Searching for Supersymmetry with Same-Sign Di-Leptons Using the Cms Experiment at the Large Hadron Collider

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Searching for Supersymmetry with Same-Sign Di-Leptons Using the Cms Experiment at the Large Hadron Collider
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Remington,Ronald C
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Doctorate ( Ph.D.)
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University of Florida
Degree Disciplines:
Physics
Committee Chair:
Yelton, John M
Committee Members:
Acosta, Darin E
Matchev, Konstantin T
Dorsey, Alan T
Koehler, Gary J

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cern -- cms -- collider -- leptons -- lhc -- physics -- supersymmetry
Physics -- Dissertations, Academic -- UF
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The year 2010 marked the beginning of a new era in collider physics as the Large Hadron Collider (LHC) began colliding proton beams at a record-setting, center-of-mass energy of $7$ TeV. The work described herein represents one of the first efforts to search for evidence of R-parity conserving supersymmetry (SUSY)using the Compact Muon Solenoid (CMS) experiment at the LHC. The analysis exploits an event topology based on same-sign di-leptons, hadronic jets, and missing transverse energy. This signature is expected to be featured in a variety of new physics scenarios and is known to be heavily suppressed by the Standard Model. The search uses data produced during the 2010 LHC run, corresponding to $\int \! L \ \mathrm{d}t = 35$ pb$^{-1}$. An extensive overview of the data-driven methods used to model the behavior of background processes is given. After imposing the event selection requirements that define the signal region, $1$ event is observed, which is statistically consistent with the total expected Standard Model background rate of $0.80 \pm 0.33$. Given this lack of an excess, exclusion limits are calculated on the parameter space of SUSY models with universal gaugino and scalar mass scales. The general limit on cross-section $\sigma$ multiplied by branching ratio $BR$ and the event selection acceptance $A^{\rm experiment}$ is $\sigma \times BR \times A^{\rm experiment} < 13$ pb at $95\%$ C.L. In order to make the results of this search accessible to the wider theoretical community, a parametrization of the experimental acceptance is presented. Using this parametrization, the viability of a large class of new physics models, not restricted to supersymmetry, can be tested against the limits set by this search.
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Statement of Responsibility:
by Ronald C Remington.
Thesis:
Thesis (Ph.D.)--University of Florida, 2011.
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Adviser: Yelton, John M.

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SEARCHINGFORSUPERSYMMETRYWITHSAME-SIGNDI-LEPTONSUSINGTHE CMSEXPERIMENTATTHELARGEHADRONCOLLIDER By RONALDC.REMINGTON ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2011

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c 2011RonaldC.Remington 2

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ACKNOWLEDGMENTS IthankmyadviserandchairJohnYeltonforthevaluablementoring,advice,and supporthehasofferedmeovertheyears.Ialsothankmyco-chairKonstantinMatchev forthemanyhelpfuldiscussions,aswellasmyothercommitteemembers:Darin Acosta,AlanDorsey,andGaryKoehlerfortheirtimeandinterestinoverseeingmy researchactivities.Iwouldliketoexpressmygratitudetomycolleaguesandthefaculty attheUniversityofFloridawhojoinedmeinmakingthisanalysiseffortasuccessfulone withintheCMScommunity:MingshuiChen,AlexeyDrozdetskiy,DidarDobur,Andrey Korytov,LanaMuniz,GuenakhMitselmakher,YuriyPakhotin,andNikSkhirtladze.Iam alsogratefultotheTier-2andHPCadministratorsfortheirtechnicalsupportandfor facilitatingallofourdataanalysisandstorageneeds. Severalpeoplehaveplayedanimportantroleinmydevelopmentasaphysicist, aprocessthatbeganseveralyearsagowhenIwasalateteen.Theseselectpeople deserveaspecialacknowledgement.Manyofthemarenotawareofhowgreatofarole theyhaveplayedandhowmuchIhavegrowntoappreciatewhattheirinuencehas doneforme. Iwouldliketorstthankmylife-longfriendChrisRogan,whoexposedmetothe someofmostinterestingandprofoundsubjectsofphysics.Ourconversationsinspired metopursueacareerasaphysicist.IthankmyundergraduateadvisorDr.Michael Rulisonforthecountlesshoursspentinhisofce,whileheindulgedmymusingsonthe variousmattersrelatedtothephilosophyofscience.Ilookbackonthoseyearsvery fondly,andtheycontinuetoinuencemyapproachtounderstandingphysicstothisday. Iamverygratefulforhavingtheopportunitytolearngraduatelevelphysicsfromoneof theUniversityofFlorida'smostgiftedphysicistsandinstructors,Dr.RichardWoodard. Thatyearofstudyunderhimimprovedmyunderstandingofphysicsandmathematicsto alevelIhadnotthoughtpersonallyattainable.Hiscandorduringourprivatediscussions willforeverbeappreciated.Unbeknownsttohimatthetime,theseconversationshelped 3

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metosettleonwhichtypeofresearchIwouldpursueformyPhD.Duringmyrstyear onCMSIhadthefortuneofworkingalongsideBobbyScurlock,RickCavanaugh,and MikeSchmitt.TheirguidanceandmentorshipprovidedmewiththetoolsIneededto makemeaningfulcontributionstotheCMScommunityveryearlyon.Workingwith themwasatruedelight,andIfeelthatmuchofthesuccessIhaveenjoyedduringmy graduatecareercanbeattributedtoeachoftheminsomeway. Theendlessloveandsupportofmyfamilyhashelpedmetoperseverethrough thefrequentandarduousperiodsoflongworkhours,sleeplessnights,andimposing deadlines.MywifeJeannettehasenduredthisprocesssincethedayIdeclaredmy majorasanundergraduateandshehasbeenunwaveringinhersupportduringeach subsequentphaseinmylongpathtobecomingaphysicist.Theroleofagraduate student'sspouseisfarfromglamorousandcanbeincrediblyunfullling.Jeannette hasnonethelessbeenutterlycommittedtoseeingthisthrough,evenasthedemands ofmyresearchbegantosignicantlycompromiseherowncareeraspirations,aprice thatcouldhavebeeneasilyviewedastomuchtobear.Sheendorsedtheideaof movingtoCERNwhenshedidnothaveto,becausesheknewitwouldbringmebetter opportunities.Shehumbledherselftoworkingasanoverqualiedau-pairwhilewelived thereinorderforustomakeendsmeet.Hersacriceshavebeenfargreaterthanmine duringthisprocess,andforthatIamgreatlyindebted.Thisdissertationisatributetomy love,Jeannette. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 3 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 10 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTION ................................... 14 2THESTANDARDMODELOFPARTICLEINTERACTIONS ........... 18 2.1OverviewandTheoreticalFoundation .................... 18 2.1.1Spin ................................... 20 2.1.2GaugeInvariance ............................ 22 2.1.3ScaleDependenceandRenormalizability .............. 25 2.1.4Chirality ................................. 27 2.1.5SpontaneousSymmetryBreakingoftheElectroweakInteraction 28 2.2TheFullParticleDescription ......................... 31 2.3Shortcomings .................................. 34 3SUPERSYMMETRY ................................. 36 3.1TheMinimalSupersymmetricStandardModel ............... 36 3.1.1Notation ................................. 36 3.1.2ParticleContentoftheMSSM ..................... 37 3.2ImplicationsofaSupersymmetricUniverse ................. 38 3.2.1TamingtheQuantumCorrectionstotheHiggsMass ........ 38 3.2.2R-Parity ................................. 40 3.2.3GaugeCouplingUnication ...................... 41 3.2.4SparticleMasses ............................ 42 3.3TheMinimalSupergravityModel ....................... 44 3.4HadronColliderPhenomenologyofthemSUGRAScenario ........ 47 3.4.1StrongProduction ........................... 47 3.4.2MissingEnergy ............................. 51 3.4.3Same-SignLeptonPairs ........................ 54 3.5CurrentExperimentalLimitsonSupersymmetry ............... 56 3.5.1ConstraintsfromAstrophysicalEvidenceofDarkMatter ...... 56 3.5.2ConstraintsfromIndirectLow-EnergyMeasurements ........ 57 3.5.3ConstraintsfromDirectExperimentalSearches ........... 58 5

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4THELARGEHADRONCOLLIDER ......................... 61 4.1Design ...................................... 61 4.2Experiments .................................. 65 4.3Performancein2009-2010andProjectionsfor2011-2012 ......... 67 5THECMSEXPERIMENT .............................. 71 5.1CMSCoordinateSystem ........................... 71 5.2DesignandPerformance ........................... 71 5.2.1SuperconductingMagnet ....................... 73 5.2.2TrackingSystem ............................ 73 5.2.3ElectromagneticCalorimeter ..................... 79 5.2.4HadronCalorimeter .......................... 82 5.2.5MuonSystem .............................. 88 5.2.6TriggerSystem ............................. 95 5.3EventReconstructionandDataAnalysis ................... 99 5.3.1TheCMSSoftware ........................... 99 5.3.2GridComputing ............................. 101 5.3.3MonteCarloSimulation ........................ 103 6THESEARCHFORSUPERSYMMETRYATTHELHCWITHTHESAME-SIGN DI-LEPTONS,JETS,AND E T SIGNATURE .................... 108 6.1Introduction ................................... 108 6.2MonteCarloSimulatedData ......................... 110 6.3TriggerStrategy ................................. 112 6.4PhysicsObjectsandDiscriminatingObservables .............. 112 6.5EventSelection ................................. 115 6.6BackgroundEvaluationandAssociatedUncertainties ........... 122 6.6.1DeterminationofPrompt-Prompt,Same-signDi-leptons: N SS p p .. 123 6.6.2DeterminationofPrompt-Prompt,Opposite-signDi-leptons: N OS p p 124 6.6.3DeterminationofFake-Fake,Same-signDi-leptons: N SS f f ..... 125 6.6.4DeterminationofPrompt-Fake,Same-SignDi-leptons: N SS p f .... 146 6.6.5ValidationoftheBackgroundCompositionintheSidebandData .. 150 6.6.6SummaryofBackgroundRates .................... 156 6.7Signalyieldanduncertainties ......................... 160 6.7.1TheoreticalUncertainties ....................... 160 6.7.2InstrumentalUncertainties ....................... 161 6.7.2.1Luminosity .......................... 161 6.7.2.2Muonselectionefcienciesandvalidation ......... 161 6.7.2.3Electronselectionefcienciesandvalidation ....... 165 6.7.2.4 H T and E T selectionefciencies .............. 168 6.7.2.5Triggerefciency ....................... 170 6.7.2.6Crosschecks ......................... 171 6.7.3Summary:SignalAcceptanceandUncertainties .......... 172 6

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6.8FinalResults .................................. 172 6.8.1Limitson BR A experiment ..................... 174 6.8.2LimitsonthemSUGRAParameterSpace .............. 174 7CONCLUSION .................................... 177 APPENDIX:ANATOMYOFTHEOBSERVEDSIGNALEVENT ............ 179 REFERENCES ....................................... 182 BIOGRAPHICALSKETCH ................................ 187 7

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LISTOFTABLES Table page 2-1Summaryoffundamentalparticleelds ...................... 21 2-2Summaryoffundamentalforces .......................... 24 2-3Quarks(Spin-1/2) .................................. 32 2-4Leptons(Spin-1/2) .................................. 33 3-1SummaryofparticlesandsuperpartnersintheMSSM .............. 38 3-2UndiscoveredparticlesoftheMSSM ........................ 44 3-3LimitsonSUSYparticlesfromtheLEPexperiments ............... 59 3-4LimitsonSUSYparticlesfromtheTevatronexperiments ............. 59 4-1SummaryofLHCbeamparameters ........................ 63 5-1 P T and d 0 resolutionformuons ........................... 79 5-2Chambermultiplicityperstationandring ...................... 93 6-1SummaryofsimulatedStandardModelbackgroundsandsignalsamples ... 111 6-2Summaryoftriggerstrategy ............................. 112 6-3Descriptionofeventselectionrequirements .................... 116 6-4Eventyieldsforthe -channel ........................... 121 6-5Eventyieldsforthe ee -channel ........................... 121 6-6Eventyieldsforthe e -channel ........................... 121 6-7Classicationofbackgroundprocesses ...................... 123 6-8Eventyieldsforprompt-prompt,same-signdi-leptonbackgrounds ....... 124 6-9Summaryofbackgroundsduetocharge-ip .................... 125 6-10BaselineyieldsfordataandMonteCarlosimulateddata ............. 128 6-11Summaryofnon-promptleptonoriginsinsimulatedQCD ............ 130 6-12SummaryofuncertaintiesonobservablesofFactorizationmethod ....... 145 6-13Controlregionyieldsforpredictionoffake-fakedi-leptons ............ 145 6-14Selectionefcienciesforfake-fakedi-leptons ................... 145 8

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6-15Data-drivenbackgroundpredictionoffake-fakedi-leptons ............ 145 6-16Data-drivenbackgroundpredictionofprompt-fakedi-leptons. .......... 150 6-17Topologiespresentinthesideband ......................... 151 6-18Controlregionsforthe d 0 TemplateFittingmethod ................ 152 6-19Statisticalerrorsoftermsusedinthecalculationof N tot bgd ............. 157 6-20Systematicerrorsinvolvedincalculationof N tot bgd .................. 157 6-21Summaryofeventyieldsforallbackgroundsourcesandassignedsystematic errors ......................................... 158 6-22Efciencyofthe H T triggers ............................. 171 6-23Parameterizationofsignalacceptance ....................... 173 6-24Signalyieldsandsystematicerrors ......................... 173 6-25Summaryofexpectedandobservedeventyields ................. 173 A-1Summaryofjetcontentinobservedsignalevent ................. 180 A-2Summaryofleptonsattributesinobservedsignalevent ............. 180 A-3Summaryof E T calculationsinobservedsignalevent .............. 180 9

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LISTOFFIGURES Figure page 2-1First-orderloopcorrections ............................. 26 3-1Gaugecouplingunication ............................. 42 3-2Strongproductionmechanismsofsuperpartners ................. 49 3-3Electroweakproductionmechanismsofsuperpartners ............. 50 3-4Gluino-squarkdecaydiagram ............................ 51 3-5SUSYsame-signdi-Leptondiagram ........................ 55 3-6D exclusionlimits ................................. 60 4-1CERN'sacceleratorcomplex ............................ 64 4-2Integratedluminosityfor2010 ............................ 69 5-1CMSdetector(fullview) ............................... 74 5-2CMSdetector( r z prole) .............................. 75 5-3Pictorialrepresentationoftransverseimpactparameter d 0 ........... 78 5-4Schematicdesignofdrifttubecell ......................... 90 5-5Schematicdesignofacathodestripchamber ................... 93 6-1LOandNLOproductioncross-sectionofcoloredsuperpartners ......... 110 6-2Pictorialrepresentationofthe RelIso observable ................. 114 6-3MonteCarlopredictionsforexpectedeventyieldswith 35 pb 1 ofdata. ..... 117 6-4Legendfordistributionsofkeyobservables .................... 117 6-5Distributionsofkeyobservablesforthe -channel ................ 118 6-6Distributionsofkeyobservablesforthe ee -channel ................ 119 6-7Distributionsofkeyobservables e -channel .................... 120 6-8Factorizationof RelIso selectionrequirements ................... 131 6-9Differential RelIso distributions ........................... 132 6-10Testsof RelIso correlations ............................. 133 6-11Factorizationof RelIso and E T selectionrequirements ............... 134 10

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6-12 RelIso ( )eventyieldandefciency ......................... 136 6-13 RelIso ( e )eventyieldandefciency ......................... 136 6-14 E T eventyieldandefciency ............................. 137 6-15Factorizationofboth RelIso selectionswithmuon-triggeredevents ....... 139 6-16PartialclosuretestsoftheFactorizationmethod ................. 140 6-17Factorizationof RelIso and E T selectionsinsingle-leptonevents ......... 141 6-18Testsofeffectsfrominvertedselectioncriteria .................. 143 6-19Final RelIso templatesformuonsandelectrons .................. 148 6-20Summaryofbackgroundcontributionstothesidebandregion .......... 151 6-21 d 0 distributionsfromthebeamspotandprimaryvertex .............. 152 6-22 d 0 distributionforelectronsandmuons ....................... 153 6-23Fitsof d 0 templatestothesidebanddata ...................... 155 6-24Finalpredictionsfortheexpectedeventratesfor 35 pb 1 ............. 159 6-25Muonreconstructionefciency ........................... 162 6-26 RelIso ( )selectionefciency ............................ 163 6-27Combinedmuonreconstructionand RelIso ( )selectionefciencies ....... 163 6-28LKTmethodusingchargedtracks ......................... 165 6-29Electronreconstructionefciency .......................... 166 6-30 RelIso ( e )selectionefciency ............................ 167 6-31Combinedelectronreconstructionand RelIso ( e )selectionefciency ...... 167 6-32Ratiosofelectronandmuoneventyieldsin Z events ............... 168 6-33 H T reconstructionperformance ........................... 169 6-34 E T reconstructionperformance ........................... 169 6-35Differencebetweenreconstructedandtruevaluesof H T and E T ......... 170 6-36Efciencyofthe H T triggers ............................. 171 6-37Eventyieldsandexclusioncontourinthe m 0 m 1 / 2 plane ............ 176 A-1 3 Deventdisplayofthe ee eventobservedinthesignalregion .......... 181 11

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy SEARCHINGFORSUPERSYMMETRYWITHSAME-SIGNDI-LEPTONSUSINGTHE CMSEXPERIMENTATTHELARGEHADRONCOLLIDER By RonaldC.Remington August2011 Chair:JohnYelton Major:Physics Theyear2010markedthebeginningofaneweraincolliderphysicsastheLarge HadronCollider(LHC)begancollidingprotonbeamsatarecord-setting,center-of-mass energyof 7 TeV.Theworkdescribedhereinrepresentsoneofthersteffortstosearch forevidenceofR-parityconservingsupersymmetry(SUSY)usingtheCompactMuon Solenoid(CMS)experimentattheLHC.Theanalysisexploitsaneventtopologybased onsame-signdi-leptons,hadronicjets,andmissingtransverseenergy.Thissignatureis expectedtobefeaturedinavarietyofnewphysicsscenariosandisknowntobeheavily suppressedbytheStandardModel.Thesearchusesdataproducedduringthe2010 LHCrun,correspondingto L d t =35 pb 1 .Anextensiveoverviewofthedata-driven methodsusedtomodelthebehaviorofbackgroundprocessesisgiven.Afterimposing theeventselectionrequirementsthatdenethesignalregion, 1 eventisobserved, whichisstatisticallyconsistentwiththetotalexpectedStandardModelbackground rateof 0.80 0.33 .Giventhislackofanexcess,exclusionlimitsarecalculatedonthe parameterspaceofSUSYmodelswithuniversalgauginoandscalarmassscales.The generallimitoncross-section multipliedbybranchingratio BR andtheeventselection acceptance A experiment is BR A experiment < 13 pbat 95% C.L.Inordertomakethe resultsofthissearchaccessibletothewidertheoreticalcommunity,aparameterization oftheexperimentalacceptanceispresented.Usingthisparameterization,theviability 12

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ofalargeclassofnewphysicsmodels,notrestrictedtosupersymmetry,canbetested againstthelimitssetbythissearch. 13

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CHAPTER1 INTRODUCTION Theyear2010markedthebeginningofaneweraincolliderphysics.TheLarge HadronCollider(LHC)surpassedtheenergyfrontier,formerlysetbytheTevatron,by collidingprotonbeamsatacenter-of-massenergyof 7 TeV.ThemaingoaloftheLHC istosucceedwhereitspredecessorshavefailed,andnallyelucidatethenatureof electroweaksymmetrybreaking(EWSB),whichisthehypothesizedmechanismfor impartingmassestothefundamentalparticlesofnature.Theparticlethatisexpected toberesponsibleforEWSBistheHiggsboson,whichtodayremainstheonlyparticle predictedbytheStandardModelofparticlephysicstoeludeobservation. WhilediscoveryoftheHiggsbosonwouldbeatruetriumphoftheStandardModel, itwouldnotmarktheendofthestory.Thepathtounderstandingthelawsofphysics atnature'smostfundamentallevelmustextendbeyondtheStandardModelforseveral reasonswhichwillbedescribedinChapters 2 and 3 .TheHiggshypothesis,ifproven tobetrue,invitesfurtherspeculationabouttheexistenceofpotentiallynumerousother particlestates,previouslynotincludedintheStandardModel.Thisspeculationcanbe attributedtotheuniquequalitiesoftheHiggsparticlethatdistinguishitfromallothersin theStandardModel,namelyitsquantumspinanditsgroundstateenergy.Manybelieve thatinorderfortheHiggsbosontotconsistentlyintotheStandardModel,anew symmetryofnaturemustbeinvoked.Thissymmetryisreferredtoas supersymmetry anditsexistenceimpliesthatahostofnewandexoticparticlestatesmightbecreated inhigh-energyparticlecollisions.Thesearchforevidenceofsupersymmetryusingdata recordedbytheCompactMuonSolenoid(CMS)experimentattheLHCisthefocusof thisdissertation. Thelawsofspecialrelativityandquantummechanics,whencombined,yield importantconsequenceswhichprovidetheunderlyingprinciplesexploitedbycollider physicsexperiments.Specialrelativitydemonstratedtheequivalencebetweenmassand 14

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energyviaEinstein'sfamousequation E = mc 2 .Quantummechanicsdemonstrated thatsmalldistances( X )canberelatedtolargeenergies( E )viaHeisenberg'sfamous uncertaintyprinciple E X # c .Thesetwotheoreticalinsightsimplythatparticles arenotindestructibleobjects,butthattheycanbeannihilatedorcreatediftheconditions areright,i.e.if E $ 2 mc 2 ,andifotherconservationlawsaresatised.Themain functionofparticlecollidersistocreatetheappropriateconditionsforparticlecreation, inessence,byforcingtwoparticlesintoasmallenough X .Clearly,ifonewantsto manufactureverymassiveparticles,thenoneneedstoacceleratethecollidingparticles toveryhighenergies. Thelawsofquantummechanicsprohibitadeterministicoutcometoanyparticular particlecollision.Instead,alloutcomesareprobabilistic.TheStandardModelcan beviewedasthemasterprobabilitydistributionfunctionofparticleinteractions.It providesaprescriptionforcalculatingtheprobabilitiesofparticularoutcomes,whichare typicallymanifestedas scatteringcross-sections .Rareoutcomes(e.g.,productionof heavyparticles)arecharacterizedbysmallcross-sections.Forexample,Higgsparticle productionattheLHCisexpectedtohaveacross-sectionoforderpicobarns( 1 pb =10 36 cm 2 ).Itismuchmorelikelytoproducelightparticles,likepairsofquarks, whichhavecross-sectionsofordermillibarns( 1 mb =10 27 cm 2 ).Thereare,ofcourse, otherfactorsbesidesmassthatinuencetheproductioncross-sectionsofvarious outcomes,forinstancethestrengthoftheforcethatismediatingtheinteractionandthe attributesofthecollidingparticles.Fromthequalitativediscussionoftheserespective cross-sections,itisclearthatforeveryonecollisionresultingintheproductionofa Higgsparticle,therewillbebillionsofcollisionsresultingintheproductionofmundane (andusuallyuninteresting)particles.Forthisveryreason,itisessentialthatacollider cannotonlyproducehigh-energycollisions,butcanalsoproducethemveryrapidly. ThisisauniquefeaturethattrulysetstheLHCapartfromitspredecessors:itis designedtocrossprotonbeamsatarateof 40 milliontimespersecondwith 25 15

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nanosecondintervals.Eachcrossingcanproduceupto 20 distinctcollisions,yieldinga nominalcollisionrateof 1 GHz.Moredetailswillbediscussedonthetechnicalaspects oftheLHCinChapter 4 Whendiscussingquantitiesinthecontextofhigh-energyphysicsitisconvenientto dosousingtheconventionof naturalunits .Thisrequiresonetomodifythedenitions oftwoconstantsofnature:thespeedoflightinavacuum c ,andPlanck'squantumof action .Normally,thesehavedimensions: [ c ] = (length) (time) 1 (11) [ ] = (length) 2 (mass) (time) 1 (12) Innaturalunits,theybecomedimensionlessandaresettounity,i.e., = c =1. (13) Inthisschemetheunitsofmassandmomentumareuniedwiththatofenergy,which typicallyismeasuredineV(electron-volts).Thecharacteristicenergyscaleofphysics attheLHCistheGeV(orTeV)whichisequivalentto 10 9 eV(or10 12 eV).Another meaningfulconsequenceofEq. 13 relatestoNewton'sgravitationalconstant G .In naturalunitsittakesondimensionsofinversemass-squared,i.e. [ G ] = 1 M 2 p (14) Thus,theforceofgravitybecomesassociatedwithamassscale(orequivalentlyan energyscale),whichistypicallyreferredtoasthePlanckmass,carryingavalueof M p % O ( 10 18 GeV).Thisvaluehasparticularimportancetotheoriesofphysicsbeyond theStandardModel,whichwillberevisitedinChapters 2 and 3 16

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Inthecontextofcolliderphysics,collisionenergiesarequotedinthecenter-of-mass referenceframe, 1 andaredenotedbythesquare-rootoftheMandelstamparameter s .TheLHCisdesignedtocollideprotonsatanenergyof & s =14 TeV,butdue toengineeringdifcultieshasthusfaronlyoperatedupto & s =7 TeV.Thisisstill signicantlyhigherthanthatofpreviouscolliders. Theorganizationofthisdissertationisasfollows.Chapter 2 providesanoverviewof theStandardModelofparticleinteractions,describingitssuccessesandshortcomings. Chapter 3 describestheimportantaspectsofsupersymmetry,whichisaleadingtheory foradescriptionofphysicsbeyondtheStandardModel.Inparticular,theexperimental signaturesofsupersymmetryarediscussed,withspecialattentiondevotedtothose whicharethefocusofthisresearch(e.g.,leptonpairswithidenticalelectromagnetic chargeplusmissingenergy).Anoverviewofthedesignandperformanceofthe LHCisgiveninChapter 4 .AcompletedescriptionoftheCMSparticledetector,the technologicalchallengesofoperatingintheLHCenvironment,andthemethods requiredtoperformanalysisofthedataisprovidedinChapter 5 .Chapter 6 gives afullaccountofthemethodsemployedandtheresultsobtainedinthissearchfor evidenceofsupersymmetrywiththedataproducedbytheLHCduring2010.Finally, someconcludingremarks,whicharegiveninChapter 7 ,relatetofuturesearchesfor supersymmetryattheLHCusingthesignatureexploitedbythisanalysis. 1 Theframeinwhichtheinitialmomentasumstozero 17

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CHAPTER2 THESTANDARDMODELOFPARTICLEINTERACTIONS 2.1OverviewandTheoreticalFoundation TheStandardModelrepresentsthesuccessfulmathematizationofnatureata veryfundamentallevel.Formally,itisalow-energy,effectivequantumeldtheory ofgauge-invariantparticleinteractions,whichhasenjoyedhugesuccessesoverthe pastseveraldecades[ 1 2 ].Itdescribesthreeofthefourknownfundamentalforces withgreatprecision(i.e.,electromagnetic,weak,andstronginteractions),withthe gravitationalforcestilleludingaconsistentquantumdescription.Atthetimeofwriting, nostatisticallysignicantdeviationsfromthepredictionsoftheStandardModelhave beenobserved,asidefromtheinterestingphenomenonofneutrinooscillations[ 3 5 ]. Allparticlesknowntoexistthusfartelegantlyintothemathematicalframeworkofthe StandardModel. Thedynamicsofaphysicalsystemcanoftenbeelegantlyandconciselydescribed usingtheLagrangianformalism.Thisholdstrueforbothclassicalandquantumsystems, whethertheyberelativisticornot.Quantumeldtheorydealswithrelativisticparticle states,whicharecharacterizedbyeldsthatpermeatespace-timeasplane-waves. TheseeldsareamenabletoaLagrangiantreatment,inthat,theeldsandtheir respectivespace-timederivativescanbecastasthegeneralizedcoordinatesina congurationspace.The action S ,whichrepresentsthetime-integraloftheLagrangian canbeminimizedaccordingly,yieldingtheso-calledEuler-Lagrangeequationsof motionwhichgovernthedynamicsoftheelds.Thevalidityoftheseequationsrelies onHamilton'sprincipleofleast-action,whichisafundamentalaxiominphysics thatencapsulatesthenotionthatobjectstravelthroughcongurationspace(on average)alonggeodesics(i.e.,viathemostefcientwaypossible).Thisprincipleis equivalenttotheassumptionthatthereisafrugaleconomyoneinwhich action isthe resourcebelongingtoallphysicalsystemsinthecosmos,regardlessofscale. 18

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Lagrangiansoffermorethansimplyaestheticappeal.Theyareusefulforseveral reasons.First,theyprovideaconvenientwaytounveilsymmetries.Symmetriesare importantbecausetheyyieldconservationlaws(i.e., universaltruths )viaNoether's Theorem[ 6 ].Forexample,theclassicallawsofmomentumandenergyconservation arebornfromthespaceandtimetranslationalsymmetriesoftheLagrangiangoverning Newtonianmechanics.Analogousconservationslawscanbederivedinquantum mechanics.Second,thecanonicaltemplateoftheLagrangian,representingthe differencebetweenkineticandpotentialenergy,iseasytointuitandcarriesover naturallytofreeelds(kineticterms)andinteractingelds(potentialterms).Ifone desirestoincorporateneweldsorinteractionsintoatheory,itissimplyamatter ofaddingmoretermstotheLagrangian,whilethepreexistingtermsremaininmost casesunaltered.Finally,aLagrangiancomposedofeldscaneasilybemadetoyield localinteractions.Non-localityor actionatadistance provedtobeoneofthemost unappealingandexperimentallycontradictoryconsequencesofsomeoftheearlier classicallawsofphysicsformulatedbyNewtonandCoulomb.Byimposingthecondition thattheeldsmustbefunctionsofspace-timecoordinates(i.e., = ( x ) )andthatthey coupleatthesamespace-timecoordinate(i.e., ( x ) ( y ) where x = y ),localitycanbe mademanifestintheLagrangian,andhencethetheory. 1 Afewguidingprinciplesareadoptedby(most)theoristswhenbuildingcandidate Lagrangiansforquantumeldtheoriesthatcouldberealizedinnature.Inparticular, whenaddingaparticleorgroupofparticlestoatheory,certainissuesneedtobe addressed.Thefollowingsubsectionswilladdresstheseissuesastheypertaintothe StandardModelLagrangian. 1 Somecarehastobemadewithrespecttothenumberofspace-timederivativesthat operateonagiveneldbecausederivatesaretantamounttospace-timetranslations. 19

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2.1.1Spin Oneofthemostimportantattributesofaparticleanditsquantumeldrelatestoits spinquantumnumber.Beforeonecanintroduceaeldorparticleintoatheorythespin mustbeknownbecausethemathematicalexpressionsfortheeldsdiffersignicantly dependingonit.Quantumspinrepresentstheintrinsicangularmomentumofaparticle andhasthesamedimensionastheaction S ,whichismeasuredinunitsofPlank's constant (MKS).Innaturalunits,itisdimensionless( [ S ]=0 ).Formassiveparticles, onecanconceptualizespinastheangularmomentumabouttheparticle'scenterof mass.Asitturnsout,masslessparticleslikephotonshavespinaswell,sothisclassical analogycanonlybeextendedsofar. Particlesknowntoexistinnaturecarryspinsof 1 (vectorbosons)or 1 / 2 (spinor fermions).ThehypotheticalHiggsparticlecarrieszerospinandifdiscoveredwould betherst fundamentalscalarboson tobeobservedinnature.Table 2-1 provides abriefsummaryofthegeneralizedLagrangiansandtheresultingEuler-Lagrange equationsthatareusedtodescribeparticlesofvariousspins,i.e.,scalar,vector,and spinoreldsrespectively[ 7 10 ].Alsoshownaretheexpressionsfortherespective eldsandtheirdimensionsinpowersofenergy,aswellasthepropagator.Spinprovides anaturalwaytoclassifydifferenttypesofparticles,andmanyobservablesrelatedto particleinteractionshavenon-trivialconsequencesasaresultofspin(e.g.theangular distributionofdecayproducts d / d ).AswillbeshowninChapter 3 ,supersymmetry, whichisanimportanttheoreticalextensiontotheStandardModel,postulatesadeep relationshipbetweenparticlesofdifferentspin,andthisinturnhasprofoundand far-reachingconsequences. 20

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Table2-1.Summaryoffundamentalparticleelds TypeSpinFreeFieldLagrangianPlaneWaveFieldExpressionPropagator Scalar 0 L =( )   ( ) m 2 #   # ( x )= 1 (2 ) 3 / 2 d 3 p 2 E # a ( p ) e ipx + b   ( p ) e ipx $ i p 2 m 2 + i $ ( ( m 2 ) =0 [ ] =1 Vector 1 L = 1 4 F F m 2 A A A ( x )= 1 (2 ) 3 / 2 % # d 3 p 2 E & a # ( p ) $ ( # ) e ipx + a   # ( p ) $ ( # ) e ipx i ( p p m 2 g ) p 2 m 2 + i $ ( #( $ $ m 2 ) g $ A =0 # A $ =1 Spinor 1 2 L = % ( i & m ) % % ( x )= 1 (2 ) 3 / 2 % s d 3 p 2 E & c s ( p ) u s ( p ) e ipx + d   s ( p ) v s ( p ) e ipx i ( / p + m ) p 2 m 2 + i $ ( ( i & m ) % =0 [ % ] = 3 2 21

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2.1.2GaugeInvariance Asdescribedearlier,theLagrangianformalismprovidesamathematicalframework thatisusefulforexposingtheintrinsicsymmetriesofatheory.Withsomebasic knowledgeofcomplexalgebra,onecaneasilyidentifyasymmetrybelongingtothe Lagrangiansforscalarandspinorelds.Thetransformationsexposingthissymmetry areshownby 21 and 22 ,respectively, ( e i $ (21) # ( e i $ # (22) Thisisasymmetryunderchangeofa globalphase ,alsoknownasa globalgauge symmetry .Itisglobalbecausetheeldvalueateveryspace-timepointismultipliedbya commonphase.Amoremeaningfulsymmetrywouldexistif $ couldtakeonanarbitrary valueateachspace-timepoint.Inotherwords,werequire $ = $ ( x ) ,whichrepresents a localgaugetransformation .Atrstglance,itappearsthatsuchapostulatewould haveadebilitatingeffectonthescalarandspinorLagrangiansfromTable 2-1 .Itisquite obviousthattheydonotallowforsuchatransformationwithoutpermanentlyaltering theformoftheLagrangian.Thisisduetothederivativeterms,whichwouldnotlonger beblindto $ intheexponent.ThesederivativetermsmustbepresentintheLagrangian toensurePoincar ` einvariance,soitappearsthatlocalgaugeinvarianceisnotpossible; however,onecouldchangethedenitionofthederivativesuchthat % and % # are invariantundersuchatransformation.Thiscanbeachievedbyintroducingthe covariant derivative ,denedas D = % igA (23) where A isavector(gauge)eldthattransformsunderalocalgaugetransformationas A ( A + 1 g % $ ( x ). (24) 22

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Theprescriptionforimposinglocalgaugeinvarianceonaquantumeldtheoryhas farreachingimplications.Weimmediatelyseethatallspinorandscalareldsarenow coupledtoavectoreldviatheirrespectivecovariantderivatives.Whentwoeldsare coupled,theyinteractwithoneanother.Thus,whenlocalgaugeinvarianceissatised, dynamics(forceexchanges)emergeasaresult. Thevectoreldsthatfacilitatethedynamicsareappropriatelynamedgaugeelds, andtheparticlesthatrepresentthequantaoftheeldsareknownasgaugebosons orforcecarriers.Asanexample,wecanthinkof # astheelectroneld,inwhichcase, A representsthephotoneld,and g wouldbethe couplingconstant relatedtothe electromagneticcharge,orthestrengthoftheelectromagneticforce.Thesymmetryin thisexampleisproducedbyasinglegenerator $ whichrepresentsthetransformation propertiesofthe U (1) symmetrygroup. Additionaltypesofsymmetrygroupsareusedtointroducetheweakandstrong interactionstotheStandardModel.Theformerisaproductofgaugeinvarianceunder an SU (2) transformationwhilethelattercomesfromgaugeinvarianceunderan SU (3) transformation.Therearemanywaystorepresent SU ( N ) symmetriesinatheory.The StandardModelinvokesthe adjoint representationofthesesymmetrygroups,which generates N 2 1 masslessgaugeeldsorvectorgaugebosonswithspin= 1 .This treatmentimpliestheexistenceof 3 bosonstocommunicatetheweakinteractionand 8 bosonstocommunicatethestronginteraction.Thus,insteadofsimplyasinglegauge eldlike A in 24 ,thecovariantderivativeincorporates 3 moreforweakinteractions, denoted W a where a =1,2,3 andanadditional 8 moreforstronginteractions,denoted G b where b =1,...,8 .Thesehavebeenexperimentallyveriedtoexistandare referredtoasweakvectorbosonsandgluonsrespectively.Together,thethreegauge 23

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symmetriesoftheStandardModelcombinetoyieldaLagrangianthatisgaugeinvariant underthetransformationlawsof SU (3) C SU (2) L U (1) Y 2 Thecouplingconstantsthatmultiplythegaugeeldsinthecovariantderivatives aredimensionlessparameters.Theyareoftendenoted g # g ,and g s 3 andrepresent thestrengthsoftheelectromagnetic,weak,andstrongforcesrespectively.Theseare freeparametersofthetheoryinthesensethattheyarenottheoreticallyconstrained andcantakeonanyvalueswhatsoever.Theyhavetobemeasuredbyexperimentand insertedintotheStandardModelLagrangianbyhandinordertomakepredictions.Table 2-2 summarizesthefundamentalforcesgeneratedbythegaugeeldsoftheStandard Model.Asisevident,theweakbosonsareobservedtohavenon-zeromasses,which breaksthegaugesymmetry.Thisisthesubjectofelectroweaksymmetrybreaking (EWSB),aninterestingandnecessaryfeatureoftheStandardModel,whichwillbe discussedinSection 2.1.5 Table2-2.Summaryoffundamentalforces[ 11 ] ForceCarrierSymbolMassRange (GeV/ c 2 )(m) Electromagneticphoton & 0 ) Weak 2 chargedbosons W 80.4 % 10 18 1 neutralboson Z 91.2 Stronggluons g 0 % 10 15 Inprinciple,theLagrangiancouldaccommodateothergaugesymmetries,but thesewouldhaveexperimentalconsequences,inthat,additionalparticlesandparticle interactionswouldbeobserveddependingonthestrengthoftheresultingcouplings. 2 Thesubscripts C L Y ,denote"Color","Left",and"Hypercharge"respectively. 3 Thesearealsocommonlydenotedas $ 1 $ 2 ,and $ 3 ,respectively. 24

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Moreinformationontheroleofgaugeinvarianceandsymmetrygroupsinquantumeld theorycanbefoundinRefs.[ 7 10 ]. 2.1.3ScaleDependenceandRenormalizability Inrelativisticquantumeldtheory,particlespropagatethroughspace-timeina complicatedway.Consideraphotontravelingfrompoint a topoint b .Ateverypointin between a and b ,thereisanon-zerochance(probability)thatthisphotoncouldsplit intoaparticle-antiparticlepair(e.g.,anelectronandpositron)foraninstantbefore subsequentlyre-annihilatingbackintoaphoton.ThisisallowedbytheHeisenberg uncertaintyprinciple.Theinteractionwouldbeprescribedbyatermliketheone introducedbythecovariantderivativeactingonaspinoreldintheLagrangian, i.e., # i & D # .DepictedbytheFeynmandiagraminFigure 2-1A ,thisphenomenon representsa virtual processknownas vacuumpolarization .Itisvirtualinthesense thattheparticlesproducedinthesplitwouldnotdirectlybemeasurablebeforethey annihilatedbackintoaphoton.Nonetheless,theintegratedeffectsofthisproduction alongthepathfrom a to b dohaveconsequencesinotherexperimentalobservables. Forexample,ifweimaginethatthepoints a and b representtheintervalspannedby anelectron-protonboundstate(i.e.,ahydrogenatom),thenwecanviewthephotonas beingexchangedfromonetotheother(e.g.tocommunicatetheforcefromtheelectron totheproton),inwhichcaseitisalsovirtual.Onesuchconsequenceofthequantum loopsfromvacuumpolarizationrelatestothestrengthofthechargeoftheelectronas perceivedbytheproton(andviceversa).Theparticle-antiparticlepairactsasacharged dipoleforthebriefinstantitexists,andthisdiminishesthestrengthoftheelectriceld emanatingfromtheelectronasperceivedbytheproton.Inrealitythereisnotjusta singlephotonbutaconstantuxofphotonsbeingexchangedbackandforthfromthe electrontotheproton,andallofthesephotonssuccumbtothisquantumidentitycrisis whileintransit.Theneteffectofthisphenomenonisknownas chargescreening 25

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Conceptually,itisconvenienttothinkofacloudofparticle-antiparticlepairs swarmingtheelectronandproton.Themoredistancethatseparatesthetwocharged particles,themoreeffectivethisephemeraldipolecloudisatdiminishingtherespective electromagneticeldsofeachparticleasperceivedbytheother.Conversely,as thedistancethatseparatestwochargedparticlesshortens,theeffectofvacuum polarizationdecreasesandastrongerelectromagneticeldisperceived.Alternatively, asdimensionsofenergyandlengthareinverselyrelatedinrelativisticquantumphysics, itisequivalenttosaythatthecouplingconstant,andhencetheforce,strengthensas higherenergiesaretransferredbetweenthetwoparticles.Thisphenomenonisaptly referredtoas scaledependence ,andhasbeenveriedexperimentally[ 12 ]. Otherobservablesaresusceptibletoquantumeffectsaswell.Themassofa particleprovestobeanotherexample.Asachargedparticlepropagatesthrough space-time,itisconstantlyemittingandreabsorbingquantafromtherespectivegauge eldstowhichitcouples.ThesimplestcaseisillustratedinFigure 2-1B ,wherean electron,forexample,ispropagatingthroughspacefromlefttoright(straightline)while emittingandreabsorbingaphoton(wavyline)alongtheway.Similartothecaseof vacuumpolarization,thisprocessaffectsthepredictedvalueoftheelectron'smass accordingtothequantumeldtheorycalculations. AVacuumpolarization BSelfenergy Figure2-1.ExampleofFeynmandiagramsrepresentingrst-orderquantumloop corrections Theequationsusedtopredicthowanobservablewillchangeduetoaquantum loopcorrectionofteninvolveintegralsoftheform a + $ 0 d x x + c (25) 26

