CONSTRAINTSONMODELSFORTHEHIGGSBOSONWITHEXOTICSPINANDPARITYByEmilyHannahJohnsonADISSERTATIONSubmittedtoMichiganStateUniversityinpartialful¯llmentoftherequirementsforthedegreeofPhysics-DoctorofPhilosophy2016ABSTRACTCONSTRAINTSONMODELSFORTHEHIGGSBOSONWITHEXOTICSPINANDPARITYByEmilyHannahJohnsonTheproductionofaHiggsbosoninassociationwithavectorbosonattheTevatrono®ersauniqueopportunitytostudymodelsfortheHiggsbosonwithexoticspinJandparityPassignments.AttheTevatrontheVHsystemisproducednearthreshold.Di®erentJPassignmentsoftheHiggsbosoncanbedistinguishedbyexaminingthebehaviorofthecrosssectionnearthreshold.TherelativelylowbackgroundsattheTevatroncomparedtotheLHCputusinauniquepositiontostudythedirectdecayoftheHiggsbosontofermions.IftheHiggssectorismorecomplexthanpredicted,studyingthespinandparityoftheHiggsbosoninalldecaymodesisimportant.InthisThesiswewillexaminetheWH!`ºb¹bproductionanddecaymodeusing9.7fb¡1ofdatacollectedbytheD0experimentinanattempttoderiveconstraintsonmodelscontainingexoticvaluesforthespinandparityoftheHiggsboson.Inparticular,wewillexaminemodelsforaHiggsbosonwithJP=0¡andJP=2+.WeusealikelihoodratiotoquantifythedegreetowhichourdataareincompatiblewithexoticJPpredictionsforarangeofpossibleproductionrates.Assumingtheproductioncrosssectiontimesbranchingratioofthesignalsinthemodelsconsideredisequaltothestandardmodelprediction,theWH!`ºb¹bmodealoneisunabletorejecteitherexoticmodelconsidered.WewillalsodiscussthecombinationoftheZH!``b¹b,WH!`ºb¹b,andVH!ººb¹bproductionmodesattheD0experimentandwiththeCDFexperiment.WhencombiningallthreeproductionmodesattheD0experimentwerejecttheJP=0¡andJP=2+hypothesesatthe97.6%CLandatthe99.0%CL,respectively,whenassumingthesignalproductioncrosssectiontimesbranchingratioisequaltothestandardmodelpredictedvalue.WhencombiningwiththeCDFexperimentwerejecttheJP=0¡andJP=2+hypotheseswithsigni¯cancesof5.0standarddeviationsand4.9standarddeviations,respectively.Copyrightby
EMILYHANNAHJOHNSON
2016Formyparents.vACKNOWLEDGMENTSI'vefoundparticlephysicsfascinatingsincehighschoolandithasbeenmyabsolutepleasuretobecomeacquaintedwiththe¯eldintheyearssincethen.Myinterestinphysicsaswellasthedriveanddeterminationnecessarytocompletemydegreedidnotsimplymaterializefromthevacuumbutweretheresultofmanypositivein°uencesfromthepeopleinmylife.Iwouldliketousethisspacetothankthosepeople.FirstandforemostIwouldliketothankmyparentsShelleyandDonaldJohnson.Icanattributemuchofmyloveofmathandsciencetotheirguidance.Theyfedmychildhoodcuriositybyalwaysattemptingtoanswermyquestionsfullyandbyengagingmeinactiv-itiesanddiscussionsthatpeakedmyinterests.Themostmemorableactivitiesinmyearlychildhoodwerethecraftingofhomemadeexperimentswithmymother.Wewatchedlimabeansandrockcandygrowinjarsandtriedto¯gureoutwhichsubstanceswouldslowtheaccumulationofrustonnails.Inadditiontofuelingmycuriositytheyalsogavemealotofencouragementandsupport.IalwaysknewthatIcouldtryforanycareer,evenonesthatwereseenasnon-traditional.Iwasshy,sosometimestheencouragementcameintheformofahealthyshove.Onesuchshoveinvolvedattendingamathandsciencemini-conferenceforgirlswhereIrealizedthat`scientist'couldbeavalidcareeroption.ForthesethingsandsomuchmoreIameternallygrateful.Ienteredhighschoolwithaninterestinscienceand¯lledmyelectiveswithadditionalscienceclasses.Ihadseveralgoodteacherswhoalldeservemythanks.Oneteacherinparticular,ThomasYocum,Icreditwithgettingmeinterestedinparticlephysics.Iaskedhimaquestionafterclassonedayandthediscussionledtohimlendingmeoneofhisbooksonspecialrelativity.AfterreadingthisbookIbegantoseekoutbooksonthetopicofviparticlephysicsthatwereaccessibletomylevel.Anotherpositivein°uenceduringhighschoolwasnotasinglepersonbutagroupofpeopleattheUniversityofMichiganwhoputtogethertheSaturdayMorningPhysicsseries.Theselectures(stillongoingatthetimeofthiswriting)showcaserecentresearchandaretailoredforthegeneralpublic.IappliedtoandgotacceptedbyMichiganStateUniversityasaphysicsmajorin2003.AsanundergraduateIhadmanypositiveexperiencesandopportunitiestolearnandgrowinthephysicsdepartment.ProbablylikemostphysicsundergraduatesthecourseIhadbeenanticipatingthemostwasquantummechanics.BothsemestersweretaughtbyWayneRepko.NotonlydidI¯ndhimtobeanexcellentteacherbutalsoagreatmentor.HeencouragedmetospendmysummersparticipatinginResearchExperienceforUndergraduates(REU)programsbothatMSUandRiceUniversity.Theseallowedmetoexperiencedi®erent¯eldsofphysicsresearch.WhenmyinterestskeptcomingbacktoparticlephysicsIaskedhimiftherewereanyresearchopportunitiesforanundergraduateinthedepartment.WetookawalkdownthehallandheintroducedmetoKirstenTollefsonandReinhardSchwienhorst.Theytookmeonandintroducedmetoparticlephysicsresearch.IwasabletolearnbybeinginvolvedinresearchatCDFandD0,thetwoexperimentsatthehighest-energyparticlecolliderintheworldatthattime.Itwastrulyanexcellentexperience.IamcertainthatIwouldnotbewhereIamtodaywereitnotfortheguidanceofthesethreepeople.Iwasinterestedingoingtograduateschoolandwasencouragedtoapply.SinceIfeltthatIhadfoundahomeatMSU,Idecidedtostay.The¯rstfewyearsofmygraduatecareerwerespentcompletingcourseworkandsupervisingundergraduatelabclasses.Istruggledsomewhatundertheloadandendedupbehindinsomeofmycourses.HereIreliedonmyfriendsandfellowgraduatestudents(youknowwhoyouare)whoworkedthroughproblemswithme.Iappreciateallofthosestudysessions.IwouldalsoliketothankVladimirviiZelevinsky;hedevotedmuchofhistimeafterclasstohelpstudentsworkthroughproblemsandprovideencouragement.IbegantoworkwithWadeFishershortlyafterhejoinedtheMSUdepartment.Iwasnervousinthebeginningtobeworkingwithsomeonenew,butWadehasatalentformakingmefeelatease.Hehasbeenanabsolutelywonderfuladvisor.Heisadedicatedteacherwhohasspentcountlesshourshelpingmetounderstandeverythingfromparticledetectorstostatistics.Hispatienceandencouragementhavebeeninvaluableduringmyyearsasagraduatestudent.Icouldnothaveaskedforabetteradvisor.AtMSUandD0Ihadthepleasureofworkingcloselywithmanypeopletosolvecommonproblemsandcollaborateonphysicsanalyses.Inparticular,IwouldliketoacknowledgeLidija·Zivkovi¶candKenHernerwhoweremycontactpointsandsurrogateadvisorsatD0.Theirhelpwiththisanalysisinparticularisgreatlyappreciated.IwouldalsoliketothankSavannaShaw,myco-graduatestudentunderWadeandanexcellentteacherinherownright.Herabilitytounderstandmythoughtsandanticipatemyquestionsisnearlyunrivaled.ThankstoBradSchoenrockandPatrickTruewhoinvitedmeouttosocialeventsandmademefeelincluded,andtoJamesKollwhoanswerednearlyallmycomputingquestions.Iwouldalsoliketothanktheo±cesta®atMSU,speci¯callyDebbieBarratt,KimCrosslan,andBrendaWenzlick,forhelpingmekeepitalltogether.Lastly,IwouldliketothankmypartnerBryanMoulewhohasbeenwithmeallthroughmyundergraduateandgraduateeducation.Hehasbeenanever-presentsourceofencour-agementandsupportandIamgladtohavehiminmylife.Fortherest:therearefartoomanypeopletolistherebyname,butknowthatyouhavemygratitude.viiiPREFACEParticlephysicsisafascinating¯eldandsomyhopeforthisThesisisthatitisreadilyaccessiblebyboththeveteransofthe¯eldandthosewhomaybeunfamiliarwiththe¯eld.TohelpwiththisgoalI'vedividedthisThesisintotwoParts.PartIisageneraloverviewofthetoolsusedinparticlephysicsaswellasatheoreticaloverviewofthe¯eld.PartIIexpandsonthisbackgroundinformationanddescribestheparticularsoftheresearchprojectthatformsthesubjectofthisThesis,fromthedevicesusedtogatherdatatothestatisticalanalysisandinterpretationofmyresults.Aveteranofthe¯eldwillbesatis¯edwithskippingPartIentirelytogetstraighttothespeci¯canalysisinPartII.SomeonelessfamiliarcanreadPartItogetabettergraspofPartII.ixTABLEOFCONTENTSLISTOFTABLES...................................xiiiLISTOFFIGURES..................................xivPartIIntroductiontoParticlePhysics.................1Chapter1Introduction...............................21.1FundamentalQuestions..............................21.2StandardModel&Predictions..........................41.3NotesonNotation................................51.3.1CoordinateSystems............................5
1.3.2MinkowskiSpaceandEinsteinNotation................71.3.3NaturalUnits...............................9Chapter2Tools...................................102.1ParticleAcceleration...............................102.1.1ElectrostaticAccelerators........................112.1.2OscillatingFieldAccelerators......................122.2ParticleProduction................................152.2.1FixedTarget...............................15
2.2.2Collider..................................17
2.2.3CollidingParticles............................192.3ParticleDetection.................................212.3.1MatterInteractions............................212.3.2Detectors.................................252.4Simulation.....................................272.4.1Generation................................27
2.4.2Propagation................................28Chapter3Theory..................................293.1Introduction....................................293.1.1ParticleZoo................................303.2StandardModel..................................323.2.1QuantumElectrodynamics........................343.2.2QuantumChromodynamics.......................35
3.2.3Glashow-Weinberg-SalamTheoryofWeakInteractions........383.2.4ElectroweakSymmetryBreaking....................403.3SearchingfortheHiggsBoson..........................443.3.1LEPSearches...............................46
3.3.2TevatronSearches.............................46x3.3.3LHCDiscovery..............................513.4BeyondtheStandardModel...........................513.4.1BSMHiggsSpin&Parity........................54PartIIConstraintsonModelsfortheHiggsBoson
withExoticSpinandParity..........................56Chapter4ExperimentalApparatus.......................574.1Introduction....................................574.2AcceleratingParticlesatFermilab........................584.3D0Detector....................................59
4.4ObjectReconstruction..............................624.4.1PrimaryVertex..............................62
4.4.2Jets....................................634.4.2.1Heavy-°avorJets........................654.4.3ChargedLeptons.............................664.4.3.1Electrons............................66
4.4.3.2Muons..............................67
4.4.3.3TauLeptons..........................684.4.4MissingTransverseEnergy........................68Chapter5ModelsfortheHiggsBosonwithExoticSpinandParity...705.1ThresholdProduction...............................715.2HelicityAmplitudes................................745.3InvariantMassasaDiscriminationTool....................76Chapter6Data&Simulation...........................816.1Data........................................826.1.1Luminosity................................82
6.1.2Triggers..................................836.2SimulatedSignalSamples............................856.3SimulatedBackgroundSamples.........................866.3.1V+jetsSamples..............................866.3.2DibosonVVSamples...........................876.3.3SingleTopQuarkSamples........................886.3.4TopQuarkPairt¹tSamples........................886.4MultijetSampleDerivation............................90Chapter7AnalysisMethod............................947.1EventSelection..................................957.1.1ReconstructingtheWBoson.......................957.1.2ReconstructingtheHiggsBoson.....................997.2MultivariateAnalysisTechnique.........................1027.3FinalObservable.................................102xiChapter8StatisticalAnalysis...........................1078.1TheHypothesisTest...............................107
8.2CLsMethod....................................1128.3SystematicUncertainties.............................1138.3.1ModelingUncertainties..........................1148.3.2TheoreticalUncertainties.........................1158.3.3JetSystematics..............................116
8.3.4LeptonSystematics............................117Chapter9ResultsandInterpretations.....................1189.1HypothesisConstruction.............................1199.2WXAnalysisResults...............................1209.2.1PureNon-SMJPStates.........................1229.3CombiningAnalyses...............................1269.4D0Combination..................................1289.4.1D0CombinationResults:PureNon-SMJPStates...........1319.4.2D0CombinationResults:AdmixturesofJPStates..........1349.4.3SummaryofD0Results.........................1359.5TevatronCombination..............................1379.5.1TevatronCombinationResults:PureNon-SMJPStates.......1389.5.2TevatronCombinationResults:AdmixturesofJPStates.......140Chapter10Conclusion................................141APPENDICES.....................................142AppendixATheFermilabAcceleratorChain....................143AppendixBTheD0DetectorinDetail........................159AppendixCAdditionalDistributions.........................185REFERENCES.....................................193xiiLISTOFTABLESTable1.1:LimitsofPhysicalLaws.........................4Table1.2:EinsteinNotationExamples......................9Table3.1:ThreeParticleFamilies.........................31Table3.2:FundamentalParticles..........................33Table6.1:IntegratedLuminosity..........................83Table6.2:SignalCrossSectionTimesBranchingRatio.............86Table6.3:W+JetsEventSample.........................88Table6.4:Z+JetsEventSample..........................89Table6.5:DibosonandTopQuarkBackgrounds.................91Table7.1:WXEventSelection..........................96Table8.1:SystematicUncertainties........................114Table9.1:SignalNormalizations..........................120Table9.2:D0CLsValuesfor¹=1:0.......................125Table9.3:D0CLsValuesfor¹=1:23.......................126Table9.4:D0Combinationp-Values........................134Table9.5:ExpectedandObservedCLsValues..................136Table9.6:Tevatron1¡CLsValues........................139TableC.1:ExpectedandObservedp-Valuesfor¹=1:23.............192xiiiLISTOFFIGURESFigure1.1:CoordinateSystems...........................6Figure1.2:PseudorapidityandPolarAngle....................7Figure2.1:Cockcroft-WaltonGenerator......................12Figure2.2:Wider¿eAccelerator...........................13Figure2.3:MicrowaveFrequencyCavities.....................14Figure2.4:MeanEnergyLossRate.........................23Figure2.5:ParticleDetectorSignatures......................26Figure2.6:SingleTopQuarkProduction......................28Figure3.1:ScalarPotential.............................42Figure3.2:IndirectHiggsBosonMassConstraints................45Figure3.3:HiggsBosonDecayBranchingRatios.................47Figure3.4:HiggsBosonMassConstraintsfromLEP...............47Figure3.5:DominantHiggsBosonProductionModes...............48Figure3.6:TevatronHiggsBosonProductionCrossSections...........48Figure3.7:TevatronHiggsBoson95%CLLimits.................50Figure3.8:TevatronLog-LikelihoodRatio.....................50Figure3.9:LHCLocalp-Values...........................51Figure4.1:FermilabCampus............................58Figure4.2:D0Detector...............................61Figure4.3:CentralD0Detector...........................62xivFigure4.4:Heavy-°avorTagging..........................66Figure5.1:WHAssociatedProduction.......................71Figure5.2:ProtonPartonDistributionFunctions.................72Figure5.3:TevatronPartonKinematics......................73Figure5.4:SimpleModeloftheInvariantMassoftheZX!``b¹bSystem...78Figure5.5:SimpleModeloftheTransverseMassoftheWX!`ºb¹bSystem..79Figure6.1:RecordedLuminosity..........................82Figure6.2:SingleTopQuarkProductionDiagrams................89Figure6.3:TopQuarkPairProductionDiagram.................90Figure7.1:WHAssociatedProduction.......................94Figure7.2:LeptonpT................................97Figure7.3:MissingTransverseEnergy.......................98Figure7.4:TransverseMassoftheReconstructedWBoson...........98Figure7.5:JetpT...................................99Figure7.6:Averageb-TaggingMVAOutput....................100Figure7.7:DijetInvariantMass...........................101Figure7.8:BDTOutput...............................103Figure7.9:TransverseMassoftheWXSystem,High-PurityRegion......105Figure7.10:TransverseMassoftheWXSystem,Low-PurityRegion.......106Figure8.1:ExampleLLRDistributions......................113Figure9.1:TransverseMassoftheWXSystem,High-PurityRegion......121Figure9.2:Log-likelihoodRatioDistributionsforJP=0¡............123Figure9.3:Log-likelihoodRatioDistributionsforJP=2+............124xvFigure9.4:VHAssociatedHiggsBosonProduction................128Figure9.5:ZH!``b¹bandVH!ººb¹bDijetInvariantMass..........129Figure9.6:InvariantMassoftheZHSystem...................130Figure9.7:TransverseMassoftheVHSystem..................131Figure9.8:D0CombinationLLRDistributionsfor¹=1:0............132Figure9.9:D0ObservedandExpectedExclusionRegions,PureJPStates...133Figure9.10:CLsasaFunctionoftheNon-SMSignalFraction..........135Figure9.11:D0ObservedandExpectedExclusionRegions,Admixtures.....136Figure9.12:LLRDistributionsfortheTevatronCombination...........139Figure9.13:TevatronObservedandExpectedExclusionRegions,Admixtures..140FigureA.1:SurfacePlasmaMagnetronSource...................144FigureA.2:ProtonSourceandAcceleratingColumn................145FigureA.3:Side-CoupledLinacSection.......................147FigureA.4:Nose-ConeField.............................148FigureA.5:400MeVChopper............................149FigureA.6:ChargeExchangeInjection.......................150FigureA.7:AccumulatorStackPro¯le.......................155FigureB.1:D0Detector...............................159FigureB.2:D0MagneticField............................162FigureB.3:D0SiliconMicrostripTracker......................165FigureB.4:CalorimeterCell.............................170FigureB.5:CalorimeterReadoutTowers......................170FigureB.6:D0MuonWireChambers........................175xviFigureB.7:D0MuonScintillator..........................176FigureB.8:ForwardMuonScintillator.......................178FigureC.1:InvariantMassofthe``b¹bSystem...................186FigureC.2:TransverseMassofthe`ºb¹bSystem,High-PurityRegion......187FigureC.3:TransverseMassofthe`ºb¹bSystem,Low-PurityRegion.......188FigureC.4:TransverseMassoftheººb¹bSystem..................189FigureC.5:D0LLRDistributionsfortheJP=0¡Hypothesis..........190FigureC.6:LLRDistributionsfortheJP=2+Hypothesis............191xviiPartIIntroductiontoParticlePhysicsPartIintroducestheconceptsessentialtounderstandinganyparticlephysicsexperi-ment.Chapter1servesasanintroductiontothe¯eld.ThenotationalinformationgiveninSection1.3willbeusefulthroughoutthisThesis.Chapter2introducesthetoolsusedbyparticlephysiciststoconductresearch.Itdescribestheequipmentnecessarytoaccelerate,produce,anddetecthighenergyparticles.AgeneraloverviewofthetheoreticalstructureisgiveninChapter3withspecialconsiderationgiventoelectroweaksymmetrybreakingandHiggsbosonphysics.1Chapter1
Introduction
1.1FundamentalQuestions
Themeaningofwhatistrulyafundamentalparticlehaschangedthroughoutthecenturies.Theatom,fromtheGreekatomosmeaning`indivisible',iscomposedofseveralparticles,sometrulyfundamentalandsomecomposite.FromexperimentsbyJ.J.ThompsonandRutherforditwasdiscoveredthattheatomconsistsofahaloofverylightnegativelychargedparticles(electrons)withaheavypositivelychargednucleusatthecenter.Rutherfordnamedthenucleusofthelightestelementhydrogen`proton'.Sincehydrogeniselectricallyneutralitwasassumedtocontainoneelectron.Itseemednaturaltoexpandthisideatoheavierelementswitheachhavingonemoreprotonandelectronthantheprevious.Whilethisisindeedtrue,itwasnotobviousfromthestartbecauseinsteadofweighingtwiceasmuchashydrogen,heliumweighedfourtimesasmuch.However,heliumdidcontaintwoelectrons,sowheredidtheextramasscomefrom?Thismysterywasn'tresolveduntilthediscoveryoftheneutronbyChadwick.Forafewyears,allmatterwasperceivedtobemadeupofprotons,neutrons,andelectrons.Physicistsatthistimewereonlyfamiliarwiththetwoforcesthatcanbeseenatworkinordinarymacroscopicexperiments:electromagnetismandgravity.ElectromagnetismwasformulatedbyMaxwellinthe1860s.Maxwell'sequationsrequiredthatthespeedofelec-tromagneticwaves(includinglight)inavacuumbeconstant.Thisledtotheideathat2thereexistedauniqueframeofreferenceinwhichelectromagneticwavespropagatedandMaxwell'sequationsheld.This(almostmagical)frameofreferencewasnamedtheaether.Indeed,astimewentonitspropertiesbecamemoreandmorefanciful;itneededtobea°uidto¯llallspacebutalsobeveryrigidtoaccommodatethehighfrequenciesofelectro-magneticwaves.Manyotherproblemsplaguedthenotionoftheaether,nottheleastofwhichwasthecontinualnegativeresultsofexperimentsdesignedtodirectlydetectit.ThefamousMichelson-Morleyexperimentin1887isfrequentlythoughtofastheturningpointinthebeliefintheexistenceoftheaether.Theyfoundthatabeamoflighttravelinginthesamedirectionasthemotionoftheearththroughtheaetherdoesn'ttakeanylongertotravelthanabeamtravelingperpendiculartothemotion.Intheend,Einsteindevelopedthetheoryofspecialrelativitythatdidn'trelyontheexistenceoftheaetherandperfectlyexplainedtheformofMaxwell'sequations.Theconstantspeedoflightinavacuum,alongwiththeprincipleofrelativity,becamethepostulatesofspecialrelativity.Inthe1910sEinsteindevelopedgeneralrelativityasarelativisticdescriptionofgravity.Itchangedthewaythecommunitythoughtaboutspaceandtime.Spacewasnolongeranunchangingvoidbutsomethingthatwasintricatelyrelatedtotime.Massandenergychangetheverynatureofspace-timeandcauseittocurve.Planetsorbitingstarsfollowcurvedpathslikemarblesonarubbersheet,respondingtothelargemassofthestar.Atthistimeitwaswellknownthattheelectronsandprotonswereboundbytheelec-tromagneticforceduetotheiropposingcharges.Bohr'sclassicaldepictionofhydrogenasasingleelectronorbitingaprotonwasverysuccessful.Whatheldtogetherthetightlypackedprotons?Sincetheyallhavethesamechargetheyshouldbeforcedapart.Itwasclearthattherewasanotherforceatwork.Whatwasitssource?Weretheproton,neutron,andelectrontrulyfundamentalparticles?Questionslikethesehavesincebeenansweredandnew3oneshavecometotaketheirplace.Thegoalofparticlephysicshasbeenanunderstandingofthefundamentalparticlesandtheforcesthatguidetheirinteractions.1.2StandardModel&Predictions
The¯eldofparticlephysicsexistsbecausethelawsofphysicsusedforspeedingtrainsand°yingcannonballsbreakdownforverysmallandveryfastobjects1.Objectsareconsidered`relativistic'(i.e.veryfast)iftheirspeedisclosetothespeedoflightc.Thebehaviorofsub-atomicparticlescanbedescribedbyquantummechanics.AvisualizationofthetheoriesthatareusedtodescribetheseregimescanbeseeninTable1.1.Thetheoriesthatdealfaster)smallerClassicalRelativisticv¿cv»c+QuantumQuantumFieldTheoryTable1.1:LimitsofPhysicalLawsAvisualizationofthephysicaltheoriesinthehigh-velocityandsmall-scaleregimes.withverysmallandveryfastparticlesarequantum¯eldtheories(QFT).Eachfundamentalforce(withtheexceptionofgravity)hasacorresponding¯eldtheorythatdescribeshowthefundamentalparticlesinteractunderitsin°uence.Thecollectionofthesetheoriesiscalledthestandardmodel(SM)ofparticlephysics.TheSMcanmakepredictionsonthetypesofinteractionsthatcanoccur,whataparticlecandecayto,andeventheexistenceofparticles.Wecanusethesepredictionsasatestofthemodel.Ifthepredictionsdon'tdescribereality,thenattheveryleastthemodelmustbeincomplete.Intheworstcase(or1Itisforthisreasonthatparticlephysicsisalsocalledhighenergyphysics{thehighvelocityoftheparticlescorrespondstotheirhighenergy.4themostinterestingcase,dependingonyourpointofview)themodelwillhavetoberebuilt.Newpredictionswilleitherpointtothemodelbeingcorrectoranotherreevaluationofthemodel.Thiscycleoftestingandreevaluationisthescienti¯cmethod.Observationsmadeleadtoahypothesisabouthowtheworldworkswhichinturnleadstopredictionsbasedonthehypothesis.Thesepredictionsareeithercon¯rmedandthehypothesisisstrengthenedorinvalidatedandthehypothesisdiscarded.Particlephysicsissimplythescienti¯cmethodatworkwiththeSMasitstestablehypothesis.
