 400
Jet Pt (GeVlc)


I oi i
02 o i



S. . .. .
0 I I I


00, ...... .. .


S100 200 300 400
Jet Pt (GeV/c)


Figure 4-19. Jet energy resolution of 0.4 cone: (a) absolute resolution and (b)

relative resolution with raw jet (open circle), benchmark correction

(triangle-down), and correction based on second moment (triangle-up)


30 ..... . . .. ........ .. .... . .



20 A.


A ... i i



: I .
^*r i --r r


002 6 .................... ... ........... ........................ ........................ ....................... ...................








i :: o


30 .... ......







I





-0 ............... ......... ..... ........... .. ....
.' I
~l '. '. '. .


400 500 600


400 500 600


500 600


500 600









































100 200 300 400
Jet Pt (GeV/c)


Figure 4-20. Jet energy resolution of 0.6 cone: (a) absolute resolution and (b)

relative resolution with raw jet (open circle), benchmark correction

(triangle-down), and correction based on second moment (triangle-up)


0





A,

01 0

* I,
0

0 l



II,,I I.
0 1 ... 1 ...... ............. ............ ............ ..........


100 200 300 400
Jet Pt (GeV/c)


Figure 4-21. Jet energy resolution of 0.8 cone: (a) absolute resolution and (b)

relative resolution with raw jet (open circle), benchmark correction

(triangle-down), and correction based on second moment (triangle-up)


SS





9 '
S. . .. .. . : . .




S.. . . . . . .


03



0 2 ............. ........................ ................................................ ........................ ....................

I
015
0 A1




10
1 i


S100o 200 300
Jet Pt (GeV/c)


i
0:








0. .4 ..................|............. ... .. .........
i A ..... ; ... .... I.. ......... ....


S1o 200 300 400
Jet Pt (GeV/c)


400 s00 600


500 600


500 600


500 600













0 A i0
2 . . . . ... . . .
i o i :,
: 0I 2 i i
2 0 6 i .......0 ;... ... .. . A.







(a) (b)

Figure 4 22. Jet energy resolution of 1.0 cone: (a) absolute resolution and (b)
relative resolution with raw jet (open circle), benchmark correction
(triangle-down), and correction based on second moment (triangle-up)


OR of various cone sizes is fitted with Eq. 4 13. The fitting results of raw jet
and corrected jet by CSM Correction are .1 . in Table 4 4.
S | | . ....... 7 4. ........ ...... .. .. ........


0 100 200 30 4D00 00 00 i0 100 200 3DD 410 600 G00
Jet Pt (GeV/c) Jet Pt (GeV/c)






( (413)


FigureTable 422. Jet energy resolution in .0 cone: (a) absolute resolution and (b)
relative resolution with raw jet (open circle), benchmark correction
(triangle-down), and correction based on second moment (triangle-up)


jR of various cone sizes is fitted with Eq. 4-13. The fitting results of raw jet

and corrected jet by CSM Correction are ili- I1 i .-' I1 in Table 4-4.


)2 -a2 + b )2 + )2 (4-13


Table 4-4. Jet energy resolution in Ir]\ < 3.0 region


Cone size Raw jet Corrected jet
0.2 0.0584 E(0.784/E-) E(4.367/Et) 0.0417 (0.669/ET) (2.763/Et)
0.4 0.0387 (1.007/ Et) (7.243/Et) 0.0278 (0.813/Et) (3.770/Et)
0.6 0.0421 E(0.907/ET) (4.648/Et) 0.0172 E(0.894/ET) (1.971/Et)
0.8 0.0274 E(1.049/E-T) (4.876/Et) 1.9E-5(0.995/Et) t(1.222/Et)
1.0 0.0028 e(1.225/ Et) (2E-4/Et) 1.8E-5e(1.009/ Et) (3.6E-4/Et)

In Table 4-4, we found similar correlation between the value of each term and

cone size for both raw jets and corrected jets. The first term (constant term) p!i-.-

an important role in the high PT region. For small cone jets, this effect is more

prominent, while for large cone jets (0.8 and 1.0), the first term almost vanishes

(which is compensated by increasing the value of the second term). The physics

aspects of the constant term highly relate to the transverse size of the hadronic









shower. Narrow cone jets are less influenced by the pileup and electronic noise. A

larger value of constant term is primarily caused by the leaking of the hadronic

shower. Two opposite effects maintain the balance of the first term, as jet energy

goes up, the width of the overall jet size decreases and the leaking from particle

showers increases.

Second term dominates JR in the jet PT range from 20 to 600 GeV/c, which

mainly relates to the stochastic effect of the calorimeter response. Wider cone jets

contain almost all the hadronic shower of the jet, so the stochastic effect is fully

manifested. This leads to a larger value of the second term.

The resolution of the narrow cone jet is generally better than that of the

wide cone ones, because most high ET towers are closer to the jet axis with higher

energy response and have relatively smaller stochastic effect than low ET towers

further away from the center of the jet. So narrow cone jets take advantage from

the intrinsic feature of the detector. The further optimization of the cone size for

the jet reconstruction and correction largely depends on the analysis need and

the interested jet PT range. Normally it can not be only based on the jet energy

resolution.

4.5.4 Performance of Correction in the I] 1> 3.0 Region

Fig. 4-23 shows calibration of jet energy of 0.6 cone in forward region (I T I>

3.0), in which the raw jet energy is alv-- over-measured. After the correction, the

linearity of jet energy response with less than ~ 1.5' error is obtained.

Results of absolute resolution (aEt) is showed in Fig. 4-24. Because the

calorimeter granularity gets larger in the HF, which may limit the accuracy of

the measured jet energy distribution, but an average improvement of absolute

resolution of 10' for forward jets with various cone size and across the PT range

from 20 to 300 GeV/c is achieved.















105 V TV
: V
0 1 .......... ..


,: I I I I

50 100 150 200 250 300
Jet Pt

Figure 4-23. Jet energy response of 0.6 cone before (triangle-down) and after
(triangle-up) the correction based on second moment


The relative resolution after the correction is fitted by Exp. 4-13, the results

are showed in Table 4-5.

Table 4-5. Jet energy resolution in Ir1 > 3.0 region

Jet cone size Corrected jet
0.2 0.0589 E(0.103/v/E) E(4.360/Et)
0.4 0.0501 (0.358/vEt) (3.660/Et)
0.6 0.0353 ((0.646/vE-) (2.446/Et)
0.8 0.0175 E(0.812/VE ) (4.423.222/Et)
1.0 0.0195 E(0.847/ /E) (0.00046/Et)


4.5.5 Stability of the Correction Algorithm and Jet Selection

As discussed in the previous section, the correction algorithm might partially

fails due to following reasons: overlapping of jets and mis-identification of jets.

These abnormal jets cause the big deviation in the energy distribution from normal

ones. The rejection of abnormal jets is important for the stability of a correction

algorithm with a complicated parameterizations. In this study, the pre-selection on

the QCD jets is not used because high PT jets are widely separate in the space and

there are very less lepton faked jets rate because of the small relative cross section

of heavy flavors producing non-isolated leptons.