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whichexhibitsalogarithmicdivergenceattheupperlimit x = ) .Observablequantities innaturemustbydenitionbenite,andcouplingconstantsandparticlemassesare certainlysusceptibletoexperimentalmeasurements.Thus,itisassumedthatthe innitiesarenotreal,andonlyreectourimpropermathematicaltreatmentofthe problem.Techniqueshavebeendevelopedtoreformulatethecalculationsinsuch awaythatdivergentintegralsliketheoneinEq. 25 canbecancelled,leavinga niteandmeasurablepredictionforthequantumcorrection.Broadlyspeakingthe employmentofthisprocedureisknownas renormalization .Whilethemathematical detailsofrenormalizationarebeyondthescopeofthisoverview,manygoodreferences existonthesubject[ 7 9 13 ].Itwasawidelyheldbeliefthatatheorythattriesto describenatureshouldberenormalizableifitistohaveanypredictivepower.Itwas demonstratedbyGerardus'tHooftinthe1970'sthatallgaugeinvarianttheoriesexhibit thisproperty[ 14 ].Thisresultplacedanevenhigherpremiumongaugeinvariance. ThefactthattheStandardModelisgaugeinvariant,andhencerenormalizable,iswhat makesita falsiable theory.Ithasbeenveriedtoallenergyscalescurrentlyaccessible byexperiment. 2.1.4Chirality Theexpressionforthespinoreld # inTable 2-1 representsaDiracfermion,which has 4 complexcomponents.Thiscanbeinterpretedas( 2 spinstates) ( 1 particlestate + 1 antiparticlestate)= 4 degreesoffreedom.Withoutintroducingmuchmorenotation, itissufcienttosaythatthesedegreesoffreedomcanbereshufedinsuchawaythat theDiracspinoreldcanbewrittenasinapairofcomplexeldswith 2 -componentsas # = # L # R (26) Thesetwocomponents # L and # R canbethoughtofastwodistinguishableparticle states(orspecies)whicheachtransformunderdifferentrepresentationsoftheLorentz group,i.e.,theso-called leftand right-handed representationsrespectively.The 27

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particles # L and # R aresaidtohavedifferent chirality ,or handedness touseamundane analogy.Chiralityisaratherabstractconceptrelatedtoaparticle'stransformation properties;although,inuniquecircumstances(i.e.,inthecasethataparticleis massless)chiralitysimpliestoaparticle'sspinorientationrelativetoitsdirectionof motion. Theweakinteraction,asitturnsout,onlyinvolvestheleft-handedcomponentof Diracspinorelds.Thus,thegaugeeldswhichcommunicatetheweakforce(e.g. W + W ,and Z )onlycoupleto # L forallStandardModelfermions.Inotherwords # R doesnotexhibitthe SU (2) gaugesymmetry,andisblindtotheweakgaugeelds. Asaconsequence,onehastotakecaretodistinguishleft-handedfermionsfrom right-handedfermions.Onespeaksofleft-handedelectronsandright-handedelectrons, forexample,asiftheyaredifferentparticles.Owingtothechiralasymmetryoftheweak force,thisdistinctionisnotanexaggeration,asithasspecialimplicationswhenthe theoryofsupersymmetryisinvoked,whichwillbediscussedinChapter 3 2.1.5SpontaneousSymmetryBreakingoftheElectroweakInteraction InSection 2.1.2 ,theclaimwasmadethattheDiracLagrangiancanbemadetobe invariantunderlocalgaugetransformationsbyconstructingacovariantderivativethat addsgaugeeldstofacilitateeachsymmetry(e.g.asin 23 ).Animplicitassumption wasmadethatthemassterm m ## wouldbeunalteredundersuchatransformationvia therelationshipsshownin 27 through 29 # ( e i % $ ( x ) # (27) # ( # e + i % $ ( x ) (28) m ## ( m ## (29) However,theweakinteractionis chiral ,meaningitonlyinvolvestheleft-handed componentsoffermionelds.Thus,only # L transformsasan SU (2) doubletinthesame 28

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wayas # doesin 27 ,while # R transformsasasinglet,i.e., # R ( # R (210) Ifthemasstermiswrittenexplicitlyintermsofthe # L and # R componentsasin 211 itisclearthattheonlywaytopreservethe SU (2) gaugeinvarianceistoimpose m =0 forallfermions.Asimilarlackofgaugeinvariancewasindeedpresentallalongforthe masstermsinvolvingthegaugebosonelds,althoughitisunrelatedtotheissueof chirality. m ## = m ( # R # L ) # L # R (211) = m ( # R # L + # L # R ) (212) Thisresultpresentsquiteaquandarybecausethefermions,aswellastheweakgauge bosonsobservedinnaturehavenon-zeromasses.Thus,someothermechanismmust beinvoked,andhenceaddedtotheStandardModelLagrangian,inordertogenerate massesfortheseparticles. ThesimplestandmoststraightforwardsolutionistoappealtotheHiggsmechanism. Therecipeisthefollowing: (i) Introduceacomplexscalareldtothetheoryandallowittotransformasan SU (2) doublet(i.e.,itis 2 -vectorin SU (2) space).Furthermore,assignitaneutraland chargedcomponent,i.e., = + 0 (213) Thecombination   isthusmanifestlyinvariantunderan SU (2) transformation. (ii) Addanewpotentialinteraction V totheLagrangianwhichislinearandquadratic in   ,i.e., V (   )= 2   + (   ) 2 (214) 29

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(iii) Require 2 < 0 andsolveforthegroundstatesolutiontoobtain   + = 2 / 2 Dene v = 2 / tobethegroundstateenergyorthe vacuumexpectation value (VEVor 0 + )ofthescalareld. (iv) Performthe SU (2) rotationon thatwillsettheneutralcomponentofthecomplex eldtothisvalue v .Sinceadirectionin SU (2) spacehasbeenpreferredbythis choice,the SU (2) symmetryissaidtobe spontaneouslybroken ,thusmaking a Higgseld .BytheGoldstonetheorem,thegaugeeldsofthebrokensymmetry acquiremasses,whichismanifestedintheLagrangianbythecovariantderivative actingonthescalareld .Newmass-liketermsoftheform ( vg ) 2 W + W are nowintroduced. (v) ThechargedfermionsacquiremassesbydirectlycouplingtotheneutralHiggs eldviatheso-called yukawacouplings & ,whicharefreeparametersinthe theorythathavetobemeasuredbyexperiment.ThesetermsentertheLagrangian andhavetheform & #"# .Neutralfermionsremainmassless. (vi) TheHiggsparticlerepresentsanexcitedstateoftheHiggseld.Ithasamass termaswell,whichisdenedas m H = 1 2 v 2 (215) TheHiggsmechanismhasyettobeproventothebethecauseofelectroweak symmetrybreaking.TheStandardModelisnotaconsistenttheorywithoutit.One ofthemainprioritiesoftheLHCistodemonstratetheexistenceoftheHiggsparticle, measureitsmass,andthuscompletetheexperimentalconrmationoftheStandard ModeluptoTeVenergyscales.Strongtheoreticalandexperimentalevidencesuggests thattheHiggsmassshouldlieintherangeofafewhundredGeV[ 15 16 ].Ifitisinthe 100 GeVrange,thentheLHCwillultimatelyrevealitsexistenceinthenextfewyears. ManydetailsofthespontaneoussymmetrybreakingandtheHiggsmechanismare 30

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omittedinfavoroftheconcisedescriptionpresentedabove.Moredetailscanbefound elsewhere[ 17 18 ]. 2.2TheFullParticleDescription ThefundamentalfermionsoftheStandardModelconsistsof 3 generationsof quarksandleptons,whicharesummarizedinTables 2-3 and 2-4 .Theyareoften arrangedintermsoftheirtransformationpropertiesunderthe SU (2) U (1) subgroup. Theleft-handedfermionsform SU (2) doublets: L-HLeptons : ( e e L , ( L , ( % ) L (216) L-HQuarks : u d L , c s L , t b L (217) Theright-handedfermionsform SU (2) singlets: R-HLeptons : e R R ) R (218) R-HQuarks : u R d R c R s R t R b R (219) Conspicuouslyabsentamongsttheright-handedleptonsareneutrinos.Indeed,they haveonlybeenobservedtoexistasleft-handedparticles,participatingonlyinthe weakinteraction(i.e.,theyareelectricallyneutral).Eachfermionhasanassociated antiparticle,whichisnotexplicitin 216 through 219 Whileallfermionsparticipateintheelectroweakinteraction,onlyquarksparticipate inthestrongcolorinteraction,whichismediatedbygluons.Thestronginteractionsof theStandardModelaredescribedbythetheoryofQuantumChromodynamics(QCD). Insection 2.1.3 thescale-dependenceofthegaugecouplingswasdescribedingeneral terms.Theimplicationwasthattheeffectsof chargescreening diminishthestrength ofthegaugeinteractionsatlargedistances.Thisisonlytruefortheelectromagnetic coupling.Fortheweakandstrongcouplings,theoppositeeffectoccursintheStandard Model,i.e.,theygrowinstrengthatfartherdistances.Fortheweakcoupling,thisistrue 31

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downtotheTeVenergyscalewhereelectroweaksymmetrybreakingoccurs.Below thisscalethestrengthoftheweakcouplingdiminishesasdoestheelectromagnetic coupling.However,thestrongforceisblindtoelectroweaksymmetrybreaking,and thuscontinuestostrengthenwellbelowtheTeVscale.Thishasveryinterestingeffects onthebehaviorofcolor-chargedparticles.Theysimplycannotexistinisolationasa resultofthe connement propertyofQCD.Quarkscanonlyexistinboundstateswith otherquarkstoformcolor-neutralsystems,knownas hadrons 4 Hadronsinclude quark-antiquarkboundstates(mesons)andtri-quarkboundstates(baryons). TheLHCwillcollideprotons,aspecictypeofbaryons.Theenergiestransferredin thecollisionswillbesufcienttodisassociatetheprotonsintotheirconstituentpartons (quarksandgluons).However,thesepartonswillinstantlyreassembleintoboundstates. Thepotentialenergythatisgainedfromthestrongcouplingasthepartonsseparate duringthecollisionwillexceedthe 2 mc 2 necessarytocreateanewpairofquarksfrom thevacuum.Thisoccursamultitudeoftimesoveruntilasystemofboundstatehadrons isformed.Thissystemisaptlycalleda jet anditrepresentsthephysicalmanifestation ofaquarkorgluon,whichhasbeenliberatedfromapreviousboundstate. Table2-3.Quarks(Spin-1/2)[ 11 ] NameSymbolChargeMass(GeV) down d 1 / 34.1 5.8 10 3 up u 2 / 31.7 3.3 10 3 strange s 1 / 30.101 +0.029 0.021 charm c 2 / 31.27 +0.07 0.09 bottom b 1 / 34.19 +0.18 0.06 top t 2 / 3172 +0.9 1.3 4 Thetop-quarkissomassivethatitdecaystooquicklytoformaboundstate.In somesense,itdoesnotlivelongenoughtonoticethatitshouldbeinone. 32

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Table2-4.Leptons(Spin-1/2)[ 11 ] NameSymbolChargeMass(MeV) electronneutrino ( e 0 < 2 10 6 electron e 15.11 10 3 muonneutrino ( 0 < 2 10 6 muon 11.05 tauneutrino ( % 0 < 2 10 6 tau ) 11.77 10 3 33

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2.3Shortcomings DespitethewonderfulsuccessesoftheStandardModel,itisanincompletetheory forseveralreasons,afewofwhicharedescribedbelow. (i) Gravity ThegravitationalinteractionsarenotincorporatedintotheStandard Modelframework.Attemptstoprovideadescriptionofgravitybasedonquantum eldtheoryhaveproventobeverychallenging.Thegravitationalcoupling constant G isnotdimensionlesslikethecouplingsoftheotherfundamental forces.Quantumgravityisthusanon-renormalizabletheory. (ii) DarkMatter Astrophysicalevidencesuggeststhatonly 4 %oftheenergyin theuniversecanbeaccountedforbytheparticlecontentoftheStandardModel. Roughly 20 %isbelievedtobefromasubstanceknownascolddarkmatter (gravitationallyattractive)andanevenmorestaggering 76 %isbelievedtobesome formofamysteriousdarkenergy(gravitationallyrepulsive). (iii) Matter-AntimatterAsymmetry Thereisnomechanismtoexplainthe preponderanceofmatteroveranti-matter.Infact,thetwoshouldbeproduced innearlyequalamountsaccordingtotheStandardModel. (iv) FreeParameters Thereare 19 freeparametersintheStandardModel, includingthefermionmasses,thegaugecouplings,aswellasothers.The StandardModeliscompletelyimpotentatconstrainingthesetoanyparticular values.Theyhavetobemeasuredbyexperimentsandfedintothetheoriesby hand.Fortunately,theyareallaccessiblebylowenergyexperiments,except fortheconstant multiplyingthequadratictermintheHiggspotential,whichis expectedtoberevealedattheTeVenergyscale. (v) MassiveNeutrinos TheoriginalincarnationoftheStandardModeldidnot accommodatemassiveneutrinos.TheHiggsmechanismimpartedmasseson theelectricallychargedfermions,andthenon-observationoftheright-handed neutrinoseemedtoprecludethekindofmasstermintheLagrangianthatappears 34

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byconventionalmethods(i.e.,theDiracmass).Proposedextensionstothe StandardModelcanincludeneutrinomassterms.Oneexampleisthe see-saw mechanism [ 19 ] (vi) HierarchyandFineTuning QuantumcorrectionstotheHiggsmassinvolve quadraticallydivergentintegrals,whichisanattributeofscalarparticles.In ordertogetasensibleresult,theupperlimitoftheintegralmustarticiallybe truncatedatsomevalue # ,whichsetstheupperboundontheenergyrangefor whichthetheoryisvalid.Atrulyfundamentaltheoryshouldbevalidatleastup tothePlanckmassscale M p ,asthisiswheregravitationalinteractionsbecome important.However,inordertoproduceaviableStandardModelHiggsparticle, thecontributionsfromsuchalargevalueof # 2 mustbecancelledtonearly 20 decimalplacesbyanothertermintheLagrangian(i.e.,the baremass term).This necessityisknownas ne-tuning ,whichrendersthetheoryunnatural.Theneed forthislarge-scalecancellationcomesbyvirtueofthePlanckscalebeing % 16 ordersofmagnitudelargerthantheelectroweakscale(setbytheHiggsVEV).This vastdisparityinenergyscalesisknownasthe gaugehierarchyproblem Thus,anothertheorymusteventuallytaketheplaceoftheStandardModeland explainoraccommodatemany(orall)oftheunexplainedphenomenadescribedabove. ManytheoreticalextensionstotheStandardModel,aswellasreplacements,havebeen triedinthispursuit,butultimately,havebeenruledoutbyexperiment.Severaltheories, however,havenotbeenexperimentallytestableuntilnow.Theirviabilitywilllikelybe exploredbythephysicsprogramsattheLHC.Supersymmetryisonesuchtheory,which isthefocusofthisworkandwillbediscussedinthenextchapter. 35

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CHAPTER3 SUPERSYMMETRY SomeoftheshortcomingsexhibitedbytheStandardModelandoutlinedin Section 2.3 canactuallybeovercomebyintroducinganewrelationshipbetweenbosons andfermions.Thisrelationshipisreferredtoas supersymmetry (SUSY)andisone oftheleadingcandidatesforatheorythatcandescribephysicsbeyondtheStandard Model.Formally,supersymmetryisrecognizedasapropertyofnaturethatwouldallow scalarandvectorbosonstotransformintofermions,andfermionstotransforminto scalars.EachparticleintheStandardModelishypothesizedtohaveaso-called superpartner (sparticle)whichmaintainsthesameattributesastheoriginalparticle(e.g., mass,couplings)butdiffersbyhalf-integerwithrespecttothespin-quantumnumber. Suchasymmetry,ifdiscovered,wouldhaveprofoundconsequences. 3.1TheMinimalSupersymmetricStandardModel TheMinimalSupersymmetricStandardModel(MSSM)representsthemostefcient wayofextendingtheStandardModeltoincludesupersymmetrictransformations. 3.1.1Notation Todenotesparticlestatessymbolically,theconventionistoplaceatildeoverthe originalparticlesymbol,i.e., ( (31) # ( # (32) ThenamesofthesuperpartnersoftheStandardModelfermionsareprepended byan"s".Quarksbecome squarks .Leptonsbecome sleptons .Thenamesofthe superpartnerstothescalarandvectorbosonsareappendedwith"ino".Thus,a supersymmetrytransformationofthescalarHiggsbosonyields higgsinos and transformationsofthevectorgaugebosonsyield gauginos 36

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3.1.2ParticleContentoftheMSSM ThechiralstructureoftheStandardModelparticlescarriesovertothesupersymmetric extension.Becausetheleft-andright-handedcomponentsoffermionsareconsidered tobeuniqueparticlestateswithuniquetransformationproperties,itisnecessarythat theyeachobtaintheirownrespectivesuperpartners,i.e., # L ( L # R ( R (33) Thesubscriptscarriedbythescalarsfermionsin 33 donotimplythattheyhave a handedness likespin1 / 2 particlesdo.Instead,theyaresimplymeanttodenote therespectivegaugetransformationpropertiesoftheirsuperpartners.Itisnaturalto arrangethefermionsandtheirscalarsuperpartnersinto chiralsupermultiplets .This arrangementpreservesthedistinctionbetweentheleft-andright-handedparticles andallowsonetoeasilyintegratethefermions'superpartnersintotheLagrangian. Gaugebosonsandtheirfermionsuperpartners(gauginos)combinetoform gauge supermultiplets Table 3-1 summarizestheStandardModelparticlesandtheirrespectivesuperpartners. Thegroupingofparticlesintosupermultipletsindicatestheircommongaugetransformation properties.Rowswithcommonentriesinthespin0 andspin1 / 2 columnsformchiral supermultiplets,whilerowswithcommonentriesinthespin1 / 2 andspin1 columns formgaugesupermultiplets.Thegaugebosonsassociatedwiththeelectroweak interaction SU (2) L U (1) Y mixafterelectroweaksymmetrybreakingtogivemass eigenstates Z 0 and & insteadofthegaugeeigenstatesof W 0 and B 0 .Thesame phenomenonoccurswithrespecttothegauginosandhiggsinos,whichyieldneutralinos andcharginos(Section 3.2.4 )asmasseigenstates.TheMSSMrequirestheexistence oftwoStandardModelHiggs SU (2) doubletsinordertoimpartmassestoup-type fermionsanddown-typefermionsrespectively.Eachdoubletcontainstwocomplex 37

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scalarelds,thuscombiningtoyield 8 degreesoffreedom.Threedegreesoffreedom areusedtogivemassestothe W and Z bosons.Theremaining 5 becomeHiggs bosons,twoofwhichareelectromagneticallycharged. Table3-1.SummaryofparticlesandsuperpartnersintheMSSM[ 20 ] Namespin0 spin1 / 2 spin1 squarks,quarks( u L d L )( u L d L ) u R u R d R d R sleptons,leptons( ( L e L )( ( L e L ) e R e R Higgs,higgsinos( H + u H 0 u )( H + u H 0 u )( H 0 d H u )( H 0 d H d )gluino,gluon gg winos, W bosons W W 0 W W 0 bino, B boson B 0 B 0 3.2ImplicationsofaSupersymmetricUniverse Ifsupersymmetryisrealizedinnaturethentheimplicationsarenumerous.The MSSMisabletocompensateinmanyareaswheretheStandardModelprovestobe inadequate.Thefollowingsubsectionswilloutlineafewoftheinterestingconsequences ofsupersymmetry. 3.2.1TamingtheQuantumCorrectionstotheHiggsMass Oneofthemostcompellingtheoreticaljusticationsforsupersymmetrycanbe foundbyexaminingtheeffectsthatsparticleswouldhaveonquantumcorrectionsto thescalarHiggsmass.Aswasdescribedearlier,aproblemexistswhichisunique toscalarparticleswithnon-zeroVEV's,i.e.therst-orderquantumloopcorrectionto theirmasseshasquadraticsensitivitytotheenergy-scalecut-off, # .Becausefermions coupledirectlytotheHiggsbosonviatheyukawainteraction,theytoosufferindirectly 38

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fromthisproblem.Atrst-order,thecorrectiontotheHiggsmasstakestheform m 2 H = / f H f f f f = / f | f | 2 8 2 # 2 + O (ln # ) (34) TheFeynmandiagramrepresentsanintegralthataccountsforthecontributionfromall fermionswhichcoupletotheHiggsboson.Theparameter f representstheYukawa couplingforeachfermion.Thus,thiscorrectionismostlysensitivetothehighest massscaleintheStandardModel,whichissetbythetop-quark,where t $ 1 .Itis fairlyobviousfromEq. 34 ,that # ,whichrepresentstheupperlimitofthemomentum integral,cannotbeoforder M P andstillpreservethe m 2 H =(100 GeV ) 2 relationship necessarytoprovidethemeasuredmassestotheStandardModelparticles.However, ifsupersymmetryisapropertyoftheuniverse,thenEq. 34 isincomplete,andthereis anothertypeofFeynmandiagramthatisinvolvedinthecalculationonethatisdue tothescalarsuperpartnersoftherespectivefermions.Thus,thecorrectionismodied, i.e., m 2 H = / f H f f f f + / f H f f = # 2 8 2 0 1 / f f / f | f | 2 2 3 + O (ln # ). (35) TheexpressiongiveninEq. 35 suggeststhatthetermproportionalto # 2 canbe vanquishedif f = | f | 2 foreachfermion f .Ifsupersymmetryexiststhenthis relationshipnotonlycanoccur,butisunavoidable[ 20 ].Itissimplyastatementthat theyukawacouplingsareidenticalbetweensuperpartners.Thisisguaranteedtobe true,astheonlydistinctionbetweensuperpartnersisthespin-quantumnumber.The 39

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factthatthespinsaredifferentbyahalf-integeramountleadstothecancellation.The integralsthatarisefromtherespectiveFeynmandiagramscarrydifferentalgebraic signs,owingtothedifferentspin-statistics,andarethusantagonistic. BytamingthequadraticallydivergentcorrectionstotheHiggsmass,supersymmetry makestheStandardModelamoreviabletheory.Thisparticularmanifestationofthe hierarchyproblemisconquered. 3.2.2R-Parity AratheraccidentalconsequenceoftheStandardModelaretheconserved quantitiesknownas baryonnumber and leptonnumber .Baryonnumberisdened simplyas B = 1 3 ( n q n q ) where n q and n q denotethenumberofquarksandanti-quarks respectively.Leptonnumberisdenedas L = n ' n ,wherewhere n and n denotethe numberofleptonsandanti-leptonsrespectively.Thesequantumnumberspertaintoall fermionsandareconservedinallStandardModelinteractions. 1 Theconservationof B and L ,forexample,explainswhyproton-decayisnotobservedinnature. InthecontextoftheMSSM,itisbothconvenientandenticing(althoughnot mandatory)toenforcethissymmetrybypostulatingaconservedquantumnumber called R-parity ,denedas P R =( 1) 3( B L )+2 s (36) Here, s referstospinquantumnumber,andensuresthatparticleswithinthesame supermultiplethavedifferentR-parities.StandardModelparticlesarethusendowedwith evenR-parity( P R =+1 )whilesquarks,sleptons,gauginos,andhiggsinosareendowed withoddR-parity( P R = 1 ).IfR-parityprovestobeaconservedquantumnumberin 1 Somerareexceptionsexistwithrespecttonon-conservationof B dueto chiral anomalies 40

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nature(whichisboththeoreticallyandexperimentallywell-motivated),thenthefollowing mustbetrue[ 20 ]: Thesparticlewiththelowestmass,oftencalledthe lightestsupersymmetricparticle orLSP,isstableandcannotdecay.IftheLSPdoesnotcarryan electromagneticcharge,thenitonlycouplesweaklytoordinarymatterandwould thusbedifculttodetect.InthiscasetheLSPwouldprovetobeaverypromising dark-mattercandidate. Sparticlesmustbeproducedinpairsinordertoconserve P R Eachsparticlecandecaytoanoddnumberoflightersparticles.Subsequent sparticledecayswilloccuruntilastableLSPisproduced. Apartfromofferingaviableandalluringdarkmattercandidate,theconservation ofR-parityhasotherimportantphenomenologicalconsequences.Theserelateto searchstrategiesforexperimentalevidenceofsupersymmetryatcolliders.Adetailed discussiononthistopicwillbedeferreduntilSection 3.4 3.2.3GaugeCouplingUnication ThegaugecouplingsoftheStandardModelareknowntoscalewiththeenergy transferoftheinteraction(seeSection 2.1.3 ).Astheenergyscaleincreases,calculations indicatethatthecouplingscometantalizinglyclosetocrossingatthesamevalue,but unambiguouslydonot.Withadditionalsparticlestatesofferedbysupersymmetry,many naturalscenariosexistwherebythegaugecouplingsuniteatacommonvaluenear theso-calledGUT 2 scaleof O ( 10 16 GeV).Sparticlescontributetoloopdiagramslike theoneshowninFigure 2-1A insuchawayastoaccomplishthisunication.This effectisshowngraphicallyinFigure 3-1 [ 20 ],wheretheinversesofthethreeStandard Modelgaugecouplingsareplottedagainsttheenergyscale.Thisapparentunication attheGUTscalecouldbeevidenceofamorefundamentaltheory,oneinwhich,the electromagnetic,weak,andstrongforcesmergeintoacommoninteraction. 2 GrandUniedTheory. 41

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!"#$%&%!%"%#%$ '() %& *+,%-./01 & %& !& 2& "& 3& #& % % % ! % 2 % Figure3-1.EvolutionoftheStandardModelgaugecouplingsasafunctionofenergy scalewithout(dashedlines)andwith(solidlines)Supersymmetry[ 20 ] 3.2.4SparticleMasses IftheMSSMexistsintheformthathasbeendescribedthusfar,thenitshouldhave beendiscovereddecadesago.ExtendingtheStandardModeltoincludesupersymmetry hastheverydirectimplicationthatthereshouldbeanidenticalcopyofeachStandard Modelparticle,whichcarriesexactlythesamepropertieswithexceptiontospin.Thus, spin0 versionsoftheelectron,muon,andtaushouldhavebeenproducedcopiously inthecollidersofdecadespast.Suchsparticleswouldhavebeeneasilydetectedand arethusruledout.Todate,nosupersymmetricparticleshavebeendiscoveredbyany experimentalmeans.Therefore,ifsupersymmetrydoesexist,thenthesuperpartners aremoremassivethantheenergiesprobedbypreviouscolliderslikeLEPandTevatron (i.e., 100 GeV).Thiscanonlyoccurifsupersymmetryexistsasabrokensymmetry. Thebreakingofsupersymmetrytoaccommodateheaviersparticlemassesis achievedbyaddinganadditionalcomponenttotheLagrangianwhichgivessparticles extramasscontributions.Itisa soft symmetrybreakinginthesensethattheseterms canstillpreservethenicefeaturesofferedbysupersymmetrythatwerediscussedin 42

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Sections 3.2.1 3.2.2 ,and 3.2.3 .ThemechanismbywhichsoftSUSYbreakingoccurs isthefocusofagreatbodyoftheoreticalwork,whichisnicelysummarizedinRefs[ 20 21 ].Whilemanyofthedetailsarebeyondthescopehere,itisworthmentioningthatin itsmostgenericform,softSUSYbreakingintroduces 110 newparameterstothetheory, noneofwhichhavecounterpartsintheStandardModel.Theseparameterstakethe formof 30 massesplus 41 phasesplus 39 mixingangles[ 22 ]. TheadditionofsoftSUSYbreakingtermscombinedwiththeelectroweaksymmetry breakingalreadyintroducedintotheStandardModelallowsforthesparticlesofthe MSSMtomix.Theparticulardetailsofthemixingisoftenmodel-dependent.Thegauge eigenstatesoffermionsuperpartnersofthethirdgeneration(i.e., t L t R b L b R ) L ) R ) areparticularlypronetomixingduetotheirlargeryukawacouplings.Additionally,the neutralhiggsinos( H 0 u and H 0 d )andtheneutralelectroweakgauginos( B 0 and W 0 )mix toformfourmasseigenstatescalled neutralinos .Thesearedenoted + 0 i ,where i = { 1 2 3 4 } .Thechargedhiggsinos( H + u and H d )andthewinos( W )mixtoformtwo masseigenstatescalled charginos .Thesearedenoted + i where i = { 1 2 } .Asummary ofthemasseigenstatesoftheMSSMisgiveninTable 3-2 Thereisstrongevidencetosuggestthatifsupersymmetryexists,andisindeed broken,themassesofthesparticleshavetobelessthanroughlyaTeV.Thiscanbe inferredfromthesecondordercorrectiontotheHiggsmass,whichfeaturesaterm proportionalto ln # .Fromdimensionalanalysisthistermactuallyhastohavetheform m 2 H m 2 ln( # m ), (37) where m representstherespectiveparticlemasses.Thus,inordertoprovidethisvery importantserviceofkeepingtheHiggsmassconstrainedtotheexperimentallyand theoreticallyfavoredvalue,thesuperpartnerscannotbemuchheavierthanaTeV. Indeed,iftheydohavemassesattheTeVscale,thentheywillingeneralbeproducedin greatnumbersoverthelifetimeoftheLHC. 43

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Table3-2.Summaryofthehypothesized,butstillundetectedparticlesofinthe MSSM[ 20 ] NameSpinR-Parity( P R )GaugeEigenstatesMassEigenstates Higgsbosons 0+1 H 0 u H 0 d H + u H d h 0 H 0 A 0 H 0 1 u L u R d L d R same squarks 0 1 s L s R c L c R same 0 1 t L t R b L b R t 1 t 2 b 1 b 2 0 1 e L e R ( e same sleptons 0 1 L R ( same 0 1 ) L ) R ( L ( % ( 1 ( R ( % neutralinos 1 / 2 1 B 0 W 0 H 0 u H 0 d + 0 1 + 0 2 + 0 3 + 0 4 charginos 1 / 2 1 W H + u H d + 1 + 2 gluino 1 / 2 1 g same gravitino 1 / 2 1 G same 3.3TheMinimalSupergravityModel Inthecasethatsupersymmetryispromotedfromaglobalsymmetrytoalocal gaugesymmetry,thensuccessivesupersymmetrytransformationscanbeshownto generatespace-timetranslations[ 20 21 ].Thisallowsthetheorytomakecontact withGeneralRelativityandhenceincludethegravitationalinteraction.Thetheory thatemergesfromthisglobal-to-localsymmetrypromotionisknownas Supergravity .Aswithanylocalgaugeinteraction,messengerparticlesmustbeintroducedto communicatetheforce.Inthiscase,itisasinglespin2 particlecalledthe graviton whichhasaspin3 / 2 superpartnercalledthe gravitino .Thesearebothlistedatthe bottomoftable 3-1 .Ifsupersymmetrywereunbroken,thenthegravitinowouldbe exactlymassless;however,theinclusionofsoftSUSYbreakingtermstotheLagrangian endowsendowsitwithanon-zeromass.Dependingontheexactmechanismofsoft SUSYbreaking,thegravitinocanbeasheavyastheothersuperpartnersintheMSSM orsignicantlylighter,inwhichcaseitwouldbetheLSP. 44

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The 110 freeparametersintroducedbythemostgenericsoftSUSYbreaking mechanismleavestheMSSMratherimpotentasapredictivemodel.However,a frameworkexiststhatreducesthisvastparameterspacetoamuchmoretractable subspace.Alargereductioncanalreadybeachievedbymakingrathermodest assumptionsaboutparameterswhichyieldavor-changinginteractions.Inthisregard, strictexperimentalconstraintscanbeusedtoeliminateseveraltermsfromthesoft SUSYbreakingcomponentoftheLagrangian.Theseexperimentalmeasurements relatetomixingsoftheneutral K D ,and B mesonsystemsrespectively,aswellas thedecayrateof ( & e .Byimposingtheseconstraints,onendsthatthesubsetof parametersisreducedto 3 gauginomasses M 1 M 2 M 3 ,whichrelatetothebino,wino,andgluino respectively. 5 squarkandsleptonmass-squaredparameters m 2 Q m 2 L m 2 u m 2 d m 2 e ,whichrelate totheleftsquarks,leftsleptons,rightup-typesquarks,rightdown-typesquarks, andrightchargedsleptonsrespectively. 3 trilinearcouplings A u 0 A d 0 A e 0 whichcoupletheleftandrightup-typesquarks,the leftandrightdown-typesquarks,andtheleftandrightchargedsleptonstotheir respectiveHiggselds.Theseparametershavedimensionsofenergy. 4 parametersfromtheHiggspotential m 2 H u m 2 H d tan( ) ,andsign( )which representthemass-squaredtermsoftheup-anddown-typeHiggseld,the ratioofthetwoHiggsVEVs( v u v d ),andthealgebraicsignofthe coefcientfrom Eq. 214 ThisreductionisreferredtoastheconstrainedMSSM(cMSSM)andleaves 15 parameters,whichismuchmoremanageable.Still,therearemoresimplicationsthat canbemade.Allofthemass-relatedparametersandcouplingslistedabovescalewith theenergytransfer,soitisnaturaltoimposesomeboundaryconditionsonthematthe PlanckorGUTscale,forexample.Onesuchsetofboundaryconditionsimposesthe 45

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followingrelationships: M 1 = M 2 = M 3 = m 1 / 2 (38) m 2 Q = m 2 L = m 2 u = m 2 d = m 2 e = m 2 H u = m 2 H d = m 0 (39) A u 0 = A d 0 = A e 0 = A 0 (310) Inthisscheme,themodeliscompletelydeterminedby 5 parameters { m 1 / 2 m 0 A 0 tan( ) ,sign( ) } .Fromtheseboundaryconditions,onecanemploytheso-called renormalizationgroupequations(RGE)todeterminehowthese 5 GUT-scaleinput parameterswillyieldthefteenTeV-scaleoutputparameterswhichareofparticular interesttoexperimentalistssearchingforsupersymmetryatmodern-daycolliders. Theframeworkwhichimposesthissetofboundaryconditionsisknownas minimal supergravity ormSUGRA.Whileotherboundaryconditionsexist,yieldingothertypesof models,themSUGRAscenarioyieldsarich,albeitconstrained,parameterspacewhich providesadiverseandmanageabletraininggroundforexperimentaliststostudythe phenomenologicalconsequencesofsupersymmetry. InasupersymmetryscenariowithmSUGRA-inspiredboundaryconditions, themassparametersoftherespectivegauginosatTeVenergyscalesistoagood approximationdescribedby M 3 : M 2 : M 2 $ 6:2:1. (311) Thus,thegluinoisusuallypredictedtobeafewtimesheavierthantheneutralinosand charginos.ThisresultcanbemostlyattributedtostrongereffectsoftheQCDcoupling whencomparedtotheelectroweakcouplingsattheTeVscale.Forthesamereason, squarksaregenerallyexpectedtobeheavierthansleptons.Owingtotheinteractions inducedbytheweakcoupling,leftsuperpartnersareexpectedtobeheavierthanright superpartners[ 20 ].Thisispertinenttotherstandsecondgenerations.Theleftand rightgaugeeigenstatesofthethirdgenerationundergoanon-trivialamountofmixing. 46

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Inmanyscenarios,thisleavesoneofthetwomasseigenstatestobelighterthanthose intherstandsecondgenerations,whileleavingtheothermasseigenstatesignicantly heavier.Thelightestsleptonislikelytobethe ) 1 ,whilethelightestsquarkisexpected tobeeitherthe t 1 orthe b 1 .Thelightestofthe 5 Higgsparticlesisexpectedtobethe h 0 withamassunderroughly 150 GeV[ 20 ],andtheotherHiggsparticlescouldbe signicantlyheavier. 3.4HadronColliderPhenomenologyofthemSUGRAScenario Ifsupersymmetryexistsinaformthatisatleastapproximatelydescribedby mSUGRA,andthesuperpartnersarebelowafewTeV,thenthereisastronglikelihood thatseveral,ifnotmany,ofthemwillbeexposedanddiscoveredbytheexperiments operatingatLHC.Thefollowingsectionswilldiscusssomeofthegeneralexperimental signaturesofsupersymmetryinthehadroncolliderenvironment.Thisismeantto motivatethestrategyadoptedinChapter 6 whichdescribesoneoftherstsearches forsupersymmetryperformedwithhigh-energycollisiondataattheLHC.Someofthe motivatingfactorsareinspiredbyvariousassumptionsmadeintheconstructionofthe mSUGRAmodel,whileothersarequitemodelindependent. 3.4.1StrongProduction TheLHCisaproton-protoncollider,buttheactualcollisionsdonotinvolvethe protonsaswhole,astheyarecompositeparticles.Rather,thecollisionsactuallyinvolve theconstituentpartonswhichcomprisetheprotons.Thesearequarksandgluons. Theprotonisaboundstateoftwoup-quarksandonedownquark( p = uud ).These arereferredtoas valencequarks .Intheclassicaldescriptionofscattering,which involvestwoincomingparticlesandtwooutgoingparticles,thevalencequarkswouldbe theonlyparticipantsinascatteringprocessoftwoprotons.However,inthequantum elddescription,thesituationismuchmorecomplicated.Thegluonswhichbindthe valencequarkstogethercanalsoserveasoneorbothoftheincomingparticles.There isacertainprobabilitydeterminedbythetheoryofQCD,thattwocollidingprotons 47

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willactuallyscattergluonsandnotvalencequarks.Evenmorebizarreisthenotion thatnon-valencequarks,i.e,thevirtualquarksthatemergefromtheQCDanalogof Figure 2-1A ,canalsoparticipateasinitialstatesinthescatteringprocess.Thisreality leadstotheconceptofa partondistributionfunction or pdf .Inotherwords,thetotal momentumcarriedbytheprotoncanbethoughtofasbeingdistributedamongsta mixtureofvalencequarks+virtualquarks+gluons.Theamountofmomentum(on average)carriedbyeachconstituentisaverydifcultquantitytocalculateandis energy-scaledependent.Atenergiesof O ( 10 TeV),whicharerelevantfortheLHC,the gluoncomponentisexpectedtodominateoverthevalencequarks.Thecontribution fromvirtualquarksisthesmallest,butstillplaysasignicantrole. BecausetheLHCisahadroncollider,theinitialstatesareguaranteedtoinvolve coloredparticles,i.e.,particlesthatparticipateinthestronginteractionsgovernedbythe theoryofQCD.Thisfactnotonlystronglyinuencestheinitialstatesbutalsothenal states.Inthesimplestandmostlikelycasewithtwoincomingparticlesandtwooutgoing particles,themostdominantproductionmechanismofsupersymmetricparticlestates areshownbytheFeynmandiagramsinFigure 3-2 .Notallofthesediagramscontribute equallytotheproductioncross-section.Dependingonthemasshierarchyofthegluino withrespecttothesquarks,somediagramswilldominateoverothers.Ifoneassumes thatthesquarkmassesareroughlydegenerate,thenthefollowingthreescenarios shouldbeconsidered: m g > m q :Inthiscasediagramswhichincludetheproductionoftwosquarks, eitherviaannihilationoftheinitialstatesintoagluonorbytheexchangeofa virtualsquark,willdominate.Theseinclude 3-2C 3-2J ,and 3-2K .Diagram 3-2D producestwonal-statesquarks,butrequirestheexchangeofagluinowhichis takentobeheavyinthisscenario.Processesinvolvingtheexchangeofheavy particlesareextremelysuppressed. m g < m q :Inthiscasediagramswhichincludetheproductionoftwogluinos, eitherviaannihilationoftheinitialstatesintoagluonorbytheexchangeofa virtualgluino,willdominate.Theseinclude 3-2B 3-2H ,and 3-2J .Diagram 3-2A 48

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yieldstwonal-stategluinosbutrequirestheexchangeofavirtualsquark,whichis assumedtobeheavyinthisscenarioandisthereforesuppressed. m g % m q :InthiscasealldiagramsinFigure 3-2 willhavenon-trivialcontributions. Particularly,contributionsfromdiagramswithasquarkandagluinointhenal statewillbeenhanced,asin 3-2E and 3-2F q q g q g 1 A( q q ( g g ) q q g g g 1 B( q q ( g g ) q q q g q 1 C( q q ( q q ) q q g q q 1 D( qq ( q q ) g q g g q 1 E( qg ( q g ) g q q q g 1 F( qg ( q g ) g q q g q 1 G( qg ( q g ) g g g g g 1 H( gg ( g g ) g g g g g 1 I( gg ( g g ) g g q g q 1 J( gg ( q q ) g g q q 1 K( gg ( q q ) Figure3-2.Asampleofstrongproductionmechanismsofsquarksandgluinos Theconclusionsdrawnabovearevalidifoneassumesthatineitherscenario,the massesarewithintherangeaccessiblebythecollider.Inthecasethatthesquarks andgluinosaretooheavytobeproduced,thenthegreaterstrengthofthestrongQCD couplingwillbeirrelevant,andtheincomingpartonswillbeforcedtodirectlyproduce lightersuperpartnersviatheelectroweakinteraction.Thiswillinvolvediagramslikethe onesinFigure 3-3 ,whichdirectlyyieldneutralinosandcharginos.Theroleofthese 49