1.3NotesonNotation
Itisprudentheretosummarizeafewnotationalquirkspresentinparticlephysics.Thissectionisdividedintoinformationoncoordinatesystems,theEinsteinsummationconven-tion,andnaturalunits.Thissectionalsohasseveraluseful¯guresdescribingthecoordinatesystemthatweuseinparticlephysicsthatmaybeusefultorefertointhefollowingchapters.1.3.1CoordinateSystems
Becauseofthephysicaldesignofparticlephysicsexperiments,thecoordinatesystemweusewhendescribingvariousaspectsoftheexperimentalsideofthe¯eldisnotthecarte-siancoordinatesystem.Collidingparticlesnaturallyleadstoacoordinatesystemwheretheincomingparticles'trajectoriesarealignedalongtheaxisofacylinder.Becausetheenergiesofthecollidingparticlesarehigh,theparticlesthatareproducedatthecollisionpointpreferentiallyhavetrajectoriesthatareatasmallanglerelativetotheaxis.Itisforthisreasonthatparticledetectorsarecylindricalindesign.However,becausetheparticlesproducedoriginatefromacollisionpoint,itisconvenienttode¯netrajectoriesbytheangle5relativetotheaxis.TheendresultofthisisthecombinationofthesphericalandcylindricalcoordinatesystemsillustratedinFig.1.1.WeusethezcoordinateofthecylindricalsystemFigure1.1:CoordinateSystemsDepictionsofthecylindricalandsphericalcoordinatesystems[1,2].Inparticlephysicsthenamingconventionisreversedfor#and'.astheaxisofourdetector.Thepolaranglefromthesphericalsystemistheanglethatde¯nesthetrajectoriesoftheparticlesproducedatthecenterofthedetector.Finally,theazimuthalanglecommontoboththecylindricalandsphericalcoordinatesystemscompletesourcoordinatesystem.Whilethesecoordinateswouldbesu±cienttodescribeparticlesintheexperimentalsetup,oneadditionalchangeisuseful.Anewquantitypseudorapiditydenotedby´isde¯nedas´=¡ln·tanµ#2¶¸(1.1)where#isthepolarangle.Therangeofthefamiliarcoordinate#is0·#·¼whiletherangeof´is¡1<´<1asimpliedbyEq.1.1.Figure1.2showsboththepolarangleandthepseudorapidityvariableforafewvaluesofeach.Theadvantageofusing´insteadof#isthatparticleproductionistypicallyuniforminpseudorapidity,butnotinpolarangle.66p = q2p = q6p5 = q = 0h = 1h = 2h34 = -2h = -1h+z+yFigure1.2:PseudorapidityandPolarAngleAcomparisonofpseudorapidity´andpolarangle#forseveralvaluesofeach.1.3.2MinkowskiSpaceandEinsteinNotation
Thetheoriesinparticlephysicsareformulatednotintraditionalthree-dimensionalEuclideanspacebutinafour-dimensionalspacecalledMinkowskispace-time.ThefourdimensionsofthisspaceconsistofthethreeEuclideanspatialdimensionsandonetimedimension.Thestandardbasisusedbyparticlephysicistsisthesetoffourmutuallyorthogonalvectorse¹suchthate0=¡e1=¡e2=¡e3=1wheree0isthetimecomponent.Thiscanbewritteninamorecompactform:g¹º=g¹º=0
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C
A(1.2)whereg¹ºiscalledtheMinkowskimetric.VectorsinMinkowskispacearecalledfour-vectors.Perhapstwoofthemosteasilyrecognizablefour-vectorsaretheposition-timefour-vector7x¹=(ct;x;y;z)andthefour-momentumP¹=¡Ec;px;py;pz¢.Whetherornottheindicesaresuperscriptorsubscriptdependsonwhetherthevectorsarecontravariantorcovariant,respectively.Covariantvectorshavecomponentsthattransformunderthesamematrixthattransformsthebasis;theyco-varywithachangeinbasis.Contravariantvectorscontra-varywithachangeinbasis{theircomponentstransformundertheinverseofthematrixthattransformsthebasis.UsingtheMinkowskimetricwecanraiseorlowertheseindices(ine®ectchangingwhetherthevectorsarecovariantorcontravariant)inthefollowingway:A¹=3Xº=0g¹ºAºA¹=3Xº=0g¹ºAº(1.3)whereg¹º=(g¹º)¡1=g¹º.InthisThesiswewilluseEinsteinnotation,asummationconventionthatiscleanandconcise.Inthisconventionatermwithrepeatedindicescarriesanimpliedsummationofthetermoverallvaluesoftherepeatedindex.Table1.2showsexamplesofcommonoperationsinboththetraditionalnotationandEinsteinnotationforthreedimensionsusinganorthogonalbasis.ThisnotationallowsustorewriteEq.1.3asA¹=g¹ºAºA¹=g¹ºAº(1.4)wheretheimpliedsummationisoverthefourspace-timecomponents.Throughoutthistextquantitiesinthree-dimensionalspacewillhaveindicestakenfromtheLatinalphabet(whosevalues2f1;2;3g)whilequantitiesinfour-dimensionalspace-timewillhaveindicestaken8fromtheGreekalphabet(whosevalues2f0;1;2;3g).QuantitySummationFormulationEinsteinNotationVectorDotProductc=a¢bc=3Pi=1aibic=aibiVectorCrossProductc=a£bci=3Pj=13Pk=1²ijkajbkci=²ijkajbkMatrixMultiplicationC=ABCik=3Pj=1AijBjkCik=AijBjkTracea=Tr(A)a=3Pi=1Aiia=AiiTable1.2:EinsteinNotationExamplesCommonoperationsinvolvingvectorsandmatricesinthreedimensionsusinganorthogonalbasis.
1.3.3NaturalUnits
Becausethetheoriesthatdescribeparticlephysicsarerelativisticquantum¯eldtheories,thespeedoflightcandthereducedPlanckconstant~makeanappearanceinmanyequations.Tosimplifyourequationsweuseasystemofnaturalunitswhere~=c=1:(1.5)Inthissystemtheunitsofmass,length,momentum,andtimearenowgivensolelyintermsofenergy.Themostcommonunitforenergyweworkwithinparticlephysicsistheelectronvolt(eV).Thisisthechangeinenergyofanelectronmovingacrossapotentialdi®erenceofonevolt.AlthoughnotanSIunitweusethestandardSIpre¯xes,mostcommonlythegiga-electronvolt(GeV).MassandmomentumwillbeinGeVwhilelengthandtimewillbeinGeV¡1.9Chapter2
Tools
Tostudyelementaryparticlesweneedtobeabletoproducethem,recordtheirinteractions,andtheninterprettheresults.ThisChapterwillbededicatedtothebasicsofparticleproductionanddetection.Itwillbebuiltuponinlaterchapterswithdescriptionsofthemachineryspeci¯ctothisDissertation.
2.1ParticleAcceleration
Toproduceinterestingandpossiblynever-before-seenparticleswecollidematterathighenergy.The¯rststepinsettingupthesecollisionsistheaccelerationofparticlestovelocitiesapproachingthespeedoflight.Currenttechnologiesusingaccelerating¯eldsnecessitatetheuseofelectrically-chargedparticles.ThereareseveralacceleratingschemesbutallarebasedontheLorentzforce:F=q(E+v£B)(2.1)whereqisthechargeoftheparticle,visitsvelocity,andEandBaretheelectricandmagnetic¯elds,respectively.Becausetheforceduetothemagnetic¯eldisperpendiculartotheparticle'svelocityitcannotbeusedtoacceleratetheparticle1.Thismeansthatallparticleaccelerationisdoneusingelectric¯elds.1Technicallythemagnetic¯eldcannotbeusedtoaccelerateaparticleinthedirectionofitsvelocity{itcanbeusedtoaccelerateaparticleperpendiculartoitsdirection,adetailthatwillbediscussedlaterinthesection.102.1.1ElectrostaticAccelerators
Thesimplesttypeofacceleratorusesastaticelectric¯eldtoimpartenergytoastreamofchargedparticles.Thisstaticelectric¯eldisproducedbygeneratingaconstantvoltagedi®erence,similartothe¯eldbetweencapacitorplates.Forafreetestchargeqmovinginauniformelectric¯eldtheenergygainedbythetestchargeisequaltotheworkdoneW=¡q(Vf¡Vi)(2.2)whereVfandViarethe¯nalandinitialvoltagerespectively.Negativetestchargeswillaccelerateinthedirectionoppositetheelectric¯eldandpositivetestchargeswillaccelerateinthedirectionoftheelectric¯eld.Toincreasetheenergygainedbytheparticlesyoucanincreasetheirchargeoryoucanincreasethevoltagedi®erencetheyacceleratethrough.Dependingontheparticlespeciesitispossibletoaddorremoveelectronstoincreasetheabsolutevalueofthecharge.Typicallythereisalimittotheamountofchargeyoucanaccumulatesowelooktoincreasingthevoltagedi®erence.Thehighvoltagesrequiredbyparticlephysicsexperimentsareobtainedbyspecializedvoltagegenerators.WhilethereareseveralschemesforgeneratingthesehighvoltageswewilldiscusstheonethatisusedtoaccelerateparticlesatFermilab:theCockcroft-Waltongenerator.TheCockcroft-Waltongeneratorisavoltagemultiplierconsistingoftwostacksofcapac-itorslinkedbydiodesasshowninFig.2.1andissometimesreferredtoastheCockcroft-Waltonladder.Thecapacitorsontheleftholdachargeandcoupletothealternatingcurrent(AC)voltagesourceatthebottomofthestackwhilethecapacitorsontheleftareDC;thechargeonthemisconstant.Duringthenegativehalf-cyclethecapacitorsontheleftarecharged.Thecapacitorsontherightarechargedduringthepositivehalf-cycle.Figure2.111Figure2.1:Cockcroft-WaltonGeneratorSchematicofatypicalCockcroft-Waltongenerator.
showsonlytwostagesofaCockcroft-Waltonladder,morecanbeaddedontoincreasetheoutputvoltage.ForaCockcroft-Waltonladderwithnstagesthe¯naloutputvoltageis2nV0.Intermsofhighenergy,thedrawbackofelectrostaticacceleratorsistherelativelylowhigh-voltageceilinglimitedbytheelectricalbreakdownofair.Gaseswithahigherdielectricconstantsuchassulfurhexa°uoridecanbeusedtoincreasethevoltagelimit.ThisgasisverycommonlyaddedtobothCockcroft-WaltonandVandeGraa®generators.Gettingparticlestotheextremelyhighenergiesusedtodayrequiresadi®erentmethodofacceleratingparticlesusingelectromagnetic¯elds.
2.1.2OscillatingFieldAccelerators
RolfWider¿e'sresonanceacceleratoriswidelyknownastheprogenitorofallmodernoscil-lating¯eldaccelerators.Itsdesigne®ectivelyside-stepsthebreakdownproblembyusingseveralconsecutivelowvoltagepushes.AschematicofasimpleWider¿eacceleratoris12showninFig.2.2.Aparticleexitingthesourcepassesthroughanumberofhollowcylin-Figure2.2:Wider¿eAcceleratorSchematicofasimpleWider¿eresonanceaccelerator.dricalelectrodesconnectedtoanACvoltagesourceinsuchawaythatadjacentelectrodescarryopposingpolarity.ThefrequencyoftheACvoltagesourceissuchthatwhenaparticleiscrossingagaptheaccelerating¯eldisatamaximum.Theparticlesreceiveakickfromtheelectric¯eldinthegapandaccelerate.Onceinsidethecylindricalelectrodestheparticlesareshieldedfromtheelectromagnetic¯eldanddriftdownthetubeatconstantvelocity.Itisforthisreasonthatthecylindricalelectrodesarereferredtoasdrifttubes.Whentheparticlesexitthedrifttubethepolarityhasreversedandthe¯eldonceagainacceleratestheparticles.Thisdoesnotallowcontinuousaccelerationofabeamofparticles.Instead,particlesmustbeacceleratedinbunches.Tokeeptheparticlesinphasewiththeaccelerating¯eldastheirvelocityincreasesthelengthsofthedrifttubesareincreased.Asparticlesasymptoticallyapproachthespeedoflight,however,thevelocitygain(andhencethelengthdi®erenceinthedrifttubes)issmall.Manyoscillating¯eldacceleratorsoperateinthesamemannerastheWider¿eacceleratorwithoneimportantimprovement¯rstmadebyLuisAlvarez.Inordertokeepthelengthof13thedrifttubesatareasonablesizethefrequencymustbeincreased.However,athighfre-quenciestheWider¿eacceleratorlosesenergythroughelectromagneticradiation.Alvarez'ssolutionwastoplacetheWider¿eapparatusinsideanevacuatedconductingcavity.Thedrivingpoweriscoupleddirectlytotheinsideofthecavityandtheelectromagnetic¯eldsarecontainedinsidetheconductor.Furthermore,iftheresonancefrequencyofthecavityisequaltothatoftheaccelerationfrequencytheenergytransferisthemoste±cient.Varia-tionsonthisdesignleadtomanydi®erenttypesofcavitiesthatdi®erinsize,shape,andconductingmaterial.Examplesofdi®erentcavitiesthatoperateinthemicrowavefrequencyrangeareshowninFig.2.3.Figure2.3:MicrowaveFrequencyCavitiesExamplesofcavityshapesthatoperateinthemicrowavefrequencyrange.AnAlvarezdrifttubecavityandasuperconductingcavitymadetooperateatverylowtemperature.Adevicewhichhasanadvantageoverthelinearacceleratorsisthesynchrotron.Accel-erationisdoneatoneormoresitesalongaringandtheparticlecanmakemanypassesthroughtheacceleratingregion(s),gainingenergywitheveryturn.Theparticlesaresteeredusingmagnetslocatedaroundthering.Theparticles'orbithasa¯xedradiusmadepossiblebyincreasingthe¯eldstrengthofthemagnetsastheparticlesaccelerate.Withthedevel-opmentofstrongfocusing,theconceptthatalternatingfocusinganddefocusingmagnetswillhaveanetfocusinge®ectonthebeam,wecanseparatethethreefunctionsofthesyn-14chrotron:acceleration,steering,andfocusing.Theaccelerationistypicallydoneinstraightsectionswithmicrowavefrequencycavities.Thesteeringishandledwithmagneticdipolesandthefocusingisdonewithquadrupoleandhighermultipolemagnets.Mostacceleratorsthatoperateonthehigherendoftheenergyspectrumaresynchrotrons.2.2ParticleProduction
Relativistickinematicsallowsfortheproductionofnewmatterthroughtheconservationofenergyandmomentum.Collidingparticlesathighenergyandexaminingtheparticlesthatareproducedasaresultistheprimarywayparticlephysicistsinvestigatefundamentalparticlesandtheirinteractions.