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diagramsmaybenegligibleorsignicantdependingonthemassspectrumofthe coloredsuperpartners. q q Z + i j 1 A( q q ( + i j ) q q Z 0 i 0 j 1 B( q q ( 0 i 0 j ) q q W i 0 j 1 C( q q ( i 0 j ) q q W 1 D( q q ( ( i ) ) q + q Z ! 1 E( q q ( ( + ( ) q ! q Z 1 F( q q ( ) ) ) Figure3-3.Asampleofelectroweakproductionmechanismsofcharginos,neutralinos, andsleptons Fromaphenomenologicalperspectivethedifferencesbetweenstrongand electroweakSUSYproductionaresignicant.Unlikethelatter,theformerinvolves heavycoloredparticles,whichmustdecaytoStandardModelcoloredparticles(i.e., quarks).Eachquarkwillhadronizeandbecomeajet.Furthermore,themultiplicity ofjetsproducedintheeventwillbelargelydependentonwhetherornotgluinosor produced.Ifagluinoisproduced,itwilldecaytoaquarkandsquark(i.e., g ( q q ). Thesquark,whichwilllikelybeoff-shell,willalsodecaytoaquarkandgaugino(i.e., q ( q + ).ThisisillustratedbythediagraminFigure 3-4 .Inthecasethatsquarksare lighterthangluinos,thentheproductionandsubsequentcascadedecaywillbegin withthesquarkinFigure 3-4 andwillonlyyieldonejetbeforedecayingtoagaugino. Becausesuperpartnersmustbeproducedinpairs(inR-parityconservingscenarios), thefollowingwillingeneralbetrue: 50

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g g productionwillleadtoatleast 2+2=4 hadronicjets. g q productionwillleadtoatleast 2+1=3 hadronicjets. q q productionwillleadtoatleast 1+1=2 hadronicjets. Inrealitytheremaybemorejetsthatariseeitherfromnalstategluonradiation(FSR) oftheoutgoingpartonsorinitialstategluonradiation(ISR)oftheincomingpartons. Thus,inthehadroncolliderenvironmentsearchesforSUSYtypicallyrelyonthe signatureofmultiplehigh-energyjets.Inordertocharacterizethetotalamountof hadronicjetactivityinacollisioneventindependentofthejetmultiplicity,itiscommonto constructavariablethatsumsthescalartransversemomentaofallofthejets.Typically, thisvariableisdenotedas H T ,andcanprovideausefuldiscriminantbetweenevents thatfeaturecoloredproductionandthosethatdonot. g q q 0 q 1 Figure3-4.Diagramofgluinoandsquarkdecay 3.4.2MissingEnergy OneofthemostimportantconsequencesofmSUGRA-inspiredmodelsisthatthey provideaviabledark-mattercandidatewhichisreferredtoastheLSP.Inmostcasesthe LSPisthelightestneutralino( + 0 1 ),whichisanelectromagneticallyneutralandweakly interactingparticle.AswasdiscussedinSec. 3.2.2 ,ifR-Parityisaperfectlyconserved quantumnumber,theneverycollisioneventwhichproducessuperpartners(inpairs) willinevitablyyieldcascadedecaysthatendintheproductionofapairofLSPs.These LSPsactlikemassiveneutrinosandwillbeinvisibletoadetector. 51

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DespitethefactthatLSPscannotinteractdirectlywiththedetectorandbe measured,theirpresencecanbeinferredindirectlybytheresultingmomentum imbalancethattheyleave.Inthecasethattwoincomingpartonswithmomentadenoted p i 1 p i 2 collideinelasticallyandproducetwosuperpartners,whichsubsequentlyundergo cascadedecaysto n nalstateobjectssuchasjets,leptons,photons,andtwoLSPs withmomentadenoted p f 1 ,..., p f n ,thentheconservationofmomentumyieldsEqs. 312 313 and 314 p i x ,1 + p i x ,2 = n / m =1 p f x m (312) p i y ,1 + p i y ,2 = n / m =1 p f y m (313) p i z ,1 + p i z ,2 = n / m =1 p f z m (314) The x and y componentsoftheinitialpartonsareequaltozeroforacollider,as thebeamsaretravelingexclusivelyinthe z direction.Thus,thetotalinitialandnal momentumtransversetothebeamdirectioniszero.Consequently,Eqs. 312 and 313 canbecombinedandrewrittenasshowninEq. 315 p i T ,1 + p i T ,2 =0= n / m =1 p f T m (315) Ifoneassumesthat n 2 nalstateparticlesarevisibletothedetectorandare well-measured,thenaconstraintcanbemadeonthetotaltransversemomentumof thetwoLSPswhichescapeundetected.Withoutlossofgenerality,thetwoLSPscan bedenotedbytheindices n and n 1 respectively.Thisconstraintyieldsanimportant quantityusedforSUSYsearchesknownasthe missingtransversemomentum ,denoted symbolicallyas P T .Inthisparticularexample,the P T wouldbecalculatedas P T = p f T n 1 + p f T n = n 2 / m =1 p f T m (316) 52

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Inthecasethatallofthenalstateobjectsarevisibleandwell-measured,then P T $ 0 (i.e,anon-SUSYevent) 3 .TheonlyparticlesfromtheStandardModelthatcanbe producedincollidersandcontributetoanon-zero P T areneutrinos,inwhichcase P T > 0 .Thus,themissingmomentumsignatureisnotexclusivetoSUSYand backgroundfromtheStandardModeldoesexist,andthiswillbediscussedinmore detaillaterinChapter 6 Forhistoricalreasonsthemissingtransversemomentumisoftenconfusingly referredtoasthe missingtransverseenergy .Thisislikelyduetothefactthatthevisible nalstateobjectsareusuallydetectedbycalorimeters,whichmeasureenergiesof particles(seeSections 5.2.3 and 5.2.4 ).Inthelimitthatthenalstateobjectsare relativistic(whichisalwaysthecaseattheLHC),themassescanusuallybeignored whendiscussingkinematicalpropertiesastheEinsteinenergy-momentumequation reducestoEq. 317 lim p % m E =lim p % m p 2 + m 2 = p (317) Thus,themomentummeasurementsimpliedinEqs. 312 313 ,and 314 are replacedbyenergymeasurementsinpractice,and P T isreplacedby E T ,eventhough theybothrepresentthesameobservable.Fromhereonthelatterwillbeusedto conformtotheconventionusedmostoftenintheliterature. Thetotalinitialmomentuminthe z direction(alongthebeams)isunknownat hadroncolliders,andwillbedifferentforeachcollision,owingtothe pdf 'sdescribed inSection 3.4.1 .Attheinstantofthecollision,thecollidingpartoncouldbecarrying anyfractionoftheproton'stotalmomentum,inprinciple.Thus,whiletherelationship inEq. 314 istrue,theinitialconditionsareunknown,andconsequentlynoobvious constraintscanbeplacedonthenalstateobjects.Forthisreason,transverseevent 3 Forconveniencethemagnitudeof P T willbedenotedby P T 53

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variablesareoftenemployedathadroncolliders.Themissingtransverseenergyisone such,veryimportant,observable. 3.4.3Same-SignLeptonPairs WhileeventsfeaturingSUSYproductionwillmostlikelybeginwithcoloredparticles (squarksorgluons)andalwaysendwithLSPs(assumingR-Parityconservation), numerouspossibilitiesexistforwhathappensinbetween.Clearly,agluinomust alwaysdecaytoaquark-squarkpair(off-shellifnecessary).Thehandednessof thequarkwillinuencethedecayofthesquark.Thestrongforcedoesnotprefera particularconguration,so50%ofthetimethequark(squark)willberight-handed(left), assumingitistheproductofagluinodecay.Theleft-squarkcouplestowinos,binos, andhiggsinos,whiletheright-squarkonlycouplestohiggsinosandbinos.Giventhatthe charginosandneutralinosconstitutemodel-dependentsuperpositionsofwino,bino,and higgsinoeigenstates,itisnotpredeterminedwhichdecaychannelswillbeaccessibleto left-andright-squarks,respectively;however,someloosegeneralizationscanbemade. InmSUGRAmodelstheLSPispredominantlyabinoeigenstate,withlittlecontribution fromthewinoandhiggsinoeigenstates.Thecharginosandheavierneutralinostend tohaveasmallerbinocomponent.Thus,ifright-squarksareproduced,eitherdirectly orthroughgluinodecay,theywilldecaytotheirquarksuperpartnerandimmediately totheLSP.Thisphenomenonwouldconstitutea jetsandmissingenergy signature.In thecasethattheleft-squarkisproduced,intermediatedecaystocharginosandheavier neutralinosareaccessibleinordertoendwithanLSP.Theseintermediatedecayswill inevitablyyieldStandardModelleptons,whichwouldconstitutea leptons,jets,and missingenergy signature. Theproductionofleptonsisakeysignatureathadroncollidersfortworeasons:1) theyindicatethatanelectroweakprocessoccurred,whichisnotfavoredbyinteractions thatbeginwithcoloredparticles(i.e.,stronginteractionsarefavored)and2)leptons aretypicallyeasiertounambiguouslydetect,andtheirnal-stateattributescanbe 54

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well-measured.OnceonedecidestofocusonleptonicsignaturesofSUSYproduction, anaturalquestionarises.HowcanSUSYproduceleptonsinacongurationthatisnot easilyproduciblebyinteractionsinvolvingparticlesexclusivetotheStandardModel?A strikinglyuniquecongurationrelatestotheproductionofapairofleptons(di-leptons) witheachleptoncarryingthesameelectromagneticcharge[ 20 23 27 ].Anexample ofsuchaneventisshowninFigure 3-5 .Thisprocessinvolvestheproductionofa gluinoandleft-squark,whicheachgiverisetoacascadedecayofStandardModel particles.Thethreequarks( q q # q ## )willeachbedetectedasjets.Thetwoleptons ( + + )canbefromthesamefamilyorfromdifferentfamiliesandwillhavethesame electromagneticcharge.Thesewillbedetectedinisolationfromotherobjectsinthe decay 4 .Theneutrinos( (( )aswellastheLSPs( + 0 1 + 0 1 )willcontributetoasignicant amountofmissingenergy.Figure 3-5 isonesimpleexampleofaSUSYeventwhich yieldssame-signdi-leptons.Therearemanymorecongurationswhichresultina similareventsignatureortopology. s g q q g q q q q !! + 1 q + 1 + # # 0 1 + # # 0 1 1 Figure3-5.Exampleofsame-signdi-leptonproductioninsupersymmetry 4 Determiningwhetherornotaleptonisisolatedisacrucialaspectofevent reconstructionandisthusthefocusofagreatamountofworkbyexperimentalists.This willbediscussedingreaterdetailinChapter 6 55

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AswillbeshownlaterinChapter 6 ,theproductionofsame-signdi-leptonsis greatlysuppressedintheStandardModel,thusmakingthe same-signdi-leptons, jets,andmissingenergy signatureoneofthemostpromisingavenuesfordetecting supersymmetry.WhilethisworkfocusesonthissignatureinthecontextofR-Parity conservingmodelsofsupersymmetry,same-signdi-leptonscanalsobefeaturedin avarietyofalternativetheoriesofnewphysicsbeyondtheStandardModel,suchas UniversalExtra-Dimensions[ 28 ],heavyMajorananeutrinos[ 29 ],andgrandunied theoryinwarpeddimensions[ 30 ]. 3.5CurrentExperimentalLimitsonSupersymmetry WhiletheparameterspacefortheMSSMisvast,notallpossiblevaluesofthe parametersareviable.AswasdiscussedinSec. 3.3 ,strongtheoreticalmotivationand compellingexperimentalevidencejustifymanyofthesimplifyingassumptionsthatwere usedtoformulatethemSUGRAmodel,whichisfullydenedwiththespecication of 5 parameters( m 1 / 2 m 0 A 0 tan( ) ,sign( )).Furtherreductionoftheparameter spacehasindeedbeenachievedbyavarietyofexperimentalresultsfromthepast fewdecades.Athoroughreviewoftheconstraintsonsupersymmetryisprovidedin Ref.[ 11 ].Abriefsummaryofthesewillbegiveninthefollowingsections,withafocus onmodelswhichconserveR-Parityandfeaturegauginoandscalarmassunicationat theGUTscale(e.g.,mSUGRA). 3.5.1ConstraintsfromAstrophysicalEvidenceofDarkMatter AnalysisoftheCosmicMicrowaveBackground(CMB)datafromtheWilkinson MicrowaveAnisotropyProbe(WMAP)showsthatthedensityofbaryonicmatterinthe universeis b h 2 =0.0227 0.0006 ,whilethetotaldensityofmatterintheuniverse is m h 2 =0.133 0.006 [ 11 ],where h istheHubbleconstantthatcharacterizesthe expansionoftheuniverse.Thematterdensityexcess,i.e. DM h 2 =( m b ) h 2 = 0.110 0.006 isgenerallyattributedtoacolddarkmattersubstance.Constraints canthusbeplacedontheparameterspacesuchthattherelicabundanceofthe 56

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LSPaccountsfortheobserveddarkmatter,i.e., ( $ DM .Theinterplayofthe mSUGRAparametersand ( isquiteinvolvedbutsomegeneralizationscanbe made.Thecross-sectionfortwothermalLSPstoannihilate(e.g., + 0 1 + 0 1 ( f f ) dependsonthecouplingsandmassesoftheexchangedandnal-stateparticles, andisinverselyproportionaltotheLSPrelicdensity ( [ 31 ].Typically,theannihilation willinvolvetheexchangeofa Z boson,aHiggsboson,orasfermionandwillresult inafermion-antifermionpair.Morenalstatesbecomeavailableasthemassof theLSPincreases(e.g,pairproductionof Z and W bosonsortopquarks).Each pointinthemSUGRAparameterspaceyieldsadistinctvaluefor ( .Whilethereis somedependenceonthevaluesofotherparameters,inordertoget ( intheright neighborhood,thevaluesof m 0 and m 1 / 2 arerestrictedtoverynarrowranges.A detailedreviewandanalysisoftheviableregionscanbefoundelsewhere[ 32 ]. 3.5.2ConstraintsfromIndirectLow-EnergyMeasurements Evidenceoftheexistenceofsuperpartnerscouldbeobservedindirectlythrough loopcontributionstovariousobservables.Onesuchexampleisthedecayofthe B -mesontoapairofoppositelychargedleptons.Suchdecaysareonlypossiblein theStandardModelthroughsecond-orderweakinteractions,andarethusheavily suppressed.However,thequantumcorrectionsthatwouldcomefromthepresenceof superpartnerscouldresultinadetectableenhancementintherespectivebranching ratiosforthe B 0 s ( + and B 0 s ( e + e (orlikewisefor B 0 ).Precisemeasurementsof thesebranchingratioswerecarriedoutattheCDFandD0experimentsattheTevatron colliderandalsoatvariousB-factoryexperiments[ 11 ].Whilenoneoftheexperiments hadthesensitivitytoconrmtheStandardModelprediction,strictlowerlimitsonthe branchingratiosof O (10 8 ) wereplaced,andaportionofthepreviouslyallowedSUSY parameterspacewasexcludedasaresult. AnothermeasurementwhichhasthepotentialtomakecontactwithvirtualSUSY particlesvialoopcorrectionsisthatofthemuonmagneticmoment( a ).Thisquantity 57

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canbecalculatedtoveryhighprecisionintheStandardModel.Itcanlikewisebe measuredtoveryhighprecisionbystudyingtheprecessionofmuonsastheycirculate aroundastorageringunderaconstantmagneticeld.TheE821experimentat BrookhavenNationalLaboratory(BNL)recentlypublishedaninterestingresultwhich suggestsa3.2 discrepancybetweenthepredictedandobservedvalueof a [ 33 ]. Whilethisisnotconclusive,itdoesaccommodateavarietyofSUSYmodelswhich predictanadditionalcontributionto a .Superpartnerswithmassesintherangeof 100 500 GeVcouldpotentiallyaccountforthedeviation.Thecorrectionisalso proportionalto tan( ) [ 11 ]. 3.5.3ConstraintsfromDirectExperimentalSearches Themostpowerfullimitssetbydirectsearchesforsupersymmetricparticles wereachievedbytheexperimentsoftheLEP(LargeElectronPosition)colliderand theTevatron p p collider,respectively.AtLEP,wherethecenterofmassenergywas & s =209 GeV,thedominantproductionmechanismoccursbyelectroweakprocesses. Table 3-3 summarizesthelimitssetforvariousspeciesofsparticles.Forsleptonsthe parametersof and tan ( )aresetto 200 GeVand 1.5 respectively.Charginomasses aresensitiveto M 2 ,and tan ( ).Thelimitsonthelightestcharginoarepresentedin 3-3 andarerobustagainstascanovertheseparameters,exceptforlargevaluesof M 2 ( 1 TeV)wherethemassdifferencebetween + 1 and + 0 1 isverysmall[ 11 ].Neutralino massesaresensitiveto M 1 inadditiontotheparametersrelevantforthecharginos.In manymodelsthelightestneutralinoiselectricallyneutral,whichimpliesdirectsearches arenotreallyfeasible.However,indirectlimitscanbeplacedonthemassoftheLSP basedonslepton,chargino,andHiggssearches.ManylimitslistedinTable 3-3 rely ontheassumptionofsfermionandgauginomassunicationattheGUTscale.In manycases,thelimitscanbetightenediffurtherassumptionsaremadeaboutmodel parameters.Theresultsfor ) L R and t 1 assumetheworstcasescenarioforL-Rmixing. 58

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Table3-3.LimitsonSUSYparticlesfromtheLEPexperiments(ALEPH,OPAL,DELPHI, L3)[ 11 ] ParticleMassComment Limit(GeV) e L R 100 Limitvalidfor M ( 0 1 < 85 GeV L R 95 Limitvalidfor M ( R , + 0 1 ) > 5 GeV ) L R 86 Limitvalidfor M ( ) R , + 0 1 ) > 7 GeV + 1 103 Limitvalidfor M > 200 GeV + 0 1 47 Limitvalidforawiderangeof tan( ) t 1 96 Limitvalidfor M ( t 1 M ( + 0 1 c )) > 5 GeV) AttheTevatroncollider,wherethecenter-of-massenergyis & s =1.96 TeV, productionofcoloredparticlesisexpectedtodominatebecausetheinitialparticles arecolored.Table 3-4 summarizesthelimitsthatwereachievedbytheCDFandD experimentsattheTevatron.MostlimitsarepresentedforanmSUGRAscenariowhere tan( )=3 A 0 =0 ,and < 0 ,butwerealsofoundtobevalidforawiderangeof parametervalues.Searchesinvolvingassociatedchargino-neutralinoproduction(e.g. qq # ( + 1 + 0 2 throughs-channel W exchange)werealsoperformed.Thesesearches exploitedthesame-signdi-leptonsignatureinordertoreducebackgroundsandset exclusionlimits[ 34 35 ]. Table3-4.LimitsonSUSYparticlesfromtheTevatronexperiments(CDF,D )[ 11 ] ParticleMassComment Limit(GeV) q L R 379 Limitvalidforrstandsecondgenerationsquarks overalargescanoftheparameterspace t 1 180 Limitvalidfor 40 # M ( 0 1 # 95 GeV b 1 240 Limitvalidfor M ( 0 1 < 80 GeV g 308 Limitvalidforalargescanoftheparameterspace + 1 164 Limitvalidfor m 0 =60 GeV, > 0 Inordertocomparethesensitivitiesofvarioussearchesacrossdifferentexperiments, aconventionhasbeenestablishedtopresentsearchlimitsasexclusioncontoursinthe m 0 m 1 / 2 planeofthemSUGRAparameterspace.Achoiceof tan( )=3 A 0 =0 ,and 59

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< 0 wasmaderatherarbitrarily.Figure 3-6 showstheexcludedregion(redshading) fromaD searchforsquarksandgluinos[ 36 ]alongwiththelimitssetbythedirect charginosearchesfromtheLEPexperiments(blueandgrayshading).Thesolidred linedelimitstheexcludedregionsetbytheanalysisandthedashedbluelinerevealsthe expectedexclusionlimit.Thedottedblacklinesenclosingtheexclusionlimitrepresent thetheoreticaluncertainties. (GeV) 0 m 0100200300400500600 (GeV) 1/2 m 0 50 100 150 200 250 (GeV) 0 m 0100200300400500600 (GeV) 1/2 m 0 50 100 150 200 250 -1 D, L=2.1 fb <0 =0, 0 =3, A tan no EWSB " # LEP2 l ~ LEP2 D II Figure3-6.ExclusionlimitsforsquarksandgluinosfromtheD experimentpresented onthe m 0 m 1 / 2 planefor tan( )=3 A 0 =0 ,and < 0 [ 36 ]. TheexperimentsoperatingattheLHCareexpectedtoextendtheexclusionlimits wellbeyondthoseinFigure 3-6 intheworstcasescenario,orconrmtheexistence ofsupersymmetryinthebestcasescenario.Forthelattercase,thenaturallylowrate ofStandardModelbackgroundstothesame-signdi-leptonsignaturemayenable ittoprovidethemostcompellingevidence.Thiswillbediscussedinmoredetailin Chapter 6 60

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CHAPTER4 THELARGEHADRONCOLLIDER 4.1Design TheLHCisasuperconductinghadronacceleratorconsistingoftworings(one foreachbeam).ThetunnelwhichhoststheLHCspans 26.7 kmincircumference andstraddlestheFranco-SwissborderintheregionnearLakeGenevaandtheJura Mountains.ConstructionofthetunnelbeganonbehalfoftheLargeElectronPosition (LEP)collideratCERNin1984andwascompletedin1989.LEPprecededtheLHC, operatingfrom1991to2000.Infact,theLHCprojectwasapprovedin1994bythe CERNcouncilwhileLEPwasstillintheearlystagesoffulllingitspotential. BudgetconcernsrequiredtheLHCtoexploittheexistingLEPtunnel.This constraintcamewithimplications,asthegeometryofthepreexistingtunnel(i.e., theproportionsofstraightandcurvedsections)isactuallybestsuitedforcirculating electronsandpositrons,whichexperiencesignicantenergylossesduetosynchrotron radiationwhileundertheinuenceofmagneticelds.Protons,forexample,donot suffersuchdramaticlossesandcouldtakebetteradvantageofamorecircularring[ 37 ]. Thetunnelgeometrycombinedwiththeexistingsuperconductingmagnettechnologies ultimatelyimposedanupperboundonthecenter-of-massenergiesachievablebythe LHCat & s =14 TeV.Thislimitwouldstillberoughly 7 timeshigherthantheenergies achievedbytheworld'smostpowerfulacceleratoratthetime,theTevatronofFermilab. OneofthemostimportantadvantagesthattheLHChasoveritspredecessorsis notonlythecollisionenergy,butalsotheinstantaneousluminosity,whichdeterminesthe rateatwhichhigh-energycollisioneventswillbeproduced.Thesimpleformulaforthe eventrateisgiveninEq. 41 n events = L ( pp ( X ) (41) 61

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where L istheinstantaneousluminosityandthecross-section ( pp ( X ) isdetermined bytheLagrangiangoverningthedynamicsof X anddoesnotdependonthebeam parameters,asidefromthevalueof & s .Itisclearthatif X israre(i.e.,hassmall cross-section),thentheimportanceofattaininghighinstantaneousluminosityis paramount.ThecommonexpressionfortheinstantaneousluminosityforaGaussian beamdistributionisgivenby[ 37 ]: L = N 2 b n b f rev & 4 */ n 1 4 1+( ) c z 2 ) 2 (42) Adescriptionofsomeoftheseandotherbeamrelatedparametersaswellas theirnominalandcommissionedvaluesisgiveninTable 4-1 .Itisworthnotingthatthe instantaneousluminosityachievedbytheLHCiftheseparameterstakeontheirnominal valuesis L peak =10 34 cm 2 s 1 ,whichisnearlyafactorofseventygreaterthanthat obtainedbytheTevatron.Itwaspartiallythishigh-luminosityambitionthatmotivated thechoiceofdualprotonbeamsfortheLHCinsteadofproton-antiprotonbeams,as isthecasefortheTevatron.Production,capture,andcirculationofantimatteralways presentsagreaterchallengeforexperimentaliststhanworkingwithordinary,stable matterparticleslikeprotonsandelectrons.However,circulatingparticle-antiparticle beamsdoesprovidetheaddedadvantageofonlyneedingasinglering.Thetwobeams cansharethesamemagneticeldandhencethesamephasespacewhileinorbit. ItshouldbenotedthattheLHCalsocirculatesheavyionbeams(Pb)duringvarious stagesofoperation.Detailsconcerningtheheavyionphysicsprogramarebeyondthe scopeofthiswork,butcanbefoundelsewhere[ 37 ]. TheLHCtunnelliesundergroundatdepthsvaryingfrom 50 mto 175 m(underthe JuraMountains)andhostsseveralexperiments,whichwillbesummarizedinSec. 4.2 AschematiclayoutoftheCERNacceleratorcomplexcanbefoundinFigure 4-1 .As onecanreadilyobserve,thereisasequenceofsmalleracceleratorswhichareusedto feedprotonbeamsintotheLHC,witheachsuccessiveoneimpartingmoreenergythan 62

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Table4-1.SummaryofLHCbeamparameters NominalCommissioned ParameterDescriptionUnitsValueValue(2010) N b protonsperbunch 1.15 10 11 1.15 10 11 n b bunchesperbeam 2808368 T bs bunchspacing ns 25150 f rev orbitfrequency kHz 11.24511.245 & relativisticboost 74613730 n transverseemittance 3.752.1 + betafunctionatIP m 0.553.5 c crossingangle rad 285200 z RMSbunchlengthin z -direction cm 7.559 L peak peakinstantaneousluminosity cm 2 s 1 10 34 2.05 10 32 & s c.o.m.energy TeV 147 theprior.Protonsareharvestedfromdi-hydrogenatoms.Onceisolated,theharvested protonsareinjectedintothePSBooster(PSB)withenergiesnear 50 MeV(viathe Linac2).ThePSBacceleratestheprotonsuntiltheyachieveanenergyof 1.4 GeV (roughlyhalfthespeedoflight)wherebytheyarefedtotheProtonSynchrotron(PS) untiltheyareacceleratedto 25 GeV(approximately98%thespeedoflight).Fromthe PStheyaresenttotheSuperProtonSynchrotron(SPS)whichistheirlastdestination beforebeinginjectedintotheLHCat 450 GeV.Thistransitionfrom 50 MeVto 450 GeVtakesjustunder5minutesundernormalcircumstances.ThedesignoftheLHC projecteda 20 minuteperiodfortheRFcavitiesintheLHCtotaketheprotonsfrom 450 GeVto 7 TeV;however,owingtounexpecteddifcultiesencounteredduringthe commissioningstagesoftheLHCin2008-2009,thisnominaldesignenergyhasnotyet proventobefeasible.Instead,theterminalenergyfortheprotonsthusfarachievedis 3.5 TeV.Thisyieldsacollisionenergyof & s =7 TeV,whichprovedtobethestateof operationforthe2010LHCrunsfromwhichthisworkisbased.MoredetailsontheLHC operationin2009-2010willbediscussedinSec. 4.3 ItisimportanttonotethatprotonsdonotarrivetotheLHCindividually.Rather, theyaresynchronizedandarriveinwhatarecalled"bunches".FromTable 4-1 itisclear thatbunchescompriseupto 115 billionprotonsundernominalconditions.Bunches 63

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Figure4-1.CERN'sacceleratorcomplex 64

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canbeseparatedinspacebyaslittleas % 7 mandseparatedintimebyaslittleas 25 ns.SteeringoftheprotonbunchesisperformedinthearcsoftheLHCby 1,232 powerfulsuperconductingdipolemagnets.For 7 TeVbeamscirculatingthe 27 kmring, amagneticeldof 8.33 Teslaisrequired.Thestrengthoftherequiredmagneticeld scaleslinearlywiththeenergyofthebeams.Thus,theenergylimitisstronglycoupled tothemagnettechnology.Focusingofthebeamsinthetransverseplaneisperformed byalatticeformationof 392 quadrupolemagnetswhicharelocatedinvarioussectors aroundthering.Therearemanyothertypesofmagnetsystemsemployedthroughout theLHC(e.g.sextupoles,octupoles)whichalsohelptocontrolthebeams. ItiscrucialthattheLHCbeampipeshostingtheprotonbeamsarecompletely evacuated.Anyresidualgasparticlesmaycauseelasticorinelasticcollisionswiththe circulatingprotons.Notonlydoesthisaffectthelifetimeofthebeam,butsuchcollisions createaso-called"machine-inducedbackground"fortheexperimentsiftheyhappento occurupstreamordownstreamoftherespectivedetectors.Themainvacuumsystemis engineeredtoreducethepressureoftheLHCbeampipestoalevelof10 13 atm. 4.2Experiments ThecollisionsproducedbytheLHCarestudiedbysixdistinctparticledetectors.A briefsummaryofeachexperimentisdescribedbelow: CMS TheCompactMuonSolenoid(CMS)isageneralpurposeparticledetectorwhich isdesignedtooperateathighluminosity(L=10 34 cm 2 s 1 ).Itsmainfeatureis 3.8Teslasuperconducting,solenoidalmagnetwhichaidsintheidenticationof variouschargedparticlespecies.ThephysicsprogramoftheCMSdetectoris diverse,coveringprecisionStandardModelmeasurementsaswellasofferingan excellentsensitivitytovariousscenariosfortheHiggsmassandmodelsofnew physics,likesupersymmetry.Over3,000scientistsfromnearly200institutes acrosstheworldcollaborateontheCMSexperiment.Itisavastscientic endeavor.MoredetailsontheCMSdetectorwillbediscussedinChapter 5 andcanalsobefoundelsewhere[ 38 ].ThisresultsshowninChapter 6 arebased ondatarecordedbytheCMSexperiment. ATLAS 65

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AToroidalLhcApparatuS(ATLAS)isalsoageneralpurposeparticledetector whichisdesignedtooperateathighluminosities.ATLASandCMSarecompeting experimentsandhavesimilarparticledetectionattributes,buthavecompletely differentdesignswithrespecttothemagneticeldemployed,andthematerials usedtobuildthetrackingdetectorsandcalorimeters.Onemaywonderwhy valuableresources(e.g.,manpowerandmoney)isdevotedtobuildingtwo separatemachineswhicharemeanttoperformthesametasks.Itisimportant thatanypotentialdiscoveryorsignalexclusionresultsreportedbyoneexperiment canbecorroboratedbyanother.Theseduelingexperimentsservethisexact purpose.Thisprovidesconsistencyandredundancytoanyground-breaking discoverieswhichmaybewaitingforusattheLHC.TheATLAScollaborationis similarinsizetotheCMScollaboration.MoredetailsontheATLASexperiment canbefoundelsewhere[ 39 ]. ALICE ALargeIonColliderExperiment(ALICE)willstudytheheavy-ioncollisions producedbytheLHC.Thesecollisionsareexpectedtoproduceanexoticstate ofmatter,theso-calledquark-gluonplasma,whichistheorizedtohaveexisted duringtheinitialstagesaftertheBigBang.Amongotherthingsthestudiesof quark-gluonplasmamayshedlightonpropertiesofconnementinthetheory ofstronginteractions(QCD).TheluminositywhichisdeliveredtoALICEbythe LHCissignicantlylessthanthatwhichwillbedeliveredtothehighluminosity experiments.ALICEwillreceiveL % 10 27 cm 2 s 1 [ 37 ].Thecompletetechnical designreportfortheALICEexperimentcanbefoundelsewhere[ 40 ]. LHCb TheLargeHadronColliderbeauty(LHCb)experimentwillstudythephysicsof b-quarksinanattempttounderstandwhytheuniverseiscomposedpredominantly ofmatterwithverylittleanti-matter.TheLHCbdesignispeculiarinthatitis asymmetricwithrespecttothetransverseplane.Itconsistsofonlyoneforward spectrometerwhichwillcatchthedebrisofproton-protoncollisionsalongthe beamlineinonlyonedirection.Becausesuchlittleenergyisneededtoproduce b-quarksinsuchcollisions,theyareproducedwithsignicantmomentumin thez-direction(alongthebeams)andthereforetravelveryneartothebeam line.Thus,onlyasmallsolidangleofcoverageisnecessarytocapturethefull decayofanyB-mesonsonewishestostudy.BydesigntheLHCbexperiment expectsluminositieswhichareabouttwoordersofmagnitudelessthanCMSand ATLAS[ 37 ].MoredetailsoftheLHCbexperimentcanbefoundelsewhere[ 41 ]. LHCf TheLargeHadronColliderforwardexperiment(LHCf)consistsoftwodetectors ofrelativelysmallsizelocated 140 mfromIP1(i.e.,theATLASinteractionpoint) andwillstudyveryforwardneutralparticlesemergingfromproton-protoncollisions occurringatIP1.Themainphysicsgoalistovalidateandcalibratethehadron interactionmodelswhichareusedinthestudyofveryenergeticcosmic-rays. 66

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TheLHCfcollaborationismuchsmallerinsizethantheotherLHCexperiments, consistingofroughly20scientistsfromabout10institutions.Thedetailsofthe LHCfprojectcanbefoundelsewhere[ 42 ]. TOTEM TheTOTalElasticanddiffractioncross-sectionMeasurement(TOTEM)experiment willalsostudytheforwarddebrisofprotoncollisionsintheregionssurrounding IP5(i.e.,theCMSinteractionpoint).Amongothergoals,theTOTEMexperiment willmeasurethesizeofprotonsandprovideanaccuratemeasurementofthe LHC'sluminosity.MoredetailsaboutthephysicsprogramofTOTEMcanbefound elsewhere[ 43 ]. 4.3Performancein2009-2010andProjectionsfor2011-2012 TheLargeHadronCollider,likemanyacceleratorsbeforeit,servesasitsown prototype.Asaconsequencemanylessonshadtobelearnedduringthedesignand commissioningstages.ManyunforeseenobstacleswereencounteredandtheLHC sufferedvarioussetbackswhichultimatelydelayedtheinitialstart-upofproton-proton collisionsbyseveralyears.Aftermuchanticipation,theLHCbegantocirculateasingle non-collidingprotonbeamatinjectionenergies( 450 GeV)onSeptember10,2008.This wasamonumentalachievementandmarkedthebeginningofwhatwasthoughttobe theLHC-eraofnewphysicsdiscoveries.Thisexcitementwasshort-livedasonlynine dayslateronSeptember19adevastatingengineeringawwasexposedwhileramping upasectionofdipolemagnetstocurrentshighenoughtosteer 5.5 TeVbeams.Inshort, afaultyelectricalconnectioncausedanelectricalarcthatpuncturedtheheliumvessel, whichsubsequentlyreleasedseveraltonsofliquidheliumintothetunnel.Thehuge pressureforcesassociatedwiththisreleasecausedseverestructuraldamagetomagnet systemandtheringinthesurroundingarea[ 44 ]. TheLHCwouldsufferayearlongdelaytonotonlyrepairthedamage,butto alsothoroughlytestandimprovetheelectricalconnectionsthroughouttherestofthe acceleratorsothatthisincidentwouldnotberepeated.Itwasdeterminedthatwhen theLHCstartsupagain,itwouldoperateforanextendedperiodwithareducedbeam 67

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energyof 3.5 TeV(insteadof 7 TeV)inordertogivetheLHCoperatorsexperiencewith runningthemachinesafely[ 45 ]. Inlate2009afterseveralmonthsofrepairsandhardwarecommissioning,the LHCbegantoinjectprotonbeamsintotheringsagain,startingwithinjectionenergies andgraduallyworkinguptohighermagneticeldstosteerhigherenergybeams.On November30,2009historywasmadeastheLHCreplacedFermiLab'sTevatronasthe highestenergyparticleacceleratorintheworldbycirculatingprotonsatanenergyof 1.18 TeV(beatingthepreviousrecordof 0.98 TeV)[ 46 ].Shortlyafter,theLHCbeganto steerthebeamsintoeachotherattheinteractionpointsalongthering,andtheparticle detectorswereobservingcollisionsatarecordc.o.m.energyof 2.36 TeV.Followinga briefshutdownperiod,onMarch19,2010theLHCbegancirculatingprotonbeamsat therecordenergyof 3.5 TeVandonMarch30begancollidingthem.TheLHCphysics programwasnowunderway. Theintentionwastocarefullyincreasetheinstantaneousluminosityoveraperiod ofseveralmonths.Gradually,thenumberofprotonsperbunchwouldincreaseand thenumberofbunchesinjectedperbeamwouldincrease.Otherparametersrelated tothebeamopticswouldbegintoapproachtheirnominalvaluesaswell.FromApril toearlyJuneof2010,onlyafewbuncheswereinjectedperll.StartinginlateJune throughtheendofJuly,theLHCincreasedthenumberofbunchesinjectedto 13 .Then inAugust,itwasupto 25 to 50 bunches.Intheperiodfrommid-Septembertolate October,llswouldcontainanywherefrom 50 to 368 bunches,insomecaseswithbunch spacingsof 150 ns.Thenalproton-protonllfor2010cameonNovember4,2010.In thesubsequentweekstheLHCtransitionedtoabrieflead-ionrun. Figure 4-2 showstheinstantaneousluminosityintegratedovertime(alsocalledthe integratedluminosity)deliveredbytheLHC(red)andrecordedbytheCMSdetector (blue)asafunctionoftime.Theintegratedluminosity L d t hasunitsofinverse length-squaredandisausefulmeasureofhowmuchdataisproducedorcollected. 68

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Foraprocessofinterestwithaknowncross-section ,onesimplyhastotakethe productof L d t todeterminetheexpectednumberofeventsproducedinthe collecteddata.Thisissimplythetime-integralofEqn. 41 .In2010theLHCdelivered roughly 47 pb 1 ofdatatotheCMSexperiment,meaningaprocesswith =1 pb couldbeexpectedtobeproduced 47 timesonaverageinadatasetofthissize. Figure 4-2 alsodemonstratestheefcientoperationsoftheCMSexperimentasthere waslittledeadtimewhiletheLHCwasproducinggoodcollisiondata.Perhaps,themost importantobservationistheexponentialriseindataproducedastheLHCwasgradually increasingtheinstantaneousluminosity.DespiteconstantoperationoftheLHCinthe periodspanningApriltoNovember,nearlyhalfofallofthedatawasproducedinthe lastweekofrunning.Thishighlightstheimportanceofrunningtheacceleratoratthe nominalinstantaneousluminosity. Figure4-2.Integratedluminosityfor2010[ 47 ] SeveralscenarioswereconsideredforthenextphaseofLHCoperationswhich wouldbegininMarchof2011.Amongotherlessimportantissues,theenergiesofthe beamsandthetotaldurationofthenextrunweretopicstobeaddressedattheannual LHCPerformanceWorkshopinChamonix,France[ 48 ].Increasingthebeamenergies 69

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to 4 TeVwasthoughttobefeasible,butultimatelyitwasdecidedtomaintainthebeams attheircurrentlycommissionedandwell-understoodenergyof 3.5 TeV.Itwasknown thatalongshutdownperiodwouldberequiredtoupgradethemachinestohandlethe designbeamenergiesof 7 TeV.Thequestionremainedastowhenthisshutdownperiod wouldoccur,asitisstronglycoupledtotheend,andhenceduration,ofthenextphysics run.Whiletheexperimentalcommunitywaseagertoanalyzethefuturedataproduced at & s =14 TeV,therewasmuchmoredemandtohavesomediscoverypowerwith thedatatobeproducedduringthenextrunoftheLHC.Therefore,theCERNcouncil decidedtobeginthenextruninMarchof2011andcarryitthroughtotheendof2012 inthehopesthattheacceleratorwouldbeabletodeliveratotalof 5 to 10 fb 1 ofdata. Thismuchdatawouldallowfortheexperimentstoexcludetheexistenceofvarious incarnationsoftheStandardModelHiggs'bosonorseenearlyconclusiveevidenceof itsexistence.AsaresultthenextphaseoftheLHCoperationisinformallybeingreferred toasthe HiggsRun 70

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CHAPTER5 THECMSEXPERIMENT TheCompactMuonSolenoid(CMS)isamulti-purposeparticledetectordesigned tooperateinthehighluminosityenvironmentprovidedbytheLHC.Locatedroughly 100 metersundergroundatInteractionPoint5(IP5)oftheLHCtunnel,theCMSdetector boastshigh-performancetracking,calorimetry,andparticleidenticationwhichis neededtoaccommodatetheambitiousphysicsgoalsoftheLHC. 5.1CMSCoordinateSystem TheCMSdetectorhasadoptedacoordinatesystemthatiswell-suitedfora cylindricalapparatusoperatinginahadroncolliderenvironment.Thepositive x -axis pointstowardsthecenteroftheLHCring,whilethepositive y -axispointstoward thesky.The z -axisliesalongthebeampipewiththepositivedirectiontowardthe JuraMountains.Theazimuthalangle ismeasuredfromthepositive x -axis.The zenithangle 0 ismeasuredfromthepositive z -axis.Thepseudorapidityisdenedas 1 = ln(tan( ) 2 )) .Thedifferenceinpseudorapiditybetweentwoparticles( 1 )represents alongitudinallyinvariantquantity. Asaconventiondifferentregionsof | 1 | withintheCMSdetectorareoftenreferenced. Themostcentralregionofthedetectorisoftencalledthe"barrel".Usually,thisregion spans | 1 | # 1.1 .Theregionroughlydenedover 1.1 # | 1 | # 3.0 isoftenreferredtoas the"endcap",andtheregionbeyond | 1 | 3.0 isreferredtoas"forward".Thevalues of | 1 | delineatingtheseregionsaretakentobequalitative,ingeneral;however,inthe contextofparticularsub-detectors,thegeometryoffersmorepreciseboundariesin | 1 | to separatetheseregions. 5.2DesignandPerformance TheCMSdetectorwasconstructedcompletelyabovegroundandthenlowered piece-wiseintotheundergroundcaverndesignedtohosttheapparatus.Fullyassembled, 71

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theapparatusspans 21 metersinthe z -dimensionwithacylindricalradiusof 15 meters andweighsnearly 12,500 tons. ThegeneraldesignoftheCMSdetectorcanbedescribedasfollows.Thedetector asawholeiscylindricalinshapeandiscomposedofseveralsub-detectors.Starting fromthenominalinteractionpointandmovingoutwardinradius,thedetectorconsists ofasilicontrackingdetector(Tracker)followedbyanelectromagneticcalorimeter (ECAL)andthenahadroncalorimeter(HCAL).Thesuperconductingmagnetliesin betweenthemainbarrelHCALsub-detectorandanouter-barrelHCALsub-detector. Beyondthemagnetliesanextensivemuonsystem.Figure 5-1 showsafullviewof theschematicdesignoftheCMSdetectorwiththemagnetandvarioussub-detectors labeled.Figure 5-2 showsthecross-sectionoftheCMSdetectorinthe r z plane.The magnetandtheindividualsub-detectorswillbediscussedinmoredetailinthefollowing sections. Itisworthdiscussingthemonumentalchallengeinvolvedinsynchronizingthe varioussub-detectors.TheLHCisdesignedtoprovidehigh-energycollisionsevery 25 ns.Theparticleswhichemergefromthecollisionsarerelativisticingeneralandhave speedscomparabletothespeedoflight c =2.98 10 8 m/s.Somesimplearithmeticleads onetothestartlingconclusionthatthedebrisfromcollision X willstillbepropagating throughvariouscomponentsoftheCMSdetectorwhilecollision X +1 isoccurring. Tobeprecise,thedebrisofcollision X willbelocatedataradialdistanceof( 2.98 10 8 m/s) ( 25 10 9 s) $ 7.5 m,whichisstillwell-insideofCMS.GiventhattheCMSdetector hasacylindricalradiusof 15 m,thedebrisfromcollision X willjustbeleavingthe peripheryofCMSascollision X +2 isoccurring.Thus,detectorsynchronizationisof paramountimportancetoensureconsistenteventreconstruction. Inthesectionsthatfollow,thegeneraldesignandfunctionofthevariousCMS sub-detectorswillbedescribed.Theroleoftriggeringisinextricablytiedtomanyof 72

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thedesignaspectsofthesub-detectors(apartfromtheTracker);however,mostofthe discussionontheCMStriggersystemwillbedeferreduntillaterinsection 5.2.6 5.2.1SuperconductingMagnet Formanyparticledetectorsofthiskind,thecongurationofthemagneticeld greatlyinuencestheoveralldesignandattributesoftheapparatus.CMSisno exception,asthesuperconductingsolenoidimposesacylindricalgeometryonthe detectorwhichmustbeaccommodatedbytheothersub-components.Astrong magneticeldisneededtobendenergeticchargedparticlesformomentummeasurements andelectromagneticchargeassignmentswithintheinnertrackingvolume(interiortothe magnet)andwithinthemuonsystem(exteriortothemagnet).Theboreofthemagnet whichhoststhequadruplylayeredcoilwindingsmustbelargeenoughtohostthethe innertrackingsystemandcalorimetryinitsinterior.Thisplacesadirectdemandonthe cylindricalradiusofthesolenoidandconsequentlyadirectdemandonthevolumeof space(orinstrumentation)whichwillbepermeatedwithmagneticelds.Magneticelds storepotentialenergyinanamountthatscaleswiththevolumeandthesquareofthe magneticeld.AsaresulttheCMSsolenoidstoresanenormousamountofenergy, roughly 2.6 GJatfullcurrent. Magneticeldlinesformclosedloops.Thus,theuxdeliveredbycoilsthrough theinteriorofthesolenoidmustbereturnedandisdonesothroughamassiveiron yokecomposedofvewheelsandtwoendcaps.Thisironyokealsohousesthemuon systems,bothinthebarrelandendcaps.Amuonthereforeexperiencescounteracting deectionsasittransitionsfromtheinteriorofthesolenoidtotheexterior. 5.2.2TrackingSystem AtdesignluminositytheLHCisexpectedtodeliver % 20 collisionsperbunch crossing(i.e.,per 25 ns),whichimpliesanumberofchargedparticlesoforder 1000 will emergefromtheinteractionregion.Theinnertrackingsystemistherstsub-detector theseparticleswillencounter.Tohandlethehugeuxofparticles,thetrackingsystem 73

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Compact Muon Solenoid Pix el Detector Silicon Tracker Very-forward Calorimeter Electromagnetic Calorimeter Had ro nic Calorimeter Pre shower Mu on Det ectors Supercondu cti ng Solenoid Figure5-1.CMSdetector(fullview) 74

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Figure5-2.CMSdetector( r z prole) mustberadiation-hardandhighlygranularwithafastresponse.Thus,thechoiceof siliconfortheactivematerialiswell-motivatedtomeetthestrictdemandsimposedby LHC. Theinnertrackingsystemconsistsoftwomaincomponents.Theinnermost componentisasiliconpixeldetector,whichconsistsofthreeactivelayersandspansa radiusof 4.4 cm < r < 10.2 cminthebarrelregion.Twodiskscomprisetheendcaps ofthepixeldetector.Behindthepixeldetectorliesasiliconstripdetector,whichisthe secondcomponentoftheinnertrackingsystemandoccupiestheregionupto r =1.1 minthebarrel.Theendcapsofthesiliconstripdetectorconsistof 12 disksintotal, yieldingatrackingacceptanceinpseudorapidityupto | 1 | < 2.5 .Toaccommodate thehugeinuxofparticles,thetrackingsystemisrequiredtobedensewithnumerous read-outchannelstodistinguishtheinteractionsfromthemultitudeofparticles.A high-densitytrackingvolumecomeswithseveralundesirableconsequences.They consumealotofpowerandthusrequiresophisticatedandefcientcoolingssystems on-board,andtheyincreasethelikelihoodofawidevarietyofdestructiveparticle 75

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interactions(e.g.nuclearinteractions,bremsstrahlung,photonconversions,and multipleparticlescattering).Theseunwantedinteractionscancompromisetheaccurate measurementofvariousparticleattributesbytheECAL,HCALandMuonsystemwhich arelocatedbehindthetrackingsystem.Thereisadelicatebalancebetweenhaving enoughmaterialtomaketheintendedmeasurementsofchargedparticlesandnot addingtoomuchmaterialtocauseunwantedinteractions;theCMStrackingsystem exempliessuchbalance,providinghigh-precisiontrackingandvertexmeasurementsat thecostof 0.4 X 0 1.8 X 0 (radiationlengths)dependingonthepseudorapidity. Thepixeldetectorprovides 3 distinctmeasurementsofpositioninspaceasa chargeparticletraversesit,whilethestripdetectoroffersfrom 9 to 14 additional measurementsdependingontheparticle'spseudorapidity.Thesolenoidprovidesa homogeneousmagneticeldof 3.8 Teslawhichpermeatesthetrackervolume,allowing forprecisionmeasurementsofchargedparticles'momentaandelectromagnetic charge.Asidefrommomentummeasurements,theCMStrackingsystemalsoallows forthereconstructionofvariousotherobservables.Perhapsmostimportantisthe reconstructionoftheeventprimaryvertex(PV).Usingtheinformationfromseveral reconstructedchargedtracks,thelocationoftheprimarycollisionin 3 -dimensional spacecanbemeasuredwithhighprecision.Withhighluminosityconditions,multiple primaryverticesareexpectedfrompile-up(PU).Thus,itisvitaltobeabletomatch chargedtracksaccuratelytotheserespectiveverticesforaconsistenteventreconstruction. Alsoimportantistheabilitytoreconstructsecondaryvertices(SV)fromshort-lived, heavy-avordecays(e.g., B and D mesons).Theseareessentialfor b -jetidentication ( b -tagging)andtau-leptonreconstruction.Relatedtosecondaryvertexreconstructionis themeasurementofthetransverseimpactparameter d 0 ,whichisusefultodiscriminate muonsandelectronsofresonancedecays(e.g. W and Z -bosons)fromthoseof heavy-avormesondecays. 76

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Figure 5-3 showsageometricrepresentationofthetransverseimpactparameter d 0 andhowitcanbecalculated.Inthisdiagramweassumethatthereexistssome relativisticshort-lived,heavy-avormeson,denoted a ,whichtravelsanitedistance V T inthetransverseplaneandthensubsequentlydecaystoparticles b and c .For simplicity,weassumeobject b isamuonandobject c representstherestofthedecay products(typicallyamuon-neutrinoandagroupofhadrons).Thetracksfromthedecay productsareusedtoreconstructasecondaryvertex.Twoobservablesareneededto reconstructthetransverseimpactparameter:1)the x y positionofthesecondaryvertex withrespecttotheprimaryvertexand2)theunitvectoralongthetransversemomentum ofthemuon.Itislefttotakethecross-productofthetwovectorsandprojectalongthe z -axis: d 0 =( P T V ) z = V x P y V y P x | P T | (51) whereweareassumingtheprimaryvertexislocatedat (0,0) forsimplicity.Whilethe reconstructionofasecondaryvertexwasassumedforthisexample,itisnotexplicitly requiredinordertocalculate d 0 foragivenchargedtrack.Whenthemomentumofa chargedparticleisreconstructedbythetracker,thevertexfromwhichitoriginatedis easilycalculatedfromthetrackt.Theerroronthesecondaryvertex,whichincludes multipletracks,willingeneralbesmallerthantheerroronthevertexofasingletrack. Nonetheless,thevertexprecisionforsingletracksisstillgoodenoughtomeasure d 0 withgoodprecisionforawiderangeoftrack p T TheCMStrackerexhibitsexcellentresolutionofkeyobservablessuchas p T and d 0 .Table 5-1 showstheirresolutionsforafewdifferentmuon p T scales[ 38 ].The spreadinvaluesreectsthe 1 dependenceontheresolutions,whichisnotexplicitly shown.Todemonstratethatthemuon d 0 resolutionismorethangoodenoughtoidentify heavy-avordecays,wecanappealtoasimpleexample.Again,referringtothediagram inFigure 5-3 ,wetakeparticle a tobeatypical B or D meson.Thesehavemasses 77

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Figure5-3.Pictorialrepresentationoftransverseimpactparameter d 0 ontheorderof 5 GeVandlifetimesontheorderof 10 12 s.Themeandistance V traveledbyarelativisticparticleasmeasuredinthelabframeis V = & v ) ,where & is therelativisticboostalsogivenbytheratioofenergytomass( E / m ), v isthevelocityof theparticlewhichisverynearlythespeedoflight c ,and ) isthemeanlifetime.Roughly 1 / e % 37% ofparticleswiththesevaluesof & v ,and ) willtravelthisdistance V before decayingasitisaPoissonprocess.Lightdecayproductsofrelativisticparticlestypically formadecayangleof 0 % 1 / 2 & withrespecttothedirectionoftheparentparticleinthe labframe.Ifweassumeparticle a tohaveanenergyof 50 GeV(notuncommon),then & = E / m =50 / 5=10 and d 0 = V sin ( 0 )= & c ) sin ( 1 2 + ) $ 1.5 mm.Inprinciple,particle a cantakeonanyvalueof | 1 | withinthetrackingacceptance.Fortheextremecasewhere 78

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| 1 | =2.4 ,then V T = V / cosh ( 1 ) $ 0.27 mm,whichisafactorof 10 greaterthanthe d 0 resolutionformuonsintherangeof p T > 10 GeV.Finally,itisworthnotingthatthescale oftheimpactparameterdependsmostlyonthecharacteristiclifetimeofthedecaying particle,asthedependenceontheenergycancelsas & growshighenoughtomeritthe small-angleapproximationofthe sin function. Table5-1. P T and d 0 resolutionformuons p T ( GeV ) ( p T )% ( d 0 )( m ) 10.7 2.090 200 100.7 2.020 30 1001.5 7.010 12 5.2.3ElectromagneticCalorimeter TheCMSElectromagneticCalorimeter(ECAL)isahomogeneousdetector composedoflead-tungstate(PbWO4)crystalscoupledtoAvalanchePhotodiodes (APDs)inthebarrelandVacuumPhotodiodes(VPDs)intheendcap.Thebarrel contains 61,200 distinctcrystalswhichcovertherangeupto | 1 | < 1.479 ,whileeach endcapconsistsof 7,324 crystalswhichspantherangeof 1.479 < | 1 | < 3.0 .Like theinnertrackingsystemtheECALisdesignedtoberadiation-tolerant,exhibitinghigh granularityandafasttimingresponse.Thedesignwasgreatlymotivatedbytheintense operatingconditionsoftheLHCandthestrictperformancerequirementsnecessaryto pursuethediscoveryoftheHiggsbosondecayintotwoenergeticphotons( H ( && ).An excellentenergyandtimingresolutionisespeciallynecessaryforthelatterpursuit. Twoguresofmeritwhichareoftenusedtocharacterizethematerialinelectromagnetic calorimetersaretheradiationlength X 0 andtheMoli ` ereradius r M .Theradiationlength representsthemeanpathlengththatahighenergyelectron(orpositron)musttravelin ordertorelease $ 63% ofitsenergythroughbremsstrahlungradiation.Forhighenergy photons,thisquantityalsorepresentsthemeandistancenecessarytotravelinorderto release 7 / 9 ofitsenergyvia e + e pair-production.TheMoli ` ereradiusrepresentsthe radiusofacylinderwhichwouldcontain $ 90% oftheelectromagneticshowerinduced 79

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byanenergeticelectronorphotoninthedimensiontransversetotheparticle'smotion. Forthelead-tungstatecrystalsintheECALthesevaluesare X 0 =0.89 cmand r M =2.2 cm.Thedimensionsofthecrystalsaretailoredwiththesevaluesinmind,asthefront (back)surfaceareais 2.2 2.2 cm( 2.6 2.6 cm)andthelongitudinaldepthisabout 23 cm,whichoffersroughly 25 radiationlengthsofmaterial.TheprobabilityfortheECAL tocompletelycontaintheelectromagneticshowerinducedbyanimpingingphotonor electroniseffectively 100% ThefrontoftheECALbarrel(EB)liesjustbeyondtheinnertrackingsystem, beginningataradiusof 1.29 meters,whiletheECALendcaps(EE)arelocatedjustover 3 metersawayfromthenominalinteractionpoint.Positionedinfrontoftheendcaps istheECALPreshowersystem(ES),whichisasamplingcalorimetercomposedofa radiation-inducinglayerofleadfollowedbyanenergy-collectinglayerofsiliconstrips. ThemainfunctionofthepreshowerdetectoristohelptheECALresolvethephoton pairscomingfrom 0 ( && ,whichisanabundantbackgroundprocesstoimportant searcheslike H ( && .Intheformerprocessthetwophotonsarelikelytobeverynear oneanother,owingtothe % 1 / & openingangle,andwouldpotentiallybereconstructed asasinglephotonintheECALendcap.However,thesephotonsimpingeuponthe preshowerdetectorrst,whichoffersamuchhighergranularitythantheECALendcap. Theresultingelectromagneticshowersfromthedi-photonsystemisseenastwo distinctshowerswiththehelpofthepreshower,insteadofone.Thisadditionalphoton discriminationpowerisavailableoverthepseudorapidityrangeof 1.653 < | 1 | < 2.6 Thepreshowerprovides 3 radiationlengthsofmaterialoverthisrange,effectively guaranteeingthatelectronsandphotonswillbegintoshowerbeforereachingthe endcaps. TheenergyresolutionoftheECALsub-detectorwasstudiedin2004withLHCtest beamdata.Thebeamsconsistedofelectronswithenergiesrangingfrom 20 to 250 GeV. 80

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Thegeneralexpressionforacalorimeter'senergyresolutioncanbewrittenas: 5 E 6 2 = 5 S & E 6 2 + 5 N E 6 2 + C 2 (52) where S representsastochasticterm(e.g.,uctuationsinphotostatistics,lateralshower containment,energyradiatedinthepreshower), N representsanoiseterm(e.g., electronics,digitization,pile-up),and C representsaconstantterm(e.g.non-uniformity oflightcollection,inter-calibrationerrors,energyleakagefrombackofcrystals).The testbeamresultssuggestedthefollowingvaluesforthesetermsinEq. 52 : S =2.8% N =0.12% ,and C =0.3% [ 38 ].Itwilltaketimetotocollectenoughdatatomeasurethe energyresolutionusingcollisionparticles.However,withtherst 250 nb 1 of pp collision dataat & s =7 TeV,theresolutionoftheneutralpionmasswasmeasuredtobejust under 10% .Theenergyscalewhichistypicallyrepresentedby | E measured E true | / E true couldalsobeestimatedwiththisearlydataandwasfoundtobeabout 1% and 3% for thebarrelandendcaprespectively[ 49 ].Thesemeasurementsdemonstratetherather impressivecapabilitiesoftheECALsub-detectorduringtheearlycommissioningphase oftheexperiment. WhentheLHCbegancollidingprotonsin2009and2010,anunexpectedrate ofanomaloushighenergysignalswasobservedintheECALbarrelsub-detector. Thesesignalsdidnotreecttheconventionalelectromagneticshowersfromimpinging electronsandphotons.Rather,theyappearedtobespuriousenergydepositsfrom directionizationofthesiliconresidingintheAPDs.ECALexpertssuspectthatthe phenomenoncanbeattributedtobackshoweringinthehadroncalorimeterorneutron decays.Fortunately,thetopologicalandtimingsignaturesoftheseanomaloussignals canbedistinguishedfromtheintendedcollision-inducedsignals,andalgorithmsarein placetorejectthesedepositsduringeventreconstruction. 81

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5.2.4HadronCalorimeter LocatedprimarilybehindtheinnertrackingsystemandECAL,theCMShadron calorimeter(HCAL)isdesignedtomeasuretheenergiesfromneutralandcharged hadrons,whichprovidethefoundationforquarkandgluon-jetreconstructionandthe calculationofthemissingtransverseenergy( E T ).TheHCALsub-detectorconsistsof fourcomponents.ThesearereferredtoastheHCALbarrel(HB),endcap(HE),forward (HF),andouter(HO).Together,theycoverapseudorapidityrangeupto | 1 | < 5.0 makingtheCMSdetectoralmostperfectlyhermetic. Whenenergetichadronsimpingeuponadensematerial,theyinitiatepion ( + * 0 )cascadesthroughnuclearinteractionswiththemedium.Because 0 's arelikelytobeproducedinroughlyequalproportionswithrespecttothechargedpions, andtheseparticlesdecayalmostinstantaneouslyintotwophotons,thereisasubstantial electromagneticshowerthatdevelops,accompanyingthehadronicshowercarriedout bythechargedpions.Thisisunlikethesituationforelectronsandphotonswhichimpact theECALandonlyinitiateelectromagneticshowers.Thetwotypesofshowershave verydifferentcharacteristicsowingtotheunderlyingphysics.Hadronicshowersare carriedoutovermuchlongerdistancesandinvolveinteractionswiththenucleonsin themediumwhichresultinsomeundetectableenergylosses(i.e.,energythatdoes notresultinscintillationlight).Thisphenomenonresultsinanintrinsicdifferenceinthe wayacalorimeterwouldperceiveanenergysignalfromanelectronversusacharged pion,ifthetwoweretoimpactthedetectorwithidenticalincidentenergies.Thisratioof theenergyresponseofhadronswithrespecttoelectronsisoftendenoted h / e ,andits deviationfromunitycausessignicantobstaclesforperformingenergymeasurementsin theeldofcalorimetry. Whiletheradiationlength X 0 isusedtocharacterizethescaleofelectromagnetic cascadesincalorimeters,theinteractionlength I isusedtodescribethescaleof hadronicshowers.Theinteractionlengthrepresentsthemeandistancearelativistic 82

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hadronmusttravelthroughamaterialinordertoreleaseroughly 63% ofitsenergyvia nuclearinteractions.Forthebrass-steelabsorberusedfortheHBandHE, X 0 $ 1.5 cmand I $ 16 cm.Thelatterisroughly 18 largerthantheradiationlengthneeded forelectronsandphotonsintheECAL.AsidefromjustifyingtheplacementoftheHCAL behindtheECAL,thescaleof I imposessomeseveredesign,andmoreimportantly, performanceconstraintsontheHCALandtheCMSdetectorasawhole. Fromthedesignperspectivehadroncalorimetersalmostalwaysarechosento performmeasurementsbysamplingthehadroninducedshowersbecauseitissimply tooexpensivetofullyinstrumentthedozeninteractionlengths(severalmeters)needed tocompletelycontaintheshowerenergywithahomogeneous,activematerial(asis doneintheECAL).Moreover,onceoneisresignedtoemployingasamplingcalorimeter forthetaskofmeasuringhadrons,theissueofcostissomewhatalleviated,buttheissue ofspaceisstillanenormousconcern.InCMStheHBisconstrainedtotinbetween theECALbarrelandtheinnersurfaceofthemagnet.Thisareaspans 1.77 mto 2.95 m inradius,andonlyaffordstheHBwithabout 5.8 ( 10.6 )interactionlengthsat 1 =0 ( 1.3 ). Thus,inrarecaseswhereasinglehadronisendowedwithanunusuallylargeenergy fromthecollisionevent,thehadronicshowerinducedintheHBmaynotbecontained andmaycarryonintothemagnetandbeyond.Thisuncontainedenergywouldnotbe accountedforandthiswouldcauseapotentiallyhigh,butspurious,missingenergy signalaswellasabadlymis-reconstructedjet.Fortunately,theCMSgeometryallowed forasafeguardtobeemployedinordertomitigatethiseffect.Locatedjustonthe exteriorofthemagnet,theHOcomponentoftheHCALismeanttoreinforcetheHB byexploitingtheadditionalabsorberofferedbythesolenoidcoilandappendingitwith additionalsamplingmaterial,thuscombiningtoyield 11.8 interactionlengthsintotal. TheHOisoftenreferredtoasa "tailcatcher" ,whichreectsitsroleincontainingthe hadronicshowersinducedbyrareenergeticparticles.Forcollisionsoccurringat & s =7 TeV,theprobabilitythattheHOwillbeneededforshowercontainmentismuchlower 83

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thanforthe & s =14 TeVcollisionscenarioinitiallyenvisionedfortheLHC;nonetheless, theHOwillserveitspurposemoreastheLHCeventuallyapproachesdesignenergies. TheHB,HE,andHOsub-detectorssharesimilardesignqualities.Theyare allsamplingcalorimeterswhichemployanadmixtureofsteelandbrassabsorber materialtoinducehadronicandelectromagneticshowers.Thephotonsgeneratedfrom theseshowersaresampledatvariouslongitudinaldepthsbyseverallayersofplastic scintillatortiles.Embeddedinthesetilesarewavelengthshifting(WS)bers,which collectscintillationlightandstreamittoHybridPhotodiodes(HPDs).Thefunctionalunit ofthisbrassandscintillatorconstructionisanHCAL tower .Towersdenethegranularity ofthesub-detector.TheHBgeometryaccommodates 72 towersinthe dimension( 5 & granularity)and 32 towersinthe 1 dimension( 0.087 granularity),whichspans | 1 | < 1.3 Theboundarytowersonthe 1 peripheryofHBaresharedwithHEinwhatisreferredto astheHB/HEtransitionregion.TheHBtowersaremountedjustbehindtheECALbarrel sub-detector,andeachonecouplesormapstoa 5 5 matrixofECALcrystalslying directlyinfrontofitwithrespecttothenominalinteractionpoint.ThisunionofECAL crystalswithanHCALtowerisreferredtoasastandard calorimetertower or calotower forshort.Intheendcapasimilarunionismade,andintheforwardregion,calotowers consistsofsolelythetowersfromtheHFsub-detector,astheECALdoesnotextend thatfarinpseudorapidity. TheHEsub-detectorcoversthepseudorapidityregionfrom 1.3 < | 1 | < 3.0 and providesabout 10 interactionlengths(includingthecontributionfromECAL).There are 72 calotowersinthe dimensionand 26 inthe 1 dimension,ifoneincludesthe two 1 -ringssharedwithHBinthetransitionregion.Thisyieldsa " 1 granularityof 5 & 0.087 for | 1 | < 1.6 andapproximately 5 & 0.17 for | 1 | > 1.6 UnliketheHB,HB,HOcomponentsofHCAL,theHFdetectorhasaverydifferent design,whichismotivatedbyitsveryvulnerablepositioningat 3.0 < | 1 | < 5.0 where theparticleuxfromcollisionswillbeextremelyintense.TheHFdetectorwillsuffer 84

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moreradiationdosagethananyothermainsub-detectoronCMS.Furthermore,theHF detectorisrequiredtosustainfunctionalityandmaintainahighlevelofperformanceto withstandapproximately 10 yearsofnominalLHCoperations.Ultimately,itwasdecided toinstrumenttheHFdetectorwithapassivesteelabsorbertoinducenuclearand electromagneticshowers,andembeddedthismediumwithquartzberstodetectthe resultingChrenkovradiationfromthesecondaries. TheHFeffectivelyconsistsoftwolongitudinalsegments.Halfofthequartzbers spantheentirelongitudinaldimension,whiletheotherhalfbeginatadistance 22 cm fromthefrontoftheHFandspantherestofthedepth.Thesetwocollectionsofbers arereferredtoas"long"and"short"bersrespectively,andtheyareread-outseparately fromeachother(notcombined)viaphotomultipliertubes(PMTs).Usingthetwosetsof quartzbers,showersfromelectronsandphotonscanbedistinguishedfromshowers inducedbyhadrons.Electronsandphotonswillreleasemostoftheirenergieswithina fewradiationlengths(i.e.,muchlessthan 22 cm).ThusthemajorityoftheChrenkov lightemittedfromtheseelectromagneticshowerswillbeconnedtothelongbers. Hadronsontheotherhandreleasetheirenergiesoveralongerdistanceonthescaleof afewinteractionlengths.Thus,signalsfromhadronswillbecollectedalmostuniformly overlongandshortbers.TheHFdetectorislocatedroughly 11.2 metersfromthe interactionpointandcontains 36 calotowersinthe dimensionand 26 calotowersinthe 1 dimension,yieldinga " 1 granularityof 10 & 0.17 for | 1 | < 4.72 andapproximately 20 & 0.30 for | 1 | > 4.72 TheHFdetectoralsoperformsluminositymonitoringoftheLHC.Employinga techniqueknownas"zero-counting",theaveragenumberoftowerswhichreportzero energysignalperbunch-crossingcanbecountedintheHFandthisnumbercanbe relatedtotheaveragenumberofinteractions,andhencetheinstantaneousluminosity canbeinferred.Moredetailsofthisandothermethodsforluminositymonitoringinthe HFcanbefoundelsewhere[ 38 ]. 85

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Theenergyresolutionforhadroncalorimetersisgenerallyworsecomparedto electromagneticcalorimeters.Duetotheirsamplingnature,theyareespeciallyprone touctuationsinthephotostatistics.Thiscontributesasignicantstochastictermtothe expressionfortheresolution(seeEq. 52 ).Thereisalsoanon-trivialconstanttermthat originatesprimarilyfromthenon-unityofthe h / e ratio.Asimpliedbythediscussionon calotowers,themeasurementofhadronenergiesupto | 1 | < 3.0 reliesonacombined measurementoftheECAL(homogeneous)andHCAL(sampling)sub-detectors.A signicantfractionofhadronswillinevitablybegintoshowerwhiletraversingthe ECAL,whichprovidesjustoveroneinteractionlengthofmaterial.Forthesecases, thehadroniccomponentoftheshowerswillcarryonwellintotheHCAL,butthemajority oftheinitialelectromagneticcomponentmayverywellbecontainedtotheECAL,which hasadifferent h / e ratio.Thus,thereisacomplicatedmarriagebetweentheenergy measurementsregisteredbytheECALandHCALtoreconstructtheincidenthadron's trueenergy.Thisunionaffectsthetotalenergyresolutionforhadronsinanon-trivial way.Somesophisticatedtechniqueswereemployedtocorrectforthediffering h / e ratios usingtestbeamdata,whichwereabletobringtheenergyresolutionforHBandEB combinedsystemdowntothefollowingvalue[ 50 ]: 5 E 6 2 % 5 84.7% & E 6 2 + 5 7.4% 6 2 (53) TheHEsub-detectorhasasimilarscaleofenergyresolutionwiththestochastic termgivingthedominantcontribution,whiletheHFhasastochasticandconstant termof 280% ( 198% )and 11% ( 8% )respectivelyforthehadronic(electromagnetic) showers[ 51 ]. AsignicanteffortisinplaceonCMStomeasuretheHCALmeanenergyresponse ofchargedpionswithcollisiondata.Thismeasurementwasperformedwiththerst 10 nb 1 ofminimum-biascollisiondatacollectedat & s =7 TeV.Thesubsetofcharged 86

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pionswhichbegintheirhadronicshowersintheHCALcanbeidentiedwithafairly simpleselection.Onejustrequiresanisolatedchargedtrackwith p T > 5 GeVas measuredbytheTracker,combinedwithaminimum-ionizingparticle(MIP)signature intheECAL.Usingthesepioncandidates,theHCALmeanresponsecanbeevaluated overthepseudorapidityrangecoveredbytheTracker( | 1 | # 2.4 ).IntheHBtheresponse ( E HCAL / p Track )variesfrom 60% at p T =5 GeVtoabout 80% at p T > 12 GeV.IntheHE, theresponsetakesonvaluesof 50% at p T =5 GeV,about 75% at p T =12 GeVand about 92% and p T > 20 GeV.Itisimportanttoextractthemeanpionresponsefunction forthecalorimeters,whichvarieswithrespectto p T and | 1 | ,asitisneededinorderto improvethereconstructedjetand E T energyscales. SomesourcesofanomalousnoiseintheHCALhavebeenidentiedeitherduring theCRAFT(CosmicRunAtFourTesla)exerciseof2008and2009orthe2010collision runs.Theyhavebeenstudiedthoroughlybyexperts.Twomainclassesofanomalous signalsareworthmentioningastheyhavereasonablyhighratesofoccurrence.The rstclassistheso-calledHPDandRBX(Readout-BoX)noisewhichexistsintheHB, HE,andHOsub-detectors.AnHPDcontains 18 readoutchannelsandthereare 4 HPDsperRBX.AnHPDcanexperiencewhatiscalled ion-feedback whichoccurswhen aphotoelectronliberatesionsfromthesilicondiode,whichsubsequentlyaccelerate acrossthehigh-voltage(HV)gapandbombardthephotocathode,thusfreeingmore photoelectrons.Thiscausesasinglereadoutchannelonaveragetoreportaspurious signalandcanoccuratarateof % 20 Hz.AnHPDcanalsoexperienceasizable dischargeduetoeffectsfromtheHVinterplaywiththeCMSmagneticeld.Thiscan leadtoupto 18 channelsreportingfalseenergysignalsandoccursatarateof % 1 Hz.ThemostcatastrophiccaseoccurswhenalloftheconstituentchannelsofanRBX registerasignal.Theexactcauseofthisphenomenonisunknown,butitcanaffectall 72 channelsandcanoccuratabout % 0.5 Hz.Theprobabilityofthesenoiseeventsto overlapwithcollisionsisquitelow,buttheyproducesignalsthatcouldmimicthoseof 87

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neworexoticphysicsprocesses(e.g., E T ,mono-jets).Thus,specialltershavebeen developedtoidentifytheseeventsbytheirtimingandtopologicalsignaturesandthey canconsequentlyberejected. ThesecondclassofnoiseexistsintheHFsub-detectorandisreferredtoas"PMT hits".ThisphenomenonoccurswhenChrenkovlightisproducedbyparticleinteractions thatoccurinthewindowmaterialofthePMTs(insteadoftheabsorberinfront)[ 51 ]. Fortunately,thesignalsthatcomefromsucheffectscanbeidentiedandrejectedvia topological,timing,andpulseshapelters. 5.2.5MuonSystem ThereisareasonwhytheCMSdetectorfeatures"Muon"asitsmiddlename.Since theearliestdesignphasesitwasalwaysenvisionedthatrobustmuonidenticationand highprecisionmomentummeasurementswouldbetwoofthekeydeliverablesofthe LHCcandidateexperimentwhichwaslatergoingtobeknownastheCompactMuon Solenoid.InpartthisdesirewasmotivatedbythediscoverypotentialoftheHiggsboson viathedecay H ( ZZ ( ) ( + + ! ,whereallfourdecayproductsaremuons.Owing totheirMIPnature,muonsareextremelycleanobjectsandeasilynavigatethroughthe materialoftheinnertrackingsystem,calorimeters,andmagnetwithoutsuccumbing tothedrasticradiativeenergylossesornuclearinteractionsasdootherdetectable particles(e.g.,electrons,photons,pions).Theyexitthesesystemswithvirtuallythe samemomentaastheyhadwhentheywerebornfromtheprimarycollision.Thus,the placementofanadditionaltrackingsub-detectoroutsideoftheseothersystemsallows formuonidenticationandanothermeasurementofthemomentumwhichiscompletely independentoftheinnertrackingsystem. TheMuonSystemconsistsofthreetypesofgaseoustrackingdetectors.Inthe barrelregion( | 1 | < 1.2 )wherethemuonrateisexpectedtobelowandthereturning magneticeldisweak,drifttubechambers(DT)areemployed.Intheendcaps( 0.9 < | 1 | < 2.4 )wherethemuonrateincreasesandthemagneticeldisstronger,Cathode 88

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StripChambers(CSC)areinstalled.AthirdsystemofResistivePlateChambers(RPC) isalsopresentinthebarrelandendcapsupto | 1 | < 1.6 andprovidescomplementary andredundanttrackingandtimingmeasurementstoaidtheCSC'sandDT'sinmuon reconstructionandtriggering. Thedrifttubesystemconsistsoffourchamberswhichformconcentriccylindrical shellsaroundthemagnetinthebarrel(denotedMB1,MB2,MB3,andMB4).They areinterspersedinbetweenthevariouslayerscomprisingtheironyokewhichreturns themagneticeldofthesolenoid.Thesechambersspanthe z -dimensionintheform of 5 wheels,whichareprovidedbytheframeoftheironyoke.Eachwheelisdivided into 12 sectorsspanningtheazimuthaldimension.Thefunctionalunitofthedrifttube chamberiswhatisreferredtoasa superlayer .Theinnermost 3 chamberscontain 3 superlayerseachwhiletheoutermostchambercontainsonly 2 .Asuperlayerisfurther granulatedinto 4 layersofradiallystaggered,butotherwiseparallel,driftcells,which havethedesigndepictedinFigure 5-4 .Ananodewireinstalledinthegeometriccenter ofthetubeischargedtoaveryhighelectricpotential(HV)of +3.6 kV.Cathodestrips whichlinetheinterioroftheI-beamsarechargedtoahighnegativeelectricpotential of 1.2 kV.Electrodestripsspanthetopandbottominteriorlayersandarechargeda potentialof +1.8 kV.Theneteffectofthisanode-electrode-cathodecongurationisa powerfulelectriceldwhichemanatesfromtheanode,issteeredbytheelectrodes,and terminatesatthecathodes. Thedriftcellperformsaspatialmeasurementviathefollowingmechanism:A chargedparticle(e.g.amuon)traversesthegaseousvolumewithinthecellandionizes thegasatomsalongitstrajectory.Theliberatedelectronsbegintodrifttothepositively chargedanodeataconstantdriftvelocitydeterminedbythegaspressureandthenet electriceld.Astheseelectronsgetclosetotheanodetheybegintoacceleratedue totheincreasingelectriceld(proportionalto % 1 / r ).Thisaccelerationendowsthe electronswithenoughkineticenergytokickoutelectronsfromneighboringgasatoms, 89

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whichthenbegintoacceleratetowardstheanodethemselves,givingrisetoa runaway chargeaccretionor chargeavalanche whichislocalizedontheanode.Thisamplication effectisoftenreferredtoasa gasgain andcanbeashighas 10 5 .Thepassageoftime betweenthetraversingparticleandthearrivaloftheliberatedelectronstotheanode constitutesthedrifttime.Withthedrifttimemeasuredandthedriftvelocityknown,the locationoftheincidentchargedparticletransversetotheanodecanbereconstructed. Thedrifttubetechnologyreliesontheresidualmagneticeldfromthesolenoidbeing weakandmostlyuniform.Ifthedriftingelectronsexperienceamagneticallyinduced Lorentzforce,theirtrajectoriesmaytakeonhelicalpatterns(insteadofdirectlyalong electriceldlines),whichcanaltertheirdrifttimesinanon-trivialway. Foratypicalchambertherstandthirdsuperlayerswillcontaindriftcellswithwires thatarealignedwiththebeamlineandthusprovideazimuthalmeasurements( ).The middlesuperlayercontainsdriftcellswithwiresthatlieorthogonaltothebeamand thusprovidemeasurementsofthe z position.Theforthchamberonlycontainstwo superlayersandthereforeonlyprovidesa measurement.IntotaltheDT'scomprise 250 chambers. Figure5-4.Schematicdesignofdrifttubecell[ 52 ] Thedrifttubeanodewiresarestainless-steelwithgoldplatingandhaveadiameter of 50 m.Thecathodeliningthedriftcellinterioredgesismadeofaluminumtape whichis 50 mthickand 11.5 mmwide.Thetubeshaveageometricalcross-sectionof 90

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13 42 mm 2 .Thegasllingthecellsisa 85% / 15% admixtureofAr/CO 2 ,whichyieldsan electrondriftvelocityuptoabout 5.4 cm/ s(saturatedvalue).Drifttimesrangefroma fewto % 400 nsdependingonthelocationoftheinitialionization.Eachwireisdesigned toprovideaspatialresolutionofabout 250 m.Whencombiningthemeasurements overseveralsuperlayers,theglobaldesignresolutioninthe r planeisontheorderof 100 m. TheendcapmuonsystemisinstrumentedwithCathodeStripChambers,whichare modeledafterthe multi-wireproportionalchamber particledetectiontechnologyrst engineeredbyCharpak[ 53 ].Eachendcapfeatures 4 stationsspanningthe z -direction. Station 1 iscomposedof 3 ringsstackedintheradialdirectionwhilestations 2 through 4 contain 2 ringsbydesign.Agivenstationandringisdenotedas MB S / R wherethe denotestheplusorminus-sideendcapwithrespecttothez-axis, S denotesthestation number,and R denotesthering.Theimplementationof ME 4 / 2 hasnotactuallybeen completedasof 2011 andplansareinplacetoinstallitinthenextfewyears. Thefunctionalunitintheendcapmuonsystemisthechamber,whichistrapezoidal inshapeasisdepictedinFigure 5-5 .Achamberconsistsof 6 anodewireplaneswhich areorthogonallyinterspersedamong 7 cathodepanels.Theanodesspantheazimuth dimensionandmeasuretheradialcoordinatewhilethestripsspanradiallyandmeasure theazimuthalcoordinate.Theanode-cathodesystemismaintainedatanHVof 3.6 kV. The 7 panelsprovide 6 gasgapswhichcontainagasmixturecomposedof 50% CO 2 40% Ar,and 10% CF 4 .Thisgasmixture,combinedwiththeHVcondition,providesa gasgainofroughly 7 10 4 TheprocessbywhichtheCSC'sperformaspatialmeasurementisthefollowing:A chargedparticle(e.g.amuon)traversesagasgapwithinachamber,ionizinggasatoms alongitstrajectory.TheHVmaintainedbetweentheanodewireandthecathodestrips createsastrongelectriceldwhichimposesadriftvelocityontheliberatedelectrons towardstheanode(similartothemechanisminthedriftcell).Asthedriftingelectrons 91

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getclosetotheanodetheybegintoexperiencealargeaccelerationwhichallowsthem toimpartenoughenergytoknockoutelectronsfromneighboringgasatoms.These freedelectronsjoinsuitandproceedtoknockoutotherelectronsandthe runaway process(or avalanche )occursinamannersimilartothatofthedriftcells.Thecharge thataccumulatesontheanodeinducesadifferentialchargedistributionacrossthe groupofnearbycathodestrips.Thisdistributionofchargewillreectthelocationon theanodewheretheavalancheoccurred.Bysynthesizingthisinformation,onecan simultaneouslydeducethe2-dimensional r spatialpositionthatwastraversedbythe incidentchargedparticle. Dependingontheringandstationpositionofthechamber,itmayspaneither 10 & or 20 & in .Thelargestchambersarelocatedat ME 2 / 2 and ME 3 / 2 andcoveranarea of 3.4 1.5 m 2 .Themultiplicityofchambersasafunctionofstationandringisgivenin Table 5-2 .Muonsinthepseudorapidityrangeof 1.2 < | 1 | < 2.4 willcross,andhencebe measured(ideally),by 3 to 4 stations,whilemuonsintherangeof 0.9 < | 1 | < 1.2 willbe measuredbothbytheDT'sandatleastoneoftheCSC's. TheCSC'sperformanceandcalibrationfortunatelydonotrelyonprecisecontrolof thetemperatureandpressureofthegas.UnliketheDT's,theCSCsdonotbasetheir measurementsondrifttimes,whichcansufferill-effectsfromunstablegaspressures orstrongmagneticelds.ThepseudorapidityregioncoveredbytheCSC'sguarantees thattheywillnotonlyseeahigherrateofcollisionmuons,whichjustiestheirfaster responsetimeswhencomparedtodriftcells,buttheywillalsoendureastrongerand non-uniformmagneticeld.Infact, ME 1 / 1 hasaslightlydifferentdesigntocopewith itsuniqueplacementclosetothebeamlineandinteractionpoint,wherethemagnetic eldisnearlyfullstrength.Theanodewires,forexample,arenotperfectlyazimuthal, buttiltedatanangleof $ 29 & tocompensateforthemagneticdeectionthatdrift electronswillexperienceastheytraveltowardsthem. 92

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cathode plane with strips wire plane (a few wires shown) 7 trapezoidal panels form 6 gas gaps Figure5-5.Schematicdesignofacathodestripchamber[ 38 ] Table5-2.Chambermultiplicityperstationandring Ring 1 Ring 2 Ring 3 Station 1727272 Station 23672 Station 33672 Station 436(72) TheResistivePlateChambers(RPC)areparallel-plategaseousdetectors, whichprovidecomplimentaryspatialandtimingmeasurementstotheDTandCSC subsystems.TheRPC'sareinstrumentedinthebarrelandendcapregionupto | 1 | < 1.6 .Initially,itwasintendedtheRPC'swouldcovertheregionupto | 1 | < 2.1 butbudgetconcernscompelledthecollaborationtodelaythisfullimplementationuntila latertime. ThefunctionalunitofanRPCisthedouble-gapmodule.Achamberwilleither containtwoorthreeofthese.Inthebarrel,thesearealignedsequentiallyalongthe beamdirection.Theindividualgapsarestackedsuchthatachargedparticlefromthe interactionpointwouldtraversebothgapsinthedouble-gapmodule.Thereissome 93