2.2.1FixedTarget
Onewaytocollidematteristouseparticlestostrikeatargetmaterial.Thiswasthemodeofoperationformanyyearsinthe¯eld.TheBevatron(namedforitsabilitytoimpartbillionsofelectron-voltsofenergy)atLawrenceBerkeleyNationalLab(LBNL)wasamachinethatacceleratedprotonsintoa¯xedtarget.The¯rstantiprotonwasdiscoveredusingtheBevatronatLBNL.Asanexampleofrelativistickinematicsandthecreationofaparticlewecancalculatetheminimumenergyrequiredtoproduceaproton-antiprotonpair.Thereactioncanbewrittenasfollows:p+p!p+p+p+¹p:(2.3)15Havingjustenoughenergytocreateaproton-antiprotonpairwouldmeantherewouldbenoextraenergyleftoverforthekineticenergyoftheproducts.Itmaybehardtoformulateconditionsforthisintheframeofreferenceofthelabbutitisrelativelyeasyinthecenterofmomentum(CoM)frame,wherethetotalmomentumofthesystemiszero.Inthisframeafterthecollisionalloftheproductswouldbeatrest.TosolvethisproblemwecanusetheLorentzinvarianceofthedotproductoftwofour-vectors,vectorsinfourdimensionalspace-time.Thismeansthatthedotproductoftwofour-vectorsisthesameinanyframeofreference.Four-momentum,P¹,isafour-vectorwithcomponentsofenergyandthreespatialcomponentsofmomentum.Theconservationofenergyandmomentummustbesatis¯edandappearsastheconservationoffour-momentum.WebeginbywritingP¹inthelabframebeforethecollisionandP0¹afterthecollisionintheCoMframe:P¹=0
B
B
B
B
B
B
B
B
B
@E+mjpj0
01
C
C
C
C
C
C
C
C
C
AandP0
¹=0
B
B
B
B
B
B
B
B
B
@4m0
0
01
C
C
C
C
C
C
C
C
C
A(2.4)whereEandparetheenergyandmomentumoftheincidentparticleandmisthemassoftheproton.Becausetheyareexpressedindi®erentframesofreferenceP¹andP0¹arenotequal.WecanremedythisbyusingtheLorentzinvarianceofthedotproductoftwo16four-vectors:P¹P¹=µE+mjpj00¶0
B
B
B
B
B
B
B
B
B
@E+m¡jpj0
01
C
C
C
C
C
C
C
C
C
A=(E+m)2¡jpj2(2.5)P0¹P0¹=(4m)2:(2.6)BysettingEquations2.5and2.6equalandusingtherelativisticenergy-momentumrelationE2=jpj2+m2toeliminatejpj,wegettheresultthattheincidentprotonmusthaveakineticenergyequaltosixtimesitsrestmass,approximately6000MeV.ThisisveryclosetotheBevatron'soperatingenergywhentheantiprotonwasdiscoveredtherein1955[3].Thisexerciseillustratesamajordisadvantageof¯xedtargetexperiments;muchoftheinitialkineticenergyisunavailableforcreatingnewmass.Therestenergyofsixprotonsisneededtocreatetwo.Inasensethisenergyis`wasted'inthekineticenergyofthe¯nalproducts.Whatifthecenterofmomentumframewasthelabframe?Itwouldthenbepossibletocreateparticlesatrestinthelabframewithoutwastinganyenergy!While¯xedtargetexperimentscertainlystillhavetheiruse,ifyouwantthemostenergyavailableforparticlecreationyoubetterbuildacollider.
2.2.2Collider
Colliderssolvetheproblemof¯xedtargetexperimentsbyhavingtheCoMframecoincidewiththelabframe.Ifweassumethattheprotonscollidehead-onwithanequalkinetic17energythefour-momentainthelabframebeforeandafterare:P¹=0
B
B
B
B
B
B
B
B
B
@2(E+m)0
0
01
C
C
C
C
C
C
C
C
C
AandP0
¹=0
B
B
B
B
B
B
B
B
B
@4m0
0
01
C
C
C
C
C
C
C
C
C
A:(2.7)RepeatingthecalculationinSection2.2.1we¯ndthatifeachprotonisgivenakineticenergyequaltoitsrestmass(¼940MeV)wecancreateaproton-antiprotonpair.Thisisindeedmuchlessenergythanisrequiredbyanequivalent¯xedtargetexperiment.Whileitisillustrativetothinkofcollidingtwosingleparticles,realitymakesthisdi±cultifnotimpossible.Weinsteadrelyonacceleratingmanyparticlesatatimeinabeamandcollidingbeamsinsteadofindividualparticles.AnimportantquantityincollidingbeamexperimentsistheinstantaneousluminosityL,thenumberofparticlespassingthroughaplaneperunittimeperunitarea.Thehighertheinstantaneousluminosity,themorechancesthereareforinteractionstooccur.Theluminosityofaparticularbeamofparticlesisdependentonthephysicalaspectsofthebeam,e.g.itssize,particlecomposition,andnumberofparticles.Relatedtoluminosityistheconceptofacrosssection,usuallydenotedby¾,withunitsofarea.Thetermcomesfromscatteringexperimentswhereparticlesareimpingedonahardsphere.Ascatteringeventwilloccuriftheincidentparticleiswithinacirculararea,thehardsphere'scrosssection.Collisionsinparticlephysicsarenotassimpleasacollisionwithahardsphere,butthetermhasstuck.Interactionboundariesarefuzzysodirectcontactisnotnecessaryforaninteractiontooccur,unlikethehardspherescattering.Additionally,thereareavarietyofoutcomeseachwiththeirownprobabilityduetothequantummechanicalnatureoftheinteraction.Forthesereasons,thecrosssectionisnota18physicaldescriptionofthesizeofaparticle,butratherane®ectivecrosssectionofaclearly-de¯nedprocess.Aprocesswithasmallcrosssectionisarareevent;theprobabilityforittooccurissmall.Knowingtheinstantaneousluminosityandaprocessyouareinterestedin,itispossibletocalculatehowmanyofthoseeventsyoucanexpectperunittime:dNdt=¾L(2.8)whereNisthenumberofevents.IntegratingbothsidesofEq.2.8tellsusthatwecanexpectNeventsequaltothecrosssectionmultipliedbytheintegratedluminosity,Lint=RLdt.Oneimportantthingtonoteisthatthecrosssectionforaprocesscanbemeasuredatanycollidingexperimentprovidedyoucanmeasuretheluminosityandcountthenumberofevents.
2.2.3CollidingParticles
Therearemanythingstoconsiderwhendecidingwhattypeofparticlestocollide.Maybethemostimportantoftheseischoosingarelativelylong-livedandchargedparticle.Itisimportanttouselong-livedparticlesthatwillnotdecaybeforetheyhaveachancetocollide.Thisisespeciallyimportantincycliccolliderswherethebeamsmaybeinrotationforhours.Havingachargedparticleisnecessarybecauseacceleratingtheparticlesisdoneusingelectromagnetic¯eldsormagnetic¯elds.Protonsandelectronsarebothchargedandverystableparticlesthataregoodcandidatesforcolliders.Anotherconsiderationiswhethertheparticleispoint-likeorcomposite.Collidingpoint-likeparticleslikeelectronsisamuchcleanerprocessthancollidingprotonsbecausetherearefewerparticlesinthe¯nalstate.Protonshavethreevalencequarksandtypicallyonly19onequarkisinvolvedinacollision,therestrecombinetoformadditionalparticles.Theseadditionalparticlesnotinvolvedinthemaininteractionnonethelessleavesignaturesinthe¯nalstateandaredetectedwiththoseproducedinthemaininteraction.Weedingouttheseadditionalparticlesisdi±cultandtheprecisionofthemeasurementsu®ers.Additionally,itisdi±culttoaccuratelycalculatetheenergyofthecollisionbecausethetotalenergyoftheparticleisdividedbytheconstituents.However,thiscurseisalsoagift;therearemoretypesofinteractionspossiblewithcompositeparticles.Ifthegoalisprecisionmeasurementsthenelectronsarethewaytogo.Ifontheotherhandthegoalisdiscoveryofnewphysicsthenprotonsaretheparticleofchoice.Sofarwe'veassumedthatbothparticlesinthecollisionareidenticalparticles.Anotherpossibilityistheuseofantiparticles:particleswiththesamemassbutoppositecharge.Insomewaysthiscansimplifythedesignoftheparticleaccelerator.Theparticlesandantiparticlescansharethesamebeampipeandthesameelectromagnetic¯eldswillacceleratetheminoppositedirections.Havingidenticalparticlesasthecollidingparticleswillrequireamorecomplicatedacceleratorcomplex.Atrelativelylowenergiesthereisanadditionalbene¯ttousingprotonsandantiprotonsduetotheenergycarriedbytheconstituentquarks.Atcollisionenergiesupto»3TeV,mostoftheenergyiscarriedbythethreevalencequarkswithminimalenergycarriedbytheseaquarksandgluons.Itismorelikelythentogetanannihilationeventbycollidingaprotonwithanantiproton.Athigherenergiestheseaquarksandgluonsgetahigherpercentageoftheenergyandthebene¯tofusingantiparticlesisreduced.Thisisfortunateinawaybecauseantiparticlesareveryhardtoproduceandstore.Requiringachargedparticledoeshaveadownsideforcycliccolliders:synchrotronradi-ation.Thisisasourceofenergylossthatisproportionaltothechargeandenergyoftheparticleandinverselyproportionaltotheparticlemassandradiusofthecurve.Colliding20verylight,chargedparticlesatveryhighenergymeansaverylargeaccelerator.Takingintoaccountallthesefactorstominimizetheenergylossisabalancingact.2.3ParticleDetection
Tolearnaboutparticlesandtheirinteractionswemusthaveawaytoobservethem.Tra-ditionalmethodsofobservationarenotfeasibleandwemustrelyontheirinteractionswithmattertolearnaboutthem.Likeparticleacceleration,particledetectionreliesheavilyonchargedparticleinteractions.Thenextsectionbrie°yoverviewshighenergyparticleinterac-tionswithmatterfocusingonelectromagneticinteractionsandintroducesparticleshowers.Section2.3.2givesanoverviewofthebasicstructureofaparticledetector.2.3.1MatterInteractions
Allenergeticchargedparticlesinteractwithmatterviatheelectromagneticforce,whichismediatedbyphotons.Theseinteractionsresultinthelossofkineticenergy.Theseinteractionscaneitherbewithorbitalatomicelectronsorwithatomicnuclei.Aninteractionwithanorbitalelectroncanresultinexcitationorionization.Excitationoccurswhentheorbitalelectrongainsenergyfromthepassingchargedparticleandispromotedtoahigherenergyorbital.Followingexcitation,theorbitalelectronrelaxesbacktoalowerenergyorbitandemitsaphotonintheprocess.Whentheenergygainedfromthepassingchargedparticleexceedsthebindingenergyofthatelectron,ionizationoccursandtheelectronbecomesunbound.Inaninteractionwithanatomicnucleusthechargedparticlemayradiateaphotonasitdecelerates,referredtoasbremsstrahlung2.Thecharacteristiclengthassociatedwith2InGerman,literally\brakingradiation".21thistypeofprocessistheradiationlengthX0,boththemeandistancethroughwhichahighenergyelectronlosesallbut1=eofitsenergyand7=9ofthemeanfreepathforahighenergyphoton.Achargedparticlecanalsoscattero®ofanucleus,losingalmostnoenergyintheprocess,andbede°ected.Thistypeofscatteringiscollectivelyreferredtoascoulombscattering.Theprecisemechanismbywhichparticlesloseenergyandtheamountofenergylostdependsonthemassoftheparticle,itsmomentum,andthematerial.Forourpurposes,wedivideourdiscussionbetweenheavy3chargedparticles,electrons,andphotons.Heavychargedparticlesinteractelectromagneticallythroughionizationandexcitation.ThemeanenergylossrateforheavychargedparticlescanbeapproximatedbytheBetheformulawhichdependsonthematerial,thevelocityoftheincidentparticle(¯=v=c),andthemassoftheincidentparticleathighenergy.Thisformulaisvalidwithinafewpercentforvaluesof¯°(°=1=(p1¡¯2))between0.1and1000.Themeanenergylossratevs¯°forseveralmaterialsisshowninFig.2.4.TheBetheformulacannotbeappliedtoelectronsandpositronsbecauseoftheirrelativelysmallmassandthefactthatelectronsthatareionizedorexcitedmustbetakenasidenticalparticlestotheincidentelectron.Athighmomentaanotherenergylossmechanismbecomesdominant.Theenergydissipatedthroughbremsstrahlungisinverselyproportionaltothesquareofthemassoftheincidentparticle.Duetotheirsmallmass,electronslosefarmoreenergytobremsstrahlungthananyotherchargedparticle.Withthistakenintoaccount,themeanenergylossratewouldlooksimilartothoseinFig.2.4withasteepriseathigher¯°toaccountforbremsstrahlungandotherradiativelosses.Althoughthephotondoesnotcarryacharge,itcaninteractelectromagneticallyasthemediatoroftheelectromagneticforce.Aphotoncanbeabsorbedbyanorbitalelectron3`Heavy'particleshererefertothosemoremassivethantheelectron.22Figure2.4:MeanEnergyLossRatePlotofthemeanenergylossrateasafunctionof¯°forseveraldi®erentmaterials.Ex-ample:aheavychargedparticlewith¯°=1:2wouldhaveameanenergylossrateof¼1:1MeVcm2/ginlead.Inmoreintuitiveunits,multiplyingbythedensityofleadgivesanenergylossof12.5MeVpercentimeterofleadtraveled[4].23andeitherbere-emittedor,iftheenergyexceedsthebindingenergy,freetheelectronfromitsboundstate.Inthepresenceoftheelectromagnetic¯eldofanelectronoranucleusaphotoncanconvertintoanelectron-positronpairprovidedithasanenergygreaterthan1.02MeV,twicethemassofanelectron.Athighenergyphotonsprimarilyloseenergyviapairproductioninthe¯eldofanucleusandtoalesserextentinthe¯eldofanorbitalelectron.Asfaraswecantell,naturehasdeterminedthatquarksandgluonsmustbecon¯nedinhadronsasdetailedbythetheorygoverningthestrongforce.Thepropertyofcon¯nementwillbediscussedinfurtherdetailinChapter3butforourpurposeshereitissu±cienttograntitsexistence.Theresultofthispropertyisthatanygluonsorquarksproducedinthecollisionimmediatelyformhadronsor`hadronize'bycombiningwithquark-antiquarkpairsfromthevacuum.Hadrons,whetherchargedorneutral,caninteractwithmatterviathestrongforce.Thecharacteristicdistanceinthistypeofinteractionisthenuclearinteractionlength¸Aandisthemeandistanceahadronicparticletravelsbeforeinteractingwithanucleiinthematerial.Whenenoughmaterialispresentandtheparticle'senergyishighenoughaparticleshowercanform.Incidentparticles,whetherchargedorneutral,interactwithmatterandproducesecondaryparticles.Iftheenergyimpartedtothesecondariesislarge,theycanalsointeractandproduceadditionalparticles.Thiscontinuesuntiltheresultingparticlesdonothaveenoughenergytoproducenewparticles.Theseparticlescontinuetoloseenergyviaionizationandexcitationuntiltheyarecapturedorabsorbedintothematerial.Twotypesofshowersoccurinaparticledetector:electromagneticshowersandhadronicshowers.EMshowersbeginwithahighenergyphotonorelectron.Anelectron,perhaps,interactswithanucleusandemitsaphoton.Thisphotonthenproducesanelectron-positronpair24andeachemitaphotonthroughbremsstrahlung.Theshowercontinuesinthismanneruntiltheenergyhasdecreasedbelowthepointatwhichpairproductionorbremsstrahlungisthedominantmodeofenergyloss.Theparticlescontinuetoloseenergybyothermethods.ThecharacteristiclengthscaleofshowerformationistheradiationlengthX0.Hadronicshowersbeginwithahighenergyhadron.Thehadroninteractswiththenucleiofthedetectormaterialproducingmorequarksandgluonswhichimmediatelyhadronize.Secondaryparticleswithenoughenergycontinuetointeractuntiltheirenergyistoolowandtheyarecapturedbythedetectormaterial.Theshowerdepthscalesasthenuclearinteractionlength¸A.Because¸Aisingenerallargerthantheradiationlength,hadronicshowerstakelongertoformthanEMshowers.Ithappensthenthatelectromagneticshowersoccurwithinhadronicshowerswhensecondaryparticlesinteractelectromagnetically.Itisworthnotingherethatofalltheparticles,neutrinosaretheonlyonesthatdon'tinteractviatheelectromagneticorstrongforce.Theyonlyinteractviatheweakforcewhichhasaveryshortinteractionrange.Neutrinoscanthereforepassthroughlargeamountsofmatterwithoutinteractingandremainundetectedbymostmultipurposedetectors.Theirexistenceisinferredfromthemomentumimbalanceormissingtransverseenergy6ETinparticlecollisions.
2.3.2Detectors
Thesecondpieceofequipmentnecessaryforaparticlephysicsexperimentisadetector.Thedetectoractsasacamerathatrecordsinformationaboutthecollisionandtheparticlesthatwerecreated.Becausethedesignofcyclicacceleratorsallowsformultipleinteractionpoints,itiscommonfortheretobemultipledetectorsateachoftheseacceleratorcomplexes.Detectorsareroughlycylindricalinshapeandaresituatedaroundthecollisionpoint.To25maximizethenumberofphysicsstudiesthatcanbedonemostdetectorsaregeneralpurpose{theyaredesignedtodetectmanydi®erenttypesofsignatures.Alldetectorcomponentsmakeuseofelectromagneticinteractions,especiallyionizationandexcitation,toobtaininformationonpassingparticles.Ionizationresultsinafreeelectronandapositiveiongenerallyreferredtoasahole.Theseelectron-holepairscanbecollectedandthechargemeasured.Photonsemittedduringexcitationscanbemeasuredaslightinaplasticscintillator.Trackingsystemsformultipurposedetectorsaredevelopedtotracethepathofaparticlewithoutdisturbingitstrajectorybyusingsmallamountsoflowatomicnumberandlowatomicmassmaterial.Theparticlemomentumcanbemeasuredforchargedparticlesbymeasuringthecurvatureoftheirtrackinamagnetic¯eld.Calorimetersareusedtomeasuretheenergyofaparticlebyinitiatingparticleshowerswithhighdensitymaterialsandmeasuringthetotalenergydepositedbychargecollectionorscintillationlight.Physicalobjectscanbede¯nedbythetrackstheyleaveandtheenergytheydepositinthedetector.Figure2.5depictshowdi®erentparticlesreactwithdetectorsubsystems.Reconstructingparticlesfromtheirsignaturesinthedetectoristhe¯nalstepinobtainingphysicsdataforanalysis.Figure2.5:ParticleDetectorSignaturesCartoondescribingthetypesofsignaturesleftbyparticlesinadetector.ThedetectorpicturedhereistheCMSdetector.262.4Simulation
Onceparticlephysicistshavecollecteddataandreconstructedobjectsitisuptothemtoanalyzethedata.Thecollecteddataiscomposedofmanydi®erentprocessesinproportiontotheircrosssections.Tolookfor(orperhapsstumbleupon)newprocessesoreventotestthestandardmodel,particlephysicistsmustbeabletocategorizeandmodeltheprocessesthatmakeupthedata.Oneveryimportanttoolistheconstructionofarti¯cialeventssimulatingknownphysicalprocesses.Therearetwostepstocreatingtheseevents:generationandpropagation.
2.4.1Generation
SimulatedeventsaregeneratedusingtheMonteCarlomethodandasaresultarecommonlyreferredtoasMonteCarloeventsorMCevents.TheMonteCarlomethodasitpertainstoparticlephysicsisacomputationalalgorithmthatrandomlysamplesprobabilitydistributionsgoverningtheoutcomeofevents.Repeatingtherandomsamplingmanytimescreatesasampleofeventsrepresentativeofalloutcomes.First,aprocessischosenthatisde¯nedbyamodeleithertheSMorotherwise.Anexamplewouldbetheproductionofasingletopquarkinassociationwithabquark,showninFig.2.6.Whencollidingprotonsandantiprotons,theinitialstateparticlesmustcomefromtheconstituentquarksandgluons.Themomentaoftheinitialstateparticlesarechosenatrandomfromthecorrespondingpartondistributionfunction(PDF).ThePDFdescribesthemomentumfractionoftheprotoncarriedbythepartonsaswellasquark°avorcontent.Finally,theinitialparticles'momentadeterminethepossible¯nalstatemomentaandoneisselectedatrandom.27Figure2.6:SingleTopQuarkProductionOneoftheFeynmandiagramsforsingletopquarkproductionattree-level.2.4.2Propagation
Aftersimulatingthephysicalprocesswhatremainsissimulatinghowitpropagatesandinteractswiththedetector.Awholehostofeventstakeplaceaftertheinteraction.Particlescanradiatephotonsorgluons,short-livedparticleswilldecayandsharetheirmomentumwiththeirdecayproducts,andanyquarksorgluonsinthe¯nalstatewillimmediatelyhadronize.Thehadronizationandradiationaspectsaremodeledbyshoweringprograms.Alloftheseparticlesandtheirdecayproductswillpropagatefromtheinteractionpointoutwardswithtrajectoriesthataredeterminedfromthemomentumandthemagnetic¯eldwithinthedetector.Theparticlesthatmakeittothedetectorvolume,mostofwhicharestable,willinteractwiththedetectormaterialasdescribedinSection2.3.1.Amodelofthedetectorisconstructedforthispurposeandincludestheactivematerial,supportstructures,magnetic¯elds,detectionthresholdsande±ciencies,andgeometricstructure.Particlesarepropagatedthroughthedetectormodelandtheirinteractionsarerecordedinthesameformatasrealdata.28Chapter3
Theory
3.1Introduction
Instudyingfundamentalparticlesandtheirinteractionsitbecomesnecessarytomoveawayfromdescribingdynamicsassystemsofparticlesandtowardssystemsof¯elds.Whilethereareseveralreasonsthisbecomesapparentperhapstheeasiestwaytocometotermswiththisisrealizingthatthereisnoreasontoassumearelativisticprocesscanbedescribedbyasingleparticlealone.Einstein'smass-energyrelationE=mc2allowsfortheproductionofparticle/antiparticlepairs.Othervirtualparticles,allowedtoexistbyHeisenberg'suncer-taintyprinciple¢E¢¢t¸~2forveryshorttimes,canappearinsecondordercalculations.Itmakesthemostsensethentoinsteaddescribesystemsof¯elds.Thischapterwilldescribethe¯eldtheoriesofparticlephysics.Innatureweknowoffourfundamentalforces:strongforceresponsibleforthebindingofquarksinhadrons;theresiduale®ectsofthisforcebindtheprotonsinanucleuselectromagneticforcethatgovernstheinteractionsbetweenchargedparticlesweakforcethataccountsforprocessessuchasnuclearbetadecayandthedecayofthemuongravitationalforcethatresultsinplanetaryorbits29Duringtheclassicalerainparticlephysicswhenallmatterwasperceivedasnothingmorethanprotons,neutronsandelectrons,thetwoknownforceswereelectromagnetismandgravity.Thiswasduetothein¯niterangeoftheelectromagneticandgravitationalforces.Thestrongandweakforcesontheotherhandhaveaveryshortrangesowerenotrecognizableuntilitwaspossibletoexamineobjectsonaveryshortlengthscale.Weshallseethateachoftheseforces(withthepossibleexceptionofgravity)ismediatedbytheexchangeofoneormoreparticles.Theseforcecarrierscanbethoughtofasmessengersbetweentwoparticlesthattellthemhowtointeractthroughtheforce.Wewillalsoseethattwooftheseforcesareactuallydi®erentaspectsofasingleforce.Alloftheseforceshavearelativisticdescription.Threeofthemhaveaquantumdescription;theirforcecarriersarethequantaofthe¯eld.Gravitypresentsabitofaproblem.Unliketheotherforces,thereisnosatisfactoryquantumtheoryofgravityatpresentandnoforcecarrierhasyetbeendiscovered.Forthisreason,itwillnotbediscussedinthefollowingchapters.Thenextsectiongivesanoverviewoftheparticletypesandfamiliesinthestandardmodel.Section3.2describesthequantum¯eldtheoriesthatmadeupthestandardmodelinparticlephysics.AnoverviewofthesearchesfortheHiggsbosonisgiveninSection3.3.AdiscussionofwhatphysicsmayexistbeyondthestandardmodelisgiveninSection3.4.