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staggeringtominimizethedeadregions.Eachofthesinglegapsinadoublegap moduleisboundedbytwoplanesofgraphite,whicharechargedtohighvoltage.The interiorofthegraphiteplanesislinedwitha 2 mmthickbakelitelayer,whichishighly resistive.Upto 96 copperreadoutstripslieintheregionbetweenthetwographite planeswhichlinethecommonborderofthesinglegapsofthedoublegapstructure. Thesinglegaphasathicknessof 2 mmandislledwithanadmixtureofgasesofthe followingcomposition: 96.2% C 2 H 2 F 4 3.5% C 4 H 10 ,and 0.3% SF 6 .Thesegasesplaya crucialroleintheoperationoftheRPC's. AnRPCdetectsthepassageofachargedparticleviathefollowingmechanism:A chargeparticlepenetratesthegasgapscausingionizationalongitstrajectory.Because thisisaparallelplatecapacitorconguration,theelectriceldwhichresultsfromthe appliedHV,isstronganduniformoverthevolumeofthegap.Thus,theelectronswhich areliberatedduringtheionizationprocessbegintoimmediatelyacceleratetowardsthe +HVsideofthegap(awayfromthestrips).Thisisunlikethecaseofthedrifttubes, wheretheelectronsexperienceacasualdriftuntiltheygettowithinafewwireradii oftheanodewire,owingtothe 1 / r dependenceontheelectriceld.TheCMSRPC's operatein avalanchemode ,whichmeanstheelectronsfromtheinitialionizationwill liberatesomeamountofadditionalelectronsenroutetotheresistiveplates,butnot enoughelectronstocausedielectricbreakdownandigniteasparkacrossthegap. Severalfactorsallowfortheavalanchetobecontrolledandlocalized.Forone,the gasmixtureinthegapnotonlyprovidescandidateatomsforionization,butitalso containsnegativechargecarriersandisabsorbenttophotonsintheUVrange.The negativechargecarrierspickupsomeoftheliberatedelectronsintheavalanche,and thephotons,whichareemittedduringthedischargeprocessastheelectronsreachthe plate,areabsorbedbythegas.Otherwise,thesephotonscouldinitiatesomeionization elsewhereintheRPC's.ThehighresistivityoftheplatesmakesitdifcultfortheHV sourcetoquicklycompensateforthechargethathasaccumulatedasaresultofthe 94

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avalanche.Thiscausesadropintheelectriceldlocaltotheavalanche,whichinduces acurrentontheread-outstrips. AchargedparticlecrossingtheplaneofanRPCwillinducesignalsinaneighborhood ofstrips.Thesestripsgetclusteredtogether,andthepathtraversedbytheincident particleisinferredbycalculatingthecentroidoftheareacoveredbythestrips.This producesaspatialresolutionofabout 10 mm;however,thenoteworthyfeatureofthe RPCisitstimingresolution,whichisontheorderof % 3 ns. TheRPC'sinthebarrelform 6 coaxialcylindersspreadacrossthefourDTstations. TherstandsecondstationsareinstrumentedwithRPC'sonboththeinteriorand exterior,whilethethirdandfourthstationsareinstrumentedonlyontheinterior.The read-outstripsinthebarrelchambersrunparalleltothebeamaxisandareabout 2.5 inlength.EachendcapisequippedwiththreeRPCstations(spanninglongitudinally) andtwotothreerings(spanningradially).TherstRPCstationisinstrumentedonthe exteriorof ME 1 / 2 and ME 2 / 3 ,whilethesecondstationisinstalledinteriorto ME 2 / 1 and ME 2 / 2 ,andthethirdstationisinstalledexteriorto ME 3 / 1 and ME 3 / 2 .ThedoublegapsoftheendcapRPC'shaveatrapezoidalgeometry. ThetwomainrolesoftheRPCsystemaretoaidinmuontriggeringandto accuratelyassignthebunchcrossingnumber.Aswasdiscussedinthebeginningof thischapter,particlesfrommultiplebunch-crossings,andhenceprimarycollisions,are propagatingthroughdifferentpartsoftheCMSdetectoratanygivenmomentintime. Itiscrucialthatthesignaturesfromtheseparticlesareappropriatelyassignedtothe correctcollisions.Forthecaseofmuons,thisisensuredtoagreatextentbytheRPC's. 5.2.6TriggerSystem TheLHCcancrossbunchesatafrequencyof 40 MHz.Separatedby 25 nsintime, eachbunchcrossing,whichcaninprincipleyieldupto 20 proton-protoncollisions, 95

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offerstheCMSdetectoranopportunitytoread-outandrecorddata 1 .Ifallofthe zero-suppressed datafromthemillionsofelectronicchannelsinthedetectorwere tobereadoutforasinglebunch-crossing(with 20 collisions),itwouldyieldabout 1 Mbyte.Bymultiplyingthisgurebythebunchcrossingfrequency,onecouldeasily concludethatitisnotonlyimpractical,buttechnologicallyprohibitive,tostreamand storesuchvastamountsofdataatsuchhighrates.Furthermore,thevastmajorityof thesecollisionswillinvolverelativelymundaneanduninterestingphysicsprocesses, suchasminimum-biasQCD(e.g.,lightquark-antiquarkproduction).Theproduction oftop-quarks,whichisaninterestingprocess,willoccurontheorderofafewHz,for example.Exoticandhypotheticalphysicsprocessescouldoccurevenmorerarely.Thus, adedicatedtriggersystemisrequiredtolterthecollisioneventsastheyoccurbefore valuableresourcesareconsumedtowritethemtotapeforextensiveanalysisbythe collaboration.ThetriggersystemconstitutesthebeginningofCMSeventselection. Therearetwostagesoftriggering,andhencetwostagesofeventratereduction, onCMS.Therststageiscalledthe Level-1Trigger (L1),whichiscomposedof customizedhardwareandelectronicsforquickandefcienton-siteprocessingof thedigitizeddatathatisreportedfromvarioussub-detectors.Thesecondstageis calledthe High-LevelTrigger (HLT),whichconsistsofalterfarmofaboutathousand commercialprocessors.TheL1ishardware-based,whiletheHLTissoftware-oriented. ThecombinedL1+HLTsystemisdesignedtoreducetheeventrateviathefollowing sequence:LHC( 40 MHz) ( L1( 100 kHz) ( HLT( 300 Hz) ( storage.Thus,therateis ultimatelyreducedbyroughly 5 ordersofmagnitude. TheL1triggersystemmakesaccept/rejectdecisionsperbunch-crossingbasedon verycoarsedata.Thecoarsenessofthedataisduetothe 3.2 stimescaleoverwhich 1 Inreality,noteverybucketislledwithaprotonbunch.Evenatnominalluminosity, 2,808 of 3,564 bucketswillbelled. 96

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theL1hastoprocessandjudgeanevent.Thehigh-resolutionversionofthedatais bufferedintheonboardfront-endelectronicsofthesub-detectorsuntiltheL1"accepts" theevent,atwhichpoint,thenerdataisthentransferreddownstreamtotheHLT,where moresophisticatedandrenedeventanalysiscantakeplace. ThreemaincomponentsortiersconstitutetheL1triggersystem:local,regional, andglobal.Thelocalcomponentbuildswhatarecalled triggerprimitives ,whichcan beunderstoodasthequantaoftheentiretriggersystem.Triggerprimitivesarecrude blocksofdata,whichreectverybasicquantitiesreportedfromthecalorimetersystems (e.g.,energydepositedinthecalotowers)andthemuonsystem(e.g.,tracksegments, hitpatterns).TheregionaltieroftheL1triggersystemperformsasynthesisofthe informationprovidedbythetriggerprimitivesandranksthemaccordingtosome predeterminedcriteria.Rankingcanbebasedonthequalityofthemeasurement representedbythetriggerprimitive.Also,sometriggerprimitivescanbejudgedtohave moreupsideorpotentialtoreectinterestingphysicsthanothers.Theglobaltierofthe L1receivestherankedinformationandexecutessomequickalgorithmstodetermineif theeventshouldbeacceptedatthisstageandpropagatedtotheHLT.IftheL1accepts theevent,thenthehigherresolutiondetectordataisreadoutandsenttotheHLTlter farmforamorethoroughscrutiny. Asidefromthecontentofthetriggerprimitiveinformation,theglobalL1decision canbecontingentonthestatusofthesub-detectorsandtheDataAcquisitionSystem (DAQ).TheLHCwilldeliverabout 128 bunchcrossingsinthe 3.2 softimeittakesthe L1torenderitsdecision.Thislatencyhasafewconsequences.Inordertoprevent bufferoverows,afew triggerrules areimposed.Nomorethan 1:2:3:4 eventsfrom theL1triggercanbeacceptedper 75:625:2500:6000 ns.Thisresultsinasmall deadtime( $ 1% )wheretheLHCisdeliveringluminosity(andhencecollisions)but theCMSdetectorcannotrecordthedata.MoredetailsrelatedtotheL1triggersforthe calorimeterandmuonsystemscanbefoundinRef.[ 38 ] 97

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TheHLToperateswithalatencyof 0.02 to 1 secondsandisonlymeanttoperform amorerenedanalysisontheL1-seededobjects.TheL1triggerwillprovidethe HLTwithmuon,electron,photon,andjetcandidates,aswellasafewothercoarsely calculatedquantities(e.g., E T H T ).Toassesstheattributesofsomeoftheseobjects, datafromtheinnertrackingsystemneedstobeunpacked.Itisatimeconsuming processtoreadoutthedatafromthemillionsofchannelsintheTracker,whichiswhy thecurrentCMSL1triggerisblindtowhatoccursintheTracker.Evenwiththeextra timeaffordedtotheHLT,onlyregionaltrackreconstructioncanbeperformedinthe vicinityoftheL1objects.Asidefromthisexception,thefulleventreconstruction-level informationisperformedandisavailabletothelteringalgorithmswhichrunattheHLT. ThedetailsofCMSeventreconstructionwillbediscussedinthesubsequentsection. TheperformanceoftheCMStriggersystemisnotsolelyevaluatedbyitsrate reduction.Likeanyeventselectionlter,thetriggersystemwilllose(orfailtoaccept) eventswhichitismeanttoaccept.Thefrequencywithwhichaneventselectionlter succeedsinacceptinganeventwhenitissupposedtoisknownasthesignalefciency. Ideally,forarobustlter,thesignalefciencyshouldbealmostalways 100% ;however,in thecaseoftriggersthisisnotingeneraltrue(dependingonthedenitionofthesignal). Forexample,amuonwithatruevalueof p T =10 GeVmaybeactuallyconstruedby theL1triggerasamuoncandidatewith p T =6 GeVduetothecoarsenessofthedata. IftheL1triggerlteronlyacceptseventswithamuoncandidateof p T > 8 GeV,then thiseventwillberejected,andaninefciencywouldresult.AttheHLTwherethedata isnerandthelteringalgorithmscanaffordtobemorecomplicated,therecouldbe anynumberofcausesforeventsbemistakenlyrejected(e.g.,eventmis-reconstruction, softwarebug,etc.).Thus,asignicantamountofeffortisinvolvedtounderstand, commission,andvalidatethetriggerlters.Thiscanbedonetoacertainextentwiththe helpofsimulation,buttobedonerigorouslynecessitatestheanalysisofrealcollision data. 98

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5.3EventReconstructionandDataAnalysis OnceaneventhasbeenacceptedbytheHLT,thedetectordatacorrespondingto theeventisthenwrittentotapeinrawform,promptlyreconstructedatCERN,andthen distributedtovarioussitesforanalysis.Thisprocessinvolvesanumberofintermediate stepsaswellasasubstantialnumberofresources,whichwillbedescribedinthe subsequentsubsections. 5.3.1TheCMSSoftware TheCMSSoftware(CMSSW)isamodular,object-orientedframeworkwhichallows usersandphysicsgroupstodothefollowing,amongmanyotherthings: DesignandapplylteringalgorithmsfortheHLT Simulate,reconstruct,analyze,andvisualizeevents Applycalibrationandalignmentcorrectionstothedatarecordedbythedetector PerformvarioustasksrelatedtoDataQualityMonitoring(DQM) ManyoftheutilitieswithinCMSSWareprovidedbytheROOTdataanalysis framework.DevelopedbycomputerscientistsatCERN,ROOTisanobject-oriented collectionoflibrariesandclasseswhichcontainmuchofthefunctionalityneededto handle,manipulate,andanalyzelargeamountsofdata[ 54 ].Experimentsacrossthe worldemployROOTforthispurpose.DatafromCMSisstoredinROOTles,andthe informationcontainedintheselesisformattedinaccordancewiththeCMSEventData Model(EDM).ThefoundationoftheEDMisthe event ,whichisaC++containerclass usedtostoreallrawandreconstructeddatarelatedtoaparticularbunch-crossing(or collision).WithinCMSSWeacheventcontainerissequentiallylledwithvariousobjects, whichrepresenttheinformationrecordedbythedetector. Asalludedtoearlier,datacanexistsinseveralformswithintheEDMformat.The mostfundamentalformistherawdata(RAW),whichmainlyconsistsofthedigitizations ofthefront-endelectronicsignalsregisteredbythemillionsofchannelsinthevarious CMSsub-detectors.TheRAWdataisnotusableforanalysis.Ithastobe unpacked 99

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and reconstructed rst,whichisanotherwayofsaying reformatted and synthesized TheCMSeventreconstructionconsistsofhundredsofalgorithmswhicharedeveloped andexecutedinseveralstageswithintheCMSSWenvironment.Insimplestterms,the unpackeddataundergoeslocaldetectorreconstruction,whichisfollowedbyphysics objectreconstructionandnallyhigh-levelreconstruction.Thelocalreconstruction algorithmsareexecutedrstandtheseproduceC++objectswhichcontaininformation aboutlowerlevelobjects,suchasthesingleandcollectivepositionmeasurementsin thetrackingandmuonssystems,aswellasenergyclustersintheECALandHCAL. Theselowerlevelobjectsareoftenreferredtoasreconstructedhitsor RecHits for short,andtheyserveasinputstothephysicsobjectreconstructionalgorithmswhere theyaresynthesizedintocollectionsoftracks,muons,electrons,photons,andjets. TheRecHitsandphysicsobjectscombinetoprovidebuildingblocksforevenhigher levelreconstructedobjects,whichincludevertexing,b-tagging, ) identication,particle ow,andthecalculationof E T -relatedquantities,tonameafew.Forthemajorityofthe 2010collisionruns,thetimerequiredtoprocessaneventthroughthefullreconstruction chainrangedfrom 1 to 2 secondsonaverage,butcanbeafactorof 10 higherinrare cases[ 55 ]. Ingeneral,astandardEDMROOTlewillcontainanyorallofthefollowinglevelsof data: RAWlevel :Containsrawdetectorinformationfromthefront-endelectronics. RECOlevel :Containsdetailedinformationaboutthereconstructedphysics objects(e.g.,jets,electrons,photons,muons)aswellastheconstituentinformation whichisusetobuildtheseobjects(e.g.,tracks,rechits,calotowers).Contains morethansufcientinformationforanalysis,andisbulkyasaresult,consuming $ 350 kB/event.Itisnotoptimalforfrequentanalysis. AODlevel :TheAnalysisObjectDatacontainsonlythesubsetofRECOlevel informationwhichisessentialforanalysis.Theeventsizeissmaller $ 100 kB/event,whichenhancestheprocessingrate,andconservesmuchlessdisk space. 100

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EventhoughtheCMStriggersystemreducestherecordedeventratetoamanageable 300 eventspersecond,theLHCwillrunforyears.Itproducedprotoncollisionsforover 800 hoursduring2010.Thus,vastamountsofdatastorageresourcesareneededto accommodatethebillionsofrecordedcollisioneventsforanalysis.Tothisend,itis essentialthatthedatalesarekeptasleanaspossible,withoutcompromisingthe users'analysisgoals.ThisiswhattheAODismeanttodo. 5.3.2GridComputing AtnominaloperatingconditionstheLHCwillproduceapproximately13million Gigabytesofdataperyear[ 56 ].TheworldwideLHCComputingGrid(WLCG)isan extensiveglobalcollaborationestablishedtomanagethisvastamountofdatathatwill beproducedbytheLHC.TheGridisanenormousentity,spanningdozensofcountries, composedofoverahundredcomputingcenters,contributinghundredsofthousandsof processors.Unliketheexperimentsofpreviousgenerations,mostofthedataanalysis willnotactuallytakeplaceon-sitewheretheexperimentsarelocatedatCERN.Itwillbe doneremotelyatvariousuniversitiesandlaboratoriesaroundtheworldbymeansofthe Grid. Thedistributionofdataacrossthegridisdoneinafewstagesandinvolvesa hierarchyofcomputingcenters.Differentlevelsinthishierarchyarecalled tiers ,which reecttheamountofCPUandstorageresourcesaninstitutionisabletoprovide.The rolesofthevarioustiersastheyrelatetotheCMSexperiment,canbesummarizedas follows: Tier-0(CERN): ReceivesRAWdatafromtheCMSOnlineDataAcquisitionandTriggerSystem SegregatesRAWdataintowhatarecalledPrimaryDatasets(PD)basedonwhich typeoftriggerltersacceptedtheevent(e.g.,MuonPD,ElectronPD, E T PD) ArchivesonecopyofeachRAWPDtotape DistributesasecondcopyoftheRAWPDtoaTier-1center 101

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Executespromptcalibrationalgorithms,whichextractthecalibrationandalignment constantsnecessarytoperformreconstructiononthedata ExecutespromptreconstructionofRAWdatayieldingRECOversionsofPDs. DistributesRECOversionofPDstotheTier-1centercontainingthesecondcopy oftheRAWversion ExtractsAODversionofPDsfromRECOversionanddistributesAODtoallTier-1 centers Tier-1(7nationallaboratories) ReceivesasubsetofRAW,RECO,andAODdatafromTier-0 Performsscheduledre-reconstructionandskimmingofPDs DistributesRECOandAODversionsofPDstoTier-2centers StoresMonte-CarlosimulateddatasetsproducedbyTier-2centers Tier-2(dozensofuniversities) : StoresRECOandAODversionsoffullPDsandskimmedPDs ProvidesGRID-basedanalysisforusersacrosstheentirecollaboration Produces,stores,anddistributesMonte-Carlosimulateddata AtypicalCMS-basedanalysisontheGridwouldbeginwithauserwritinga CMSSWexecutableanalysisprogramoralgorithmonhisorherpersonalcomputer. TheuserwouldthenconnecttotheGridviaasharednetworkfromaTier-0,Tier-1,or Tier-2institution.TheGridwouldreceivetheuser'sexecutableprogramaswellassome parametersrelevanttothedesiredPDtobeanalyzed.AfterlocatingthePDatafew Tier-2centers,forexample,andassessingtheavailableresources(CPU,storage,etc), theGridwouldcreatejobsthatwillexecutethealgorithmsinaparallelfashionoverthe data.TheusercanmonitortheactionsoftheGridaswellastheprogressofhisorher jobs.Whenthejobsarenished,theuserexecutessomeretrievalcommandsandthe outputsofthealgorithms(typicallyROOTlescontaininghistograms)aredelivered. WiththecombinedresourcesoftheGrid,acollisioneventcanoccurattheLHC,be 102

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recordedbytheCMSdetector,andbedistributedtothevariousTier-1andTier-2sites inAODformatforuserstoanalyzeintheperiodofroughly 48 hours.Forhigh-priority, low-latencyanalysiswork,resourcesdoexiston-siteatCERN(Tier-0),butthemajority ofanalysisisconductedovertheGrid. 5.3.3MonteCarloSimulation Theroleofsimulationincolliderphysicsexperimentscannotbeoverstated. ItisessentialtoeveryaspectofoperationonCMS,includingdetectordesignand calibration,triggeremulation,machine-inducedandcosmic-raybackgroundstudies,and reconstructionperformance,tonameafew.Perhaps,themostvaluableserviceoffered byMonteCarlosimulationsatthisstageoftheexperimentisthehigh-statisticstraining grounditprovidesforphysiciststoexploreandoptimizesearchstrategiesforvarietiesof newphysicsmodels.Withthehelpofsimulation,theexpectedbackgroundandsignal yields,andhencediscoverypotential,ofanewphysicssearch(e.g.supersymmetryvia same-signdi-leptons)canbeevaluated.Ifaparticularsearchstrategyisnotfeasible accordingtoMonteCarlosimulations(e.g.backgroundsaretoohigh),thenitisvery unlikelytobefeasiblewithrealdata.Theinverseofthisstatementisnotguaranteed tobetrue,however,andthisfactmotivatesasignicantamountofeffortrelatedto so-called data-driven analysismethods(i.e.,notMonte-Carlobased).Thediscussion ondata-drivenmethodswillbedeferreduntilChapter 6 TheproductionofaMonte-Carlosimulatedeventisfactorizedintoafewstages. Therststageisperformedbyan eventgenerator suchasMadGraph[ 57 ]orPythia[ 58 ]. ThesesimulatetheparticlecollisionsthattheLHCwillcopiouslyproduceinreallife. Despitetakingplaceoversub-femtosecondtimeintervals,anLHCcollisioneventhasa rathercomplicatedgenesisandevolution,whichtheeventgeneratormusttrytoreplicate correctly.ThesequenceofimportantprocessesissummarizedsuccinctlyinRef.[ 58 ] andwillonlybebrieyparaphrasedhere.Inshort,protonsfromthetwoLHCbeams approacheachotherfromoppositedirectionscarryingthebeammomentum.Protons 103

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havesubstructure,i.e.quarksandgluons,andthebehaviorandcharacteristicsofthese needtobeaccuratelysimulated.Thisisdonebypartondistributionsfunctions( pdf 's) whichmodelthemomentumphasespaceavailabletoeachspeciesofparton.The interactionbeginsasonepartonfromeachprotonbeginsabranchingsequence(e.g., g ( gg or q ( qg )whichrapidlybreedsmanymorepartons.Typicallyonepartonfrom eachoftheseshowersisinvolvedinahard-scatteringprocessthatresultsinanumber ofoutgoingpartons(oftentwo).Thedetailsofthishard-scatteringprocessdetermine theoutcomeoftheevent.Thecreationofashort-livedresonanceboson(e.g. Z 0 or W )mayoccur,whichsubsequentlydecaystoleptonsorotherpartons.Themostlikely interaction(i.e.highestcross-section)isamundaneQCDprocesswheretheincoming partonssimplyexchangeagluon,whichresultsinamodestmomentumtransfer.While thisisthemostcommon,anyinteractionprescribedbytheStandardModelwillhave someprobabilityofoccurrenceforagivenevent. Manygeneratorsstoponcetheoutcomeofthehard-scatterissimulated,andsimply providealistofthefewparticleswhichresultalongwiththeirrespective 4 -momenta, etc.Theevolutionoftheeventisnonethelessstillincompleteatthisstage.Any outgoingpartonsfromthehard-scattercouldalsoundergoabranchingsequence similartotheincomingpartons.Thisisknownasnalstateradiation(FSR).Some typesoflarge-angle(hard)FSRcanbecalculatedbytheeventgenerator;however, thesoft,collinearFSRismoredifculttotreatanalyticallyandhastobemodeledby partonshowerprograms(e.g.,Pythia).Furthermore,thelawsofQCDonlyallowfor color-neutralnalstates(connement),soeachcolor-chargedparton(i.e.,individual quarkandgluon)producedinthehard-scattermustbeundergoafragmentationand hadronizationprocess.Someoftheresultinggroupsofhadronsmaybeextremely short-livedandwilldecayimmediatelyuponcreation,andsomecouldhavelifetimesthat allowthemtotraversemeasurabledistancesinthelaboratoryframebeforedecaying (e.g. D and B mesons)oreveninteractwiththedetector(e.g. K 0 L ,and K ).Allof 104

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thishastobeprobabilisticallysimulatedaccordingtofragmentationandhadronization models,whicharenotwell-knownfromrstprinciples,butareoftenparameterizedwith data. Thenalnumberofdistinctparticlesinvolvedinthehardscatteringeventfrom genesistohadronizationcanbewelloverathousand.Thus,thereisanimmense amountofdetailedcalculationsandbookkeepingrequiredforeventgenerationand partonshowering.Theindustryisrifewithactivityinordertobettersimulatehard collisionsandbetteraccountforquantumeffects.Somegeneratorscanaccount forquantumspincorrelations,andsomecanfeatureeventswithupto 6 outgoing partonsbeforehadronization(insteadof 2 ),whileothersspecializeinnon-leadingorder contributionstothematrixelement(scatteringamplitude)forvariousprocesses.Asa result,CMSemploysavarietyofeventgeneratorstoaccommodateitsMonteCarlo needs. Whilethecreationofoutgoingintermediateandnalstateparticlesresultingfrom theLHCcollisionsisunderthepurviewofeventgenerators,adifferentframework musttaketheseparticlesandpropagatethemthroughtheCMSdetector,simulating interactionswiththevariousmediumsalongtheway.TheisdonebytheGEANT4 simulationtoolkit[ 59 ].TheentireCMSdetector'sgeometry,it'smaterialcomposition (activeandpassive),aswellasitsmagneticeldmapisimplementedintheGEANT4 program.Thisallowsforuserstosimulatehowparticleswillbehavewhiletraversing thedetectorandhowthedetectorwillconsequentlyperformmeasurementsofsuch particles.GEANT4attemptstomodelallknownphysicsprocessesthatareinvolvedin thepassageofparticlesthroughmatterpermeatedbyanintensemagneticeld(e.g., ionizationlosses,bremsstrahlung,nuclearinteractions,multipleparticlescattering, electromagnetic/hadronicshowering,photonconversions,etc.).Theprogramsimulates theseprocessesforeachgeneratedparticleandproducesasimulatedhitinthedetector (SimHit)whichisthenusedtosimulateafront-endelectronicssignal(electronicsnoise 105

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isemulatedontop).ThecollectionofthelatterconstitutesasimulatedversionofRAW data.ThissimulatedRAWdataisthenprocessedbythereconstructionalgorithmsjust asrealRAWdatawouldbe. Allofthesefactorizedstepsfromeventgenerationtodetectorsimulationand reconstructionoccurwithintheCMSSWenvironment.Theendresultistheproduction ofanEDMROOTlewhichcontainshundredsofsimulatedeventswithnearlythe samelecontentasthatofrealcollisiondata.Animportantdifferencebetweenreal dataandsimulateddataisthatwiththelatter,theuserhasaccesstothe Monte CarloTruth information,whichallowshimorhertoidentifycertainsignaturesinthe detectorandattributethemtocertainparticles.Thisaffordsonetheabilitytoperforma varietyofreconstruction-levelandtrigger-levelefciencystudiesaswellasassessthe performanceofvariouseventselectionrequirementsattheanalysislevel. TheutilityofGEANT4islimitedbyitsper-eventprocessingrate.Itisquite CPU-intensivetofaithfullysimulatehoweachparticlewillinteractwitheachcubic micronofdetectormaterialthatitencountersalongitsway.TofullysimulateasoftQCD interactionevent(e.g. p T > 15 GeV),GEANT4requiresabout 90 secondsofCPUtime, withvariationsthataresensitivetotheparticlemultiplicityoftheevent.Recall,thatthe LHCcanmanufacturearealQCDeventeveryfewnanosecondsatnominaloperating conditions.Thus,parallelprocessingisanecessityformassproductionofsimulated data.Fortunately,suchprocessingiseasilyfacilitatedbytheGrid,andspecicallythe resourcesoftheCMSTier-2centers. DespitetheadvantagesthattheGridprovides,inordertosimulatejust 1 pb 1 worth ofsoftQCDdataitwouldrequireover 800 millionevents,asthecross-sectionisover 8 10 8 pbatleadingorderfor p T > 15 GeV.Consideringthatusersgenerallywanttheir MonteCarlostatisticstobecommensuratewiththeintegratedluminosityofrealdata theyareanalyzing,oneimmediatelyseesthelimitationsfromemployingaprogramlike GEANT4tosimulatethedetector'sresponse.In2010theLHCdeliveredover 40 pb 1 106

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ofdata.Thisisexpectedtoincreasebyroughlytwoordersofmagnitudebytheendof 2012.ItissimplyimpossibletosimulatethatmuchQCDdatawithGEANT4,although processeswithmuchsmallercross-sections(e.g.high p T QCDorelectroweak)willnot ingeneralbelimitedbythelargeprocessingtime. AnalternativetoGEANT4istheCMSFastSimulationsoftware(FastSim),which offersaparameterizedtreatmentofthephysicsinteractionsthatoccurasparticles propagatethroughmatter.Dependingonthetypeofcollisioneventbeingsimulated, FastSimcanproducetheeventseveralhundredtimesfasterthanGEANT4can,and withcomparableaccuracyformostoftheobservablesuserswishtostudy[ 60 ].Withthe helpofFastSim,high-statisticssamplescanbeproducedforanynumberofprocesses. Oneimportantuse-case,whichwillbeencounteredinChapter 6 ,isthemassproduction ofsimulateddataforamultitudeofnewphysicsmodelswithinavastparameterspace (e.g.mSUGRA).Thesetypesofparameterspacescansareusefulinordertocalculate statisticalexclusionlimitsfornewphysicssearches. 107

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CHAPTER6 THESEARCHFORSUPERSYMMETRYATTHELHCWITHTHESAME-SIGN DI-LEPTONS,JETS,AND E T SIGNATURE 6.1Introduction Theanalysisdescribedhereinconstitutesoneofthreemajorcomponentsof therstefforttoidentifysupersymmetryattheLHCwiththesame-signdi-leptons, jets,and E T signatureusingtheCMSdetector.Themainfeatureofthisanalysisthat distinguishesitfromtheothercomponentsisthefocusonnalstateswithsoftleptons (i.e.,smalltransversemomentaorlowp T ),includingthedi-muon( ),di-electron( ee ), andelectron-muon( e )channels.Theothertwocomponentsfocusonnal-stateswith hardleptons(highp T )andnalstateswithhadronicallydecayingtau-leptons(also calledhadronic ) 's),respectively.Thesethreecomponentshavebeensynthesizedintoa commonresult,whichisbasedonanintegratedluminosityof 35 pb 1 andcanbefound elsewhere[ 61 ].Thefollowingdiscussionwillberestrictedonlytothecomponentrelated tosoftleptons. Pairsofsame-sign,promptleptons(notarisingfromjets)areveryrareinthe StandardModel,Synchrotronbutappearverynaturallyinmanynewphysicsscenarios[ 20 23 25 28 30 ].Thismakessearchesfornewphysicswithsame-signdi-leptonpairs veryattractive.The minimal SUSY-inspired(butnotlimitedtoSUSY)prerequisites fortheappearanceofsame-signdi-leptons,andthecorrespondingexperimental consequences,areasfollows: Bydefault,weassumethatthelightestsupersymmetricparticle(LSP)isstable(or semi-stable)andweaklyinteracting(e.g., + 0 1 ).Fromthephenomenologicalpointof view,theLSPsetsanewandhithertounknownmassscale, m C .Theexpectation ofsuchanLSPmakes E T anaturalpartoftheexperimentalsignature. Next,weassumethattheprimeproductionmechanismisviaQCDprocesses,i.e. viaproductionofgluinosandsquarks,whosemassesbecomethesecondmass scale m A .Thisleadstolargecrosssectionsandthusdetectionintheearlydata apossibility.Theexperimentalconsequencesaresuchthatoneshouldexpect jets(inacascadefromacoloredobjecttotheLSP),whichbecomeasecond ingredientintheanalysis. 108

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Finally,weshouldassumeachargedElectroweak(EWK)particlecouplingto quarksandsquarksandhavingamassresidingbetweenthesquarksandtheLSP. InthecontextofSUSY,thisparticlewouldbeachargino.Suchamasshierarchy opensthepossibilityforacascadedecaychainwhichincludesasinglelepton (e.g., q ( + + q ( l + ( + 0 1 q )and,consequently,allowsfortwosame-signleptonsper event.Theobviousphenomenologicalimplicationofinsertingacharginobetween squarks/gluinosandtheLSPisthatwehaveintroducedyetanother,thirdmass scale, m B ,withtheoverallorder m A > m B > m C NotethattheEWKproductiondoesnotnaturallyleadtoexclusivesame-sign di-leptons;theywouldappearonlyasapartoftri-orquad-leptonnalstates, whicharebettersearchedforindedicatedanalyseslookingexclusivelyfor 3 or moreleptons.Itisalsoworthmentioningthat,shouldgluinosbeveryheavy,the dominantproductionmechanismwouldbeviasquark-antisquarkpairs,which, asinthecaseoftheEWKproduction,doesnotleadtoexclusivesame-sign di-leptons. Anexampleofaprocessgivingthedesiredsignatureoftwosame-signleptonswithjets and E T wasshowninFigure 3-5 .Figure 6.1 showsthetotalnext-to-leadingorder(NLO) andleadingorder(LO)cross-sectionscalculatedwiththeProspino[ 62 ]softwarefor gluino-gluino,squark-squarkandsquark-gluinoproductionsin pp collisionsat & s =7 TeVasafunctionofthegluino-squarkmass( M g = M q for q g production). Thethreemassscalesinherenttothesame-signdi-leptonsignaturedene theexperimentalenergyscalesforhadronicactivity,leptonmomenta,andmissing transverseenergyinthenalstate. Jetsappearintherststepofthetwo-stepprocess: q ( + q or g ( + q q Consequently,thenumberofhardjetsperdecaychainisoneortwo,whilethe masssplitting, m AB ,denesthetotalamountoftheenergyavailabletojets. Giventhatthecharginomassmustbeabove 100 GeVandthatsquark/gluino massesabove 400 500 GeVwouldnotbeproducedattheLHCwiththedata collectedthusfar,charginosappearingintherstcascademustlikelyhaveavery modestboost.Consequently,the p T ofleptonsappearingintheseconddecayare goodindicatorsofthesecondmasssplitting m BC Themagnitudeofthe E T willhavesomedependenceonbothmasssplittings,but neverbecomessmallaslongasthereisalargemassdifference, m AC ,between squarks/gluinosandtheLSP. 109

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, GeV q ~ = M g ~ M 0 200 400 600 800 1000 Cross Section, pb -3 10 -2 10 -1 10 1 10 2 10 3 10 4 10 = 7 TeV S LHC NLO LO g ~ g ~ g ~ q ~ q ~ q ~ q ~ q ~ + g ~ g ~ + g ~ q ~ GeV q ~ = M g ~ M 0 200 400 600 800 1000 Cross Section, pb -3 10 -2 10 -1 10 1 10 2 10 3 10 4 10 Figure6-1.ThetotalNLO(solid)andLO(dashed)cross-sectionsforgluino-gluino( g g ), squark-squark( q q )andsquark-gluino( q g )productionsvsgluinoorsquark massesattheLHC( & s =7 TeV). 6.2MonteCarloSimulatedData ForthisanalysisanassortmentofsimulatedStandardModelMonteCarlo datasamplesareusedtostudytheperformanceofeventselectioncriteriaandto validatebackgroundpredictionmethods.ThesesamplesrelyoneitherPythia[ 58 ] orMadGraph[ 57 ]foreventgenerationandGEANT4[ 59 ]forsimulationoftheCMS detector.Tomodelthesignal,areferencepointfromthemSUGRAparameterspaceis usedwithparameters: m 1 / 2 =160 GeV, m 0 =200 GeV, tan( )=10 A 0 = 400 GeV, > 0 .ThismodeliscommonlyreferredtoasLM0andfeatureslow-masssquarksand gluinos.Asaresultoftheselowmasses,theproductioncross-sectionisrelativelyhigh ( % 57 pb),allowingforthepossibilityofdiscoverywiththerst 35 pb 1 ofdata,should itexist.WhileitisbeyondtheexclusionreachesoftheLEPandTevatronsearches, ithasrecentlybeenexcludedat95%CLbysearcheswiththeATLAS[ 63 ]andCMS 110

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detectors[ 64 65 ],whichwereperformedconcurrentlywiththisone.Despitethis,LM0 stillprovidesausefulmodelofthegenericsignaltopology(i.e.,same-signdi-leptons, jets,andmissingenergy),whichcanhelptoinspireseveraloftheeventselection criteria.AlloftherelevantbackgroundsaswellasLM0arerepresentedanddetailedin Table 6-1 .Leadingordercross-sectionsarecombinedwithk-factors,wherethelatter areavailable.Alleventsfromthesesamplesarereconstructedwithversion3.5.6ofthe CMSSoftWare(CMSSW). Table6-1.SummaryofsimulatedStandardModelbackgroundsandsignalsamples ProcessGenerator (LO)k-factorEquivalent (pb) L d t (pb 1 ) b b : H T [100,250] GeVMadGraph 23820 21.4 b b : H T [250,500] GeVMadGraph 7002 148.3 b b : H T [500,1000] GeVMadGraph 172 6.14 10 3 b b : H T [1000, ) ] GeVMadGraph 2.4 1.22 10 5 QCD: H T [100,250] GeVMadGraph 7.0 10 6 1.5 QCD: H T [250,500] GeVMadGraph 1.71 5 28.7 QCD: H T [500,1000] GeVMadGraph 5200 805 QCD: H T [1000, ) ] GeVMadGraph 83 2.00 10 3 t t MadGraph 951.669.35 10 3 singlet (s-channel)MadGraph 4.21 9.79 10 4 singlet (t-channel)MadGraph 64.6 8.18 10 3 singlet (tW-Channel)MadGraph 10.6 4.40 10 4 & + jetsMadGraph 173 6.28 10 3 W + jetsMadGraph 242001.2322 Drell-Yan ( ( + ( : m Z [50,120] GeVMadGraph 24001.17356 Drell-Yan ( ( + ( : m Z [20,50] GeVPythia 4998 (NLO) 523 Drell-Yan ( ( + ( : m Z [10,20] GeVPythia 10371 (NLO) 278 W + W + Pythia 0.188 5.3 10 4 W W Pythia 0.064 2.9 10 5 2 ( qq # ( W ) Pythia 0.203 2.2 10 5 ZZ Pythia 4.31.372.0 10 4 W Z Pythia 10.51.746.3 10 3 W W Pythia 281.532.9 10 3 SUSYModelPointLM0Pythia 38.91.483.6 10 3 111

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6.3TriggerStrategy AstheinstantaneousluminositydeliveredbytheLHCincreasedoverthe2010data takingperiod,theCMStriggermenuswereforcedtoevolveaccordingly.Forasearch relyingonhighH T andlowP T leptons,thetriggerstrategybecomesquitecomplicated, astriggerthresholdswerefrequentlyraisedtoaccommodatetheincreasingcollision rates.Asaconsequence,varioustriggerpathswereexploredforeachchannelin thisanalysis.Ultimately,the H T -basedtriggerpathsprovidedthebestsensitivity,and sotheyareusedhere.Somecomplicationsarisefromthefactthatdenitionfor H T usedonlinebythehigh-leveltrigger(HLT)isnotthesamedenitionusedofinein theanalysis.Thisisduetothelimitedandcoarseinformationthatisavailabletothe HLTforsuchcalculations.Thesecomplicationssimplyforceonetoimposeanevent selectionrequirementonthe H T observableofinethatiswellabovetheonethatis usedonline.Thisisdoneinordertoensurethattheprobabilityforaneventwithan ofinevalueof H T tosatisfytheonline H T selectionrequirementwillbegreaterthan 95%.Thisprobabilityisoftenreferredtoasthetriggerefciency,andismeanttobe closeto100%inidealcases.The H T triggerefciencycanbemeasuredbyappealing tootherorthogonaltriggers.ThismeasurementwillbediscussedinSection 6.7.2.5 Table6-2.Summaryoftriggerstrategy RunRange L d t (pb 1 )TriggerRequirement 140160-1471167.4Online H T > 100 GeV 147196-1480589.5Online H T > 140 GeV 148822-14929417.8Online H T > 150 GeV 6.4PhysicsObjectsandDiscriminatingObservables Themainphysicsobjectsemployedbythisanalysisaremuons,electrons,jets,and missingtransverseenergy.Allofthemarereconstructedusingstandardtechniqueson CMS[ 38 ]. Muonsarerequiredtobereconstructedusingtwoalgorithms[ 66 ].Onealgorithm, calledtheTrackerMuonreconstructionalgorithm,matchestracksinthesilicondetector 112

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withmeasuredhitsinthemuonsystem.Anotheralgorithm,knownastheGlobalMuon reconstructionalgorithm,performsasimultaneousglobaltracktusingmeasurements fromboththesilicondetectorandthemuonsystem.Tracksbelongingtothemuon candidatemusthaveaminimumnumberof 11 hitsinthesilicontracker,atleast 1 hitin themuonsystem,andhaveahigh-qualityglobaltracktwithanormalized + 2 valueof lessthan 10 .Thecalorimetersignalwhichliesinthetrajectoryofthemuoncandidate mustbeconsistentwiththatofaminimumionizingparticle. Electronsarereconstructedbeginningwithanenergyclusterlocatedinthe ECAL.Theclusteristhenmatchedtohitsinthesilicondetector.Owingtothehigh possibilityforotherobjects(e.g.,photons,jets)tomimicthecharacteristicsignatures ofelectroncandidates,acollectionofdedicatedelectronidenticationvariablesare employedtofurtherestablishtheexistenceofatrueelectron.Thesevariableshave beenoptimizedusing W ( e ( events,andcantakeonavarietyofvaluesinorder toallowtheusertochoosethedesiredbalancebetweenreconstructionefciency andpurityofelectrons[ 67 ].Forthisanalysistheidenticationcriteriaarechosen atavaluethatensuresthatapproximately80%oftrueelectronsarereconstructed, whilethemis-reconstructionofotherobjectsaselectronsaregreatlydiminished.This identicationcriteriaisoftenreferredtoasVBTF80. 1 Muonsareabletobereconstructedandwell-measureddownto p T > 5 GeV,while electronsmustbeselectedwithahighertransversemomentumof p T > 10 GeV.Both muonsandelectronsaremeasureduptoapseudorapidityof | 1 | > 2.4 ,andarerequired tooriginatefromtheprimarycollisionvertex.Inordertoselectleptonsfromso-called prompt electroweakdecays(e.g.,from W Z + 0 + particles)andnotfromhadronic decaysorjets,averyimportantdiscriminatingvariableisemployed,knownas relative isolation ,whichisoftenabbreviatedas RelIso .The RelIso observableiscalculatedby 1 Vector-BosonTaskForceworkingpoint80%. 113