3.1.1ParticleZoo
Beforewediveintothedescriptionofthestandardmodeltheories,itishelpfultogiveanoverviewofthemanytypesofparticles,bothcompositeandfundamental,thatexistintheSM.Fundamentalparticlescanbedividedintoquarks,leptons,andmediators.Quarksarethebuildingblocksofprotons,neutrons,andotherparticleslikethem.Thegroupofleptons30includethefamiliarelectronandneutrino.Themostrecognizablemediatoristhephoton,thelightquantum.Thesixquarksandsixleptonsaredividedintothreefamiliesoftwoeachdi®eringonlyinmass.The¯rstfamilyconsistsoftheupquark(u),thedownquark(d),theelectron(e),andtheelectronneutrino(ºe).Thisfamilyisallthatisneededtomaketheordinarymatteraroundus:protons,neutrons,nuclei,andatoms.Table3.1givesthenamesandsymbolsforthethreefamiliesofquarksandleptons.QuarksLeptonsFirstFamilyupuelectronedowndelectronneutrinoºeSecondFamilycharmcmuon¹strangesmuonneutrinoº¹ThirdFamilytopttau¿bottombtauneutrinoº¿Table3.1:ThreeParticleFamiliesAlistofthequarksandleptonsineachofthethreefamilies.Oneattributeofparticlesistheintrinsicquantumnumberspin.Spindoesnotrepresentanysortofmotionwithrespecttoanaxis,butisanintrinsicpropertyofaparticle.Youcandividethegroupofallparticlesintotwocategoriesbasedonspin:fermionsandbosons.Fermionshavehalf-integerspinwhilebosonshaveintegerspin.Thedi®erenceinspinleadstoaverystrangeproperty.FermionsfollowthePauliexclusionprinciple:notwoidenticalparticlescanoccupythesamestate.Bosonsdonotfollowthisruleandarbitrarilymanybosonscanoccupythesamestate.Allleptonsandquarksarefermionsandallforcemediatorsarebosons.Parity(P)isanotherintrinsicquantumnumberofparticles.Itreferstohowtheparticlewavefunctiontransformsunderaparityoperation.Infour-dimensionalspace-timeaparity31operationisthecompleteinversionofthethreespatialcomponents:P:0
B
B
B
B
B
B
B
B
B
@txyz1
C
C
C
C
C
C
C
C
C
A!0
B
B
B
B
B
B
B
B
B
@t¡x¡y¡z1
C
C
C
C
C
C
C
C
C
A:(3.1)AssuminganeigenstateÃPoftheparityoperatorPandusingthefactthattwoapplicationsoftheparityoperatorleavethestateunchanged(withtheexceptionofaphase)P2ÃP=eiÁÃPweseethatPÃP=§eiÁ=2ÃP.IntrinsicparityisthereforeaneigenvalueoftheparityoperatorwithvaluesP=+1(even)orP=¡1(odd).Theforcemediatorshaveoddintrinsicparitywhilethequarksandleptonsarede¯nedtohaveevenintrinsicparity.Theantiparticlesofthequarksandleptonsarede¯nedtohaveoddintrinsicparity.Parityisamultiplicativequantumnumberwhichisconservedinthestrongandelectromagneticinteractions.Itisviolatedintheweakinteractions.Forreference,Table3.2listsalltheknownfundamentalparticlesinthestandardmodel:theirsymbol,mass,electriccharge,spin,andparity.
3.2StandardModel
Thestandardmodel(SM)ofparticlephysicsencompassestherelativisticquantum¯eldtheoriesofthestrong,electromagnetic,andweakforces.Itdescribestheuni¯cationoftheelectromagneticandweakforcesintotheelectroweakforce.ItsmostrecenttriumphisthediscoveryoftheHiggsboson,aparticlepredictedbytheSMandalsothesubjectofthisthesis.32NameSymbolMassCharge(e)JPQuarksupu2:3+0:7¡0:5MeV2/31/2+downd4:8+0:5¡0:3MeV-1/31/2+stranges95§5MeV-1/31/2+charmc1:275§0:025GeV2/31/2+bottomb4:18§0:03GeV-1/31/2+topt173:21§0:87GeV2/31/2+Leptonselectrone0:511MeV¡11/2+electronneutrinoºe<2eV01/2+muon¹105:7MeV¡11/2+muonneutrinoº¹<2eV01/2+tau¿1776:86§0:12MeV¡11/2+tauneutrinoº¿<2eV01/2+Mediatorsphoton°001¡WBosonW§80:385§0:015GeV§11¡ZBosonZ91:1876§0:0021GeV01¡gluong001¡HiggsbosonH125:09§0:24GeV00+Table3.2:FundamentalParticlesAlistofalltheknownfundamentalparticles:theirsymbol,mass,charge,spinJ,andparityP.Thestandardmodelisa¯eldtheoryandisbestdescribedusingaLagrangianformalism.TheLagrangianLfortheSM¯eldtheorywillbeafunctionofthe¯eldsandtheirderivativesL(Á;@¹Á).ThetheoriesthatcomprisetheSMaregaugetheories;theirLagrangiansareinvariantunderasetoflocaltransformationsthatformasymmetryorgaugegroup.ThegeneratorsofthesymmetrygrouparedescribedbyaLiealgebra.Associatedwitheachgenerator(ngeneratorsforagroupofdimensionn)isavector¯eld.Thequantizationofthesevector¯eldsgivesrisetophysicalstatescalledgaugebosonswhicharetheforcecarriersoftheSM.AswewillseeinthefollowingsectionstheSMisanon-abeliantheorywithsymmetrygroupU(1)£SU(2)£SU(3)withatotaloftwelvegaugebosons.First,Sections3.2.1and3.2.2describethe¯eldtheoriesoftheelectromagneticandstrongforces.33Section3.2.3describestheuni¯cationoftheelectromagneticandweakforcesundertheGlashow-Weinberg-Salam(GWS)theoryofweakinteractions.Finally,Section3.2.4givesanoverviewofelectroweaksymmetrybreakingandanintroductiontotheHiggsboson.3.2.1QuantumElectrodynamics
Quantumelectrodynamics(QED)wasthe¯rstformulationofatheoryofparticleinteractionsthattookintoaccountbothquantummechanicsandspecialrelativity.Itisarelativisticquantum¯eldtheorythatdescribestheinteractionsbetweenelectricallychargedparticles.Thetheorywasatremendoussuccessinexplanatoryandpredictivepowerandtothisday,itboaststhehighestagreementwithexperimentaldata.Becauseitwasthe¯rsttheoryofitskind(and,inpart,becauseofitswildsuccess)otherquantum¯eldtheories,suchasquantumchromodynamics(QCD),aremodeledafterit.WebeginbywritingtheLorentz-invariantDiracLagrangianforafreeelectron:LDirac=Ã(i°¹@¹¡m)Ã(3.2)whereÃisaDiracspinorwithaLorentz-invariantadjointÃ=Ãy°0andthe°¹aretheDiracmatrices°0=0
B
@01
101
C
Aand°i=0
B
@0¾i¡¾i01
C
A1.Wethenrequireour¯eldtobeinvariantunderthefollowingtransformation:Ã(x)!ei®xÃ(x):(3.3)Thistransformationisaphaserotationthroughanangle®(x)anditde¯nesthesymmetry1Herethe¾iarethePaulimatrices¾1=µ01
10¶,¾2=µ0¡ii0¶,and¾3=µ10
0¡1¶.34groupU(1),theunitarygroupofdimension1.ThesecondterminEq.3.2isinvariantunderthistransformationbutthe¯rsttermisnot.Itisunclearwhatthederivativeofthecomplex¯eldshouldbewhenthe¯eldtransformationateachpointinspaceisdi®erent.Wemustintroduceanewderivativethattransformslikethe¯eld:thecovariantderivative.ForthetransformationunderU(1)symmetry,thecovariantderivativetakestheformD¹=@¹+ieA¹whereeistheelectronchargeandA¹isanewvector¯eld.Wecanidentifythenewvector¯eldwiththefamiliarelectromagneticfour-potential.Thisisthesinglegauge¯eldexpectedbytheLiealgebraofU(1)andthequantumofthis¯eldisthephoton.TocompletetheQEDLagrangianwemustincludeakinetictermforthefour-potentialthatislocallyinvariantanddoesnotdependonthe¯eld.Weintroducetheelectromagnetic¯eldtensorF¹º=@¹Aº¡@ºA¹forthispurpose.ThefullQEDLagrangiancanthenbewrittenas:LQED=Ã(i°¹@¹¡m)Ã|{z}LDirac¡eð¹A¹Ã|{z}Lint+14(F¹º)2|{z}LMaxwell:(3.4)The¯rsttermofEq.3.4isjusttheDiracequationwebeganwithandthemiddletermdescribestheinteractionbetweenthe¯eldandthefour-potential.ApplyingtheEuler-LagrangeequationtothelasttermyieldstheinhomogeneousMaxwellequations.TheQEDLagrangiandescribestheinteractionsofallmassivespin-1/2particleswiththeelectromagneticforcewhichincludesallthequarksandchargedleptons.
3.2.2QuantumChromodynamics
Quantumchromodynamics(QCD)isthetheorythatdescribesstronginteractions.Itsdevel-opmentbeganwiththeconceptionofthequarkmodel,usedtoexplainthemanymesonsandbaryonsdiscoveredinthe'50sand'60s.Theearlyquarkmodelhadtwoproblems:quarks35thatdidn'tappeartoobeyFermi-Diracstatisticsandparticleswithafractionalchargecouldnotbefound.Quarksarefermions;theirwavefunctionsmustbeantisymmetricunderex-change.Thisproblemwiththeearlyquarkmodelcanbeillustratedbythe¢++particle,aspin-3/2particlewithcharge+2.Thisparticlecanbeexplainedasaboundstateofthreeupquarkswithparallelspin{symmetricin°avorandspin.Tosolvethis,itwasproposedthatanadditional(hidden)quantumnumberwascarriedbyquarksandthatallbaryonswereantisymmetricinthishiddenquantumnumber.ThisquantumnumberiscalledcoloranditrepresentsaninternalSU(3)symmetry.Closelyrelatedtothesecondproblemwiththeearlyquarkmodelisthediscoverythatelectron-protonscatteringexhibitedBjorkenscaling2;athighenoughenergies(orashortenoughtimescale)theconstituentsoftheprotonbehavedasfreeparticles.Howisitpossiblethenthatquarksonlyweaklyinteractyetaresotightlyboundthattheydon'texistfreelyinnature?Theanswertothisliesinasymptoticfreedom,thecornerstoneofQCD.Asymptoticfreedomisapropertythatcausesinteractionsbetweenparticlestobecomeweakerathighenergiesandshorttimescalesandstrongeratlowenergiesandlongtimescales.TheNobelPrizeinphysicsfor2004wasawardedtoWilczek,Gross,andPolitzerfortheir1973discoveryofasymptoticfreedominnon-abelian3gaugetheoriesandtheirrelationtostrongdynamics[5,6].QuantumChromodynamicsisanon-abeliangaugetheorywithlocalSU(3)colorsym-metry.InitsmostcompactformtheQCDLagrangianlooksalmostidenticaltotheQED2PropertiesthatexhibitBjorkenscalingarefoundtobeindependentoftheenergyatwhichtheexperimentisperformedwhiledependingondimensionlesskinematicquantitieslikeascatteringangle.NamedforJamesBjorkenwhofoundthatstructurefunctionsofnucleonsexhibitedthisbehavior,stronglyimplyingthatthenucleonshadpoint-likesubstructure.3UnliketheabeliangaugetheoryQED,thegeneratorsofanon-abeliangaugetheorydonotcommute.Itisthischaracteristicthatallowsnon-abeliangaugetheoriestobeasymptoticallyfree.36Lagrangian:LQCD=Ã(i°¹D¹¡m)á14(Ga
¹º)2;Ga
¹º=@¹Caº¡@ºCa¹+gfabcCb¹Ccº:(3.5)HereGa
¹ºisthenew¯eldstrengthwiththeindexasummedovertheeightgeneratorsofSU(3),gisthecouplingconstant,andthefabcarethestructureconstantsofSU(3).Thecovariantderivativeisde¯nedasD¹=@¹¡igCa¹tawherethetaarethegeneratorsofSU(3).Theeightnewvector¯eldsCa¹arethegluon¯elds.UnlikeQED,wherethereisonlyonegaugebosonQCDhaseightgaugebosons{thegluons.WritingouttheLagrangianmoreexplicitlyyields:LQCD=Ã(i°¹@¹¡m)á14(@¹Caº¡@ºCa¹)2|{z}free¯eld+gCa¹Ã°¹taÃ|{z}fermion¡gfabc(@ºCa¹)CºbC¹c|{z}three-vertex¡14g2(feabCaºCb¹)(fecdCºcC¹d)|{z}four-vertex:(3.6)The¯rstterminEq.3.6isthefree¯eldLagrangian(g=0)thatdescribesthedynamicsofthequarksandthegauge¯eld.Thesecondtermisthefermioninteractionterm;itdescribestheinteractionbetweenafermionwithcolorquantumnumbers(quarks)andagluon.ThelasttwotermsareinterestingbecausesimilartermsdonotappearintheQEDLagrangian.Theyareself-interactiontermscorrespondingtoFeynmandiagramverticeswiththreeandfourgluons.Gluonscanself-interactbecausetheythemselvescarrycolorunliketheelectrically-neutralphotonsinQED.373.2.3Glashow-Weinberg-SalamTheoryofWeakInteractions
Formulatingatheoryoftheweakforceinteractionspresentsafewproblems.First,ithasbeenexperimentallyobservedthattheWbosononlycouplestoleft-handedparticles.Worse,itappearsthatright-handedneutrinosdonotexist.Second,¯eldtheorieswithunbrokensymmetriesonlyhavemasslessgaugebosonsbutthemassesoftheWandZbosonsarecertainlynotzero{theyarequiteheavy!AsweshallseeinSection3.2.4themechanismforgivingtheweakvectorbosonsmassinvolvesspontaneouslybreakingthesymmetryoftheelectroweaksector.The¯rstproblemcanbesolvedinpartbyassigningright-andleft-handed¯eldstodi®erentrepresentationsofthegaugegroup.Thesedi±cultiesareasmallpricetopayfortheendresult:atheorywhichgivesauni¯eddescriptionoftheelectromagneticandweakinteractions.Thismeansthattheelec-tromagneticandweakforcesarereallydi®erentaspectsofthesameforce,theelectroweakforce.Glashow[7],Weinberg[8],andSalam[9](GWS)introducedthetheorywhichdescribestheweakinteractionsandalsoagreeswithexperiment.ForthistheywontheNobelPrizeinphysicsin1979.Webeginasalwaysbyrequiringalocalgaugeinvariance.FortheGWStheoryitisaSU(2)£U(1)gaugeinvariance:Ã!ei!iTiei¯YÃwheretheTiarethegeneratorsofSU(2)withi=1;2;3,¯and!iarearbitraryphases,andYistheweakhypercharge4ofU(1).Forafermion¯eldbelongingtothegeneralrepresentationofSU(2)thecovariantderivativehastheformD¹=@¹¡igWi¹Ti¡ig0YB¹(3.7)wheretheWi¹arethevector¯eldsofSU(2)andB¹isthevector¯eldofU(1).Thekinetic4WeakhyperchargerelatestheelectricchargeQtothethirdcomponentofweakisospinT3byQ=T3+Y.Infact,thisequalitywillbecomeevidentinourdiscussionofelectroweaktheory.38energytermsintheLagrangianforthegauge¯eldsareLkinetic=¡14Wi¹ºW¹ºi¡14B¹ºB¹ºWi¹º=@¹Wiº¡@ºWi¹+g²ijkWj¹WkºB¹º=@¹Bº¡@ºB¹(3.8)whicharesimilartothekinetictermsinQEDandQCD.WenowincorporatethefactthattheWbosonsonlyinteractwithleft-handedfermionsbyassigningtheleft-handedfermionstodoubletsofSU(2)andright-handedfermionstosingletsofSU(2).Toreinforcethefactthatthedoubletsandsingletsbelongtodi®erentrepresentationsofSU(2)wewilldenotethedoubletsasÃLandthesingletsasÂR.ThesingletsofSU(2)onlyinteractwiththeB¹¯eldleadingtotheLagrangianLR=iÂR°¹(@¹¡ig0YB¹)ÂR.Thedoubletsinteractwithboth¯eldsLL=iÃL°¹(@¹¡igWi¹Ti¡ig0YB¹)ÃL.ThevaluesofthechargeYaredeterminedbythespeciesoffermion.Thequark¯eldsconsistofoneleft-handeddoubletQL=(ud)Landtworight-handedsingletsuRanddR.Similarlyfortheleptons,EL=(ºee¡)LandeR.Itistemptingtoassignthethreegauge¯eldsWi¹tothethreeweakvectorbosonsW§andZandtheB¹¯eldtothephotonbutthatwouldimplythattheZbosondoesnotcoupletoright-handedfermionsandthisisnotthecase.TheroleofWi¹andB¹inproducingthevectorbosonsismadeclearifweinsteadwriteEq.3.7intermsofthemasseigenstatesofthe¯elds.ForthisweneedtobreakthesymmetryoftheGWStheory.393.2.4ElectroweakSymmetryBreaking
Themethodofgeneratinggaugebosonmassesthroughspontaneoussymmetrybreakingwas¯rst5describedindependentlybyHiggs[10];BroutandEnglert[11];andGuralnik,Hagen,andKibble[12].In2013HiggsandEnglertwontheNobelPrizeinphysicsforthiswork.Spontaneouselectroweaksymmetrybreaking(EWKSB)canbeincorporatedintotheGWStheory.Tobreaktheelectroweaksymmetryspontaneouslyweintroduceadoubletofcomplexscalar¯elds©=1p20
B
@Á+Á01
C
AwithÁ+=Á1+iÁ2andÁ0=Á3+iÁ4(3.9)withaself-interactionpotentialoftheformV(©)=¹2©y©+¸(©y©)2.Topreservethesymmetryoftheelectromagneticsectorweassignthescalar¯eldahyperchargeYof+1/2which¯xestheelectromagneticchargesofthecomponentsof©.Thecovariantderivativeof©followsfromEq.3.7:D¹©=(@¹¡ig2Wi¹¾i¡ig02B¹)©whereTihasbeenexpandedas¾i2.WecanwritetheLagrangianasakinetictermandapotentialtermL=jD¹©j2¡V(©)=jD¹©j2|{z}kineticterm¡¹2©y©¡¸¡©y©¢2|{z}potentialterms:(3.10)Let's¯rstlookatthepotentialtermsintheLagrangian.Assuming¹2<0and¸>0,onecomponentofthepotentialV(©)isplottedintheimaginaryplaneinFig.3.1with5SpontaneoussymmetrybreakinginanabeliangaugetheoryhadalreadybeenusedtoexplaintheMeiss-nere®ectinsuperconductivity.Theapplicationtonon-abeliangaugetheoriesandtheimplicationstoparticlephysicswaswhatwas¯rstdescribedbyHiggs,etal.40arbitraryunits.Theminimumofthispotentialisacircleinthecomplexplane:v=§pRe2(Á)+Im2(Á)=§p¡¹2=¸withanothercriticalpointatÁ=0.Thevacuum(orgroundstate)expectationvalue(vev)ofthe¯eldÁwilloccurataminimuminthepotential.Sincethegroundstateisdegeneratethe¯eldwillspontaneouslychooseandthesymmetrywillbebroken.Wewillconsiderthepositivesolution.Forthedoubletscalar¯eld©wechooseÁ1=Á2=Á4=0andÁ3=v.Inthiscasethepositively-chargedcomponentÁ+iszeroandonlytherealpartoftheneutralcomponentisnon-zero.Tosimplifythediscussion,wewillworkintheunitaritygauge,achoiceofgaugethatreducesthescalar¯eldtoonephysicaldegreeoffreedom.Next,weconsidersmalloscillationsabouttheminimumandwrite©(x)=1p20
B
@0v+h(x)1
C
A(3.11)whereh(x)isareal¯eldinourgaugechoice.WecannowevaluatetheLagrangianinthegroundstate.LV=¡¹2h2¡¸vh3¡14¸h4+14¹2v2=¡12mhh2¡r¸2mhh3¡14¸h4+14¹2v2:(3.12)The¯rsttermintheLagrangianisamasstermfortheh¯eld,mh=p2¹.Thisrepresentsaparticlewithnon-zeromass,whichwerefertoastheHiggsboson.NoticethatthemassfortheHiggsbosonisnotspeci¯ed;itdependsonlyonunknownparameters.LookingatthekineticenergytermofEq.3.10weseethatittakestheformofthecovariantderivativeofÁ,squared.Sincethesymmetryhasbeenbrokenwecanevaluatethis41Figure3.1:ScalarPotentialThepotentialV(Á)=¹2ÁyÁ+¸(ÁyÁ)2assuming¹2<0and¸>0foracomplexscalar¯eldplottedinarbitraryunits[13].
termatthevevofÁ.Atthispointwecanevaluatetheproductexplicitly:jD¹Áj2=12(@¹h)2+12v24£g2(W1¹¡iW2¹)(W1¹+iW2¹)+(gW3¹¡g0B¹)2¤¢µ1+hv¶2:(3.13)Thetermsinsidethebracketsaremasstermsfortheweakvectorbosons.Ourbosonshaveacquiredmass!Wecande¯nethemasfollows.W§¹=1p2(W1¹¨iW2¹)mW=gv2Z¹=1pg2+g02(gW3¹¡g0B¹)mZ=v2pg2+g02(3.14)TheWbosonsareactuallyacombinationofthe¯rsttwocomponentsoftheWi¹.TheZboson,ontheotherhand,doesn'treceiveanycontributionsfromtheseandisinsteadacombinationofthethirdcomponentofWi¹andB¹.Thephotonofcourseremainsmasslessandthereforedoesnotappearin3.13.ItisalsoacombinationofW3¹andB¹andisorthogonal42toZ¹:A¹=1pg2+g02(g0W3¹+gB¹)m°=0:(3.15)Wecanwritethetransformationthatchanges(W3;B)to(Z;A)asarotationthroughtheweakmixingangleµw:0
B
@ZA1
C
A=0
B
@cosµw¡sinµwsinµwcosµw1
C
A0
B
@W3B1
C
Acosµw=gpg2+g02;sinµw=g0pg2+g02:(3.16)WritingthecovariantderivativesintermsofthemasseigenstatesandidentifyingtheelectricchargequantumnumberQasT3+Yandthecoe±cientofthephoton¯eldgg0=pg2+g02aseweobtainD¹=@¹¡igp2(W¹+T++W¹¡T¡)¡igcosµwZ¹(T3¡sin2µwQ)¡ieA¹Q:(3.17)Thefermionmassesmfaremoredi±culttoincludeintheLagrangianbecausetheright-andleft-handed¯eldsliveindi®erentrepresentations.Puttinginamassterminthiswaywouldviolategaugeinvariance.UsingtheHiggsmechanismwecanconstructthesetermsbycontractingthefermiondoubletsFLwiththespinorÁevaluatedatthevacuumexpectationvalue.Newdimensionlesscouplingconstantsarerequired.AgainusingtheunitaritygaugewewriteLfermion=¡¸f¹FL¢ÁfR=¡vp2¸f(1+hv)¹fLfR=¡mf¹fLfR(1+hv):(3.18)43Ourchoiceoftheunitaritygaugeobscuressomeoftheunderlyingmechanicsofthescalar¯eldthatareworthmentioninghere.LookingbackatFig.3.1,thepotentialtakestheshapeofthebottomofachampagnebottle.Atsu±cientlyhighenergiesthe¯elddoesnotseethepotentialandthesystemissymmetric.Whenthesystemisinitslowestenergystatethe¯eldwill`settle'intothetheminimumofthepotentialandthesymmetryisbroken.Wesawthatsmalloscillationsofthe¯eldintheradialdirectioncorrespondtothemassiveHiggsboson.Wecanalsoconsideranothertypeofexcitationinthispicture:thosearoundtheverticalaxis.Sincethereareanin¯nitenumberofequivalentminimathegroundstateisdegenerateandoscillationsaroundthebottomofthebottlemovethesystemtoadi®erent,equivalent,groundstate.ThesemodescorrespondtomasslessNambu-Goldstonebosons.InEWKSBtherearethreeoftheseNambu-Goldstonebosons,oneforeachgeneratorbelongingtoabrokensymmetry.Beingableto`remove'themfromtheLagrangianmeansthattheyarenotphysicalstatesbutrepresentextradegreesoffreedom.Wesaythattheyare\eaten"bytheweakvectorbosonswhichgainanadditionaldegreeoffreedom:alongitudinalpolarizationstate.
3.3SearchingfortheHiggsBoson
ThemechanismofelectroweaksymmetrybreakingdiscussedintheprevioussectionpredictsamassivephysicalparticlewhichhasbeennamedtheHiggsboson.Inthestandardmodelitisascalarbosonwithzerospinandnoelectricorcolorcharges.Theonlypropertynotpredictedbythestandardmodelisitsmass,mh=p2¹,whichonlydependsonunknownparameters.Itcouplestoallparticlesroughlyinproportiontotheirmass;verylightparticlescoupleweaklytotheHiggsboson.Unfortunately,mostoftheparticleswecaneasilycreate44areverylightandmakeitdi±culttoobserve.WecanplaceconstraintsontheHiggsbosonmassdirectly,bysearchingforexcessesoveralargemassrange,orindirectlybyprecisemassmeasurementsonstronglycoupledparticles.ManyexperimentsovertheyearshavesearchedfortheHiggsbosonbothdirectlyandindirectly.Thefollowingsectionsbrie°yreviewsearchesfortheHiggsbosonatcolliders.AsregionsofpossibleHiggsbosonmasseswereexcluded,precisionmeasurementsoftheWbosonandtopquarkmassesimproved.Figure3.2showsthemeasuredmassoftheWbosonversusthemassofthetopquark. [GeV]tm140150160170180190 [GeV]WM80.2580.380.3580.480.4580.568% and 95% CL contours measurementst and mWfit w/o M measurementsH and Mt, mWfit w/o M measurementst and mWdirect Ms 1± world comb. WM 0.015 GeV± = 80.385 WMs 1± world comb. tm = 173.34 GeVtm = 0.76 GeVs GeV theo 0.50Å = 0.76 s = 125.14 GeVHM = 50 GeVHM = 300 GeVHM = 600 GeVHMGfitterSMJul '14Figure3.2:IndirectHiggsBosonMassConstraintsThe68%and95%con¯dencelevelcontoursresultingfromaglobal¯tusingprecisionelec-troweakmeasurementsofthemassoftheWboson,themassofthetopquark,andtheorycalculationstoconstrainthemassoftheHiggsboson.AlsoincludedarethemeasurementsofthescalarbosondiscoveredattheLHC[14].453.3.1LEPSearches
TheLargeElectron-Positron(LEP)collideratCERNcollidedelectronsandpositronsatcenterofmassenergiesbetween189GeVand209GeV.From1989to2000thefourexper-imentsatLEP(ALEPH,DELPHI,OPAL,andL3)collectedatotalof2461pb¡1ofdata.ThedecaybranchingratiosfortheHiggsbosonareplottedasafunctionsoftheHiggsbo-sonmassinFig3.3.ForaHiggsbosonwithlowmasstheprimarydecayistopairsofbquarks.ThiswastheprimarysearchmodeforLEPexperiments,buttheyalsoperformedsearchesthatlookedfortheHiggsbosondecayingtopairsofvectorbosonsandtauleptons.TheprimaryproductionmechanismconsideredwastheHiggsbosonproducedinassociationwithaZbosonintheprocesse+e¡!ZH.TheZbosondecayedtoeithertwoquarks,twochargedleptons,ortwoneutrinos.Theywereabletosetalowerboundonmhof114.4GeVatthe95%con¯dencelevel[15].Figure3.4showsthevalueofCLsasafunctionofthetestedHiggsbosonmass.HiggsbosonmassesareexcludedifCLs·0:05.3.3.2TevatronSearches
TheTevatroncollideratFermilabcollidedprotonsandantiprotonsfrom1985to2011atcenterofmassenergiesupto1.96TeV.TheexperimentsattheTevatron,CDFandD0,collectedupto10fb¡1perexperiment.AtthecenterofmassenergyoftheTevatronthedominantHiggsbosonproductionmodesaregluon-gluonfusion,associatedVHproduction,vectorbosonfusion,andassociatedtopquarkpairproductionttH.Tree-levelFeynmandiagramsfortheseproductionmodesaregiveninFig.3.5.TheproductioncrosssectionsfortheseprocessesareplottedoverarangeofHiggsbosonmassesinFig.3.6.ThedecaybranchingratiosfortheHiggsbosonareplottedasafunctionoftheHiggsbosonmassin46 [GeV]HM80100120140160180200Higgs BR + Total Uncert101010101LHC HIGGS XS WG 2013bbttmmccgggggZWWZZFigure3.3:HiggsBosonDecayBranchingRatiosHiggsbosondecaybranchingratiosasafunctionoftheHiggsbosonmass[16].Figure3.4:HiggsBosonMassConstraintsfromLEPShownhereisthevalueofCLsforarangeofHiggsbosonmasses.Theyellowandgreenbandscorrespondtothe68%and95%con¯dencelevelsforthemedianexpectedvalue[15].47HqZq'Zb
bFigure3.5:DominantHiggsBosonProductionModesShownherearethetree-leveldiagramsforthedominantHiggsbosonproductionmodesattheTevatron.110102103100125150175200225250275300mH MGeVNs(pp¾5H+X) MfbNTevatron
Rs¾=1.96 TeVpp±5H (NNLO+NNLL QCD + NLO EW)pp±5WH (NNLO QCD + NLO EW)pp±5ZH (NNLO QCD + NLO EW)pp±5qqH (NNLO QCD + NLO EW)pp±5tt±H (NLO QCD)Figure3.6:TevatronHiggsBosonProductionCrossSectionsHiggsbosonproductioncrosssectionsforgluon-gluonfusion(blue),WH(green)andZH(gray)associatedproduction,vectorbosonfusion(red),andassociatedtopquarkpairpro-duction(purple)[16].48Fig.3.3.ThemostdominantdecaysaretoapairofbquarksuptoaHiggsbosonmassof135GeVandtoapairofWbosonsathighermasses.ThecenterofmassenergyoftheTevatronrestrictsthemassrangethatcanreasonablybeprobedto·200GeV.SearchesfortheHiggsbosonattheTevatronconcentrateontheproductionmodesinFig.3.6withtheHiggsbosondecayingtob¹bortoapairofWbosons.WhensearchingforthedecayH!b¹bweusuallyconsiderproductionmodeswhichhaveleptonsinthe¯nalstate.MostoftheinteractionsthatoccuratahadroncolliderliketheTevatronproducequarks.Finalstateswithquarkstendtogetoverwhelmedbythesebackgroundinteractions.Byrequiringleptonsinthe¯nalstate(whicharerarerathadroncolliders)wecanlimitpotentialbackgroundsources.TheTevatronwasabletoexcludeHiggsbosonmassesintheranges90<mH<109GeVand149<mH<182GeV[17]atthe95%con¯dencelevelwhencombiningallproductionprocessesanddecaymodes.ForadiscussionofthestatisticalmethodsemployedherepleaserefertoChapter8.Figure3.7showstheobservedandexpected95%con¯dencelevelupperlimitdividedbythestandardmodelproductioncrosssectionforarangeofHiggsbosonmasses.WhencombiningonlyVHassociatedproductionprocesseswiththeHiggsbosondecayingtotwobquarkswealsosawevidence6ofanewparticleinthemassrange120<mH<135whichwasconsistentwiththeSMHiggsboson[18].Figure3.8showstheexpectedandobservedlog-likelihoodratioasafunctionoftheHiggsbosonmass.Thehighestlocalsigni¯canceisatmH=120GeVandcorrespondsto3.3s.d.withaglobalsigni¯canceof3.1s.d.6Thetermsevidenceandobservationordiscoveryhavespeci¯cconnotationsinparticlephysics.Havingevidenceofanewparticlemeansthateveniftheparticledoesn'texist,theprobabilityofgettingaresultatleastasextremeasthedatais0.3%correspondingtoap-valueof0.003orathreestandarddeviation(s.d.)°uctuationabovethebackgroundexpectation.Observationordiscoverycorrespondstoap-valueof3£10¡7ora5s.d.°uctuationabovethebackgroundexpectation.49110100120140160180200mH (GeV/c2)95% C.L. Limit/SMTevatron Run II, Lint £ 10 fb-1SM Higgs combinationObservedExpected w/o HiggsExpected ± 1 s.d.Expected ± 2 s.d.Expected if mH=125 GeV/c2SM=1Figure3.7:TevatronHiggsBoson95%CLLimitsExpectedandobserved95%con¯dencelevelupperlimitsdividedbytheSMproductioncrosssectionforarangeofHiggsbosonmasses.Thegreenandyellowbandscorrespondto1s.d.and2s.d.onthemedianbackground-onlyprediction.)2(GeV/cHm100105110115120125130135140145150051015201 s.d.±  bLLR2 s.d.±  bLLRbLLRs+bLLRobsLLRLLR expected for2=125 GeV/cHm 9.7 fb£ intTevatron Run II, LFigure3.8:TevatronLog-LikelihoodRatioExpectedandobservedlog-likelihoodratio(LLR)asafunctionoftheHiggsbosonmass.Thegreenandyellowbandscorrespondto1s.d.and2s.d.onthemedianbackground-onlyprediction.503.3.3LHCDiscovery
OnJuly4,2012itwasannouncedthatanewparticlehadbeendiscoveredconsistentwiththeSMHiggsbosonattheLargeHadronCollider(LHC)almost50yearsafteritsexistencehadbeenproposed.BothexperimentsattheLHC,ATLASandCMS,wereabletoindependentlyclaimdiscovery[19,20].AtthecenterofmassenergiesattheLHC(thediscoveryuseddataat7TeVand8TeV)choosing¯nalstateswithuniquesignaturesbecomesevenmoreimportant.EventhoughthebranchingratioforthedecayH!°°ismuchsmallerthanH!b¹bitsuniquesignaturemakesitmuchmoresensitive.ThediscoverycombinedH!°°,H!ZZ,H!WW,H!b¹b,andH!¿¿decaychannelswithmostofthesensitivitycomingfromthe¯rsttwomodes.Figure3.9showsthelocalbackgroundp-valuefortheATLASandCMSexperiments. [GeV]Hm1101151201251301351401451500Local p10101010101010101010110210310410510610710Obs. Exp. +4lggObs. +4lggExp. +bbtt+nlnObs. l+bbtt+nlnExp. lò = 8 TeV:  sò = 7 TeV:  sATLASs0s1s2s3s4s5s62011 + 2012 DataFigure3.9:LHCLocalp-ValuesLocalbackgroundp-valuesfortheATLASandCMSexperiments.3.4BeyondtheStandardModel
Thestandardmodelhasbeenagreatsuccess;itspredictionshavefueledexperimentalprogressanddiscoveryfordecades.TheHiggsbosonwastheverylastofthesepredic-51tionstobecon¯rmed.However,thisdoesnotmeanthatthestandardmodelisacompletetheory.Therearestillopenquestionsandissuesthatitdoesnotaddress.Someoftheseproblemsareinherent,whilemanyareexternaltothestandardmodel.Belowisalistofsomeoftheproblemsfrombothcategories,butitisbynomeansexhaustive.Thereareissueswhichareoutsidethepurviewofthestandardmodel.Thesearequestionsforwhichthestandardmodelsimplydoesn'thaveananswer.
²GravityTheforceofgravityisresponsibleforthelarge-scalestructureoftheuniverse.Itisalsotheforcewithwhichwearemostfamiliaryetitisnotdescribedbythestandardmodelofparticlephysics.Asofthiswritingtherehasneverbeenasuccessfultheoryofquantumgravity.²DarkmatteranddarkenergyCosmologicalstudiesofthematter/energydensityoftheuniversehaveshownthatthematterdescribedbythestandardmodelconstituteslessthan5%ofthetotalmass-energycontentoftheuniverse.Theremainingmattercontent,whichcontributes¼27%doesnotinteractelectromagneticallyandremainsunseen.Theremainingmass-energycontentisanunknowntypeofenergywhichisacceleratingtheexpansionoftheuniverse.Forthisreasonwerefertothemasdarkmatteranddarkenergy,respectively.TheparticlesandenergiesintheSMcannotaccountforthesetwostrangequantities.²Matter-antimatterasymmetryTheabundanceofmatterintheuniversesuggeststhattherewasanimbalanceofmatterandantimatterintheearlyuniversewhichcannotbeaccountedforinthestandardmodel.²Uni¯cationInthe¯rstepochoftheuniverseknownasthePlanckeraitispredictedthatthegravitationalforcewascomparabletoalltheotherforcesandthatitdominated52matterinteractions.TheenergyscaleatwhichthisoccurredisreferredtoasthePlanckscaleandisapproximately1019GeV.Itistheorizedthatatthisscalealltheforcesweredi®erentaspectsofasingleuni¯edforce.ForthistooccurthecouplingconstantsfortheelectroweakandstrongforceswouldbecomeequalatanenergyscalelessthanthePlanckscale.Unlessthereisnewphysicsbeyondthestandardmodelthisdoesnotoccur.Problemsinherentinthestandardmodelareeitherbasedondisagreementsbetweentheoryandexperimentorarephilosophicalinnature.