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rstformingaconein 1 spaceofradius R = 1 2 + 2 =0.3 centeredaround theleptoncandidate.Thenthesumofthetransversecomponentsofallthetracks, ECALtransverseenergydeposits,andHCALtransverseenergydeposits,whichliein thiscone,isdividedbythetransversemomentumofthelepton 2 .Figure 6.4 provides apictorialrepresentationofhow RelIso isconstructed.Algebraically,theexpression for RelIso isgiveninEq. 61 .Forthisanalysis,arequirementof RelIso < 0.15 is imposedonallleptons.Arequirementisalsomadeonthetransverseimpactparameter (Figure 5-3 )ofleptonsasmeasuredfromthebeamspotatavalueof d 0 < 0.2 mm.This helpstoensurethattheleptonsdonotcomefromdecaysoflong-lived,heavy-avor mesons. RelIso= % i p Track T i + % i E ECAL T i + % i E HCAL T i p T (61) Figure6-2.PictorialrepresentationofhowtheRelIsovariableiscalculated. 2 Asmallconeofradius R = 1 2 + 2 =0.01 surroundingamuoncandidate isremovedfromtheisolationsum,inordertoprohibitthemuon'sown p T andenergy depositfromcontributing.Forelectrons,amorecomplicatedgeometricalshapeis removedinordertoprohibitcontributionsfrombremsstrahlung. 114

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Jetsand E T arereconstructedbasedontheparticle-owtechnique[ 68 69 ]. Theanti-K T algorithmisusedforclusteringhadronicjetswithadistanceparameter of R =0.5 [ 70 ].Jetsarerequiredtopassstandardqualityrequirementsinorderto reducetheeffectoffalselyreconstructedjetsfromcalorimeternoiseorotherspurious signals[ 71 ].Jetenergiesarecalibratedtocompensateforthenonlinearityofthe calorimeterresponse[ 72 ].Selectedjetsmusthave p T > 30 GeVandbewithin | 1 | < 2.5 The H T observableisusedtocharacterizethetotalamountofhadronicjetactivityinthe event.Itconsistsofthescalarsumoftransversemomentafromallselectedjetsinthe event.Atleasttwojetsmustbeusedinthecalculationof H T 6.5EventSelection Aftersatisfyingthetriggerrequirements,theeventischeckedtoensurethata goodprimaryvertexisreconstructedwith | Z | < 15.0 cm, N dof > 3 and d 0 < 2.0 cm. Furthereventselectionisdoneinthreestages: pre-selection baselineselection ,and nalselection .Eachsubsequentstageimposesstricterrequirementsthantheprevious stage.Thepre-selectionrequirementsaremeanttoprovidearelativelyhigh-statistics samplethatcanbeusedfordirectcomparisonswithMonteCarlosimulateddata. Thebaselineselectionisusedasacontrolregionforpredictingasub-dominant,but important,backgroundfromQCDmulti-jetproduction.Thenalselectionrepresentsall oftheselectionrequirementsthatareusedforthecountingexperiment(i.e.,thesignal search).ThedetailsoftheseselectionstagesareprovidedinTable 6-3 Additionalleptonsarealsoallowedtobepresentintheevent.Inthecasethat therearemultiplepairsofsame-signleptonsintheevent,priorityisassignedby e andlastly ee .Iftherearemultiplepairswithinthesamechannel,thenthepairwiththe highestscalarsumof p T ischosen. Tables 6-4 6-5 and 6-6 showtheeventyieldsastheeventselectionrequirements areappliedinsuccession,startingfrompreselection,forvarioussimulatedStandard Modelprocesses,theLM0signalmodel,anddata.Distributionsofthe H T RelIso 115

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Table6-3.Descriptionofeventselectionrequirements SelectionLevelRequirementDescription Pre-selection N jets # 2 Coloredproduction H T > 100 GeVMinimalhadronicactivitynecessary formeaningfulMonteCarlocomparisons N # 2 or N e # 2 Di-lepton(ormulti-lepton)event or N + N e # 2 q 1 = q 2 Same-signelectromagneticcharge M 1 2 > 5 GeVInvariantmassabove characteristicheavy-avordecay M + i j / [76,106] GeVNeitherleptonshouldcome fromaZ-bosondecay Baselineselection H T > 300 GeVSignicanthadronicactivityindicative ofdecayofheavy,coloredsuperpartners. Alsonecessaryforconsistencyw/trigger. Finalselection RelIso < 0.15 Leptonsmustbeisolated, indicatingtheyareprompt E T > 30 GeVNon-trivialmomentumimbalance, indicatingtheescapeofinvisibleparticles ofthemostandleastisolatedleptonsrespectively,and E T aftereachsubsequent selectionrequirementareshowninFigures 6-5 6-6 and 6-7 forthe -, ee -,and e -channels,respectively.Preselectionisrepresentedbytherstrow.Baseline selectionisrepresentedbythesecondrow.Thethirdandfourthrowsincludethe RelIso requirementsonthemostandleastisolatedleptons,respectively.Thenalrow furtherincludesthe E T requirementandrepresentstheyieldsafterthenalselection. AgraphicalrepresentationoftheexpectedeventyieldsfromsimulatedStandard Modelprocessesafterthenaleventselectionasdescribedaboveisshownin Figure 6-4 for 35 pb 1 .Thedominantbackgroundsaresingle-topandtop-antitop pairproduction( t t ).Duetotheextremelyhighproductioncross-sectionofQCD multi-jetprocesses,thelimitedstatisticsfromMonteCarlosimulationscannotbe 116

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usedtoevaluatethisbackground.Whileitisexpectedtobesub-dominantorsmall,the contributionofthisbackgroundmustbeaccountedforandderivedfromdata. m u m u e e e m u 0 0 0 1 0 2 0 3 E x p e c t e d e v e n t s D i l e p t o n e v e n t c a t e g o r y L M 0 t t + t W + t b q + t b q q W W W Z & Z Z M o n t e C a r l o f o r 7 T e V 3 5 p b 1 C M S P r e l i m i n a r y Figure6-3.MonteCarlopredictionsforexpectedeventyieldswith 35 pb 1 ofdata. Data LM0 t t W+Jets Z+Jets WZ + W + W ZZ tW Single-t W W W) (qq' 2 QCD Figure6-4.LegendforFigures 6-5 6-6 ,and 6-7 117

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050100150200250300350400450500 -2 10 -1 10 1 10 050100150200250300350400450500 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 2 10 0123456 -2 10 -1 10 1 10 2 10 0123456 -2 10 -1 10 1 10 2 10 0123456 -2 10 -1 10 1 10 2 10 050100150200250300 -2 10 -1 10 1 10 2 10 050100150200250300 -2 10 -1 10 1 10 2 10 050100150200250300350400450500 -2 10 -1 10 1 10 050100150200250300350400450500 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 2 10 0123456 -2 10 -1 10 1 10 2 10 050100150200250300 -2 10 -1 10 1 10 050100150200250300 -2 10 -1 10 1 10 050100150200250300350400450500 -2 10 -1 10 1 10 050100150200250300350400450500 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 050100150200250300 -2 10 -1 10 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 050100150200250300 -2 10 -1 10 H T RelIso ( 1 ) RelIso ( 2 ) E T Figure6-5.Distributionsofkeyobservablesforthe -channel.Fromlefttoright: H T RelIso ( 1 ), RelIso ( 2 ),and E T .Therowsfromtoptobottomrepresent successiveeventselectionrequirements:preselection,baselineselection, RelIso ( 1 ) < 0.15 RelIso ( 2 ) < 0.15 E T > 30 GeV. 118

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050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 H T RelIso ( e 1 ) RelIso ( e 2 ) E T Figure6-6.Distributionsofkeyobservablesforthe ee -channel.Fromlefttoright: distributionsof H T RelIso ( e 1 ), RelIso ( e 2 ),and E T .Therowsfromtopto bottomrepresentsuccessiveeventselectionrequirements:preselection, baselineselection, RelIso ( e 1 ) < 0.15 RelIso ( e 2 ) < 0.15 E T > 30 GeV. 119

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050100150200250300350400450500 -2 10 -1 10 1 10 050100150200250300350400450500 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 2 10 0123456 -2 10 -1 10 1 10 2 10 0123456 -2 10 -1 10 1 10 2 10 0123456 -2 10 -1 10 1 10 2 10 050100150200250300 -2 10 -1 10 1 10 2 10 050100150200250300 -2 10 -1 10 1 10 2 10 050100150200250300350400450500 -2 10 -1 10 1 10 050100150200250300350400450500 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 050100150200250300 -2 10 -1 10 1 10 050100150200250300 -2 10 -1 10 1 10 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 10 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 050100150200250300350400450500 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 0123456 -2 10 -1 10 1 050100150200250300 -2 10 -1 10 050100150200250300 -2 10 -1 10 H T RelIso ( l 1 ) RelIso ( l 2 ) E T Figure6-7.Distributionsofkeyobservablesforthe e -channel.Fromlefttoright: distributionsof H T RelIso ( 1 ), RelIso ( 2 ),and E T .Therowsfromtopto bottomrepresentsuccessiveeventselectionrequirements:preselection, baselineselection, RelIso ( 1 ) < 0.15 RelIso ( 2 ) < 0.15 E T > 30 GeV. 120

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Table6-4.Eventyieldsaftereachcutforthe -channelfor 35 pb 1 CutLevelLM0DataTotBgd t tW + jets Z + jets WZW W # ZZtW singletW W 2 x ( qq $ ( W ) QCD Pre-selection2068527722.34.880.9950.08070.03640.01420.5312.460.05940.000638245 Baseline17.122379.610.61.410.390.03460.012100.1850.6530.0312066.3 RelIso ( 1 )12.92211.47.221.30.2920.0288000.1170.5370.030701.9 RelIso ( 2 )3.4200.2240.125000.00576000.002720.0250.022200.043 E T 3.3200.1570.103000.00576000.002040.0250.020600 Table6-5.Eventyieldsaftereachcutforthe ee -channelfor 35 pb 1 CutLevelLM0DataTotBgd t tW + jets Z + jets WZW W # ZZtW singletW W 2 x ( qq $ ( W ) QCD Pre-selection5.043013.64.932.280.5420.02310.03640.01770.1520.4910.03470.0001595.06 Baseline3.8263.041.440.1080000.003550.01630.07490.013601.39 RelIso ( e 1 )3.4641.511.210.1080000.003550.01220.07490.013600.0859 RelIso ( e 2 )1.7410.06290.044200000.0035500.004160.01100 E T 1.6710.04760.03320000000.004160.010200 Table6-6.Eventyieldsaftereachcutforthe e -channelfor 35 pb 1 CutTotLM0DataTotBgd t tW + jets Z + jets WZW W # ZZtW singletW W 2 x ( qq $ ( W ) QCD Pre-selection21.432423427.46.721.970.1610.06070.04440.8753.320.09120.000638193 Baseline16.87841.49.11.190.1520.05190.02430.00710.1430.5620.0391030.1 RelIso ( ( 1 )14.52113.57.361.190.1250.04610.02430.003550.1190.4870.038104.11 RelIso ( ( 1 )510.2350.166000.017300.001770.001360.02080.02800 E T 4.8600.2050.147000.017300.001770.001360.01250.024800 121

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6.6BackgroundEvaluationandAssociatedUncertainties Inthissectionthebestestimatesofthebackgroundeventrateswiththeassociated systematicuncertaintiesaregiven.TheStandardModelprocessesleadingtoprompt, same-signdi-leptonpairshaveverysmallcross-sections.Hence,themainbackgrounds associatedwiththisanalysiscomewithso-called"fake"leptons(e.g.,non-prompt leptonspassingtightisolationcuts,promptleptonsmis-reconstructedwiththewrong charge,etc.)OnecannotreallyexpectthattheMonteCarlosimulationwouldaccurately predictratesofsuch"fake"leptons.Thus,thisanalysislargelyreliesonmeasuring thedominantandleastcertainbackgroundsdirectlyfromdata,whichreectsthe organizationofthissection.Backgroundpredictions,whicharederivedfromthedata itselfareusuallyreferredtoas data-driven ,whilebackgroundpredictionsthatcome fromsimulationsarereferredtoas Monte-Carlobased .Thisterminologywillbeused throughouttheremainderofthischapter. Beforegoingfurtheritshouldbenotedthattherespectivedata-drivenmethods ofbackgroundestimationdonotnecessarilymapone-to-oneontodistinctphysics processes.Insomecases,onemethodmaycovermorethanjustonebackground.For example,allprocesseswithasinglepromptleptoncombinedwithanothercomingfrom ajet(e.g., t t tW W + jets, Z + jets)areevaluatedtogetherbythesamemethod.In othercasesasinglephysicsprocesscanleadtomorethenonedistinctwayofentering thesignalregion.Forexample, t t cancomeviaitsprompt-fakecomponent( t t ( ( .( b )( jj b ), b jet ( + X )orviatheprompt-promptcomponent( t t ( ( + ( b )( ( b ) whereoneofthetwopromptleptonsismis-reconstructedwiththewrongcharge.) Thecategorizationofthemainbackgroundstothissearchissummarizedin Table 6-7 .Thenotationintroducedinthistablemaybereferencedinotherpartsofthis chapter.Anygenericnon-promptleptonwillhenceforthbereferredtoasa"fake"lepton. 122

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Table6-7.Summaryofbackgroundstothesame-signdi-leptonsearch. BackgroundTypeSourcesMethod Same-signprompt-prompt( N SS p p ) WZ ZZ W W Monte-Carlobased Opposite-signprompt-prompt( N OS p p )Charge-ipinData-driven t t tW ,DY, W W ,etc(Charge-ipmethod) Same-signprompt-fake( N SS p f ) t t tW W + jets, Z + jetsData-driven (BTag&Probemethod) Same-signfake-fake( N SS f f )QCD,all-hadronic t t Data-driven (Factorizationmethod) Equation 62 providesthecalculationforthetotalbackgroundprediction.The termspresentinthisequationwillbedescribedindetailinthefollowingsections,aswell astheirrespectiveuncertainties. N tot bgd = N SS p p + N OS p p + N SS f f + N SS p f (62) 6.6.1DeterminationofPrompt-Prompt,Same-signDi-leptons: N SS p p Potentialsourcesofprompt,same-signdi-leptonnalstatesin pp -collisionsare: (i) di-bosonproduction: q q ( WZ and ZZ (ii) double"W-sstrahlung": qq ( q # q # W W (iii) doublepartonscattering: 2 ( q q ( W ) Theseprocessesarenotyetestablished,norwell-measuredattheLHC(thougha fewcleaneventcandidateshavebeendetected).Therefore,topredicteventrates associatedwiththeseprocessesonesimplyhastorelyonthetheoreticalpredictions andtheassociatedtheoreticaluncertainties. Thedoublepartonscatteringeventsareexpectedtobeheavilysuppressedbythe selectionrequirementsbasedonhadronicactivity.Therefore,suchcontributionscan simplybeignored.However,thedouble"W-sstrahlung" qq ( q # q # W W hasallofthe prerequisitestomimicthesignal(i.e.,samesignleptons, E T ,jets)anddoescontribute attheend. 123

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Fromthephenomenologicalpointofview,theseprocessesareverymuch "signal-like"andwouldhaveverysimilarexperimentalsystematicerrorstothoseofthe signal(Section 6.7 ).Table 6-8 summarizestheexpectedeventyieldsandassociated systematicerrorsforthissourceofbackground,whicharebasedonMonteCarlo simulation. Table6-8.Eventyieldsandsystematicerrorsforadouble"W-sstrahlung" qq ( q # q # W W anddoublepartonscattering 2 ( q q ( W ) Di-leptonchannel eee total Numberofexpectedeventsfor VV 0.0060.0000.0190.025 Theoreticalsystematicerror 0.003 0.007 0.010 0.013 Numberofexpectedeventsfor qq ( q # q # W W 0.0210.0120.0250.058 Theoreticalsystematicerror 0.011 0.006 0.013 0.029 TotalPrompt-Promptbackgrounds0.0260.0120.0440.083 Experimentalerrors 0.005 0.002 0.008 0.015 Totalerrors 0.014 0.007 0.023 0.044 6.6.2DeterminationofPrompt-Prompt,Opposite-signDi-leptons: N OS p p BasedonphysicsconsiderationsanddirectMonteCarlostudies,thechargeof electronsismuchmorelikelytobemis-reconstructedthanisthechargeofmuons. Infact,theprobabilityofthelatteroccurringcansimplybeignored,asitisnegligible duetotheminimumionizingnatureofmuonsinthemomentumrangetargetedforthis analysis.Electrons,ontheotherhand,caneasilyemitbremsstrahlungphotonswhile passingthroughthedensevolumeofthesiliconTracker.Thisprocesscancausesmall kinksinthereconstructedtrackthatmayleadtochargemisassignment.However,the electron'senergymeasurement,largelydrivenbytheECAL,ishardlyaffectedsincethe electronanditsbremsstrahlungphoton(s)aremostlycollinearandformonecommon ECALsuperclusterwiththetotalenergyoftheoriginalelectron.Thelatterfeatureallows theevaluationofthechargemis-reconstructionrate(chargeiprate)bymeasuringthe numberofsame-signdi-electronpairswhichformaninvariantmassthatlieswithina smallwindowsurroundingthe Z -bosonmass.Thedi-electronpairscontributingtothe Z -bosonmasspeakshouldinherentlybeoppositelycharged( Z ( e + e ). 124

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Therststepinpredictingthisbackgroundistosimplycountthenumberof same-signdi-electronswithinthe Z masswindowafterimposinga E T veto(tosuppress neutrinoactivityfrom W + jetsand t t ),anddividethisnumberbytheyieldof Z ( e + e events,asinEq. 63 2 ip = 1 2 N Z ( e e ) N Z ( e + e ) (63) Theipratefortheelectronsusedinthisanalysisismeasuredtobe 2 ip =0.5 (5 / 3642)=0.0007 0.0003 andisconsistentwiththeexpectationfromMonte-Carlobased studies. Next,ananalysisisperformedwiththenalselectioncriteria,exceptnowasking fortwoopposite-signdi-leptons.Theobservedeventyieldsare: 8 + 6 e + e and 6 e events.Usingthemeasuredyieldsofopposite-signdi-leptonsandthe measuredchargeiprate,onecanpredictthebackgroundrateofeventsduetoprompt, opposite-signdi-leptons( e and ee ),whereoneelectronhasbeenreconstructedwith thewrongcharge.TheresultsareprovidedinTable 6-9 .Withthecurrentamountof data,theerroronthismeasurementislargelydrivenbythesmallnumberofsame-sign di-electroneventsobservedinthe Z -bosonmasswindow. Table6-9.Eventyieldsfortheanalysiswithopposite-signdi-leptonpairs,measured probabilityofachargeipforelectrons,andnaldata-drivenpredictionofthe rateofeventswheretwooriginalleptonsareprompt,butoneofthemis mis-reconstructedwiththewrongcharge. Di-leptonchannel eee total NumberofobservedOSdi-leptons 86620 ExpectedrateofSSdi-leptons( $ =0.0007 0.0003 )2 N ee $ N e $ 0.00820.00410.0124 Statisticalerror 0.0050 0.0025 0.006 6.6.3DeterminationofFake-Fake,Same-signDi-leptons: N SS f f ThebackgroundfromQCDmulti-jetprocesses,althoughnotexpectedtodominate, neverthelessneedscarefulinvestigationbecauseitisnotwellknown.Amethodfor 125

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evaluatingtheQCDbackgroundcontributionhasbeendeveloped,whichreliesonthe factorizationofthreeselectioncriteria:two RelIso requirements(i.e.,oneforeachlepton) andthe E T requirement.Thefollowinggenericnotationwillbeusedtodenotethese respectiveselectionrequirements: SelectionRequirement a RelIso ( 1 ) < 0.15 (64) SelectionRequirement b RelIso ( 2 ) < 0.15 (65) SelectionRequirement c E T > 30 GeV (66) TheFactorizationmethodreliesontheansatzthatthesethreeselectionrequirements areuncorrelatedforQCDprocesses(fake-fakedi-leptons).Thisassumptionis well-motivatedbecausebothleptonsareguaranteedtobenon-promptandshould comefromdistinctjets.Thus,the RelIso variableshouldbeconstructedwithaunique setoftracksandcalorimeterenergydepositsforeachlepton,respectively.Themain sourceof E T isexpectedtobeduetojetenergymismeasurementandnotfromthesoft neutrinoactivityaccompanyingthenon-promptleptons.Basedontheseexpectations, theprobability( 2 a )foraneventtopassrequirement a shouldbethesameregardless ofwhetherornotrequirements b or c havealreadybeenimposed.Thisshouldbetrue forallpermutationsof a b ,and c .ThisistheprinciplethatunderliestheFactorization method. Inordertoemploythemethod,itisimportanttoverifythatthechosenselection requirementscanindeedbyfactorized.Thismustbedonebyprovingtherelationshipin Eq: 67 2 abc = 2 a 2 b 2 c (67) Thus,eachprobability(orselectionefciency)mustbeindividuallymeasuredon theyieldssurvivingthebaselineselection,whichareexpectedtobedominated byQCDevents.Theproductoftheserespectiveefcienciesshouldagreewiththe 126

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cumulativeselectionefciency( 2 abc ),whichisobtainedafterapplyingeachrequirement successively. 3 Thepredictionforthenumberofeventssurvivingthenalselection requirementsfromthefake-fakedi-leptonbackgroundswillbeproductofthethree factorizableefcienciesalongwithbaselineselectionyieldsforeachchannel.Thisis shownmoreformallyinEq. 68 ,wheretheabstractindices a b ,and c arereplaced thoseindicatingtheparticularselectionrequirementforeachchannel. N SS f f = N baseline 2 2 2 E T + N baseline ee 2 e 2 e 2 E T + N baseline e 2 e 2 2 E T (68) FromTables 6-4 6-5 and 6-6 ,itwasobservedthatthetotalSMbackground,which passesthebaselineselectiondoesnotcompareverywellwithdata.Thisisdueto thefactthattheMonteCarlosimulationscannotfaithfullyaccountforthelargeQCD contribution.Thesimulatedyieldsarelowerbyroughlyafactoroftwo.Despitethis,itis stillworthwhiletouseQCDMonteCarlosimulationstovalidatetheFactorizationmethod becausetheabsoluteeventratesarenotneeded.Onlytheprincipleoffactorizability needstobedemonstrated,butthisstillrequiresanadequateamountofstatistics, however.ToaugmentthestatisticsintheinclusiveQCDmulti-jetMadGraphsamples, onecanappealtoadedicatedsampleofeventswhichfeature b b production.Theseare listedinTable 6-1 ,butwerenotusedtocalculatetheyieldsinTables 6-4 6-5 and 6-6 TheexpectationisthatasignicantfractionofleptonsinQCDeventsactuallyoriginate fromtheparticularsubsetofprocesseswhichfeature b -quarksor b -jets.Forthispart oftheanalysis,wenditconvenienttocombinetheinclusiveQCDsampleswiththe 3 Thecumulativeselectionefciencycanalsobeunderstoodastheprobabilityto passthenalselectionrequirementsgiventhattheeventhaspassedthebaseline selectionrequirements. 127

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b b samplesinordertoenhancethenumberofsimulatedeventswithleptons.Special careistakentoavoiddoublecountingastheinclusiveQCDsampledoeshaveasmall componentof b b events(roughly 4 %).Table 6-10 showsthebaselineeventyieldsfrom thisQCD+ b b cocktailsample(scaledbycross-sectionto 35 pb 1 )alongwiththedata. Thescalingfactorofthecocktailincludesanadditionalfactoroftwoinordertoroughly normalizetheyieldstodata. 4 Onecanarguethatthisfactorcouldbeevenhigher.The totalbaselineyieldsfromallStandardModelprocesses,includingtheQCDcocktail, isprovidedinordertoillustratethefactthatthesampleisdominatedbyQCDevents beforethe RelIso and E T requirementsareimposed.Thisfactisvitaltothesuccessof themethodbecausethebaselinesampleisusedasaQCDcontrolsampletoderive 2 2 e ,and 2 E T Table6-10.BaselineyieldsfordataandMonteCarlosimulateddata Process N N e N ee b b : H T [100,250] GeV 000 b b : H T [250,500] GeV 32.615.11.94 b b : H T [500,1000] GeV 2.870.9150.0821 b b : H T [1000, ) ] GeV 0.01670.005180.00115 QCD: H T [100,250] GeV 000 QCD: H T [250,500] GeV 84.4460 QCD: H T [500,1000] GeV 14.26.220.361 QCD: H T [1000, ) ] GeV 0.01670.005180.00115 TotalQCD+ b b Cocktail 13468.32.39 TotalStandardModel 14879.84.1 Data 223786 Thebaselineyieldsarenoticeablylopsidedinfavorof events,givingaratio of N / N ee =37.2 indata.Thisenhancementcanbeattributedtoacombinationof 3 factors(orderedbyimportance): 4 Next-to-leadingordercross-sectionsforsuchQCDmulti-jetprocessesarenot available,norareproperk-factors.This adhoc normalizationtodataisacommon procedure. 128

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(i) lower p T requirementsonthemuons (ii) tighteridenticationrequirementsontheelectrons(VBTF80) (iii) higherreconstructionefcienciesforbothnon-promptandpromptmuons Theeffectofthedifferencesin p T requirementscanbestudiedsimplybyequalizing themto 10 GeVformuonsandelectrons.Thisyields 38 events( 26 e events),which reducesthedi-muon/di-electronasymmetrytoafactorof 6.3 .Onemusttakethesquare rootofthisnumbertoobtaintheasymmetryinthesingleleptonproductionrate,i.e., & 6.3=2.5 .ByappealingtotheQCDsimulation,wecaninvestigateandvalidate thesourcesleadingtotheremainingasymmetry.LookingattheMonteCarlotruth 5 weobservethatmuonsfromheavy-avordecaysareroughly 3 to 5 timesmorelikely thanelectronstopasstheirrespectiveselections.Theeffectfromthissourceaswell asothersaredetailedinTable 6-11 .Insomecases,asourcefavorselectronsover muons.Sourcesdenotedby(*)arenotexplicitlymatchedviaagenerator-levellepton intheMonteCarlotruth.Inthesecases,thelistofgeneratorparticlesissearchedfora stableparticlewithinaconeof R < 0.01(0.02) ofthereconstructedmuons(electrons). Thesumofallofthesesourcesyieldsaratioofobservedmuonstoelectronsinour acceptanceof 1.9 ,whichisroughlyconsistentwithourobservationsindata. HavingestablishedthatthebaselineselectionisindeeddominatedbyQCD,itis nowlefttoshowthattheselectionefcienciescanbefactorized.Thedemonstrationwill bedonepiece-wise.Firstitwillbeshownthatthe RelIso requirementsareindependent foreachlepton(i.e., 2 ab = 2 a 2 b ).Inthecasethatwearedealingwiththe or ee channels,therelationshipcanbesimpliedto 2 ab = 2 2 a .Then,itwillbeshownthatthe RelIso requirementisindependentofthe E T requirement(i.e., 2 ac = 2 a 2 c ). 5 TheMonteCarlotruthconsistsofthelistofparticlesthatwereactuallygeneratedin theevent,asopposedtothosethatwerereconstructedbytheCMSdetector 129

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Table6-11.Summaryofnon-promptleptonoriginsinsimulatedQCD Source N N e N / N e b 2.34 e +036563.56 b ( / 59153.93 b ( c 328585.66 c 1.01 e +031875.4 lightavor 15420.357 p(*) 7380.184 0 (*) 4404770.922 k (*) 3421063.23 k L (*) 120.5 & (*) 2500.04 unmatched 57590.00659 Total 4.54 e +032.39 e +031.9 Itisfairlystraightforwardtoshowthatthe RelIso ofoneleptoniseffectively independentofthe RelIso oftheotherindi-leptonQCDevents.Figure 6-8 shows thatthefactorizationholdsinboththedataandthesimulationforallthreechannels towithinstatisticalerrors.Here, / a isrepresentedbydarkbluelledcircles, / ab is representedinredlledsquares,and / a / b isrepresentedinlightbluelledrectangles. Forthecaseofthe e channel, / b / = / a ,so / b isrepresentedseparatelybyblacklled triangles.Asonecanreadilyobserve,theagreementispresentforallchannelsindata andsimulation.Itisworthemphasizingthatonegreatlyreducesthestatisticalerrors forthemeasurementofthe RelIso selectionefciency / ab byexploitingtherelationships givenabove.Thevaluesof / a and / b aremeasuredtogoodstatisticalprecision,while / ab cannotbebecauseitrequiressimultaneouslyapplyingtheselectiontobothleptons, asisillustratedbythesizableerrors(red)inFigure 6-8 .Theresimplyarenotvery manyeventsthatsurvivethisrequirement.Whiletheactualdata-drivenmeasurement oftheseselectionefcienciesmeantfortheQCDpredictionwillbeextractedfromthe baselineselectionyields,thedistributionsshowninFigure 6-8 comeafterrelaxingthe H T requirementto 200 GeV.Thisisdoneinordertoenhancestatistics. Forcompletenessafewmorechecksareperformedtoensurethat / a and / b are mutuallyindependentofeachother.Figure 6-9 showsthedifferential RelIso ( 2 ) 130

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Relative Isolation Cut -1 10 1 Efficiency -4 10 -3 10 -2 10 -1 10 1 ) a only ( 1 ) ab ( 2 and 1 ) 2 a ( 2 and 1 Prediction of -1 = 35 pb L = 7 TeV, s CMS Preliminary A (MC) Relative Isolation Cut -1 10 1 Efficiency -5 10 -4 10 -3 10 -2 10 -1 10 1 ) a e only ( ) b only ( ) ab ( e and ) b a and e ( Prediction of -1 = 35 pb L = 7 TeV, s CMS Preliminary B e (MC) Relative Isolation Cut -1 10 1 Efficiency -4 10 -3 10 -2 10 -1 10 1 ) a only ( 1 e ) ab ( 2 and e 1 e ) 2 a ( 2 and e 1 Prediction of e -1 = 35 pb L = 7 TeV, s CMS Preliminary C ee (MC) Relative Isolation Cut -1 10 1 Efficiency -3 10 -2 10 -1 10 1 ) a only ( 1 ) ab ( 2 and 1 ) 2 a ( 2 and 1 Prediction of -1 = 35 pb L = 7 TeV, s CMS Preliminary D (Data) Relative Isolation Cut -1 10 1 Efficiency -3 10 -2 10 -1 10 1 ) a only ( ) b e only ( ) ab and e ( ) b a and e ( Prediction of -1 = 35 pb L = 7 TeV, s CMS Preliminary E e (Data) Relative Isolation Cut -1 10 1 Efficiency -2 10 -1 10 1 ) a only ( 1 e ) ab ( 2 and e 1 e ) 2 a ( 2 and e 1 Prediction of e -1 = 35 pb L = 7 TeV, s CMS Preliminary F ee (Data) Figure6-8. RelIso selectionefcienciesinQCDsimulation(top)anddata(bottom)for the e ,and ee channelsrespectively. distributioninbinsof RelIso ( 2 ).Unfortunately,differentialdistributionssuchasthese arestatisticallylimitedandonlycoarsebinningin RelIso ( 1 )isfeasible.However,since wehaverelaxedthe H T cutfrom 300 to 200 GeVforthisdemonstration,someefciency islostintheeventyieldsduetotheslowturn-onofthe H T triggers.Tocombatthiswe canappealtoanothertrigger,namely,adouble-muontriggertoaugmentthestatistics collectedbythe H T triggers.Thisenablesaviewof RelIso ( 2 )forathinnerslicenear oursignalregionof RelIso ( 1 ).Inallthreeplots,theshapesofthetwodistributionsare inagreementtowithinstatisticalerrors.Similardistributionsforthe e and ee channels aretoostatisticallylimitedtorevealanythingofsubstance,sotheyarenotshownhere. Analcheckofthecorrelationbetweentherespective RelIso selectionrequirements canbeperformedbyplottingthe 2 -dimensionaldifferentialdistributionof RelIso ( 2 )vs 131

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RelIso ( 1 )for e ,and ee eventsrespectively.ThisisdoneinFigure 6-10 fordataand QCDsimulation,andthecorrelationfactorsaredisplayedinredtextineachsubgure. Forthe channelasmall,butnon-negligible,negativecorrelationfactoratavalue ofabout 0.06 isobservedinthedataandtheQCDsimulation.Forthe e channel thecorrelationfactorsarenegligibleandforthe ee channelstatisticsaretoolimitedto drawanyfurtherconclusions,soweareforcedtorelyonFig 6-8 asevidencethatthe factorizationprincipleisvalid.Furtherstudiesshowthatthecorrelationfactorgoesfrom 0.06 toto 0.01 intheQCDsimulationasthe H T requirementisrestoredtoisnominal valuesof 300 GeV.Whileitiscomfortingtoseesmallcorrelationfactors,therewill inevitablybenon-QCDprocessespresentinthedatasurvivingthebaselineselection, whichcouldcontributetosomesubtlecorrelations.Theprocessof t t ( b bW + W for example,willlikelyhaveoneisolatedlepton(froma W -decay)andonenon-isolated lepton(froma b -quark)ifitpassesthebaselinerequirements.Thepresenceofsmall correlationswillhaveanimpactontheclosuretestsandwillthusbeincorporatedinthe systematicerrorsquotedforthemeasurement. 2 Relative Isolation of 0246810 Normalized Events 0.02 0.04 0.06 0.08 0.1 0.12 0.14 channel (MC) ) < 1.5 1 0.0 < RelIso( ) < 10.0 1 1.5 < RelIso( -1 = 35 pb L = 7 TeV, s CMS Preliminary AQCDMC 2 Relative Isolation of 0246810 Normalized Events 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 chael (Data) ) < 1.5 1 0.0 < RelIso( ) < 10.0 1 1.5 < RelIso( -1 = 35 pb L = 7 TeV, s CMS Preliminary BData 2 Relative Isolation of 0246810 Normalized Events 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 chael (Data) ) < 0.4 1 0.0 < RelIso( ) < 10.0 1 0.4 < RelIso( -1 = 35 pb L = 7 TeV, s CMS Preliminary CData(muon-triggered) Figure6-9.Differential RelIso ( 2 )distributionoffor 0.0 < RelIso( 1 ) < 1.5 (blue)andfor 1.5 < RelIso( 1 < 10.0 (red)forQCDsimulation(left)anddatawithonlythe H T triggers(middle)andaugmentedbymuontriggers(right). Havingjustiedthefactorizationofthe RelIso selectionrequirementsonthetwo leptonsintheevent,itisnowlefttoshowthattherequirementon E T canbefactorized 132

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1 Relative Isolation of 012345678910 2 Relative Isolation of 0 1 2 3 4 5 6 7 8 9 10 Mu1RelIsoVsMu2RelIso Entries 2290 Correlation Factor : -0.0651 A channel(QCDMC) Relative Isolation of 012345678910 Relative Isolation of e 0 1 2 3 4 5 6 7 8 9 10 MuRelIsoVsElRelIso Entries 609 Correlation Factor : -0.0155 B e channel(QCDMC) 1 Relative Isolation of e 012345678910 2 Relative Isolation of e 0 1 2 3 4 5 6 7 8 9 10 El1RelIsoVsEl2RelIso Entries 46 Correlation Factor : -0.1434 C ee channel(QCDMC) 1 Relative Isolation of 012345678910 2 Relative Isolation of 0 1 2 3 4 5 6 7 8 9 10 Mu1RelIsoVsMu2RelIso Entries 974 Correlation Factor : -0.0669 D channel(Data) Relative Isolation of 012345678910 Relative Isolation of e 0 1 2 3 4 5 6 7 8 9 10 MuRelIsoVsElRelIso Entries 381 Correlation Factor : -0.0058 E e channel(Data) 1 Relative Isolation of e 012345678910 2 Relative Isolation of e 0 1 2 3 4 5 6 7 8 9 10 El1RelIsoVsEl2RelIso Entries 23 Correlation Factor : 0.01580 F ee channel(Data) Figure6-10.Differentialdistributionof RelIso ( 2 )vs RelIso ( 1 )forQCDsimulation(top) anddata(bottom). fromthe RelIso requirementononeofthetwoleptons.Figure 6-11 showsthe RelIso selectionefciencyformuons(left)andelectrons(right)fordifferentvaluesofthe E T requirementforQCDsimulation(top)anddata(bottom).ThecurvesfromtheQCD simulationareingoodagreement,andthisdemonstratesthatthefactorizationholds forQCDevents.Itisworthemphasizingthatwedonotexpectthecurvestooverlap perfectlyinthedataduetothepresenceofnon-QCDprocesses(e.g t t ).Becausewe willmeasurethe RelIso efcienciesindata,whichwillpresumablycontainnon-QCD events,wewillimposeaninverted E T requirementatavaluebelow 20 GeV,wherewe expectcontributionsfromQCDtodominate.Theeffectsofthisinvertedrequirementon datacanbeseenbythelightblue-shadedcurveinFigure 6-11 133

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Muon Relative Isolation Cut -1 10 1 Efficiency -3 10 -2 10 -1 10 1 MET > 0 GeV MET > 20 GeV MET > 30 GeV -1 = 35 pb L = 7 TeV, s CMS Preliminary AQCDMC Electron Relative Isolation Cut -1 10 1 Efficiency -3 10 -2 10 -1 10 1 MET > 0 GeV MET > 20 GeV MET > 30 GeV -1 = 35 pb L = 7 TeV, s CMS Preliminary BQCDMC Muon Relative Isolation Cut -1 10 1 Efficiency -1 10 1 MET > 0 GeV MET > 20 GeV MET > 30 GeV MET < 20 GeV -1 = 35 pb L = 7 TeV, s CMS Preliminary CData Electron Relative Isolation Cut -1 10 1 Efficiency -1 10 1 MET > 0 GeV MET > 20 GeV MET > 30 GeV MET < 20 GeV -1 = 35 pb L = 7 TeV, s CMS Preliminary DData Figure6-11.Efciencyof RelIso ( 1 )asafunctionofthe E T requirementforsimulated QCD(top)anddata(bottom)for 1 = (left)and 1 = e (right).The distributionsindata,arenotexpectedtodemonstratefactorizationdueto thenon-negligiblepresenceofotherbackgrounds. 134

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Withthemutualindependenceofthethreeselectionrequirementsestablished,itis nowlefttomeasurethevaluesfor 2 2 e ,and 2 E T individuallyfromtheeventspassingthe baselineselection.Figure 6-12 showstheeventyieldsandcutefcienciesasafunction oftheselectionrequirementon RelIso formuonscomingfrom and e candidate eventsforcollisiondataandMonteCarlosimulateddata.Itisworthreemphasizingthat whilemeasuringtheselectionefciencyofthe RelIso requirement,the E T requirement isinvertedatavalueof 20 GeVtomitigateanybiasesdueto t t andpotentiallysignal. Here,theQCDportionofthesimulateddataisshownseparatelyfromtheStandard Modeltoillustrateitsbehavior.Figure 6-13 showsthesamedistribution,onlynowfor electronscomingfrom ee and e candidateevents.Again,theQCDisshownseparately from,aswellascombinedwith,therestoftheStandardModelsimulationsamples. Figure 6-14 showstheeventyieldsandefcienciesasafunctionoftherequirementon E T for events.Theshapesarequalitativelyverysimilarforallthreechannels.When measuringthecutefciencyonthe E T observable,the RelIso requirementisinverted onbothleptonsatavalueof 0.2 toavoidpotentialbiasesfromsignalandnon-QCD processes. Thelargestuncertaintywithrespecttothismeasurementisexpectedtobe statistical.Thisisduemainlytothefactthatthemeasurementconsistsofmultiplying thevaluesoffourobservables,whicheachobeyPoissonstatisticsandwillderive fromsamplesthatarescantlypopulated.Aswillbeshownthestatisticalerrorsforthe QCDpredictionforeachchannelwillrangefrom 50% 100% despitecleverattempts toincreasethesamplepopulationwithoutbiasingthemeasurement.Nonetheless, despitethelargeuncertaintieswhichwillcomefrompoorstatistics,othersystematic uncertaintiesneedtobeaccountedforinthemeasurement. Acommonmethodforassessingsystematicerrorsandbiasesinadata-driven measurementusuallyinvolvesperforminga"closuretest"onaMonteCarlosimulated samplethatismeanttoserveaspseudo-data.Insuchatestwewouldmeasurethe 135

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Muon Relative Isolation Cut -1 10 1 Events -1 10 1 10 2 10 Data QCD (MC) (MC) t t -1 = 35 pb L = 7 TeV, s CMS Preliminary AEventYield Muon Relative Isolation Cut -1 10 1 Efficiency -3 10 -2 10 -1 10 1 Data QCD (MC) All SM (MC) -1 = 35 pb L = 7 TeV, s CMS Preliminary BEfciency Figure6-12.Eventyields(left)andselectionefciency(right)givenasafunctionofthe cutonthemuonRelativeIsolationtakenfrom and e eventspassingthe baselineselection. Electron Relative Isolation Cut -1 10 1 Events -1 10 1 10 Data QCD (MC) (MC) t t -1 = 35 pb L = 7 TeV, s CMS Preliminary AEventYield Electron Relative Isolation Cut -1 10 1 Efficiency -2 10 -1 10 1 Data QCD (MC) All SM (MC) -1 = 35 pb L = 7 TeV, s CMS Preliminary BEfciency Figure6-13.Eventyields(left)andselectionefciency(right)givenasafunctionofthe cutontheelectronRelativeIsolationtakenfrom ee and e eventspassing thebaselineselection. 136