²NeutrinomassesInthestandardmodelthereisnowaytoaddmasstermsforneutrinostotheLagrangianwithoutdestroyinggaugeinvariance.ThefermionmasstermsinEq.3.18areconstructedusingboththeleft-handeddoubletandright-handedsingletstatesoftheparticlesandneutrinosdonotexistinaright-handedstate.However,neutrinoexperimentshavefoundthatneutrinosundergo°avoroscillation{somethingthatwouldnotbepossibleiftheydidnothavemass.²HierarchyproblemIfuni¯cationispossibleatthePlanckscaletheSMo®ersnoexpla-nationastowhythePlanckscaleissomuchhigherthantheotherenergyscalesoftheSM.TheelectroweakscaleisequaltotheHiggsbosonvacuumexpectationvalueof246GeV.Fromthisscaleallthewayupto1019GeVisdevoidofanyinterestingphysicsaccordingtothestandardmodel.²Fine-tuningQuantumcorrectionstothethirdterminEq.3.12producecontributionstotheHiggsbosonmasswhicharequadraticallydivergent.Theyremain¯niteuptothePlanckenergyscalebutthecontributionsareverylarge.InorderfortheHiggsbosonmasstoremainsmalltheremustbeveryprecisecancellationstothelarge53contributionstotheHiggsbosonmass.Thisamountstoanunacceptable¯ne-tuningofmodelparameters.Amodelwhichadequatelydescribesrealityshouldnotrelyona¯ne-tuningofitsparameters.Alloftheseproblemspointtosomethingbeyondthestandardmodel.Therearemanytheoreticalproposalsonhowtodealwiththeseproblems.SomeinvolveextensionstotheSMwhichtypicallyincludeadditionalSM-liketermstotheLagrangian.Thesetermsofcourserequireadditionalparameterswhicharenotpredictedbythestandardmodel.Otherproposalsgivethetheoryacompleteoverhaulbypositingsomeunderlyingstructuretothestandardmodelitself.ThesetheoriesmustreproduceSMpredictionsaswellasprovidenewtestablepredictions.Perhapsoneofthemostfamousbeyond-the-SM(BSM)theoriesissupersymmetry[21,22].Likeallofthequantum¯eldtheories,supersymmetryisbasedonanunderlyingsymmetry.Itpositsasymmetryrelatedtoparticlespinandpredictsafermionicsuperpartnerforeverybosonandabosonicsuperpartnerforeveryfermion.Ifsupersymmetrywereanunbrokensymmetry(likethechargesymmetryinGWS)thenthesuperpartnerswoulddi®eronlyby1/2-spin{theywouldhavethesamemassandchargesastheirSMcounterparts.Sincethishasn'tbeenobservedweknowthatifsupersymmetryexistsithastobeabrokensymmetry.3.4.1BSMHiggsSpin&Parity
Oneoftheplacestolookforphysicsbeyondthestandardmodelisoneofitsnewestdiscov-eries:theHiggsboson.IftherecentlydiscoveredbosonistheSMHiggsbosonitwillhavezerospinandevenparity.Thereareotherpossibilitiesforthespinandparityofthediscov-eredbosonifitisnottheSMHiggsboson.Manyofthesepossibilitiescomefromtheories54thatsolvesomeoftheproblemswiththestandardmodel,mostnotablythe¯ne-tuningandhierarchyproblems.ApseudoscalarwithJP=0¡ispredictedfortwoHiggsbosondoubletmodelsoftypeII[23]suchasthosefoundinsupersymmetry[24].TheoriespostulatingextradimensionspredictmassiveparticleswithtensorcouplingsandJP=2+[25,26].Knowingthespinandparityofthediscoveredbosonorbeingabletoexcludespeci¯cvaluesofJPtellsusaboutthestructureoftheunderlyingtheory.PartIIofthisThesisisdesignedtoaddressthisissue.55PartIIConstraintsonModelsfortheHiggsBosonwithExoticSpinandParityPartIIprovidesanin-depthdiscussionofthedataanalysisandconclusions.Itbeginswithadescriptionoftheequipmentusedtoproduce,detect,andrecordthedatainChapter4.Chapter5discussesthemotivationsbehindthisanalysis.Itincludesanoverviewofthetheoreticalframeworkspeci¯ctoanalyzingthespinandparitynatureofaHiggsbosonattheTevatron.ThedataandsimulatedsamplesusedinthisanalysisarediscussedinChapter6.ThedataanalysismethodisdescribedinChapter7.Chapter8givesanoverviewofthestatisticalanalysismethodemployedanddiscussessourcesofsystematicuncertainties.Finally,Chapters9and10discusstheresultsoftheanalysisindetail.56Chapter4
ExperimentalApparatus
4.1Introduction
FermiNationalAcceleratorLaboratory1isalargeacceleratorcomplex.Priorto2008itwasthesiteofthehighest-energyparticlecollisionsintheworld.ThattitlenowbelongstotheLargeHadronCollider(LHC)nearGeneva,Switzerland.Thelabbeganlifein1965withtheapprovalofahighenergyphysicsproposalaimedatbringingtogetherexpertsfromuniversitiesacrossthecountryandtheworld.Theprojectbrokegroundin1968forthe¯rststageoftheprotonacceleratorandwasabletoreachitsdesigncollisionenergyof200GeVbyearly1972.Bytheendof1972ithaddoubleditsenergyto400GeV.From1972to1985theacceleratorprovidedbeamsolelyfor¯xedtargetexperiments.Duringtheearly`80sthelabapprovedandimplementedaplantousetheacceleratorchaintocollideprotonsandantiprotons.Inthefallof1985the¯rstproton-antiprotoncollisionswereseenatacenterofmassenergyequalto1.6TeV.Whencollisionsstoppedinthefallof2011thecenterofmassenergywas1.96TeV.TheD0experimentisoneoftwoexperimentsthatdetectedcollisionsatFermilab.TheD0Collaborationwasfoundedin1983,twoyearsbeforeFermilabsawits¯rstcollisions.Constructionofthe5,000ton,three-storytalldetectorthatwasthecenterpieceoftheexperimentwascompletedinearly1992.Ittookdatauntil1996whenitwasgivenamajor1LocatedinBatavia,Illinois.57upgrade.Aftertheupgradewascompletein2001itcollecteddatauntilcollisionswerehaltedinthefallof2011.Thecollaborationhas68memberinstitutionsfrom15countriesand,asof2015,isstillanalyzingitsdata.
4.2AcceleratingParticlesatFermilab
Figure4.1showsabird's-eyeviewoftheFermilabacceleratorcomplex.DuringthecollidingbeamserathecenterpieceoftheFermilabacceleratorcomplexwastheTevatron,asupercon-ductingproton-antiprotonsynchrotron.Thismachinewastaskedwithboostingtheenergyofeachbeamtotheir¯nalenergyof980GeVaswellasinitiatingandmaintainingcollisionsattwopointsarounditsring.However,theFermilabacceleratorcomplexishometoatotalFigure4.1:FermilabCampusAerialviewoftheFermilabacceleratorcomplex.ThelargeringistheTevatron.oftenacceleratorsandstoragerings.ParticlesstartinoneoftwoPreaccelerators(1&2)wheretheyareacceleratedto750keV.The¯rstsectionofthelinearaccelerator(3),theLinac,furtheracceleratesthemto116MeVwhilethesecondsection(4)acceleratesthemto58400MeV.AftertheLinactheparticlesaresenttothe¯rstsynchrotron,theBooster(5),andgivenaboostupto8GeV.Fromtheretheymoveontothesecondsynchrotron,theMainInjector(6),andleavewithanenergyof150GeV.Antiprotonsbeginintheantiprotonsourceandareshu²edtoasetofstorageringscalledtheDebuncher(7)andtheAccumulator(8)whichcondenseandaccumulatethem.TheyarethensenttotheRecycler(9),apermanentmagnetstoragering.Eventually,whenenoughantiprotonshavebeenaccumulated,theyareacceleratedintheMainInjectoralongwiththeprotonsto150GeV.TheTevatron(10)isthe¯nalstepwheretheparticlesreachanenergyof980GeV.MoredetailsontheFermilabacceleratorchainatthetimeitceasedtooperateasacollidingbeamfacilitycanbefoundinAppendixA.
4.3D0Detector
TheD0detectorwasoneoftwogeneral-purposehadroncolliderdetectorssituatedaroundtheFermilabTevatronring.Designbeganin1983duringconstructionofitssisterdetector,theColliderDetectoratFermilab(CDF).Thistimingmotivatedadesignthatwascomple-mentarytoCDF'sstrengthsandweaknesses,namelyonewithanenhancedabilitytodetectleptons.Physicsgoalsatthetime,reachableattheexpectedcenterofmassenergyoftheTevatronat2TeV,includedprecisionmeasurementsoftheW§andZbosons;explorationofnewphenomenaatandabovetheirmassscales,includingsearchesforthetopquark;andinvestigationofhightransversemomentumpTparticles.Thisrequiredgood,fullsolidanglecoveragetoobtainanaccuratemeasurementofmissingtransverseenergyindicatingthepresenceofneutrinos.MeasurementofhighpTparticlesrequiredthedevelopmentofasophisticatedhadroniccalorimeter.Allofthesespeci¯cationsweretakenintoaccountinthe59designoftheD0detector.Constructionofthedetectorwascompletedinearly1992.ItoperatedduringRunIoftheTevatronfrom1992-1996.DuringRunI,theTevatronoperatedatacenterofmassenergyof1.8TeVwithsixbuncheseachofprotonsandantiprotonswithabunchspacingof3500ns.Ithadatypicalpeakinstantaneousluminosityof1{2£1031cm¡2s¡1.D0collectedapproximately120pb¡1ofdataandwasabletomeetmostofitsphysicsgoalsincludingthediscoveryofthetopquarkalongsideCDFin1995[27,28].From1996-2001theFermilabacceleratorcomplexreceivedanupgradethatincludedtheinstallationoftheMainInjectorandRecycler.DuringthistimetheD0detectorwasalsoupgradedwithabrandnewtrackingsystemandelectronicstohandlethenewTevatronoperatingconditions.RunIIbeganin2001andendedonSeptember30,2011withtheshutdownoftheTevatron.TypicalpeakluminosityneartheendofRunIIwas2{3£1032cm¡2s¡1.TheTevatronoperatedwiththreetrainsoftwelvebuncheseachofprotonsandantiprotonswithabunchspacingof396ns.ThetotalintegratedluminositydeliveredbytheacceleratorduringRunIIwas11.9fb¡1.D0wasabletocollect10.9fb¡1ofdataduringthistime.Afterdataqualitycutsthetotalintegratedluminosityavailableforphysicsanalyseswas9.7fb¡1.TheoriginaldetectorisdescribedindetailinRef.[29]withtheupgradeddetectorofRunIIdescribedinRef.[30].Anadditionalupgradeofthetrackingsystemwasinstalledin2006andisdescribedinRef.[31].ForthepurposesofthisThesisthenextsectionsdescribethedetectorinthestateitwasinaftertheupgradein2006.TheD0detectorisalargemachineweighingapproximately5500tonswithapproximatedimensions300£300£500.Thedetectorisroughlycylindricallysymmetricaroundthebeamlineandnearlycoversthefullsolidangle.TherearethreemaincomponentstotheD0detector:thetrackingsystem,thecalorimeter,andthemuonsystem.Thesecomponents60arearrangedsimilartotheskinofanonion.Fromtheinsidemovingradiallyout,aparti-clewouldpassthroughtheberylliumbeampipe,thesilicontrackingdetector(SMT),thescintillating¯bertracker,asolenoidmagnet,intotheliquidargon(LAr)/depleteduraniumelectromagnetic(EM)andhadroniccalorimeters,onelayerofthemuonsystem,anirontoroidmagnet,andasecondlayerofthemuonsystem.TheEMandhadroniccalorimetersaredividedintothreecryostats:twoendcryostats(EC)andonecentralcryostat(CC).Thecentralcryostatcoverstheregionj´j.1andtheendcryostatcoversthej´j.4region.AcutawayviewofthedetectoranditssubsystemsisshowninFig.4.2.ThecentralregionisillustratedinFig.4.3.Inadditiontothesethreemaincomponentsaretwoothersystemses-sentialforrecordingandanalyzingdata:thetriggeringsystemandtheluminositydetectors.AdditionaldetailsoneachcomponentoftheD0detectoraregiveninAppendixB.Figure4.2:D0DetectorCutawayviewoftheD0detectorshowingtheonionskinlayeringofthedetectorsub-components.61Figure4.3:CentralD0DetectorCutawayviewofthecenteroftheD0detector.4.4ObjectReconstruction
InordertostudythecollisionsrecordedbytheD0detectorwemusthaveanaccuratemeasurementofthefour-momentumoftheparticlesproduced.Wemustreconstructphysicsobjectsfromthesignaturesleftinthedetector.FortheD0detectortherearethreemaintypesofsignatures:jetswhichresultfromhadronicparticleshowers,chargedleptons,andmissingtransverseenergy6ETwhichsigni¯estheproductionofanundetectableneutrinointhe¯nalstate.
4.4.1PrimaryVertex
InteractionsintheD0detectordonotingeneraloccurinthecenterofthedetectorandmaybeo®setspatially.Sinceallotherreconstructedobjectsarede¯nedinreferencetotheinteractionpointorprimaryvertex,caremustbetakentoreconstructitaccurately.TrackswithatransversemomentumpTofatleast0.5GeVandatleasttwohitsintheSMTare62clusteredin2cmintervalsbasedonthezcoordinatesoftheirdistanceatclosestapproachfromthebeamline.Thesezclustersarethenre¯nedbyremovingoutlyingtrackswithrespecttothebeamline.Selectedtracksinaclusterarethen¯ttoacommonvertex.Severalverticesmaybefoundresultingfrommultiplep¹pinteractionsperbeamcrossing.Manyaretheresultofsoftp¹pinteractionsandsomearetheresultofhardscatterinteractionsdistinguishedbytheirhigherthanaveragetrackpT.Thevertexthatismostlikelytohavebeentheresultofhardscatteringischosenastheprimaryvertex.
4.4.2Jets
Quarksproducedintheinteractionwillhadronizeandproduceahadronicshowerofparticleswhichdepositmostoftheirenergyinthehadroniccalorimeter.Theseenergydepositionsinthecalorimeterarereferredtoasjets.Byidentifyingtheshowerstructureandmeasuringtheenergydepositedbythejetwecanreconstructpositionandenergymeasurementsoftheinitialquark.Inthefollowing,jetsareonlyreconstructedinthecentralcalorimeterwhichcorrespondstotheregionj´j·2:5.Whilethereareseveralgoodtechniquesfor¯ndingjetsintheenergydepositioninthecalorimeter,weuseasimpleconealgorithminthisanalysis.TheRunIIMidpointConeAlgorithmisaclusteringalgorithmthatassignscalorimetertowerstojetswithina¯xedconeofradiusRcone=p(¢´)2+(¢Á)2=0:5in´-Áspace.TheRunIIMidpointConeAlgorithmcanbedescribedinfoursteps:towerreconstructionandpre-clustering,clusteringintoproto-jets,additionofmidpoints,andmergingandsplitting.Thesefourstepsaredescribedbrie°ybelow.1.Towerreconstructionandpre-clustering:Pseudo-projectivecalorimetertowersofthesame´andÁ(seeshadedregionsofFig.B.5)arereconstructedbyassigninga(mass-63less)four-momentumvectortoeachcalorimetercellde¯nedwithrespecttotheprimaryvertexandthenaddingthefour-momentumofallcellsinatower.CalorimetertowerswithapT¸1GeVareusedasseedsinthepre-clusteringalgorithm.Towerswithin¢R<0:3oftheseedtowerareclusteredtogether.2.Clustering:AconeofradiusRconeplacedaroundeachpre-clustercenteredatitscentroidde¯nesaproto-jet.Towerswithintheconeareaddedtotheproto-jetanditscenterisadjustedaccordingtothescheme:p¹=(E;~p)=Xi(Ei;~pi)Á=tan¡1µpypx¶pT=qp2
x+p2
yy=12lnµE+pzE¡pz¶(4.1)wherethedirectionofthefour-momentumde¯nesanewcone.Thisprocedurecon-tinuesuntilthefour-momentumofproto-jetcoincideswiththeaxisoftheconeandisconsideredstable.Proto-jetswithmomentumlessthan3GeVarediscarded.3.Additionofmidpoints:Toreducethealgorithm'ssensitivitytosoftradiationwerepeatthepreviousstepusingpT-weightedmidpointsbetweenpairsofproto-jetsasseeds.4.Mergingandsplitting:Toavoiddouble-countingtheenergy,overlappingproto-jetsmustbemergedorsplit.Inthisanalysiswemergetheproto-jetsifmorethan50%ofthepTofthelowerenergyproto-jetisintheoverlapregion.Otherwisethecellsintheoverlapregionareassignedtothenearestjet.Thefour-momentaofthejetsarerecomputedaccordingtoEqs.4.1andthosewithpT<6GeVarediscarded.Toavoidtheinclusionof\noisy"jets{jetsthatcontainalargeportionoffakecalorimeterenergy{inphysicsanalysesweimposeadditionalrestrictionsontheselectedjetswiththe64aimofensuringreasonableenergydeposits.Weuseanalgorithmtoremovecalorimetercellswhosenearestneighborsareunlikelytobefromatruejet.Thefractionofajet'senergydepositedintheEMcalorimetermustbebetween5%and95%andtheenergyfractioninthecoarsehadroniccalorimetershouldbelessthan40%.
4.4.2.1Heavy-°avorJets
Heavyquarks(speci¯callycharm(c),bottom(b),andtop(t))areimportantasthedecayproductsofheavyparticlessuchastheWandHiggsbosonsandareofinterestwhenlookingforphysicsbeyondthestandardmodel.Withtheexceptionofthetopquark(whichdecaysbeforeithadronizes),thesequarkshadronizeandaredetectedasjets.Toacertaindegreeweareabletodistinguishlight-°avorfromheavy-°avorjetsandtoalesserdegreebetweencandbquarkjetsbytheirlifetime.Hadronswithcharmandbottomcontenthavearelativelylonglifetimecomparedtothetopquarkandcantravel¼3mmbeforedecaying.Thisdistanceisjustshortenoughthattheproductsarestillinthetrackingvolumeofthedetector.Figure4.4depictsaneventwithapossibleheavy-°avorjet.Somecharacteristicsofheavy-°avorjetswemightlookforinthedetectorareadisplacedvertexandtrackswithlargeimpactparametersdenotedbyd0inFig.4.4.D0exploitsthesefeaturesusingmultivariateanalysis(MVA)techniquesto`tag'jetsasoriginatingfrombandcquarks.TheoutputoftheMVAisacontinuumusedtoidentifyjetsoriginatingfromthehadronizationofbquarks.Usingthisoutputwecande¯nerequirementsthatcorrespondtocharacteristic\true"bquarkjettagginge±cienciesandlight-°avorjetrejectionrates65Figure4.4:Heavy-°avorTaggingGraphicrepresentationofaheavy-°avorjetdepictingthesecondaryvertexandimpactpa-rameterresultingfromthedecayoftheheavy-°avorhadron.
4.4.3ChargedLeptons
ChargedleptonsintheD0detectorallhavetheabilitytoleavetracks.AsdescribedinSection2.3.1,itisthewaytheyinteractinmatterthatdeterminestheirsignatureinthedetector.
4.4.3.1Electrons
Electronsleavetracksinthetrackingdetectoranddepositthebulkoftheirenergyintheelectromagneticsectionsofthecalorimeter.PhotonsleavesimilarshowersignaturesinthedetectorandareincludedinthereconstructionofEMenergyclusters.ThereconstructionoftheEMclustersproceedsinasimilarmannerasthehadronicjets.Electromagneticclustersarereconstructeddi®erentlyintheCCandECcalorimeters.Pseudo-projectivetowersinthecalorimeterareformedandthetransverseenergyissummedinthefourlayersoftheEM66calorimeterandthe¯rstlayerofthe¯nehadronicsectionofthecalorimeter2.TowerswithET<500MeVarediscarded.IntheCC,beginningwiththetowerwiththehighestETadjacenttowerswithinaconeofradius0:4in´-ÁspaceareaddedtoformanEMcluster.IntheEC,clustersareformedfromadjacenttowerswithinatransversedistanceof10cmfromthecellwiththehighestenergyinthethirdlayeroftheEMcalorimeter.ElectronsaredistinguishedfromphotonsbyrequiringatrackwithpT>1:5GeVwithina¢´£¢Á=0:05£0:05windowaroundthecenterofthecluster.ForclustersintheCC(EC)werequirethat97%(90%)oftheirenergybedepositedinaconeofradiusp(¢´)2+(¢Á)2=0:2intheEMcalorimeterlayers.IntheCCregion,areconstructedisolatedtrackmustbeassociatedwiththeEMcluster.Additionalinformationsuchasthetransverseandlongitudinalshowershape,theEMenergyfraction,numberofhitsinthevariouslayersofthetrackingdetector,andclusterinformationfromthepreshowerdetectorsisusedtotrainamultivariatetoolcalledaboosteddecisiontree(BDT)toidentifyelectrons.
4.4.3.2Muons
Incontrasttoelectrons,muonsdonotproduceshowersintheEMcalorimeter.However,theyleavetracksinboththetrackingdetectorandthemuonsystem.Hitsinbothmuonscintillatorandwirechambersareusedtoformtracksegmentsinthemuonsystem.Thesetracksegmentsarethenmatchedtotracksinthecentraltrackingdetectortoformmuoncandidates.Muoncandidatesarecategorizedbasedonthenumberofhitsinthemuonsystem,thequalityofthetrackreconstructioninthecentraltracker,andisolationparametersinboththecalorimeterandtrackingsystem.Themuonsystemhasdetectorsbothinsideandoutsidethetoroidandwerequireanymuoncandidatestohavehitsinbothofofthese2The¯nehadroniclayerisincludedinthesumtoaccountforleakageofEMshowersintothehadronicsectionofthecalorimeter.67regions,exceptwherethedetectorsupportsystemlimitscoverage.Toreducethecosmicraybackgroundweusescintillatorhittiminginformationtoensurethathitscoincidewithabeamcrossing.
4.4.3.3TauLeptons
Tauleptonsareveryshort-livedanddecaybeforetheycanleaveatrack.Becausethetauleptonhasachargeof1,itdecaysmostoftentooneorthreechargedparticlesandsomenumberofneutralparticles.Thirty-¯vepercentofthetimetheydecayleptonicallytoamuonoranelectronandtwoneutrinos.Theother65%ofthetimetheydecayhadronically.Thisanalysisdoesnotattempttoreconstructorrejecttauleptons.Thee®ectoftheirinclusioninthedataandsimulatedsamplesontheanalysisisnegligible.