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MET Cut [GeV] 020406080100120140 Events -1 10 1 10 2 10 Data QCD (MC) (MC) t t -1 = 35 pb L = 7 TeV, s CMS Preliminary AEventYield MET Cut [GeV] 020406080100120140 Efficiency -3 10 -2 10 -1 10 1 Data QCD (MC) All SM (MC) -1 = 35 pb L = 7 TeV, s CMS Preliminary BEfciency Figure6-14.Eventyields(left)andselectionefciency(right)givenasafunctionofthe cutonthe E T takenfrom eventspassingthebaselineselection. fourobservables, N baseline 2 2 e 2 E T ,thentaketheappropriateproducttoderivethe predictionforeachchannel,andnallycomparethepredictionwiththenumberofevents whichsurviveoncealloftheselectionrequirementsareapplied(i.e.,baselineselection, RelIso ( 1 ), RelIso ( 2 ), E T ).Thesetwonumberswillbereferredtoas N predicted and N observed ,respectively.IfthemethodisvalidthentherelationshipinEq. 69 isveried andtheclosuretestissatised. N observed = N predicted ( N baseline 2 abc = N baseline 2 a 2 b 2 c (69) Unfortunately,acompleteclosuretestasdescribedbyEq. 69 cannotbe performedbecausetheresimplyarenotenoughQCDeventsavailableinthesimulation. Thisisoneofseveralfactorswhichheavilymotivatedthedata-drivenmeasurementof theQCDbackgroundintherstplace.WewillneverbeabletosimulateenoughQCD 137

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eventstocheckEq. 69 directly.Asaconsolationwecanredene N observed and N predicted andinsteadtestforthefollowingrelationshipsinapiecewisemanner: N baseline 2 ab = N baseline 2 a 2 b (610) N baseline 2 ac = N baseline 2 a 2 c (611) Wehavealreadyshownthattheserelationshipsholdqualitativelybytheagreement showninFigures 6-8 and 6-11 ,butmorequantitativecomparisonscanhelptoreveal anysystematicuncertainties.Webeginwithatestoftherstrelationshipandwefocus onthe channelasithasthemoststatistics.Eventhoughwedonotperformthefull QCDpredictionherebymultiplyingallthreeefciencies,thesingleleptonefciencyis smallenough,thatwhensquared(ormultipliedbytheopposite-avorleptonefciency forthe e channel),veryfew(ifany)eventsareexpectedtosurvive.Unfortunately,the QCDsimulationsamplesdonotprovideenoughstatisticstoallowforatestofeventhis partialclosuretest.However,wecantrytoperformthepartialclosuretestdirectlyinthe data,whichisQCD-dominated(particularlyoncetheinvertedcutonthe E T isapplied), andcansupplythesufcientstatisticstotestEq. 610 .Asonecanreadilyobserve bycomparingtheredpointsinFigure 6-8A withFigure 6-8D ,thelatter(data)isbetter populatedatlowvaluesofthe RelIso observable.Still,giventhatthenalselection requires RelIso < 0.15 ,wewillhavetotestforclosureatthatvalueandwebarely cannot,evenwithgreaterstatisticsaffordedbythedata.Toovercomethiswecantry toinvitemoreeventsintothebaselineselectionyieldsbyappealingtomuon-triggered data.Recall,werelaxthe H T selectionrequirementfrom 300 GeVto 200 GeVto validatetheFactorizationmethodandcheckforclosure.Thisrelaxationcomesatthe costoftriggerefciencyfromthemain H T triggersemployedinthisanalysis(Table 6-2 ), butwecanrecovermanyeventsforthispurposebysupplementingthemaintriggers withmuontriggers.BydoingthisweobtainasimilardistributioninFigure 6.6.3 to 138

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whatwasobtainedin 6-8D withsolelythe H T triggers,exceptnowthelowestbinsare occupied,albeitscarcely. InFigure 6-16A ,weshowtheresultsofthepartialclosuretestondataofEq. 610 .Atthenominalselectionrequirementof RelIso < 0.15 ,weseethatthemethod closes,althoughthereissomevariationattheadjacentselectionrequirementvalues whicharelikelyduetostatisticaluctuationscombinedwithnebinning.Thetrend isquiteclearthatforthemajorityof RelIso selectionrequirements,thereisverygood agreementbetweenpredictionandobservation.Thegraybandrepresentsa 25% spreadwhichforeshadowsthesystematicuncertaintythatwillbeassignedtothe methodfromtheresultsoftheclosuretest.Withfewexceptions,allpointsarewithinthis band. Relative Isolation Cut -1 10 1 Efficiency -3 10 -2 10 -1 10 1 ) a only ( 1 ) ab ( 2 and 1 ) 2 a ( 2 and 1 Prediction of -1 = 35 pb L = 7 TeV, s CMS Preliminary Figure6-15. RelIso factorizationinthe channelafteraddingmuon-triggeredevents. TotestforclosureoftherelationshipinEq. 611 ,weareforcedtorelyonsimulation ifwewanttoperformthetestwiththesame-signdi-leptontopology,asitistoodifcultto performthetestinacontrolregionindata.Figures 6-16B and 6-16C showresultsfrom theMonte-CarlobasedclosuretestoftherelationshipinEq. 611 .Moreconcretely, wecomparethevaluesofthe RelIso ( )selectionefciencyobtainedinthecontrolregion ( E T < 20 GeV)withtheefciencyobservedinthesignalregion( E T > 30 GeV).The formerconstitutesthepredictionwhilethelatterconstitutestheobservation.Theratio 139

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Relative Isolation Cut -1 10 1 Observed/Predicted 0.5 1 1.5 2 2.5 3 3.5 -1 = 35 pb L = 7 TeV, s CMS Preliminary A Relative Isolation Cut -1 10 1 Observed/Predicted 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -1 = 35 pb L = 7 TeV, s CMS Preliminary B Relative Isolation Cut -1 10 1 Observed/Predicted 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -1 = 35 pb L = 7 TeV, s CMS Preliminary C Figure6-16.ClosuretestsofrelationshipsinEqs. 610 for H T > 200 GeV(left)and Eqs. 611 for H T > 200 GeV(middle)and H T > 100 GeV(right)using single-leptonevents. ofthetwoisplottedasafunctionofthe RelIso ( )requirementforthecasewherethe H T requirementisrelaxedto 200 GeVandfurtherrelaxedto 100 GeV.Fortheformer ( 6-16B )theclosuretestisquitestableacrossawiderangeofvaluesforthe RelIso requirementandmostpointsresidewellwithinthe 25% bandsurroundingunity. Theloneoutlieroccursatthenominalvalueofthe RelIso requirement( 0.15 )where statisticaluctuationsarequiteprobable.Toseeiftheoutlierat RelIso < 0.15 isdue tonon-statisticaleffectsonecanchecktoseeiftheuctuationpersistsafterthe H T requirementisrelaxedto 100 GeV,whichisdoneinFigure 6-16C .Itisobservedthattest ofclosureisachievedinthiscaseandallpointsmaintainashortdistancefromunityand residewellwithinthe 25% band. OnecanalsoattempttotestforclosureoftherelationshipinEq. 611 byusinga single-leptonQCDcontrolregionindata,wherestatisticsaremuchmoreplentifulthan inthesame-signdi-leptoncase.Thisallowsthe H T requirementtobemaintainedat itsnominalvalueof 300 GeV,withoutsacricingtoomanyevents.Figure 6-17 shows the RelIso selectionefciencyformuons(red)andelectrons(blue)asafunctionofthe requirementonthe E T .Asonecanreadilyobserve,thedependenceisstrongandthe cutsdonotfactorizeintheregiondenedby d 0 < 0.1 mm,whichiscontaminatedby 140

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manyeventscontainingpromptleptonsfrom W -decays.Theregiondenedbythe inversionofthis d 0 requirement,however,isdominatedbyeventswithnon-prompt leptonsfromheavy-avordecaysorhadrondecays-in-ight,andthusconstitutesavery pureQCDcontrolregionwheretheclosuretestcanbeperformed.Itisworthexploring howdramaticallythecocktailofnon-promptleptonschangesincompositionasonegoes fromthesignalregion( d 0 < 0.2 mm)tothisQCDcontrolregion( d 0 > 0.1 mm).This wascheckedinQCDsimulation.Inthesignalregion,thecompositionoffakeleptonsin QCDis 45% fakeand 55% heavy-avor,whileforthecontrolregionitis 25% fakeand 75% heavy-avor.Itisobservedthatthe RelIso selectionefciencyisquitestablewith respecttotherequirementonthe E T inthisQCDcontrolregion,andthisobservation isexpectedtoholdindependentoftherelativefractionsoffakeleptonsfromfakeand heavy-avorsourcesrespectively. Cut [GeV] T E 01020304050 Relative Isolation Efficiency 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 < 0.1 mm) 0 Muons (d < 0.1 mm) 0 Electrons (d > 0.1 mm) 0 Muons (d > 0.1 mm) 0 Electrons (d -1 = 35 pb L = 7 TeV, s Figure6-17.Demonstrationthatthe RelIso and E T selectionsfactorizeusingasingle leptonQCDcontrolregionindata. Itcanbeconcludedthatthethreeselectionrequirementschosenafterthebaseline selectiondoindeedfactorizequitewell.Auniform 25% systematicuncertaintyis 141

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assignedtothemeasurementof N SS f f and 100% correlationforallthreechannelsis assumedinordertocoverthespreadofvaluesobtainedintheclosuretests. Anotherpossiblesourceofsystematicuncertaintythathasnotdirectlybeen discussedmaycomefromtheinversionofthe E T requirementwhenmeasuringthe RelIso selectionefciencyorlikewisefromtheinversionofthe RelIso requirementwhen measuringthe E T selectionefciency.Thisissimplyanotherwayforcorrelationsof thetwoobservablestobiastheefciencymeasurementofeitherone.AsFigures 6-8 6-9 6-10 ,and 6-11 demonstrated,anyexistingcorrelationswhetherpresentinthe underlyingphysicsorintroducedbythedetectorarehardlynoticeable.Nonetheless, onecanseehowtheselectionefciencyof RelIso variesastheinvertedrequirementfor the E T ischangedandviceversa.ThisisdoneinFigure 6-18 forboth RelIso (bottom) and E T (top)forboth H T > 300 GeV(left)and H T > 100 GeV(right).Ascanbereadily observedthemeasuredselectionefcienciesareverystablewithrespecttothevalues oftheinvertedselectionrequirements.Deviationsareobservedonthelevelof % 1% Thus,nosystematicuncertaintyisattributedtothiseffect. Asdiscussedearlierthesampleofeventspassingthebaselineselectionis expectedtobedominatedbyQCD,butitmostcertainlywillnotbewithoutother backgrounds,andpotentiallysignal.Thepresenceoftheseotherbackgroundsdirectly enhancesthevalueof N baseline andwillhencedirectlyenhancethevalueof N predicted FromtheMonte-Carlobasedbaselineselectionyields N baseline isobservedtohave 6.4% 11.6% ,and 34.5% contaminationfromnon-QCDprocessesforthe e ,and ee channelsrespectively.Thesebiasescanbefactoredinasymmetricallyasasource ofsystematicuncertaintyforthenalmeasurement.Thisuncertaintyisasymmetric becausethepresenceoftheseotherbackgroundswillserveonlytoincreasethevalue of N predicted fromthetruenumberofQCDevents.Theirpresencecannotmakethe predictednumberanysmallerthanitwouldotherwisebe. 142

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Inverted RelIso Cut 00.20.40.60.81 MET Cut Efficiency 0.1 0.15 0.2 0.25 0.3 0.35 -1 = 35 pb L = 7 TeV, s CMS Preliminary AQCDMonteCarlo( H T > 300 ) Inverted RelIso Cut 00.20.40.60.81 MET Cut Efficiency 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 -1 = 35 pb L = 7 TeV, s CMS Preliminary BQCDMonteCarlo( H T > 100) 102030405060708090 Muon RelIso Efficiency 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 -1 = 35 pb L = 7 TeV, s CMS Preliminary Inverted MET Cut [GeV] 102030405060708090 Electron RelIso Efficiency 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 CQCDMonteCarlo( H T > 300 ) 102030405060708090 Muon RelIso Efficiency 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 -1 = 35 pb L = 7 TeV, s CMS Preliminary Inverted MET Cut [GeV] 102030405060708090 Electron RelIso Efficiency 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 DQCDMonteCarlo( H T > 100 ) Figure6-18.Testingthestabilityoftheobserved E T selectionefciency(green)for variousvaluesoftheinverted RelIso requirment(top)andthestabilityofthe observed RelIso selectionefciencyofmuons(red)andelectrons(blue)for variousvaluesoftheinverted E T requirement(bottom). Similartothesituationwith N baseline ,thereexistssomecontaminationfromnon-QCD processesintheeventsthatsurvivethe RelIso and E T requirementsrespectively. Theamountofcontaminationforeachmeasuredselectionefciencycanbeinferred bycomparingthegreenandbluedistributionsinFigures 6-12B 6-13B ,and 6-14B respectively.Anticipatingtherequirementontheseobservablestobe 0.15 and 30 GeV for RelIso and E T respectively,itisdeterminedthattheformerwillinviteasystematic uncertaintyof 10% and 80% forthecasesofmuonsandelectronsrespectively,while thelatterwillinviteasystematicuncertaintyof 3% Analsourceofsystematicerrormaycomefromthepresenceofpile-upevents (PU).Theeffectsofpile-uponthe RelIso selectionefcienciescanbetakentobe negligible.Theproofofthisliesinthefactthatthetwo RelIso requirementsdoindeed 143

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factorizeinthedata(implyingasuccessfulclosuretestonthesetwoobservables). Thus,whatevereffectsareinthedataduetopile-updonotaffectthisunderlying premise,whichisvitaltothesuccessofthemethod.Itisworthexploringtheeffectsof pile-uponthe E T requirement,sinceitisaglobalobservablethatissensitivetoallofthe activityreconstructedintheevent.Thiscanbestudiedbyevaluatingthe E T selection efciencyforbothsingleandmultiplevertexevents. 6 Thistestwasperformed,andfor singlevertexeventsanefciencyof 18 / 71=25.4% 6.0% isobserved,whileformultiple vertexeventsanefciencyof 50 / 180=27.8% 4.0% isobserved.Thesecalculated efcienciesarestatisticallyconsistentwithoneanother. Aseparatetestwasalsoperformedtostudyhowpile-upmayaffectthebaseline selectionefciency,whichissimplyconstitutedbyan H T requirement.Eventspassing thepre-selectionrequirementswereseparatedintosingle-vertexandmultiple-vertex samples.Theefciencyforeventsfromtheformersampletofurtherpassthebaseline selectionrequirementisobservedtobe 51 / 120=44.6% 6.0% ,whiletheefciency foreventsfromthelattersampletopassthebaselineselectionisobservedtobe 204 / 478=41.6% 3.0% .Thetwoefcienciesarestatisticallyconsistent,indicatingthat theeffectsofpile-up,ifpresent,arebenign.Therefore,thismeasurementdoesnotincur anysystematicerrorsduetopile-upeffects. InTable 6-12 ,allofthesourcesofuncertaintyforboththeindividualobservables andthenalmeasurementof N SS f f aresummarized.ValuesshowninTable 6-12 reect thenalselectionrequirementsfor RelIso and E T ,respectively.Therelativeuncertainty ontheclosuretestsgiveninTable 6-12 willbeappliedtothenalmeasurementofeach channel.Thenalingredientsforthedata-drivenpredictionaregiveninTables 6-13 6-14 6-15 .Theuncertaintieswhichareasymmetricwillbetakenconservativelytobe symmetric(usingthelargererror)forthenalpredictions. 6 Thepresenceofmultipleprimaryverticesindicatesthepresenceofpile-up 144

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Table6-12.SummaryofuncertaintiesonobservablesofFactorizationmethod. ObservableUncertaintyComment N baseline 14.93(7%)statistical 14.27(6.4%)biasduetop-fcontamination(Table 6-10 ) N baseline e 8.83(11%)statistical 9.05(11.6%)biasduetop-fcontamination(Table 6-10 ) N baseline ee 3.28(55%)statistical 2.07(34.5%)biasduetop-fcontamination(Table 6-10 ) RelIso ( )efciency 0.015(42%)statistical 0.004(10%)biasduetop-fcontamination.(Figure 6-12 ) negligiblebiasdueto E T cutinversion.(Figure 6-18C ) RelIso ( e )efciency 0.077(70%)statistical 0.089(80%)biasduetop-fcontamination.(Figure 6-13 ) negligiblebiasdueto E T cutinversion(Figure 6-18C ) E T efciency 0.028(10%)statistical 0.008(3%)biasduetop+fcontamination.(Figure 6-14 ) negligiblebiasduetoisolationcutinversion(Figure 6-18A ) N predicted (allchannels) 0.45(25%)statisticaluncertaintyonclosuretest(Figure 6-16 ) Table6-13.Controlregionyieldsforpredictionoffake-fakedi-leptons Observable eee total Baselineeventyields 223678317 Numberofeventsforthe RelIso measurements( E T < 20 GeV) 94232128 Numberofmuonspassing RelIso < 0.156 28 Numberofelectronspassing RelIso < 0.15 134 Numberofeventsforthe E T measurements( RelIso > 0.2 ) 194255251 Numberofeventspassing E T > 305801068 Table6-14.Selectionefcienciesoffake-fakedi-leptons ObservableSelectionEfciency RelIso ( )selectionefciency $ =0.036 0.015 RelIso ( e )selectionefciency $ e =0.111 0.077 E T selectionefciency $ E T =0.271 0.028 Table6-15.Data-drivenbackgroundpredictionoffake-fakedi-leptons N $ 2 $ E T N ee $ 2 e $ E T N e $ e E T total Prediction 0.0780.0200.0840.183 Statistical+Systematicerror 0.060 0.028 0.084 0.169 145

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6.6.4DeterminationofPrompt-Fake,Same-SignDi-leptons: N SS p f AsMonte-Carlobasedstudiessuggest(Tables 6-4 6-5 and 6-6 ),itisexpectedthat themainbackgroundcomponentinthissearchisdueto t t production.In t t eventsitis naturaltohaverelativelylarge H T and E T .Twoisolated,same-signleptonsappearin t t eventswhenoneleptoncomesfroma W -decay(promptlepton)andanotherfakelepton froma b -jet(isolatedbychance).Inordertoevaluatethisbackground,adedicated data-drivenmethodhasbeendevelopedreferredtoastheBTag-and-Probemethod. Usingtheknowledgethatthefakeleptonsfrom t t productioncomefromsemi-leptonic b -decays,onecanattempttomodelthe RelIso distributionsformuonsandelectronsby studyingQCDeventswhichfeature b b production.Inordertogetagoodsample ofleptonsoriginatingfrom b -jets,onemuststudyjet-triggereddataandemployan algorithmtotag b -jets.Forthisanalysis,analgorithmwhichusesinformationfrom awell-reconstructedsecondaryvertexisemployed,whichgivesapurityof 99% AccordingtostudieswithQCDsimulation,leptonswhicharereconstructedfarawayin 1 spacefromachosentagged b -jet,i.e.with R (jet, ) > 1 ,havea 95% probability tooriginatefromtheotherrecoiling b -jetintheevent. 7 Thetagged b -jetconstitutesthe tag andthedistantleptonconstitutesthe probe forthistag-and-probemethod.Avariety ofdata-drivenmeasurementsinmanydifferentcontextsrelyontag-and-probemethods. Themainadvantageofsuchmethodsisthatitallowsonetostudyadesiredobservable (e.g., RelIso )byselectingadesiredtopology(inthiscase b b events)withoutbiasingthe measurementoftheobservablewithanysystematicuncertaintiesfromthetechniqueor algorithmusedtoselecttheevents.Forthisstudy,itmayseemnaturaltosearchnear orwithinthe b -taggedjetforalepton,butthiswillcertainlybiasthe RelIso measurement insomeunknownwaybyconvolutingthesystematicuncertaintiesinvolvedinthe b -jet 7 Inroughly 5% ofthecasestheleptonwilloriginatefromanadditionaljetintheevent fromFSR,ISR,ormulti-jetproduction. 146

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taggingalgorithmorthejetreconstructionalgorithm.Instead,weusetheknowledge that b -quarksareproducedinpairsviaQCDprocesses,sothatfromthetaggingofone b -jet,onecaninferthepresenceofapartner b -jet(usuallypointedoppositein fordi-jet events). Eventsarerequiredtohave H T > 100 GeV,whichyieldsa p T distributionof thepartner b -jetsthatisverysimilarto b -jetsin t t events.Alternatively,byrequiring H T > 150 or H T > 50 GeV,the b -jetsinthiscontrolsamplebecomenoticeablyharder orsofterwithrespecttothecharacteristic p T scaleof b -jetsin t t production.Although the H T > 100 GeVselectionrequirementgreatlyhelpstounitethekinematicsof b -jets inthecontrolsamplewiththatof t t production,theresidualdifferencesarestilltoolarge toignore.Are-weightingproceduremustbedonetocompensatefortheseremaining differences. Inordertore-weightthe b b events,itisnecessarytoappealtotwootherobservables: theprobe-lepton'stransversemomentum, p T ,andthetotaljetmultiplicityintheevent, N jet .The RelIso selectionefciencydemonstratesadependenceonthesetwovariables, whichhaveverydifferentspectrainQCDand t t events.However,foragivenrangein p T andjetmultiplicity,itisobservedthatthedistributionsof RelIso inQCDand t t are verysimilar.Therefore,thefollowingmeasurementsareneededtoderivetheprediction of t t eventsinthesignalregionindata: (i) RelIso selectionefciencies, / ( i j ) ,where i and j representbinsin p T and N jet in b -taggedevents. (ii) Probabilitydensityfunction, 3 ( i j ) ,ofndingaleptonwithtransversemomentum p T ( i ) froma b -jetin t t eventswithjetmultiplicity, N jet Boththemuonmomentumspectrafrom b -jetsandthejetmultiplicityareexpectedtobe muchbettermodeledintheMonteCarlosimulationthanisthe RelIso observable,soit issafetocalculate 3 ( i j ) usingsimulated t t events.Atotalselectionefciencycanbe 147

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obtainedformuonsandelectronsrespectively,bymultiplyingthesetwoquantities,i.e., < 2 > ( b ) = / i j / ( i j ) 3 ( i j ) (612) InFigures 6-19A and 6-19B thenalre-weighted RelIso templatesformuonsand electrons,asmeasuredinthe b -enrichedcontrolsampleareshown.Forcomparison, theresultsobtainedfromre-weightingsimulatedQCDeventsisshownaswell,along withtheexpected RelIso distributionfromfakeleptonsin t t simulation.Thelevelof agreementbetweenthere-weightedQCDsimulationand t t simulationconstitutes asuccessfulclosuretestofthemethod.Itisnotexpectedthatthere-weighteddata shouldmatchthe RelIso distributionfrom t t simulation.Asmentionedearlier,the simulationcannotbetrustedtofaithfullymodelthebehaviorofthe RelIso observable forfakeleptons.The RelIso selectionefcienciesareexplicitlystatedinthetextonthe plotsinFigures 6-19A and 6-19B ,whichrepresentthefractionofeventsintherst bin(ofwidth 0.15 ).Formuonstheobservedefciencyis < 2 > ( b ) =0.029 +0.003 0.002 while forelectronstheobservedefciencyis < 2 > ( b ) e =0.036 +0.013 0.008 .Theuncertaintiesare statisticalonly. Relative Isolation(Muon) 0 1 2 3 4 5 6 Events(Normalized)/0.15 0 0.05 0.1 0.15 0.2 Efficiency(RelIso<0.15) 0.003 : 0.017 t t 0.001 QCD: 0.018 -0.002 +0.003 data : 0.029 -1 =35 pb int =7 TeV L s BTag-and-probe (data) BTag-and-probe (MC) (MC) t t A Relative Isolation(Electron) 0 1 2 3 4 5 6 Events(Normalized)/0.15 0 0.05 0.1 0.15 0.2 0.25 BTag-and-probe (data) BTag-and-probe (MC) (MC) t t Efficiency(RelIso<0.15) 0.012 : 0.037 t t 0.006 QCD: 0.028 -0.008 +0.013 data : 0.036 -1 35pb int =7 TeV L s B Figure6-19.Final RelIso templateformuons(left)andelectrons(right). 148

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Tofullyexecutethisdata-drivenbackgroundpredictionindata,theanalysisis performedbyimposingallofthenalselectioncriteriausedinthesignalsearch,with oneexception.The RelIso requirementontheleastisolatedleptonisinvertedand requiredtobeabovethenominalvalue 0.15 .Thissemi-nalselectionwillbereferred toasthe sidebandregion .Theobservedeventsareexpectedtobemostlyfrom t t production(withaverysmallcontributionfrom W +jets).Thereisalsopotentially anon-trivialcontributionfromthefake-fakebackgroundswhichwerediscussedin Section 6.6.3 ,butthiscanbesubtractedfromthesidebandyieldsusingtheefciencies derivedforthefake-fakeprediction.Beforeperformingthissubtractioninthedata,the followingnumbersofsame-signdi-leptoneventsareobservedinthesideband: 11 2 ee 6 e ,and 5 e (thelastleptondenotestheonethatisleastisolated). Afterthefake-fakesubtractionisperformed,thesesidebandyieldsforeach channelcanbemultipliedbythecorrespondingaverageprobabilitiestopassthe RelIso requirement,whichnallygivesthedata-drivenpredictionforthetotalnumber ofprompt-fakedi-leptonswhichpopulatethesignalregion: N SS f f =0.52 0.24 (stat) 0.26 (sys).Thisnumberrepresentsthecombinationofallchannels.Thedetailsofthe calculationareprovidedinTable 6-16 Asindicatedbytheuncertaintiesgivenfor N SS f f ,afewdifferentsourcesof systematicerrorhavebeenstudiedfortheBTag-And-Probemeasurement.Thelargest contributioncomesfromthestatisticalprecisionoftheMonte-Carlobasedclosure test.Anothersourceoferrorisdeterminedbyevaluatinghow < 2 > ( b ) changesin responsetovariationsintheeventselectionconditions(e.g., H T > 150 GeVor H T > 50 GeV).Thisisfoundtobesub-dominant.Anattemptismadetoaccountfortheunknown W + jetscontaminationinthesidebandbyarticiallyenhancingitsMonte-Carlobased expectationbyafactoroftwo,andevaluatingifthemeasuredvaluesof < 2 > ( b ) deviates awayfromthevaluegivenby t t simulation.Inasimilarvein,testswereperformedin simulationtocheckifanarticiallyenhancedfractionoffakeleptonsfromsourcesother 149

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than b -decayscanleadtoanysignicantvariationsinthemeasuredvalueof < 2 > ( b ) Thecontributionsfromallofthesepossiblesourcesofsystematicuncertaintyareadded inquadraturetoarriveatatotalsystematicuncertaintyon < 2 > ( b ) of 54(29)% for electrons(muons). Table6-16.Data-drivenbackgroundpredictionofprompt-fakedi-leptons. Observable eee e total Eventsinsideband 11 3.32 1.46 2.25 2.424 4.9 f-f(sideband) 4.2 2.20.3 0.42.3 2.50.7 0.47.5 4.5 p-f(sideband) 6.8 4.21.7 1.53.7 3.64.3 2.616.6 6.4 p-f(signalregion) 0.20 0.140.06 0.070.12 0.110.16 0.140.52 0.35 6.6.5ValidationoftheBackgroundCompositionintheSidebandData Asanalchecktoillustratethatthecompositionofthebackgroundtothissearchis understood,onecanattempttoaccountfortheindividualcontributionstothesideband yieldsusingStandardModelMonteCarlosamplescombinedwiththedata-driven predictionoftheQCDbackgrounds.Figure 6-20A showstheSM MC +QCD data prediction forthesidebandforeachchannelseparatelyandcombined.Theactualyieldsin dataarerepresentedbyblackmarkers.ThedataandSM MC +QCD data agreequite well.TheFactorizationmethodpredictsthattheQCDcomponent(fake-fake)ofthe sidebandshouldbe 31% 19% .Figure 6-20B ismeanttoillustratethesameprinciple, butappliedtotheopposite-signdi-leptontopology.Here,thedata-drivenfake-fake measurementisperformedonopposite-signbaselineselectionyields,butwiththe RelIso and E T selectionefcienciesderivedfromthesame-signdi-leptonyields.Again, goodagreementbetweendataandSM MC +QCD data isobserved. TheFactorizationmethod'sclassicationofthebackgroundsinthesidebandcan befurthervalidatedbyappealingtoanotherindependentdata-drivenmethod,whichcan bereferredtoasthe" d 0 TemplateFittingmethod".Thismethodexploitsthedifferences inthe d 0 spectraofpromptandnon-promptleptons.Again,itisassumedthatthe sidebandyieldisdominatedbytwotopologies(i.e.,"fake-fake"and"prompt-fake")as indicatedbyTable 6-16 .TheseassumptionsaresummarizedinTable 6-17 .Relying 150

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0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 T O T A L e e E v e n t s S a m e S i g n S i d e b a n d o b s e r v e d f a k e f a k e ( Q C D ) d a t a d r i v e n V + j e t s M o n t e C a r l o t t + t b q + t W M o n t e C a r l o V V M o n t e C a r l o C M S P r e l i m i n a r y s q r t ( s ) = 7 T e V L i n t = 3 5 p b 1 e e A 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 T O T A L e e E v e n t s O p p o s i t e S i g n S i d e b a n d o b s e r v e d f a k e f a k e ( Q C D ) d a t a d r i v e n V + j e t s M o n t e C a r l o t t + t b q + t W M o n t e C a r l o V V M o n t e C a r l o C M S P r e l i m i n a r y s q r t ( s ) = 7 T e V L i n t = 3 5 p b 1 e e B Figure6-20.Summaryofbackgroundcontributionsforsidebandeventsindataand simulationshownforthesame-signdi-leptontopology(left)andthe opposite-signdi-leptontopology(right).Here,thecutontheleastisolated leptonisrelaxed. onthiswell-motivatedassumption,the d 0 requirementiscompletelyrelaxedonthe isolatedleptoninthedi-leptonpair.Then,two d 0 templatesmustbederivedfromdata. Onetemplateismeanttomodelthe d 0 spectrumforpromptleptonsandistakenfrom a Z controlregionindata.Theothertemplateismeanttomodelthe d 0 spectrumfor non-promptleptonsandistakenfromaQCDcontrolregionindata.Theselection requirementsusedtodenethesetwocontrolregionsareprovidedinTable 6-18 Table6-17.Topologiespresentinthesideband IsolatedLeptonNon-isolatedLeptonProportion PromptPromptnegligible PromptFake 1 FakePromptnegligible FakeFake 1 1 Beforederivingthetemplatesafewissuesmustbeaddressed.Inparticular,one mustdeterminewhetherornottheprecisionandaccuracyofthe d 0 observableis sufcientwhenitismeasuredwithrespecttothebeamspot(asisdonethroughoutthe restofthisanalysis)versussomeotherreferencepoint,liketheeventreconstructed 151

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Table6-18.Controlregionsforthe d 0 TemplateFittingmethod ObservableZ-ControlQCD-Control Leptons 2 withopposite-sign # 1 RelIso < 0.15 > 0.4 Mass[GeV] [76,106] [5,76] or [106, ) ] H T [GeV] > 100 > 300 E T [GeV] < 20 < 20 primaryvertex,whichischosensimplyastheonewiththemostdegreesoffreedom (i.e.,mosttracksemergingfromit)inthecaseofmultiplepile-upevents.Figure 6-21 showsthe d 0 spectraforthesetwochoicesinthe Z controlregion(left)andtheQCD controlregion(right).Fortheformer,isclearthattheprimaryvertexgivesamore 4 -like function,whichisdesirable,whileforthelatterasofterspectrumisobservedinthecore, whichisundesirable.Thetrade-offdoesnotseemtomeritaswitchtotheprimaryvertex here.Thus,itisjustiedtocontinuetotakethemeasurementfromthebeamspot,which iscommononCMS. D0 [cm] 00.010.020.030.040.050.06 0 0.2 0.4 0.6 0.8 1 1.2 Data (Z-Control) Beamspot (2050) Primary Vertex (2050) A Z control D0 [cm] 00.010.020.030.040.050.06 0 0.1 0.2 0.3 0.4 0.5 0.6 QCD control (data) Beamspot (32554) Primary Vertex (32554) BQCDcontrol Figure6-21.Thedistributionof d 0 measuredfromthebeamspot(blue)andmeasured fromthereconstructedprimaryvertex(black)fortheZ-controlregion(left) andtheQCDcontrolregion(right). 152

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Anotherdetailthatcannotbeoverlookedistheslightdifferencein d 0 spectra betweenfakemuonsandfakeelectrons.ThisisshowninFigure 6-22 .Asdiscussedin Section 6.6.3 ,inheavy-avordecayselectronsarelesslikelytobereconstructedthan muons.Thus,thetailofthedistributionforfakeelectronsismilder.Differencesbetween promptmuonsandpromptelectronsareshowntobenegligible.Intheidealcaseit wouldbedesirabletoavoidcombiningelectronsandmuonsintoacommon d 0 template andsimplyperformtwoseparatetsonthesidebanddata(oneforisolatedelectrons andoneforisolatedmuons);however,thesidebanddataistoostatisticallylimitedto performsuchatreatment.Asanalternative,itisenoughtosimplyderivethetemplates forelectronsandmuonsindividuallyandthencombinethemintoasingletemplatein proportiontotheelectron:muonratiointhesideband.Theelectron:muonratiointhe sideband,oncethe d 0 cutisrelaxed,provestobe 1:2 [cm] bs D0 00.010.020.030.040.050.06 0 0.2 0.4 0.6 0.8 1 Data (Z-Control) Electrons (1138) Muons (912) A Z control [cm] bs D0 00.010.020.030.040.050.06 0 0.1 0.2 0.3 0.4 0.5 QCD control (data) Electrons (3666) Muons (28892) BQCDcontrol Figure6-22.Thedistributionof d 0 forelectrons(blue)andmuons(black)forthe Z controlregion(left)andtheQCDcontrolregion(right). Oncerespectivetemplatesforpromptandnon-promptleptonsarederived,they canbeaddedtogetherwithweights $ and 1 $ ,whichareoptimizedviaabinned maximum-likelihoodttothe d 0 spectrumoftheisolatedleptoninthesidebanddata. 153

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Figure 6-23A showsthepromptandnon-prompttemplatesnormalizedtounityon overlaidwiththedata,whichisalsonormalizedtounity.Theextendedtailisclearly visiblefornon-promptleptons.Figure 6-23B showsthesameplot,butnowthe templatesarescaledtobesttthedata.Themaximumlikelihoodtyieldsavalue of $ =0.51 0.24 ,whichrepresentstheproportionofeventsattributabletothe "prompt-fake"topology.Theproportionofeventsattributabletothe"fake-fake"topology istherefore 1 $ =0.49 0.24 .Thevalueof 2ln( likelihood ) isplottedasafunctionof $ inFigure 6-23C InordertocomparewiththeresultsfromtheFactorizationmethodthevalueof 1 $ mustbeadjustedtothevalueitwouldbewiththe d 0 requirementrestoredtoitsnominal valueof 0.2 mm.Thiscanbedoneifoneknowsthe d 0 selectionefcienciesforprompt andnon-promptleptons,respectively.Fortunately,thiscanbemeasuredthesedirectly fromthetemplates,whichgives 2 d 0 =80.2%(100%) fornon-prompt(prompt)leptons. Thus,the"fake-fake"contributiontothesideband 2 d 0 (1 $ ) / ( 2 d 0 (1 $ )+ $ ))= 0.43 0.25 ,whichisstatisticallyconsistentwiththepredictionfromtheFactorization method. 154

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[cm] bs D0 00.020.040.060.080.1 -2 10 -1 10 1 Data (27) Non-prompt Template (32556) Prompt Template (2050) ATemplates(beforet) bs d0 00.020.040.060.080.1 -1 10 1 10 bs d0 00.020.040.060.080.1 -1 10 1 10 data prompt + nonprompt nonprompt BTemplates(aftert) 0.20.40.60.81 -2ln(likelihood) -208 -206 -204 -202 -200 -198 -196 -194 C 2 ln (likelihood)vs. 1 Figure6-23.Prompt(blue)andnon-prompt(red)templatesnormalizedtounityontopof data(top-left).Thesametemplatesscaledbyweightswhichwere optimizedbyamaximumlikelihoodt(top-right).Thevalueof 2ln (likelihood)asafunctionof $ (bottom). 155

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6.6.6SummaryofBackgroundRates Table 6-21 andFigure 6-24 summarizetheexpectedeventyieldsforallbackground contributions.Wecannowre-writeEq. 62 inallofitsdetail.ThisisdoneinEq. 613 wherethedependenceoftheprompt-fakemeasurementontheefcienciesderivedfor thefake-fakemeasurementisclearlyillustrated. N tot bgd = N SS p p + N OS p p + N baseline 2 2 2 E T + N baseline e 2 2 e 2 E T + N baseline ee 2 e 2 e 2 E T + ( N sideband N baseline 2 (1 2 ) 2 E T ) < 2 > ( b ) + ( N sideband e N baseline e + e 2 e (1 2 ) 2 E T ) < 2 > ( b ) + ( N sideband e N baseline e + e 2 (1 2 e ) 2 E T ) < 2 > ( b ) e + ( N sideband ee N baseline ee 2 e (1 2 e ) 2 E T ) < 2 > ( b ) e (613) Thealgebraicexpressionfor N tot bgd giveninEq. 613 helpstoguidetheerrorpropagation. Thecalculationisperformedbyvaryingthisexpressionseparatelyforeachsourceof uncertainty.Table 6-19 showstheabsolutestatisticaluncertaintyforeachterminthe expressionaswellasitsabsolutevariationonthetotalbackgroundestimate N tot bgd .Table 6-20 summarizessystematicuncertaintiesfortherespectivemeasurementsandtheir respectiveimpactsonthetotalbackgroundestimate.Itshouldbeemphasizedthatthe errorsareinmostcasesdominatedbythelowstatisticsoftheeventsinthecontrol samples;hence,inthefuturetheyareexpectedtoscalewithluminosityas 1 / 4 L d t 156

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Table6-19.Statisticalerrorsoftermsusedinthecalculationof N tot bgd Term (Term) ( N tot bgd ) N OS p p 0.0060.006 N baseline 14.93 < 0.01 N baseline ee 3.28 < 0.01 N baseline e 8.83 < 0.01 N sideband 3.320.10 N sideband ee 1.410.05 N sideband e 2.240.08 N sideband e 2.450.07 $ 0.0150.03 $ e 0.0770.03 $ E T 0.028 < 0.01 < $ > ( b ) 0.0030.03 < $ > ( b ) e 0.0130.08 Table6-20.Systematicerrorsinvolvedincalculationof N tot bgd Source ( N tot bgd ) Uncertaintyon N SS p p 0.041 Biasesduetof-pcontaminationin 0.02 N baseline $ $ e $ E T Uncertaintyonclosuretestfor N f f 0.05 UncertaintiesonBTag-and-Probe < $ > ( b ) 0.21 Uncertaintyon W + jetscomponentin N p f 0.15 157

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Table6-21.Summaryofeventyieldsforallbackgroundsourcesandassignedsystematicerrors. PhenomenologicalSorting eee totalcomments Prompt-Promptsame-signdi-leptons 0.0260.0120.0440.083 theory+simulation qq ( q # q # W W 2 ( q q ( W ) WZ ZZ 0.013 0.006 0.022 0.041 Prompt-Promptopposite-signdi-leptonswithachargeip0.0080.0040.012 fullydata-driven ( t t tW WW ) 0.005 0.003 0.006 Prompt-fakesame-signdi-leptons 0.1970.0600.2640.522 fullydata-driven ( t t tX W + jets ) 0.136 0.067 0.110 0.354 Fake-fakesame-signdi-leptons 0.0780.0200.0840.183 fullydata-driven (QCD,all-hadronic t t ) 0.060 0.028 0.042 0.169 Totalbackgroundestimate(astobeusedintheanalysis) 0.300.100.400.80 mostlydata-driven 0.13 0.07 0.18 0.33 Totalbackgroundaspredictedbysimulation(withoutQCD) (0.16)(0.05)(0.21)(0.41) forcomparisononly 158

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0 0 0 5 1 0 T O T A L e e E v e n t s S i g n a l R e g i o n f a k e f a k e p r o m p t f a k e O S p r o m p t p r o m p t S S p r o m p t p r o m p t C M S P r e l i m i n a r y s q r t ( s ) = 7 T e V L i n t = 3 5 p b 1 e A 0 5 1 0 T O T A L e e E v e n t s S i g n a l R e g i o n o b s e r v e d L M 0 ( N L O c r o s s s e c t i o n ) f a k e f a k e p r o m p t f a k e O S p r o m p t p r o m p t S S p r o m p t p r o m p t C M S P r e l i m i n a r y s q r t ( s ) = 7 T e V L i n t = 3 5 p b 1 e B Figure6-24.Finalpredictionsfortheexpectedeventratesat 35 pb 1 (left)andwithLM0 included(right).Allpredictionsexceptfor qqWW + WZ + ZZ arefully data-driven. 159

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6.7Signalyieldanduncertainties Beforeproceedingwiththediscussionofsystematicerrorsassociatedwiththe signaleventyield,itisimportantnottoentangletwodistinctgoals:Onemaypursue thegoalofexploringone(orasetof)fullydenedmodel(s)(e.g.mSUGRAwith somesetofparameters).Settinglimitsinthiscaseisreducedtoayesornoanswer foragivensetofthemodelparameters.Thetheoreticaluncertaintiesonthemodel itselfwouldinuenceone'sjudgmentonwhetherornotthemodel(orsomerangeof modelparameters)canbeexcluded.Alternatively,giventheenormousrangeoffree parametersintheunconstrainedMSSM,scanningoveraveryconstrainedsubsetof parameters(e.g.mSUGRA)maynotyieldasatisfactoryorreliableresult.Thus,one maywanttopresentsearchresultsasmodel-independentlimitsontheproductofthe crosssection( ),branchingratios( BR ),andtheexperimentalacceptance( A ).This iscertainlyaveryattractiveoption;however,itrequiresstatingcertaindisclaimerson whichmodelscanandcannotbetriedagainstsuchgenericallystatedlimits.Themain concernhereisthattheexperimentalreconstructionofaparticularobservableisnot alwaysconstantandhasaniteresolution.Thisleadstothefactthattheacceptancefor aparticularsignalisnotauniversalquantityanddependsontheactualdistributionsof theprimeobservablesinthemodel. Systematicerrorswillbediscussedinthecontextofthesetwoapproaches.The model-dependentsystematicerrorswillbeillustratedontheexampleoftheLM0 benchmarkpoint.Inordertomakethelimiton BR A applicabletoanymodel,itis necessarytoprovidetheparameterizedacceptancefunctionsforallobservablesusedin theanalysis. 6.7.1TheoreticalUncertainties Theseuncertaintiesareapplicableonlyforsettinglimitsonaconcretemodelwith agivensetofparameters.Themaincontributionstotheoreticaluncertainties(once 160

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allmodelparametersarexed)areassociatedwiththescaleoftheQCDcoupling (Section 2.1.3 )andtheprotonpartondensityfunctions( pdf 's). Forgluino/squarkproductioninmSUGRAmodels,the pdf uncertaintiestranslateto abouta 10 13% systematicerroronthecross-sections[ 73 ].Thecitedrangecovers theenergyscalefrom 2 TeV(Tevatron)to 14 TeV(LHC).Thisanalysiswillapplya 13% uncertaintyinordertobeconservative. Thesystematicerrorsofthecross-sectionarisingfromQCDscalevariations dependverystronglyontheenergyofcollisions.AttheNLOlevelcalculations,they wereestimatedtorangefrom 40 50% attheTevatronto 5 10% at 14 TeVLHC[ 73 ]. The 7 TeVcollisionenergyusedinthe2010LHCrunfallsrightinbetween;hence,it isnecessarytoevaluatethemSUGRAcross-sectionsensitivitytorenormalizationand factorizationscalesusedinthepQCDcalculations[ 62 ]byvaryingthembyafactorof 2 upanddown,whichoverthelastfewyearshasbecomeacommonconvention.Thus, theuncertaintyobtainedfortheLM0benchmarkpointis 18% ,whichisconsistentwith theexpectationgiventhenumbersmentionedabove. 6.7.2InstrumentalUncertainties 6.7.2.1Luminosity ThecurrentuncertaintyontheintegratedluminosityinCMSis 11% [ 74 ],whichis measuredbythemethodof"zero-counting"usingtheHFcalorimeter. 6.7.2.2Muonselectionefcienciesandvalidation ThemuonreconstructionefciencyasobtainedfromMonteCarlosimulation isshowninFigure 6-25 .Theresultsareshownasafunctionof p T ofthesimulated muonforthebarrelandendcapmuonsystems,respectively.Themuonreconstruction efciency,asderivedfromdatausingtheclassicalTag-and-Probemethodusing J / # and Z events,isconsistentwiththeMonteCarlomodelingatalevelbetterthan5%[ 66 ]. AlsoshowninFigure 6-25 arecurves(blue)whicharettothepoints.Thefunctional 161

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formusedforthetsreliesonthreeparametersandisgivenby: / ( p T )=par(1)+par(2) 7 erf 7 p T p ,thresh T par(3) 8 1 8 (614) where p ,thresh T representsthemuon p T thresholdof 5 GeVusedinthisanalysis. The RelIso ( )selectionefcienciesforLM0eventsareshowninFigure 6-26 asafunctionofthe p T ofthereconstructedmuonforthebarrelandendcapmuon systems,respectively.Thebluecurvesrepresenttsbasedontheformulagivenin Eq. 614 .ItshouldbenotedthattheselectionefciencyforpromptmuonsinLM0 eventsisgenerallylowerthanitisforpromptmuonscomingfrom Z ( eventsof theStandardModel.ThisisduetotheincreasedpresenceofhadronicactivityinSUSY eventsfeaturingcoloredproduction.Promptleptonsinsucheventscanoverlapwith jetsfromotherpartsofthecascadedecaysbyaccident,thusgivingtheappearance ofanon-isolated,andhencenon-promptlepton.Figure 6-27 showstheproductofthe reconstructionand RelIso selectionefciencieswithsimilartsperformed. / ndf 2 1694 / 16 Prob 0 p0 0.0002 0.9409 p1 0.0045 0.1126 p2 0.213 4.487 in Barrel gen T Muon p 0 20 40 60 80 100 120 140 160 180 200 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 1694 / 16 Prob 0 p0 0.0002 0.9409 p1 0.0045 0.1126 p2 0.213 4.487 reco pt > 5 / ndf 2 914.4 / 16 Prob 0 p0 0.0002 0.9488 p1 0.00205 0.08828 p2 0.229 8.473 in Endcap gen T Muon p 0 20 40 60 80 100 120 140 160 180 200 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 914.4 / 16 Prob 0 p0 0.0002 0.9488 p1 0.00205 0.08828 p2 0.229 8.473 reco pt > 5 Figure6-25.Muonreconstructionefciencyversussimulatedmuon p T with | 1 | < 1.2 (left)and 1.2 < | 1 | < 2.4 (right).Thereconstructedmuonisrequiredto have p reco T > 5 GeV. ItisimportanttonotethatthetraditionalTag-and-Probemethodwhichisusedto measure RelIso selectionefcienciesinadata-drivenwayisnotapplicabletoSUSY 162

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/ ndf 2 140.9 / 16 Prob 4.864e-22 p0 0.0049 0.9057 p1 0.0054 0.2968 p2 2.2 50.9 >5) in Barrel reco T (with p gen T Muon p 0 20 40 60 80 100 120 140 160 180 200 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 140.9 / 16 Prob 4.864e-22 p0 0.0049 0.9057 p1 0.0054 0.2968 p2 2.2 50.9 reliso < 0.15 / ndf 2 44.44 / 16 Prob 0.0001688 p0 0.0080 0.9294 p1 0.008 0.181 p2 5.51 51.69 >5) in Endcap reco T (with p gen T Muon p 0 20 40 60 80 100 120 140 160 180 200 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 44.44 / 16 Prob 0.0001688 p0 0.0080 0.9294 p1 0.008 0.181 p2 5.51 51.69 reliso < 0.15 Figure6-26. RelIso ( )selectionefciencyforreconstructedmuonsversus p T for | 1 | < 1.2 (left)and 1.2 < | 1 | < 2.4 (right). / ndf 2 153.6 / 16 Prob 1.505e-24 p0 0.0027 0.7992 p1 0.0066 0.2789 p2 1.29 30.07 in Barrel gen T Muon p 0 20 40 60 80 100 120 140 160 180 200 combined efficiency for reco & iso 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 153.6 / 16 Prob 1.505e-24 p0 0.0027 0.7992 p1 0.0066 0.2789 p2 1.29 30.07 / ndf 2 47.58 / 16 Prob 5.525e-05 p0 0.0034 0.8362 p1 0.0091 0.1968 p2 1.8 22.3 in Endcap gen T Muon p 0 20 40 60 80 100 120 140 160 180 200 combined efficiency for reco & iso 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 47.58 / 16 Prob 5.525e-05 p0 0.0034 0.8362 p1 0.0091 0.1968 p2 1.8 22.3 Figure6-27.Productofmuonreconstructionand RelIso selectionefcienciesversus p T for | 1 | < 1.2 (left)and 1.2 < | 1 | < 2.4 (right). foratleasttworeasons.First,leptonsfromSUSYproduction,althoughprompt,may neverthelessbemuchsofterthanthosein Z and W decays.The p T spectrumof leptonsintheprocesswilldenitelybeimportantifoneusesthe RelIso variabletoselect events.Second,leptonsfromSUSYproduction,liveinasubstantiallybusierhadronic environmentthanleptonsin Z and W decays.Suchintensehadronicenergyow, inherenttotheprocessesbeingsearchedfor,willcertainlyhaveadetrimentaleffecton theperformanceofthe RelIso selectionefciency. 163

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Toevaluatethe RelIso ( )selectionefciencyforLM0-likepromptmuonsinthe LM0-likemulti-jetenvironment,themethodofLeptonKinematicTemplates(LKT)is used,whichwasdesignedforevaluatinga RelIso selectionefciencyforeventswith multiplepromptleptonsfromanarbitrarymomentumspectrumandwithanarbitrarily densejetactivity.Themethodnaturallytakesintoaccountkinematiccorrelations betweenmultiplemuonsinsignalevents.TheLKTmethodwasrstintroducedin[ 66 ] andwasusedintherst W / Z cross-sectionmeasurementsonCMS[ 75 ]. Inbrief,theLKTmethodcanbedescribedasfollows: Z ( eventsareselected fromdataandrandomisolationconesin 1 spacearethrownatregionsinthe detector.Then,the 3 -momentaof n leptonsfromsimulatedsignaleventsaresampled andcombinedwiththeactivityinsidetherandomisolationconetoperformthe RelIso calculation.Thevalue n canvaryonaneventbyeventbasisandshouldalsobe sampledfromthesignalmodelunderstudy.Next,theselectionefciencyperevent(not perlepton)fordifferentvalues(bins)ofhadronicactivityin Z -eventsismeasured.The numberofchargedtracksintheeventisusedasaconvenientmeasureofthehadronic activity.Finally,themeasuredefcienciesinbinsofhadronicactivityarere-weightedto matchthehadronicactivitydistributionexpectedinthesignalunderthestudy. Figure 6-28 (left)showsthetrackmultiplicitydistributionfor Z ( eventsin simulation(redline)anddata(bluepoints).ThesamedistributionfromLM0(black dashedline)isalsoshown.Thedifferenceinhadronicactivitybetweenthetwo processesisreectedintheseparationofthecurves.Figure 6-28 (right)showsthe LKTmethodappliedtotheLM0benchmarkpoint.Theredpointsshowthe RelIso ( ) selectionefciencyforLM0-likeLKT'sthrowninsimulated Z ( events.The bluepointsshowthesamedistributionfor Z ( eventsindata.Onecanclearly seethestronglineardependenceofthe RelIso ( )selectionefciencyonthelevelof hadronicactivityin Z eventsforbothsimulationanddata.Theblackcrossesshow the RelIso ( )selectionefciencyintheLM0benchmarksampleafteralloftheother 164

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nalselectionrequirementshavebeenapplied.Thesinglehollow-squaredmarker representstheaverageselectionefciencyforLM0accordingtosimulation.Itisevident thatthemeasurementsdonewith Z eventscanbelinearlyextrapolatedusingthetrack multiplicitytomatchthe RelIso selectionefciencyinthecontextofabusierenvironment whichischaracteristicofaSUSYprocess.ThisconstitutestheclosuretestoftheLKT method.Therefore,thesimulationcanbetrustedtofaithfullymodelthe RelIso selection efciencyforprompt,signal-likeleptonsinabusyhadronicenvironment.Thevariations betweentheLM0 RelIso selectionefciencyandextrapolationsusing Z eventseither fromsimulationorfromdatagivesameasureofapossiblesystematicerrorofabout 3% Number of tracks 0 10 20 30 40 50 Probability -2 10 -1 10 (MC) Z (data) Z mSUGRA LM0 (MC) CMS preliminary -1 =7TeV, 35pb s Number of tracks 0 20 40 Muon isolation cut efficiency 0.6 0.7 0.8 0.9 1 (MC, LKT method) Z (data, LKT method) Z mSUGRA LM0 (MC, LKT method) mSUGRA LM0 (MC, muons) Figure6-28.Distributionsofnumberoftracksinsimulated Z ( events(red),data (blue),andinLM0events(black)(left).Predictionof RelIso ( )selection efciencyforLM0eventsobtainedbyextrapolationofmeasurementsdone withsimulated Z events(right). 6.7.2.3Electronselectionefcienciesandvalidation Theelectronreconstructionand RelIso ( e )selectionefcienciesasobtainedfrom simulationareshowninFigures 6-29 and 6-30 ,respectively,whiletheproductofthe twoareshowninFigure 6-31 .ThefunctionalformgiveninEq. 614 isusedtota curve(blue)toeachefciencydistribution.Here, p e ,thresh T representstheelectron p T 165

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thresholdof10GeVthatisusedforthisanalysis.Theparametersforthetsperformed onthecombinedefcienciesaregiveninSection 6.7.3 Electronssufferfromsignicantlymoresourcesofreconstructioninefciencies,than muonsdo.Muonspassthroughmattermuchmoreeasily,owingtotheirminimum-ionizing nature,andasaconsequencearelesslikelytohavedestructiveinteractionswhich couldjeopardizetheirmeasurements.Thefaithfulsimulationofanelectron'spassage throughthedetectormaterialisconsequentlymuchmoredifculttoachieve.Thus, relyingonthereconstructionefciencyfromsimulationmustbedonewithcare.To evaluatethesensitivityoftheLM0signaleventyieldtothepossibleuncertaintiesinthe electronreconstructionefciency,are-weightingprocedureisperformedonallsimulated eventscontainingreconstructedelectronsaccordingtopossiblevariationsfromthe expectedefciency.TheobservedyieldsofLM0eventsareobservedtovaryby 8% as aresultofthistest. / ndf 2 1318 / 15 Prob 0 p0 0.0004 0.8376 p1 0.0017 0.3504 p2 0.1 12.8 in Barrel gen T Electron p 0 20 40 60 80 100 120 140 160 180 200 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 1318 / 15 Prob 0 p0 0.0004 0.8376 p1 0.0017 0.3504 p2 0.1 12.8 reco pt > 10, ecalDriven / ndf 2 306.3 / 15 Prob 0 p0 0.0007 0.6221 p1 0.0022 0.3839 p2 0.12 13.48 in Endcap gen T Electron p 0 20 40 60 80 100 120 140 160 180 200 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 306.3 / 15 Prob 0 p0 0.0007 0.6221 p1 0.0022 0.3839 p2 0.12 13.48 reco pt > 10, ecalDriven Figure6-29.Electronreconstructionefciencyversussimulatedelectron p T for | 1 | < 1.5 (left)and 1.5 < | 1 | < 2.4 (right).Thereconstructedelectronisrequiredto have p reco T > 10 GeV. Tovalidatethefullelectronselectionefciency,itisconvenienttoexploitthe previouslyobservedagreementbetweendataandsimulationfortheselectionefciency ofmuons.Sincetheexpectedratesof Z ( and Z ( ee eventsarethesame,it 166

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/ ndf 2 26.8 / 15 Prob 0.0304 p0 0.0089 0.9391 p1 0.0075 0.1534 p2 7.46 67.99 >10) in Barrel reco T (with p gen T Electron p 0 20 40 60 80 100 120 140 160 180 200 isolation efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 26.8 / 15 Prob 0.0304 p0 0.0089 0.9391 p1 0.0075 0.1534 p2 7.46 67.99 reliso < 0.15 / ndf 2 21.66 / 15 Prob 0.1172 p0 0.037 0.968 p1 0.03319 0.07982 p2 59.58 82.37 >10) in Endcap reco T (with p gen T Electron p 0 20 40 60 80 100 120 140 160 180 200 isolation efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 21.66 / 15 Prob 0.1172 p0 0.037 0.968 p1 0.03319 0.07982 p2 59.58 82.37 reliso < 0.15 Figure6-30. RelIso ( e )selectionefciencyversus p T for | 1 | < 1.5 (left)and 1.5 < | 1 | < 2.4 (right). / ndf 2 264.1 / 15 Prob 0 p0 0.0019 0.7574 p1 0.0049 0.3467 p2 0.57 21.29 in Barrel gen T Electron p 0 20 40 60 80 100 120 140 160 180 200 combined efficiency for reco & iso 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 264.1 / 15 Prob 0 p0 0.0019 0.7574 p1 0.0049 0.3467 p2 0.57 21.29 / ndf 2 50.7 / 15 Prob 9.258e-06 p0 0.0027 0.5742 p1 0.0076 0.3756 p2 0.49 13.52 in Endcap gen T Electron p 0 20 40 60 80 100 120 140 160 180 200 combined efficiency for reco & iso 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 50.7 / 15 Prob 9.258e-06 p0 0.0027 0.5742 p1 0.0076 0.3756 p2 0.49 13.52 Figure6-31.Productofelectronreconstructionand RelIso ( e )selectionefciencies versus p T for | 1 | < 1.5 (left)and 1.5 < | 1 | < 2.4 (right). issufcienttocomparetheratiosofelectronandmuonyieldsindataandsimulation using Z events.Figure 6-32 showssuchratioswithallelectronidenticationand RelIso selectionrequirementsapplied.Electronsandmuonsusedfortheseplotsaretaken fromdi-electronanddi-muoneventsthatagreewiththe Z bosondecayhypothesis: | m e + e m Z | < 30 GeV.Thepurityofsuchaselectionisveryhigh.Onecansee that e -to ratiosindataandsimulationagreetowithin 5% ,whichgivesameasureof 167

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possiblesystematicerrorsinthemodelingoftheelectronreconstruction,identication, and RelIso performance. in Barrel [GeV] T Electron p 10 20 30 40 50 60 70 80 R = Electron/Muon 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 data: 35 pb Monte Carlo: Zjets in Endcap [GeV] T Electron p 10 20 30 40 50 60 70 80 R = Electron/Muon 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 data: 35 pb Monte Carlo: Zjets [GeV] T Electron p 10 20 30 40 50 60 70 80 90 100 R = Electron/Muon 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 data: 35 pb Monte Carlo: Zjets Figure6-32.Ratiosofelectronandmuonyields(dataandsimulation)in p T binsfor eventswithdi-electronsanddi-muonswithinthe Z -peakfortheECAL barrel(left),ECALendcap(middle),andcombined(right). 6.7.2.4 H T and E T selectionefciencies Figure 6-33 (left)demonstratesthatthereconstructed H reco T isnotexpectedtohave anyoffsetswithrespecttothetrue(generator-level)valueof H gen T formedbythescalar p T sumoftheoutgoingpartonsinthehard-scatter 8 .Thisagreementisexpectedin principleoncethejetenergyscale(JES)isproperlycalibrated.Figure 6-33 (right) showstheprobabilityofreconstructing H reco T withavalueof 300 GeVorhigherasa functionofthegenerator-levelvalue H gen T .SimilardistributionsareshowninFigure 6-34 forthe E T observable 9 Figure 6-35 illustratesthedifferencebetweenthereconstructedandgenerator-level H T (left)and E T (right)observables.ThesedistributionsaretwithaGuassiancurveto demonstratetheeffectofthenitedetectorresolution.Theresultingstandarddeviations 8 Thegenerator-level H gen T isbuiltfrom"stable"(status=1)generatorparticlesprovided intheMonteCarlotruth. 9 Thegenerator-level E T iscalculatedfromthestableparticlesprovidedintheMonte CarlotruthwhichwouldbevisibletotheCMSdetector. 168

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1 10 2 10 gen HT 0100200300400500600 reco pf HT 0 100 200 300 400 500 600 / ndf 2 9.266 / 27 Prob 0.9994 p0 0.0048 0.9976 p1 0.0425 0.3334 p2 6.84 58.86 gen HT 0 100 200 300 400 500 600 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 9.266 / 27 Prob 0.9994 p0 0.0048 0.9976 p1 0.0425 0.3334 p2 6.84 58.86 reco HT > 300 Figure6-33.Reconstructed H reco T vs.generator-level H gen T (left).Probabilityof reconstructinganeventwith H T > 300 GeVforagiven H T atthegenerator level(right). 0 20 40 60 80 100 120 140 gen met 020406080100120140160180200 reco pf met 0 20 40 60 80 100 120 140 160 180 200 / ndf 2 0.624 / 14 Prob 1 p0 0.0029 0.9998 p1 0.0607 0.4374 p2 2.06 19.18 gen MET 0 20 40 60 80 100 120 140 160 180 200 efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 0.624 / 14 Prob 1 p0 0.0029 0.9998 p1 0.0607 0.4374 p2 2.06 19.18 PF met > 30 Figure6-34.Reconstructed E T reco vs.generator-level E T gen (left).Probabilityof reconstructinganeventwith E T > 30 GeVforagiven E T atthegenerator level(right). ( H T and ! E T )oftheseGaussiantscanbeusedforsmearingthetruevaluesofthese observablesgivenbytheMonteCarlotruth,inordertomodeltheresponseoftheCMS detector. Systematicerrorsontheefcienciesofthe H T and E T selectionrequirementsare stronglycorrelatedandarethusevaluatedonsimplythecombinedselectionefciency ofthetwo.Toevaluatethesystematicerrorduetouncertaintiesinthejetenergyscale, 169

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/ ndf 2 338.3 / 102 Prob 4.19e-27 Constant 2.55 70.39 Mean 1.566 4.822 Sigma 1.45 51.84 gen HT reco HT -400-300-200-1000100200300400 entries 0 10 20 30 40 50 60 70 80 90 / ndf 2 338.3 / 102 Prob 4.19e-27 Constant 2.55 70.39 Mean 1.566 4.822 Sigma 1.45 51.84 / ndf 2 51.59 / 33 Prob 0.0207 Constant 6.5 225.6 Mean 0.406 -7.572 Sigma 0.34 18.06 gen MET reco MET -200-150-100-50050100150200 entries 0 50 100 150 200 250 / ndf 2 51.59 / 33 Prob 0.0207 Constant 6.5 225.6 Mean 0.406 -7.572 Sigma 0.34 18.06 Figure6-35.Distributionsof H reco T H gen T foreventswith H gen T > 300 GeV (left)and E T reco E T gen foreventswith H gen T > 300 GeV and E T gen > 30 GeV (right). theLM0sampleisusedtovarysimultaneouslytheenergiesofalljetsand E T (after subtractingthecontributionfromleptons)by 5 %.Theobservedchangeintheevent yieldsafterapplyingthe H T > 300 GeV, N jets # 2 ,and E T > 30 GeVrequirementsis +4.4% and 7.5% ,respectively.Anoverallsystematicerrorof 8% isthusappliedto the H T and E T selectionrequirements. 6.7.2.5Triggerefciency The H T triggerefcienciesaremeasureddirectlyfromdatausingeventsrecorded viaamuontriggerpath,whichisassumedtobeorthogonal.Muonsdonotinuencethe H T trigger,sincetheyinteractonlyminimallywiththecalorimetersand,hence,donot biasthemeasurement.Figure 6-36 showsthe H T triggerefcienciesforeventswitha given H T reconstructedofine.MoredetailscanbefoundinTable 6-22 .Onecansee thateventswith H T > 300 GeVreconstructedofinepassthe H T triggersusedinthis analysiswithnearly 100% efciency.Thesystematicerrorsonthetriggerefciency measurementsaredrivenbythestatisticsofthemeasurement.BasedonFigure 6-36 ,a conservative 5% errorisassigned. 170

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[GeV] T H 100 150 200 250 300 350 400 Efficiency 0 0.2 0.4 0.6 0.8 1 > 100 GeV T Online H > 140 GeV T Online H > 150 GeV T Online H Figure6-36. H T triggerefciencyvsreconstructed H T .Theefciencyismeasuredusing dataobtainedwithmuontriggers. Table6-22. H T triggerefcienciesforthedatasetusedintheanalysis. TriggersusedduringdifferentrunningperiodsHT100UHT140UHT150U Integratedluminosityrecorded/used(pb 1 ) 7.49.517.8 Efciencyofindividualtriggers 100%95%90% 6.7.2.6Crosschecks Tovalidatethatthenalselectionefcienciesareunderstoodforeventsfeaturing twosame-signpromptleptons, H T > 300 GeV,and E T > 30 GeV,theanalysis isrepeatedforopposite-signdi-leptoneventswiththeexactsamenalselection requirements.Intotal, 20 eventsareobserved( 8 6 e e ,and 6 e ),which areinreasonableagreementwiththeexpectedbackground(about 14 events).The opposite-signdi-leptontopologyisexpectedtobedominatedby t t eventswithtwo promptleptons.Thiscross-checkfurthervalidatesthenalselectionefciencyfor signal-likeevents. 171

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6.7.3Summary:SignalAcceptanceandUncertainties Inordertoconstructanupperlimiton BR A experiment ,whichisapplicabletoa widerangeofmodels,itisnecessarytoprovideparameterizationsthatcanallowoneto calculatetheexperimentalacceptanceforanysignalmodelwitharbitrarydistributions fortheobservablesusedintheanalysis.Theproductioncross-section( )andthe branchingratios( BR )dependonthemodelofinterest.Theexperimentalacceptance A experiment relatestotheoverallefciencyofthenalselectioncriteriausedinthe analysis(Table 6-3 ).Theparameterizationisasfollows: Generator-level H T shouldbesmearedusingaGaussiandistributionwith H T from Figure 6-35A andthenarequirementof H T > 300 GeVistobeapplied, Generator-level E T shouldbesmearedusingaGaussiandistributionwith ! E T from Figure 6-35B andthenarequirementof E T > 30 GeVistobeapplied 2 promptsame-signleptonsmustbeproducedintheevent Muonsmusthave p T > 5 GeVand | 1 | < 2.4 Electronsmusthave p T > 10 GeVand | 1 | < 2.4 Non-promptmuonsandelectronsfromsignaleventscanbeconsideredtobelost Selectionefciency(includingreconstruction,identicationand RelIso )forprompt muonsandelectronsisparameterizedasinEq. 614 Byapplyingtheserequirementstothegenerator-levelobjectscomingfromtheMonte Carlotruth,oneobtainstheoverallexperimentalacceptance A experiment forawiderange ofmodelstopassthenalselection. Table 6-23 showsthevaluesofparameters par(1) par(2) ,and par(3) .Table 6-24 summarizesthethevaluesofthesignalacceptancesystematics(andalsotheoretical uncertaintiesfortheLM0benchmarkpoint). 6.8FinalResults Table 6-25 andFigure 6-24 summarizetheexpectedandobservedeventyields, togetherwiththeestimatedsystematicerrors.Only 1 eventisobservedtopassthenal 172

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Table6-23.Observablesusedintheanalysisandparameterizationoftheiracceptance forsignal-likeevents. Observableusedintheanalysis par(1)par(2)par(3) Promptmuonswith p T > 5 GeVand | 2 | < 1.20.790.2830 Promptmuonswith p T > 5 GeVand 1.2 < | 2 | < 2.40.840.2022 Orwithoutsubdividingintocentral/forward 2 regions 0.760.2321 Promptelectronswith p T > 10 GeVand | 2 | < 1.50.760.3521 Promptelectronswith p T > 10 GeVand 1.5 < | 2 | < 2.40.570.3814 Orwithoutsubdividingintocentral/forward 2 regions 0.680.3717 H T > 300 GeV,builtfrom > 1 jetswith E T > 30 GeVand | 2 | < 2.4 H T =52 GeV E T > 30 GeV,builtfromobservabletransverseenergyow E T =18 GeV Table6-24.Signalyieldsandsystematicerrors eee Total Expectedsignalevents(LM0) 3.321.674.869.85 Isolated(prompt)muonswith p T > 5 GeVand | 2 | < 2.4(6%)12% 6% Isolated(prompt)electronswith p T > 5 GeVand | 2 | < 2.4(10%) 20%10% Hadronicenergyowreconstruction--8% Trigger--5% Luminosity--11% TotalExperimentalAcceptanceErrors 19%23%19%18% LM0crosssectionatNLOduetoPDFuncertainties--13% LM0crosssectionatNLOduetoQCDscaleuncertainties--18% TotalerrorsforLM0 29%32%29%32% selection,whichisconsistentwiththetotalbackgroundexpectationof N tot bkd =0.80 0.33 Forcomparison,ifsupersymmetryexistedwiththemodelparametersofLM0,arateof 9.9 eventswouldbeexpected(notcountingthebackground).The"anatomy"ofthe observedeventisdiscussedintheAppendix. Giventhereisnoobservedexcessofeventsinthesignalregion,itisnaturalto calculateexclusionlimits.Tothisend,tworesultswillbepresented: (i) Limitsoncrosssectiontimesacceptance BR A experiment (ii) LimitsonthemSUGRAparameters Table6-25.Summaryofexpectedandobservedeventyields,togetherwiththeoverall systematicerrors eee total Totalbackgroundestimate 0.30 0.130.10 0.070.40 0.180.80 0.33 Observedevents 0101 LM0expectation 3.321.674.869.9 LM0signalyieldsystematicerrors 27%30%27%26% 173

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6.8.1Limitson BR A experiment Tocalculatelimitsoncross-sectiontimesacceptance BR A experiment ,itis convenienttocombinethethreechannelstogetherintoasinglecountingexperiment. 10 Tables 6-24 and 6-25 provideallofthenecessaryinformationforsettingtheexclusion limitsfromthissearch.Theexpectedbackgroundrateis 0.80 witharelativeuncertainty of 38% .Theerroronthesignalacceptancewasdeterminedtobe 18% .Itisassumed thattheerrorsonthebackgroundmeasurementandthesignalacceptanceare uncorrelatedandthattheyeachfollowalog-normaldistributionforerrorpdf's.The Bayesianapproachisusedtosetthelimitsusingaatpriorpdfon BR A experiment Technically,thecalculationisperformedbytheLandSsoftware[ 76 ],whichgivesusthe followingresult: BR A experiment < 0.13 pbat95%C.L. Forcomparison,theLM0modelpredicts BR A experiment =9.85 / 35=0.28 pbandis thereforereliablyexcludedbythissearch. Table 6-23 showsthevaluesoftheexperimentalacceptanceparameterization. Theseparametersallowonetopredict BR A experiment foranygivenmodeltotest whetheritisbeexcludedat 95% C.L.bythissearch.TheNLOcross-sectionforLM0is 57.6 pb.Thetheoreticalacceptancefortheselectionrequirementsusedintheanalysis isabout 1.2% ,andtheexperimentalacceptanceisabout 38% 6.8.2LimitsonthemSUGRAParameterSpace Theeventyields(usingLOcross-sections)fora m 0 vs. m 1 / 2 mSUGRAparameter-plane with tan( )=3 A 0 =0 GeV,and > 0 areshowninFigure 6-37A .The SoftSUSY program[ 77 ]isusedtocalculatetheSUSYparticlemassspectrum.The SUSY-Hit program[ 78 ]isthenappliedinordertoaccountforradiativecorrectionstothemass 10 Itwascheckedthatdoingamoresophisticatedcombinationofthreechannelswitha propercorrelationsofsystematicerrorsgivesnegligibleimprovement 174

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spectraandbranchingratios.SignaleventsarethengeneratedwithPythia6[ 58 ]and lteredfortwopromptleptons( e and ) )with p T > 4 GeVand | 1 | < 2.5 .Finally,the eventsarepropagatedthroughtheCMSFastSimulation,whichsimulatesthedetector response,andthenaresubsequentlyreconstructedusingversion3.8.6ofCMSSW.Due tothelterappliedduringtheeventgenerationstep,someeventsinwhichoneofthe same-signleptonsisnon-prompt,buthappenstobeisolatedbyaccident,arelost.This lossisevaluatedtobeatthelevelof 5% accordingtotheLM0simulationsample.All modelspointsontheplanethatareexpectedtoyieldmorethan 4.5 eventspassingthe nalselectionper 35 pb 1 aresubsumedbythecontour,andarehenceexcludedat 95% C.L. Itisimportanttoshowthelevelofprecisionobtainablefromtheparameterization providedinTable 6-23 .Figure 6-37B comparestwoexclusioncontoursonthe m 0 vs. m 1 / 2 plane.OneisderivedfromtheCMSFastSimulationsamples(solidblue curve),wherethemagentabandrepresentsthetheoreticaluncertainty.Anotheris derivedfromthesignalacceptancemodeldescribedinSection 6.7.3 ,whichisapplied togenerator-levelobjects(blackdashedcurve).NLOcross-sectionsareusedforboth curves. 11 Theagreementbetweenthetwocurvesdemonstratestherobustnessof thesignalacceptanceparameterizationinthecontextofmSUGRA.Itgivesthosewho areexternaltotheCMScollaborationandcannotaccessoremployCMSSWorthe CMSFastSimulationareliablewaytotestvariousmodelsofnewphysicsagainstthe exclusionlimitssetbythissearch.AlsoshowninFigure 6-23 aretheexclusionscurves setbyprevioussearchesperformedbyotherexperiments,whichareweaker,ingeneral, thanthelimitssetbythissearch. 11 Acommonk-factorof 1.5 isusedforallmodelpointsontheplane 175

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(GeV) 0 m 200 400 600 (GeV) 1/2 m 100 150 200 250 300 350 event yields ( LO ) 1 10 2 10 same-sign dileptons -1 7 TeV, 35 pb |<2.4 e/ > 10(5) GeV, | ) e( T p >30 GeV reco >300 GeV, MET reco HT plane 1/2 vs. m 0 mSUGRA m ) > 0 = 0, sign( 0 = 3, A tan AEventyieldsatLO (GeV) 0 m 0 100 200 300 400 500 (GeV) 1/2 m 200 300 400 500 (500)GeV q ~ (500)GeV g ~ (650)GeV q ~ (650)GeV g ~ (800)GeV q ~ (800)GeV g ~ = 7 TeV s -1 = 35 pb int CMS preliminary L > 0 = 0, 0 = 3, A tan LM0 LM1 <0 =5, tan q ~ g ~ CDF <0 =3, tan q ~ g ~ D0 1 # LEP2 l ~ LEP2 2 0 1 D0 = LSP $ # NLO observed limit NLO limit (efficiency model) (GeV) 0 m 0 100 200 300 400 500 (GeV) 1/2 m 200 300 400 500 (GeV) 0 m 0 100 200 300 400 500 (GeV) 1/2 m 200 300 400 500 BExclusioncontours Figure6-37.ExpectedeventyieldsformSUGRAmodelsonthe m 0 m 1 / 2 planefor 35 pb 1 ofdata(top).Exclusioncontourinthe m 0 m 1 / 2 plane(bottom). ContourssubsumeallmSUGRAmodelpointsthatyieldmorethan 4.5 eventsper 35 pb 1 ofdata(i.e., BR A experiment > 0.13 pb). 176

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CHAPTER7 CONCLUSION Theresultsofasearchforasignalofnewphysicsinvolvingeventswith 2 same-sign leptons,jets,andmissingtransverseenergyhavebeenpresented.Thisistherst searchfeaturingthiseventtopologytobeperformedattheLHCwiththeCMS experiment.Itreliesondatacollectedinthe2010LHCrunatacollisionenergyof & s = 7TeV,andcorrespondstoatotalintegratedluminosity 35 pb 1 .Inthesignalregion denedbytheeventselectioncriteriaofthisanalysis, 1 eventisobserved,whichis statisticallyconsistentwiththetotalexpectedbackgroundratefromtheStandardModel of N tot bgd =0.80 0.33 events.Themainbackgroundstothissearcharepredictedusing avarietyofrobustdata-drivenmethods,whichhavebeenthoroughlyvalidatedwith collisiondataorinsomecaseswiththehelpofsimulations. Giventhelackofanobservedexcessofeventsinthedenedsignalregion, exclusionlimitsarecalculatedontheparameterspaceofsupersymmetrymodels withuniversalscalarandgauginomassesattheGUTscale.Thegenerallimitonthe cross-section timestheeventacceptance, A ,describedaboveis BR A experiment < 0.13 pbat95%C.L.Aparameterizationoftheexperimentalacceptance, A experiment ,is alsoprovided,whichcanbeusedtotestavarietyofmodelsagainstthelimitssetbythis search. EffortsareunderwaytoperformasimilarsearchwiththedatarecordedbytheLHC in2011,whichisexpectedtobeasmuchasafewinversefemtobarnsbytheendof theyear.Preliminarystudiesindicatethattheselectioncriteriausedinthisanalysis willcontinuetobegreatlysensitivetonewphysicsprocessesfeaturingthestudied topologyuptoapproximately 400 pb 1 ,beyondwhichthesystematicuncertainties prohibitanyfurtherlimitsettingordiscoverypotential.Itisexpectedthatthestatistical uncertaintiesincurredonthevariouscomponentstothebackgroundmeasurements willscaleinverselywiththesquare-rootoftheintegratedluminosity.Somedata-driven 177

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methodsemployedinthisanalysismayalsobeimprovedtoperhapsdecreasethe incurredsystematicuncertainties.Itinanticipatedthatsomeversionofthisanalysiswill becarriedoutbytheSummerof2011,whentheLHCincreasestheamountofcollision databyoveranorderofmagnitude.Thisauthoreagerlyawaitsthisnewopportunityto possiblymakeadiscoverythatwillforeverchangeourunderstandingofthefundamental particles. 178

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APPENDIX:ANATOMYOFTHEOBSERVEDSIGNALEVENT Afterapplyingallthenalselectionrequirementson 35 pb 1 ofdata,asingleevent survivesfromthe ee channel.Event 156279004 wasrecordedduringLHCFill 1439 and CMSRun 148822 onOctober24,2010. A 3 -dimensionaldisplaydepictsthetopologyofthissurvivingeventinFigure A-1 Forillustrationpurposesthemuonsystemandtrackingdetectorsaresuppressed inthedisplay.Labelsdenotethereconstructedparticleowjets,thetwocandidate same-signelectrons,andtheparticleow E T vector.Tracksaredepictedingreenand aresuppressedbelow p T < 0.5 GeV.Hadronicandelectromagneticcomponentsofthe calorimetertowersarerepresentedbyblueandredrespectively.Energycomponents fromcalotowerswith E T < 0.3 GeVaresuppressed.Reconstructedparticleowjets areshowninturquoise,whiletheelectrontracksaredisplayedinblue.The E T vector isdepictedbyaredarrowandlabeled"PFMet".Therearetworeconstructedprimary verticeswhicharenotvisibleinFigure A-1 ,butbothelectronsemergefromthesame vertexlocatedat( 0.08593 cm, 0.0190 cm, 3.406 cm). Kinematicandotherdetailspertainingtothesereconstructedobjectsareprovided inTables A-1 A-2 ,and A-3 forthejets,electrons,and E T respectively.The H T calculationforthiseventyieldsavalueof 337.6 GeV,whichissafelyabovethethreshold usedintheanalysis.Noneofthejetsareidentiedasoriginatingfromb-quarksbythe "TrackCountingHighPurity"discriminatordenotedbythecolumnheading"B-Tag"in Table A-1 .Typically,b-jetswillhavevaluesabove 3.0 forthisvariable.Theleadingjet doespointdirectlytowardthetransitionregionoftheECALBarrelandECALEndcap, wherethejetenergyresponsecantendtobecompromised.Thiseffectshouldbe compensatedforbythejetenergyscalecorrectionsperformedontheparticleowjets. AscanbeseenfromFigure A-1 ,theeventisratherclean.Theelectronsarewell separatedfromoneanotheraswellasthejetsintheevent.Thelesserisolatedofthe twoelectrons(i.e. e 2 )justbarelypassesthe RelIso < 0.15 requirement(calculatedwith 179

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conesizeof R =0.3 );however,itwouldfailiftheconewereenlargedto R =0.4 whilethemoreisolatedelectronwouldcontinuetopasseasilyasisshowninTable A-2 Thismaybeahintthattheformermaynotactuallybeapromptelectron. Table A-3 showsthe E T calculationsasperformedbyvariousalgorithmswhichare executedduringtheeventreconstruction.ParticleFlow E T andTrack-CorrectedCalo! E T areconsideredtohavethebestperformanceandtheirmagnitudesagreetowithin 7 GeV.Theformer,whichisusedinthisanalysis,iswellbeyondtheselectionrequirement of 30 GeV. Moredatawillbeneededtodrawanyfurtherconclusionsabouttheviabilityofthis eventtoserveasacandidatefornewphysics.Itsobservationisperfectlyconsistentwith theStandardModelexpectationforthisanalysis. TableA-1.Summaryofjetcontentinobservedsignalevent Label P T (GeV) 2# (rad)EMFractionB-Tag R(jet, e 1 ) R(jet, e 2 ) J 1 156.91.47 2.140.3101.693.640.91 J 2 83.5 1.35 2.900.045 0.732.992.95 J 3 58.92.031.950.093 0.503.531.37 J 4 38.61.450.260.2940.202.593.00 TableA-2.Summaryofleptonsattributesinobservedsignalevent Label P T 2# q d 0 RelIso (GeV)(rad)(mm)(Cone= 0.3 )(Cone= 0.4 ) e 1 75.9 1.140.40 10.0150.0000.0458 e 2 20.01.60 3.04 1 0.0060.1440.363 TableA-3.Summaryof E T calculationsinobservedsignalevent Algorithm E T (GeV) # (rad) Particle-Flow E T 45.60.52 Track-correctedcalorimeter E T 52.60.66 Rawcalorimeter E T 23.51.00 TypeI-correctedcalorimeter E T 113.00.43 180

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FigureA-1. 3 Deventdisplayofthe ee eventobservedinthesignalregion 181

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BIOGRAPHICALSKETCH RonaldCharlesRemington("Ronny")wasborninDaytonaBeach,Florida toThomasandAngelRemington.RonnygrewupinOrmondBeach,Floridaand attendedSeabreezeHighSchool.Duringthewinterof2002,hewasinvitedtocompete againstahundredotherhighschoolstudentsfortheJamesEdwardOglethorpe(JEO) scholarship,aprestigiousawardthatgranted 4 yearsoffulltuition,roomandboardto attendOglethorpeUniversity,aselectiveliberalartsschoolinAtlanta,Georgia.The competitionfeaturedadiscussionsessionandawritingcomponent,witheachfocused onThomasKuhn'sphilosophicalwork,"TheStructureofScienticRevolutions".It wasduringhispreparationsforthiscompetitionthatherstencounteredsomeofthe revolutionaryideasthatinitiatedtheeraofmodernphysics.Hewasquicklyromanticized bytheseideas,andasaresultwasabletodiscussthemuentlyinthecontextofKuhn's work.Hisperformanceduringthecompetitionearnedhimthescholarship.Heaccepted andenrolledintheFallof2002asastudent-athleteplayingforthevarsitysoccerteam andasaJEOscholar.WhileatOglethorpe,RonnyearnedaB.Sc.degreeinphysics withhonorswithasecondmajorinmathematics.Upongraduatingheenrolledatthe UniversityofFloridaforgraduateschoolinphysics,wherehejoinedtheexperimental high-energyphysicsgroupandlatertheCMScollaborationunderthedirectionof ProfessorJohnYelton. 187