4.4.4MissingTransverseEnergy
AsdescribedinSection2.2.2,collidingbeamsofparticleswithequalmomentumresultsinalabframethatisequivalenttothecenterofmomentumframeandtheinitialmomentumiszero.However,thehardscatterinteractionoccursbetweenthepartonsinsidetheprotonandantiproton.Thepartonsdonotcarrythefullmomentumoftheprotonbutinsteadshareitwiththeotherconstituents.Thismeansthatthetotalmomentumoftheinteractionisnotzero.Fortunatelyforusthepartonscarryverylittletransversemomentumandthetotaltransversemomentumcanbeassumedtobezero.Thisisessentialtoourreconstructionofneutrinos.Neutrinosonlyinteractviatheextremelyshort-rangeweakforceandhenceleavethedetectorwithoutatrace.Theirpro-ductioninaneventmustbeinferred.Welookforanimbalanceinthetransverseenergyoftheeventtoidentifyneutrinos.This\missing"transverseenergyor6ETiscalculatedfrom68thetransverseenergy.Thetransverseenergyofindividualcalorimetercellsintheelectro-magneticand¯nehadroniccalorimetersectionsandclusteredenergyinthecoarsehadronicsectionareaddedvectoriallyandthe6ETistakentobeavectorwiththesamemagnitudewithadirectionof180±withrespecttothetotalsum.Anyidenti¯edmuons,whichdonotleaveshowersinthecalorimeter,aresubtractedfromthetotaltransverseenergy.69Chapter5
ModelsfortheHiggsBosonwith
ExoticSpinandParity
InChapter3wediscussedthepossibilityoflookingforphysicsbeyondthestandardmodelbyexaminingthespin(J)andparity(P)oftherecentlydiscoveredHiggsboson.IfitistrulytheHiggsbosonpredictedbytheSMthenitshouldhaveJP=0+.Twoofthemosthighly-motivatedBSMJPstatesareJP=0¡andJP=2+.ThepseudoscalarstateJP=0¡canresultfromtwoHiggsdoubletmodelsoftypeII[23]suchasthosefoundinsupersymmetricmodels[24].AbosonwithtensorcouplingsJP=2+canariseinmodelswithextradimensionssuchasgenericmodelspredictingabulkRandall-Sundrumgraviton[25,26].TheexperimentsattheLHChavemademeasurementsonthespinandparityoftheHiggsbosonintheH!WW,H!°°,andH!ZZdecaychannels.TheabilityoftheLHCexperimentstodistinguishbetweendi®erentJPassignmentsisbasedprimarilyontheangularanalysisoftheHiggsbosondecayproducts.ThemeasurementshavebeenconsistentwiththeSMJPassignmentofJP=0+andtheyhavebeenabletoexcludesomemodelswithexoticspinandparity[32,33].TheexperimentsattheTevatronhavefoundevidenceofaparticledecayingtotwobquarks[18],whichisconsistentinmassandproductionratewiththeHiggsbosondiscoveredattheLHC[19,20].ThisisuniquerelativetotheLHCmeasurementswhichrelyonbosonic70¯nalstates.Thus,weareinauniquepositiontostudythespinandparityofthisbosoninitsdirectdecaytofermions.Thisiswell-motivatedbecauseiftheHiggssectorismorecomplexwemightexpectmultipleHiggsbosonswhichcoupleseparatelytofermionsandbosons.ItisthereforeimportanttostudytheJPcharacteroftheHiggsbosoninitsdecaystobothbosonsandfermions.TheVHassociatedproductionchannelsareamongthemostsensitivechannelsattheTevatronando®eramethodforstudyingthespinandparityoftheHiggsbosonina(mostly)model-independentway.InthisThesiswewillfocusontheWHassociatedproductionchannelbutthegeneralmethodofanalysisisnearlyidenticaltotheZHassociatedproductionchannels.InChapter9wewilldiscusstheresultsofthecombinationofVHchannelsbothattheD0CollaborationandwiththeCDFCollaboration.HqWq'Wb
b`Figure5.1:WHAssociatedProductionExampletree-levelFeynmandiagramoftheWHassociatedproductionchannelwiththeHiggsbosondecayingtoapairofbquarksandtheWbosondecayingleptonically.5.1ThresholdProduction
Anexampletree-levelFeynmandiagramofthisprocessisshowninFig.5.1.Bystudyingthekinematicsofthis¯nalstatewecandistinguishdi®erentJPstates.Atahadroncolliderthehard-scatterinteractionoccursbetweentheconstituentpartonsofthe(anti)proton.71Sincethepartonscarryonlyafractionofthetotalmomentumoftheprotontheamountofenergyavailablefortheproductionof¯nalstateparticlesissigni¯cantlyreducedrelativetothetotalcenter-of-massenergyofthecollidinghadrons.Iftheinteractingpartonscarrymomentumfractionsx1andx2thenthecenter-of-massenergyofthepartonsp^sisrelatedtothecenter-of-massenergyofthecollidingbeamspsby^s=x1x2s.Themomentumfractionsoftheinteractingpartonsaredescribedbyprobabilitydensitiescalledpartondistributionfunctions(PDFs).ThePDFsdescribetherelationshipbetweenthemomentumfractionxandthemomentumexchangeQ2oftheinteractionandarederivedfromexperiment.TheprotonpartondistributionfunctionsareplottedasafunctionofxfortwovaluesofQ2inFig.5.2.Toestimatethemomentumfractionsneededtoproducea¯nalstatewithmassMweusetheruleofthumbp^s»M»Q.Figure5.3depictsthepartonkinematicsattheTevatronasafunctionofthemomentumexchange.x-410-310-210-1101)2xf(x,Q00.20.40.60.811.2g/10dduuss,cc,2 = 10 GeV2Qx-410-310-210-1101)2xf(x,Q00.20.40.60.811.2x-410-310-210-1101)2xf(x,Q00.20.40.60.811.2g/10d
duuss,cc,bb,2 GeV4 = 102Qx-410-310-210-1101)2xf(x,Q00.20.40.60.811.2MSTW 2008 NNLO PDFs (68% C.L.)Figure5.2:ProtonPartonDistributionFunctionsProtonpartondistributionfunctionsfromtheMSTW2008next-to-next-leading-ordercalcu-lationfortwodi®erentvaluesofthemomentumexchange[34].7210-710-610-510-410-310-210-1100100101102103104105106107108109  WJS2008fixed
targetHERAx1,2 = (M/1.96 TeV) exp(±y)Q = MTevatron parton kinematicsM = 10 GeVM = 100 GeVM = 1 TeV42204y =Q2   (GeV2)xFigure5.3:TevatronPartonKinematicsTevatronpartonkinematicsasafunctionofthemomentumexchange[35].73ProducingtheWH¯nalstaterequiresanenergyofatleast125+80=205GeV.ThenecessarymomentumfractionforM2¼4£104»Q2canbereadfromFig.5.3.Assumingarapidityofzerothiscorrespondstoamomentumfractionofapproximatelyx=0:1.Atamomentumfractionx=0:1theparton-partonluminosityisnearalocalmaximumandtheWHsystemisalmostalwaysproducednearthreshold.Wecande¯nehowfartheWHsystemisfromthresholdas¯=2p=pswherepistheWHthree-momentuminthecenter-of-massframeofthecollidingbeamsinunitsofthecenter-of-massenergy.5.2HelicityAmplitudes
ThemethodofdeterminingtheHiggsbosonspinandparityassignmentsusedinthisanalysiswas¯rstdescribedinthecontextofelectron-positroncollisions[36],butitsapplicationtohadroncollisionsisstraightforward.TheformoftheproductioncrosssectionandangulardistributionsatthresholddependontheJPcharacteroftheHiggsboson.Becauseweareonlyinterestedinthebehavioroftheseobservablesatthresholditisnotnecessarytoknowtheexactformofthecouplings.Thisallowsustodistinguishdi®erentJPassignmentsinamodel-independentway.Inthefollowingwewillworkinthehelicityformalism(seeforexampleRef.[37])whichiswell-suitedforanalyzingstateswithde¯nitespinandparity.Helicityisde¯nedasthedotproductofthespinoftheparticlewiththeunitvectorinthedirectionofitsmomentumh=~S¢^p1.AmassiveparticlewithspinS=Jhas2J+1helicitystateswithvalues¸=¡J;¡J+1;:::;J.Masslessparticlesontheotherhandhaveonlytwohelicitystates¸=§Jduetothefactthattherearenocomponentsofspin1HereIuseStorefertothespinoftheparticletobeprecise;helicitydependsonthespinoftheparticle~Snotthetotalangularmomentum~J=~L+~Swhichisde¯nedtobeperpendiculartothemotion.Incollisionphysicswede¯neouraxessuchthattheorbitalangularmomentum~Liszeroand~J=~S.74transversetothedirectionofmotion2.ThehelicityamplitudeAoftheW¤!WHprocesswiththeazimuthalanglesettozerotakestheformA/d1
M;¸(µ)A¸W¸Hwhered1
M;¸(µ)aretheWignersmalldmatriceswhichrelatearotatedstatetoanoriginalunrotatedstateand¸=¸W¡¸Harehelicities.TheA¸W¸HarereducedamplitudeswhichonlydependonthehelicitiesoftheWandHbosons.ThereducedhelicityamplitudesarerelatedtostateswithnegativehelicitybyA¸W¸H=nHA¡¸W¡¸H.ThenormalityoftheHiggsbosonnHisde¯nedbynH=(¡1)JP.Theangulardi®erentialcrosssectionisproportionaltothesquareofthehelicityamplitudessummedoverthe¯nalstatehelicities¸Hand¸W.Performingthesummationweobtain:1¾d¾dcosµ=34A2sin2µ£jA00j2+2jA11j2¤+(1+cos2µ)£jA01j2+jA10j2+jA12j2¤A2=jA00j2+2jA11j2+2jA01j2+2jA10j2+2jA12j2:(5.1)Equation5.1isthegeneralformforaHiggsbosonspinJ·2andnotalltermsarenonzeroforaspeci¯cJ.Tostudythethresholddependence,wecanparametrizethereducedamplitudesasafunctionof¯.AsanexamplewecanexaminetheSMcase:JP=0+.ThespinoftheSMHiggsbosonrestrictsthereducedhelicityamplitudestothoseoftheformA¸W0.TheWbosonhasJP=1¡withhelicityvalues¸W=0;§1.OnlytwotermsinEq.5.1remain:A00andA10.SubstitutingthestandardmodelvaluesA00=¡EW=mWandA10=¡1andrearrangingEq.5.1yields1¾d¾dcosµ=34¯2sin2µ+8m2
W=s¯2+12m2
W=s:(5.2)Atthreshold¯!0andWHproductionisisotropic.Toleadingorder,thetotalcross2Becausemasslessparticlestravelatthespeedoflightitisimpossibletoboostintotherestframeoftheparticle;ithasnorestframe.Youcanonlymeasurethespinalongitsmomentum.75sectionnearthresholdgoesasonepowerof¯fromthephasespaceintegration.Athighboosts(large¯)ithasacharacteristicsin2µdependence.Nearthreshold,wherethecrosssection»¯,theproductionmechanismisthusreferredtoass-waveproduction.TofurtherinvestigatetheimplicationsofEq.5.1wecanexamineastatewithnegativenormality:JP=0¡.TheequationrelatingreducedhelicityamplitudeswithpositiveandnegativehelicitiesforbidstheA00termforstateswithnegativenormality.EverythingelseremainsthesameandthisleavesonlytheA10term.ForaspinandparityassignmentofJP=0¡,theA10termisoftheform¡i¯sa1wherea1isacoe±cientthatdoesnotdependonthemomentanearthreshold.Atthresholdtheproductionisisotropicanddevelopsacos2µdependenceathigher¯.Thecrosssectionrisesas»¯3andtheproductionmechanismisd-wave.Otherspinandparityassignmentscanbeexaminedinthesamemanner.Ingeneral,thecrosssectionrisesasthesquareoftheleadingorder¯dependenceofthereducedamplitudesplusonefactorof¯fromthephasespaceintegration.5.3InvariantMassasaDiscriminationTool
Theformoftheangulardistributionabovethresholdandthe¯-dependenceofthecrosssectionnearthresholda®ectthe¯nalstatekinematicsinobservableways.Theangulardis-tributioncanbeexaminedbymeasuringtheangularcorrelationsbetweenthedecayproductsinthe¯nalstate.AttheLHCthisistheprimarymethodofmeasuringthespinandparityoftheHiggsboson.ComparedtotheLHC,theTevatronhasamuchsmallerintegratedluminosityandthebehaviorofthecrosssectionnearthresholdismoreimportant.The¯-dependenceofthecrosssectiona®ectsthe¯nalstatekinematicsbyenhancingorsuppressingthecontributionsofparton-partoninteractionswithaparticularmomentumfraction.Asan76example,considerthecaseofJP=0¡pseudoscalarversustheSMHiggsboson,JP=0+.JustabovethresholdtheJP=0¡crosssectionisheavilysuppressedbythe¯3dependencecomparedtothe¯dependenceofthestandardmodel.ThispushesproductionoftheWHsystemtohigherenergiesand,thus,tohighermomentumfractions.Thise®ectisobservableintheinvariantmassdistributionofthe¯nalstate.Thesquareoftheinvariantmassisde¯nedastheMinkowskiinnerproductofthefour-momentumP¹P¹.Asaninvariantitisthesameinallreferenceframes.IntherestframeoftheW¤bosontheinvariantmassissimplythemassoftheW¤bosonM.ReferringbacktoSection5.1wesawthatM2»x1x2sandthresholdproductionoftheWHsystemrequiresthemomentumfractionstobe»0:1.LargeraveragemomentumfractionswillincreasethemassoftheW¤bosonandtheinvariantmassofthesystem.ForWHproductiontheinvariantmassasde¯nedinthelabframeis:m=p(EW+EH)2¡(~pW+~pH)2:(5.3)Asaproofofconcept,theauthorsofRef.[38]producedMonteCarloeventsamplesforZX!``b¹b,WX!`ºb¹b,andVX!ººb¹bproductionwithspinandparityassignmentsofJP=0+;0¡,and2+andappliedthesamecutsastheD0andCDFpublishedanalysesofthesameproductionchannels.Figure5.4showstheinvariantmassoftheZX!``b¹b¯nalstateusingD0cuts.Asexpected,theJP=0¡statehasonaverageahigherinvariantmass.Thee®ectisstrongerfortheJP=2+statebecausethecrosssectionrises»¯5abovethreshold,thusforcingxvalueshigher.BecausethelifetimesoftheWandHbosonsaresoshortwemustinsteadmakemea-surementsontheirdecayproducts.WhenconsideringleptonicdecaysoftheWorZboson77Figure5.4:SimpleModeloftheInvariantMassoftheZX!``b¹bSystemPlotoftheinvariantmassoftheZX!``b¹bsystemfromthesimplemodelinRef.[38]usingtheselectionrequirementsfromthepublishedD0ZH!``b¹banalysis[39].78withoneormoreneutrinostheinvariantmassofthe¯nalstatecannotbemeasured.Wecanonlyinferthepresenceofneutrinosbytheapproximateconservationofmomentuminthetransversedirection;theirmomentainthezdirectionisnotmeasured.Weinsteadde¯neaquantitythatisinvarianttoboostsinthezdirectionandbehavesinthesamemannerastheinvariantmass:thetransversemassmT.FortheWX!`ºb¹bproductionchannelthetransversemassism2
T=(EWT+EXT)2¡(~pW
T+~pX
T)2;pW
T=6ET+p`
T:(5.4)Figure5.5isthetransversemassdistributionfortheWX!`ºb¹bchannelusingtheselectioncutsfromtheCDFexperiment'spublishedWH!`ºb¹banalysis[40],againfromRef.[38].Figure5.5:SimpleModeloftheTransverseMassoftheWX!`ºb¹bSystemPlotofthetransversemassoftheWX!`ºb¹bsystemfromthesimplemodelinRef.[38]usingtheselectionrequirementsfromthepublishedCDFWH!`ºb¹banalysis.Thedi®erenceintheaveragevalueofthetransversemassoftheWXsystembetween79theJPassignmentsisthekeytodeterminingiftheexcessofHiggs-likeeventsobservedattheTevatronisindeedaHiggsbosonandifithassimilarspinandparityquantumnumbersasthebosondiscoveredattheLHC.Thismakestheanalysismethodrelativelysimple:1)generateMonteCarlosamplesforWX!`ºb¹bproductionwithJP=0¡andJP=2+,2)re-analyzethedatausingthepublishedanalysismethod,thistimeincludingthenewsamples,and3)usethetransversemassoftheWXsystemtodiscriminatebetweenJPassignments.TherestofthisThesiswilldescribethisanalysismethodindetail.Chapter6describesthedataandthesimulatedeventsamples.TheanalysismethodincludingtheselectioncriteriaisdescribedinChapter7.ThestatisticalmethodusedtoanalyzethetransversemassdistributionisdiscussedinChapter8.Finally,theresultsandconclusionsaregiveninChapters9and10.80Chapter6
Data&Simulation
ThedatastudiedinthisanalysiswerecollectedoveraperiodoftenyearsusingtheD0detector.ThedataweretakenstartingafterthecommissioningoftheMainInjectorandtheupgradeoftheD0detector,andisreferredtoasRunII.RunIIisdividedintotwomajorsubsets,RunIIaandRunIIb,bytheadditionofanewlayertothesilicondetector.RunIIbisfurtherdividedintofourepochs;RunIIb1,RunIIb2,RunIIb3,andRunIIb4;eachrepresentingroughlyayearofrunning.Eachofthe¯veepochs(includingRunIIa)aretreatedseparatelytoaccountfordi®erencesbetweenepochssuchasinstantaneousluminositypro¯les,trackingdetectore±ciency,anddetectorchanges.WeproducesimulatedeventsamplesviaMonteCarlo(MC)foreachepochtoproperlymodelthedetectorresponse.Withtheexceptionofthemultijetsample,weusedMonteCarlotosimulatenearlyallSMprocesseswhichcouldresultinour¯nalstatesignature.AllsimulationsusetheCTEQ6L1[41]leading-orderpartondistributionfunction(PDF)setintheeventgeneration.Partonshoweringandhadronizationisdonewithpythia[42]forallMCsamples.Eventsareprocessedthroughafulldetectorsimulationusinggeant[43].Tosimulatetheoperatingconditionsofthedetectorsuchasresidualsignalsfromthepreviousbeamcrossing(referredtoaspile-up),noiseinthedetector,andadditionalp¹pinteractions(orunderlyingevents)weoverlayeventsfromrandomlyselectedbeamcrossingswiththesameluminosity.Finally,thesimulatedeventsareputthroughthesamereconstructionprocessasdata.816.1Data
6.1.1Luminosity
OverthecourseofRunII,theacceleratordivisionwasabletodeliver11.9fb¡1ofintegratedluminositytotheD0experiment.Figure6.1showsthedeliveredandrecordedintegratedluminosityoverthecourseofRunII.TheD0detectorwasabletorecord10.7fb¡1ofdataduringthisperiod.Detectorlatencyanddeadtimeaswellasunexpectedmalfunctionsreducethedatacollectione±ciencytobelow100%.Oncedataarerecordedweenforcerequirementsonthequality;ifanypartofthedetectorwasfunctioninginamannerthatcompromiseditsabilitytoidentifyphysicsobjectstherecordeddataduringthattimeiscut.Afterdataqualitycutsthetotalintegratedluminosityusedinthisanalysisis9.74fb¡1.Table6.1showstheintegratedluminositydistributionacrossallepochs.Theuncertaintyontheluminositymeasurementis6.1%.Figure6.1:RecordedLuminosityShownaboveisagraphoftheintegratedluminosityoverthewholeofRunII.Atotalintegratedluminosityof11.9fb¡1wasdeliveredbytheacceleratordivision.D0wasabletorecord10.7fb¡1.82EpochIntegratedLuminosity(fb¡1)RunIIaRunIIa1:08RunIIbRunIIb11:22RunIIb23:04RunIIb31:99RunIIb42:40Table6.1:IntegratedLuminosityTotalintegratedluminosityafterdataqualityrequirementsforeachepoch.6.1.2Triggers
Thedatasampleforthisanalysiswasobtainedthroughtheuseofspeci¯ctriggersde¯nedbyD0tocaptureeventswiththesignatureofhigh-pTelectroweakinteractions.Ofparticularimportancetothisanalysisaretriggersbasedonsingle,chargedleptons.FortheelectronchannelweusethelogicalORofthesingleEMandEM+jetstriggersuites.BothtriggersuitesrequireagoodEMtriggerobjecttobeabovepre-de¯nedthresh-oldsandtheEM+jetstriggerrequiresatleastonehigh-pTjet.MinimumelectronandjetpTthresholdsaredi®erentforeachtrigger.Thee±ciencyofthesetriggersisapproximately(90-100)%fortheeventspassingtheeventselectionoutlinedinSection7.1dependingontheindividualtriggerandthelocationoftheelectroncandidateinthedetectorvolume.WemodelthetriggerresponseinMonteCarlobyapplyingaweighttoevents.Theweightiscalculatedbymeasuringthetriggere±ciencyasafunctionofelectronÁ,´,andpT.Inthemuonchanneltheequivalenttriggersuites{singlemuonandmuon+jets{haveane±ciencyofapproximately70%forourselectedevents.Toincreasetheacceptanceinthemuonchannelwedonotrequireanyspeci¯ctriggerandinsteadusethelogicalORofallavailableD0triggerswiththeexceptionofthoseaimedatidentifyingheavy-quark83jets.Thefullcomplementoftriggerswhichcontributetothisinclusiveeventsampleislargeandvaried,makingitdi±culttomodelintheMonteCarlo.Wethereforetakeatwo-stepapproachtomodelingthemuontriggerresponse.First,weverifygooddataandsimulationagreementforeventsselectedbythewell-modeledsinglemuonandmuon+jetstriggersuites,collectivelyT¹OR.WethencomparethedataeventsselectedbytheinclusivetriggerTincltothedataeventsselectedbyT¹ORandde¯neatriggercorrectionforMCintendedtoaccountfortheadditionalcontributionfromTincl:Pcorr=(NData¡NMJ)incl¡(NData¡NMJ)¹ORNMC:(6.1)HereNMCisthetotalnumberofMCeventswithtriggere±ciencysetto1,NDataisthenumberofdataevents,andNMJisthenumberofmultijetevents.Multijetevents,asdetailedinSection6.4,areestimatedfromdataanddonothavethiscorrectionapplied;theirin°uenceonPcorrisremovedbysubtractingthemfromthedataevents.The¯naltriggere±ciencyappliedtoeachMCeventisthesumofPcorrandthee±ciencyofT¹ORwiththeconstraintthatthetotale±ciencymustbelessthanunity.Themostsigni¯cantcontributionstoTinclbeyondT¹ORtriggersarebasedonjetsand6ET.Toaccountforthis,thetriggercorrectionPcorrisparametrizedasafunctionofthescalarsumofthepTofalljetsandthe6ET.Toaccountforthechangingtriggercompositionasafunctionofdetector´andthepartialmuoncoverageduetosupportstructureswederiveseparatecorrectionsforregionsinmuon´andÁ.846.2SimulatedSignalSamples
TotestthecompatibilityofmodelsforaHiggsbosonwithnon-SMJPassignmentswithdatawestudytheWH!`ºb¹bprocess.WeincludetheZH!``b¹bprocessinoursignalsamplestoaccountforscenarioswhereonlyoneoftheleptonsisidenti¯edandtheothercontributestothe6ET.AllsampleshavebeengeneratedforaHiggsmassmHof125GeV.TheSMHiggsbosonsignalprocesses,whichhaveJP=0+,aregeneratedusingpythia.Bothnon-SMHiggsbosonsignals,thepseudoscalarJP=0¡andthegraviton-likeJP=2+signals,aregeneratedusingmadgraph[44].WeuseaRandall-Sundrum(RS)extra-dimensionalmodel[25,26]whichhasaJP=2+particlewithgraviton-likecouplingstosimulateanon-SMJP=2+Higgsboson.Agenericmodelofthistypehasbeenimplementedinmadgraph[45,46].TogenerateeventsusingthismodelweassigntheJP=2+particleamassof125GeVandspecifytheproductionmechanismand¯nalstate.Inadditiontothemodelsavailableinmadgraph,itispossibletoimplementuser-de¯nedmodels.Themodelusedforthegenerationofeventswithanon-SMJP=0¡HiggsbosonwaswrittenbytheauthorsofReference[38].Wehaveveri¯edthattheSMHiggsbosonsamplegeneratedwithpythiaagreeswithaSMHiggsbosonsampleproducedwithmadgraph.Allsignalsamplesarenormalizedtothecrosssectiontimesdecaybranchingratioaspredictedbythestandardmodel.Thesignalcrosssectionsarecalculatedatnext-to-next-to-leadingorder(NNLO)usingtheMSTW2008NNLOPDFset[34].Weusehdecay[47]toobtainthedecaybranchingfractionfortheHiggsboson.Table6.2listsallthesignalpro-cesses,thespinandparityvalues,theeventgenerator,andthecrosssectiontimesbranchingratio¾£BR.85ProcessJPGenerator¾£BR[pb]WH!`ºb¹b0+pythia0:02425ZH!``b¹b0+pythia0:00458WX!`ºb¹b0¡madgraph0:02425¤ZX!``b¹b0¡madgraph0:00458¤WX!`ºb¹b2+madgraph0:02425¤ZX!``b¹b2+madgraph0:00458¤Table6.2:SignalCrossSectionTimesBranchingRatioSignalcrosssectionstimesbranchingratio.Itemsmarkedwith¤donothaveatheoreticallyde¯nedcrosssectionsotheyarenormalizedtotheSMprocess.
6.3SimulatedBackgroundSamples
WeconsiderSMprocesseswhichareabletoreproducethe¯nalstateproductsasback-grounds.Theseincludemultijetevents,vectorbosonplusjetsevents(V+jets),dibosonproductionVV,singletopquarkproduction,andtopquarkpairt¹tproduction.Thesebackgrounds,withtheexceptionofmultijet,areallsimulatedbyD0andhavestandardcorrectionsapplied.Thetypeofcorrectiondependsonthebackgroundsample.6.3.1V+jetsSamplesOurV+jetssamplesaregeneratedwithalpgen[48].WeproduceseparatesamplesforWandZbosons.BothbosonsdecayleptonicallywiththeZbosondecayingtotwoleptons(!``)andtheWbosondecayingtoaleptonandaneutrino(!`º).Weproducevectorbosonsandlight-°avor(lf)jetsseparatelyfromvectorbosonsandheavy-°avor(hf)jets.TheW+lfsampleconsistsofeventswithoneWbosonandbetween1{5light-°avorjets.Heavy-°avorjetsarede¯nedashavingborcquarkcontentandtheW+hfsampleconsistsofoneWboson,twob(c)jets,and1{3light-°avorjets.TheZ+lfandZ+hfsamplesare86generatedinasimilarmannerwithoneZbosonand1{3light-°avorjetsortwob(c)jetsand1{2light-°avorjets,respectively.TheZ+jetssamplesareproducedinfourregionsdependingonthemassoftheZbosontoincreasestatistics.WereweightourV+jetssamplestoaccountforknownissues(seeforexampleRef.[49])inalpgenleadingtoincorrectmodelingofcertainkinematicdistributions.Thereweightingsaredesignedtocorrecttheshapeofthedistributionwithouta®ectingtheoverallnormal-ization.Tominimizecontaminationfromsignalwederivethecorrectionbeforeeventsareb-tagged.Correctionsarederivedineventsamplesselectedwiththemuon+jetstriggersbyadirectcomparisonbetweenV+jetsMCanddatawithallnon-V+jetsbackgroundssubtractedandareappliedtobothelectronsandmuons.Wecorrectthe´distributionofthetwohigh-estpTjetsforbothW+jetsandZ+jetsevents.Thelepton´distributioninW+jetseventsisalsocorrected.DiscrepanciesinthetransversemomentumoftheWbosonpW
Tandthejetseparationin´-Áspace¢R(j1;j2)arecorrelatedandatwo-dimensionalcorrectionisderived.ThepW
TreweightingisonlyappliedtoW+jetseventswhilethe¢R(j1;j2)reweightingisappliedtoallV+jetsevents.TheV+jetssampleandthemultijetsamplearenormalizedtodataaftertheeventselection.Asimultaneous¯toftheV+jetsandmultijetsamplestodatawithallotherSMbackgroundssubtractedisperformedinthemW
Tdistribution.Tables6.3and6.4summarizetheeventsgeneratedfortheV+jetssample.6.3.2DibosonVVSamplesDibosonprocessesincludeWW,ZZ,orWZproductionwhereoneweakvectorbosondecaysleptonicallyandonedecayshadronically.Alldibosonprocessesaregeneratedwithpythia.Table6.5summarizesthecrosssectiontimesbranchingratioforthedibosonprocesses.87Process¾£BR[pb]W+jj+0lightparton5875:679+1lightparton1656:399+2lightpartons388:983+3lightpartons91:519+4lightpartons20:920+5lightpartons6:599W+bb+0lightparton17:828+1lightparton8:127+2lightpartons2:971+3lightpartons1:392W+cc+0lightparton45:684+1lightparton25:639+2lightpartons10:463+3lightpartons5:08Table6.3:W+JetsEventSampleCrosssectiontimesbranchingratioforW+jetsevents.Allprocessesaregeneratedusingalpgen.6.3.3SingleTopQuarkSamples
TheelectroweakproductionofasingletopquarkoccursattheTevatronintwomainchan-nels:s-channelandt-channel.ThetwoproductionchannelsareillustratedinFig.6.2.WeconsidertopquarksdecayingintoaWbosonandabquarkwheretheWbosondecaysleptonically.Weproduceboths-channelandt-channelsamplesseparatelyforeachlepton°avorusingsingletop[50].TheircrosssectionsmultipliedbybranchingratioareoutlinedinTable6.5.
6.3.4TopQuarkPairt¹tSamplesTopquarkpairproductionisillustratedinFig.6.3.Weconsiderthedecaychaint!WbwheretheWbosonseitherbothdecayleptonicallyoronedecayshadronicallyandtheother88ProcessMassRange[GeV]¾£BR[pb]Z+lfProductionZ(!``)+lf15{751488:080075{130710:7280130{2505:3353250{19600:4380Z+hfProductionZ(!``)+b¹b+lf15{754:548275{1304:0986130{2500:0353250{19600:0034Z(!``)+c¹c+lf15{7534:836075{13010:9150130{2500:0965250{19600:0085Table6.4:Z+JetsEventSampleCrosssectiontimesbranchingratioforZ+jetsevents.Forallprocesses`=e;¹;¿.TheZ+lfprocessesareproducedwithanadditional0,1,2,or3lightpartons.TheZ+hfprocessesareproducedwithanadditional0,1,or2lightpartons.Allprocessesaregeneratedusingalpgen.Figure6.2:SingleTopQuarkProductionDiagramsRepresentativeFeynmandiagramsforsingletopquarkproductioninthes-channelandt-channel.decaysleptonicallyforallt¹tsamples.ThecontributionfromeventswherebothWbosonsdecayhadronicallyisnegligibleinthisanalysis.Samplesareproducedwithanadditional0,1,or2lightquarkjet(s)toaccountforpossibleadditionaljetsinthe¯nalstatefromhigher-89orderdiagramsandmultiplecollisions.Weusealpgentogenerateeventsinclusivelyforalllepton°avors.Table6.5outlinesthegeneratedprocesses.Figure6.3:TopQuarkPairProductionDiagramRepresentativeFeynmandiagramfortopquarkpairproduction.6.4MultijetSampleDerivation
RatherthanbeingsimulatedwithMonteCarlo,themultijetsampleisderivedusingdata.Atemplatesampleiscreatedbyreweightingindividualdataeventsandisthenscaledaftertheeventselectiontoestimatethenumberofmultijeteventsthatpassourselection.Todothiswemakeuseofthe\loose"and\tight"leptonidenti¯cationcriteriadescribedinSection7.1.Eventsthatpassthetightleptonidenti¯cationcriterionareconsideredintheanalysiswhilethoseeventsonlypassingtheloosecriterionarenot.ThenumberofeventsindatawithaleptonthatpassestheloosecriterionNLwillbeNL=N`+NMJ(6.2)whereN`isthenumberofeventswitharealleptonintheloosesampleandNMJisthenumberofmisidenti¯edmultijeteventsintheloosesample.Toobtainthenumberofevents90ProcessGenerator¾£BR[pb]WWinclusivepythia11:34ZZinclusivepythia1:20WZinclusivepythia3:22Singletopquarks-channel(tb!eºb¹b)singletop0:1050Singletopquarks-channel(tb!¹ºb¹b)singletop0:1180Singletopquarks-channel(tb!¿ºb¹b)singletop0:1260Singletopquarkt-channel(tqb!eºbq¹b)singletop0:2520Singletopquarkt-channel(tqb!¹ºbq¹b)singletop0:2470Singletopquarkt-channel(tqb!¿ºbq¹b)singletop0:2630t¹t!b¹b+`+º`¡¹º+0lightpartonalpgen0:4900+1lightpartonalpgen0:1980+2lightpartonsalpgen0:0941t¹t!b¹b+`º+2j+0lightpartonalpgen2:0340+1lightpartonalpgen0:8270+2lightpartonsalpgen0:4050Table6.5:DibosonandTopQuarkBackgroundsCrosssectionstimesbranchingratioandnumberofeventsfordibosonandtopquarkback-grounds.
indatawithaleptonthatpassesthetightrequirementNTwede¯netwoe±ciencies:i)thee±ciencyforarealleptonthatpassesthelooserequirementtoalsopassthetightrequirement²`andii)thee±ciencyforajetmisidenti¯edasaleptonthatpassedthelooserequirementtosubsequentlypassthetightrequirementfj.NTisthende¯nedasNT=²`N`+fjNMJ:(6.3)Becauseourgoalistoreweightactualdataeventstocreateabackgroundsamplewemustbecarefultokeepoursamplesorthogonaltoavoidcorrelated°uctuationsinourresults.Wedothisbycreatingthetemplatesamplesuchthatitonlycontainsthoseeventswhichpassthelooserequirementbutfailthetightrequirement.Thetemplatesamplethendoesnot91containanyeventswhicharealsoconsideredintheanalysis.Equations6.2and6.3canbecombinedto¯ndthenumberofmisidenti¯edmultijeteventsinthetightsampleNTMJasafunctionofthenumberofloose-not-tighteventsNL¡T:NTMJ=fj1¡fjNL¡T¡fj(1¡²`)(1¡fj)²`NT`(6.4)whereNT`isthenumberofeventswitharealleptoninthetightsample.Thisequationillustratesthecompositionofthemultijetbackgroundsample;itisthenumberofloose-not-tighteventsmodi¯edbyafactorminusthenumberofrealleptoneventsinthetightsamplemodi¯edbyanotherpositivefactor.Itwouldbesu±cientheretoderiveweightsfortheloose-not-tightevents,butIwillmakeonemoreadjustmentforclarity.SubstitutingEq.6.4intoEq.6.3weobtainthetotalnumberofeventsinthetightsample:NT=fj1¡fjNL¡T+µ1¡fj(1¡²`)(1¡fj)²`¶NT`:(6.5)Ratherthanbeingconstantvalues,thee±cienciesfjand²`arefunctionsoftheeventkinematicsqi.Usingthisinformationwecandeviseanevent-by-eventweightingschemetocalculatethenumberofeventsinthetightsample.NT=NL¡TXi=1fj(qi)1¡fj(qi)+NT`Xi=1µ1¡fj(qi)(1¡²`(qi))(1¡fj(qi))²`(qi)¶=NL¡TXi=1i+NT`Xi=1(1¡j!ij)(6.6)Theweightsiand1¡j!ijareappliedtotheloose-not-tightsampleandrealleptoneventsinthetightsample,respectively.Realleptoneventsinthetightsampleareasourceofsignal92contaminationinthemultijetbackgroundsample.Theweightappliedtotheseeventsisexpectedtobeasecond-ordere®ectandassuchisonlyappliedtothedominantsourceofrealleptonsinthetightsample:V+jetsevents.Theleptone±ciencies²`arederivedfromasampleofZ=°¤!`¹`eventsandarefunctionsofleptonpT.Thejete±cienciesfjarecalculatedinaneventsamplewith5<6ET<15GeVandnotrianglecut(seeSection7.1)meanttoreducethemultijetbackground.Allothereventselectioncriteriaareapplied.Intheelectronchannelthee±ciencyisparametrizedasafunctionofdetectorj´jinregionsofelectronpTandtheminimumÁanglebetweenthevector6ETandjet¢Á(6ET;jet).Thee±ciencyinthemuonchannelisparametrizedasafunctionofmuonpTinregionsofdetectorj´jand¢Á(6ET;¹).93Chapter7
AnalysisMethod
AsdescribedinChapter5,searchesfortheassociatedproductionofaHiggsbosonHandavectorbosonV(V=W;Z)aresensitivetothedi®erentkinematicsofnon-standard-model(non-SM)spinandparityJPstates,X,inseveralobservables,namelytheinvariantmassortransversemassoftheVXsystem.InthisanalysiswesearchforaHiggsbosonproducedinassociationwithaWbosonwheretheHiggsdecaystoapairofbquarksandtheWbosondecaysleptonicallytoachargedleptonandaneutrino.Thetree-levelFeynmandiagramforthisprocessisshownforreferenceinFigure7.1.HqWq'Wb
b`Figure7.1:WHAssociatedProductionTree-levelFeynmandiagramoftheWH!`ºb¹bprocess.Manyotherstandardmodelprocessescanhavethesame¯nalstateasoursignalprocesses,andareundesirablebackgroundsinthesearchforthesignalprocesses.AsdiscussedinChapter6,thelargestsourcesofbackgroundstoWHassociatedproductionaremultijetevents,V+light-°avorjets,V+heavy-°avorjets,dibosonproductionVV,single-topevents,andtoppairproduction(t¹t).94Inanysearchitisnecessarytobeabletodiscriminatebetweensignalandbackgroundeventsthrougheventselectionandbackgroundrejection.Carefuleventselectionmaximizesthenumberofsignaleventsincludedwhileminimizingtheamountofbackground.Section7.1describestheeventselectionindetail.Signalscanbefurtherdiscriminatedfrombackgroundsbytrainingamultivariateanalysistooltodi®erentiatebetweensignalandbackgroundeventsusingmanyobservables.WeuseaBoostedDecisionTree(BDT)asdescribedinSection7.2forthispurpose.The¯nalobservable,thetransversemassoftheWXsystem,isdiscussedinSection7.3.
7.1EventSelection
WiththegoalofreconstructingtheWandHiggsbosons,wesearchforeventswithonechargedlepton(eor¹)1,signi¯cantmissingtransverseenergy,andatleasttwojets.Ad-ditionalrequirementsontheeventandobjectswithintheeventareappliedtohelprejectbackgroundsandaidinobjectreconstruction.Theeventselectionusedinthisanalysisisdescribedinthefollowing.Table7.1summarizestheeventselection.7.1.1ReconstructingtheWBosonToreconstructtheWbosonwerequireexactlyoneelectronormuonintheeventalongwithsigni¯cant6ET.Electronsandmuonsareidenti¯edfollowingtheprescriptioninSection4.4.The6ETiscalculatedasdescribedinSection4.4.Oursamplesaredividedintochannelsbasedonthe°avoroftheidenti¯edlepton.Inthisanalysistwosetsofidenti¯cationrequirementsareappliedtoleptonsinordertoform\loose"and\tight"leptonsamples.Thelooselepton1Wedonotselecttauleptonsdirectlyandtheircontributiontotheeventsampleissmall.95Leptons(`=eor¹)6ETJets1electron6ET>15GeV2or3jetsj´j<1:1(CC)ordividedinto4b-taggingcategories:1:5<j´j<2:5(EC)pe
T>15GeVone-tight-tag(1TT)D>0:151muon6ET>20GeVtwo-loose-tag(2LT)0:02<¹D·0:35j´j<2:0two-medium-tag(2MT)0:35<¹D·0:55p¹
T>15GeVtwo-tight-tag(2TT)¹D>0:55Table7.1:WXEventSelectionSummaryoftheeventselectionusedintheWXanalysis.Theoutputoftheb-taggingMVAdiscriminantDde¯nesthesingle-b-taggedcategorywhileitsaverage¹Dde¯nesthedouble-b-taggedcategories.sampleisusedtoestimatethemultijetbackgroundasdescribedinSection6.4whilethetightsampleisusedtoperformtheanalysis.Figure7.2showsthepToftheleptonforallchannelscombined.Electronsareselectedinthepseudorapidityregionsj´j<1:1and1:5<j´j<2:5corre-spondingtotheCCandECcalorimetersrespectively.Theyarerequiredtohaveatransversemomentumofatleast15GeV.Electronsthatpassthesecutsarerequiredtosatisfyaddi-tionalidenti¯cationrequirementstoformlooseandtightsamples.Theselooseandtightsamplesarede¯nedbymakingdi®erentrequirementsontheoutputoftheelectronidenti-¯cationBDT2.Thesesamplesarechosentoretainahighelectronselectione±ciencywhilesimultaneouslyrejectingbackgroundsatdi®erentrates.MuonsarereconstructedasdescribedinSection4.4.3.2andareselectedinthepseudo-rapidityregionj´j<2:0.MuoncandidatesmustalsosatisfypT>15GeV.Wealsorequireaminimumseparationbetweenthenearestjetandthemuoncandidateof0:5in´-Áspacefortheloosemuonsample.Thetightmuonsamplesatis¯estheaboverequirementsand2Thiscriteriondiscriminatesbetweenrealandfakeelectrons,allowingforthesamplepuritytobede¯nedaccordingtothecutmade.96hasadditionalisolationrequirements:i)thescalarsumofthepToftrackswithinaconeofradiusR=0:5mustbelessthan0:4£p¹
Tandii)thetransverseenergyinthecalorimeterwithinahollowconeof0:1<¢R<0:4mustbelessthan0:12£p¹
T.Themissingtransverseenergy6ET,showninFig.7.3,mustexceed15GeVintheelectronchanneland20GeVinthemuonchannel.Withtheinformationfromthe6ETandtheleptonweareabletoreconstructthetransversemomentumpW
TandthetransversemassmW
T=q(EWT)2¡(~pW
T)2oftheWboson.ThetransversemomentumoftheWbosonisshowninFig.7.4.ToreducethemultijetbackgrounddescribedinSection6.4weapplyatwo-dimensional\triangle"cutofmW
T>40¡0:56ET. [GeV]TLepton p20406080100120Events / 2.62 GeV050001000015000200002500030000DØ, 9.7 fb)+2 jets, pretagnl®V(DataVVTopV+hfV+lfMultijet 1000)´Signal (=125 GeVHMFigure7.2:LeptonpTDistributionsofleptonpTforallchannelscombined.97 [GeV]TE2030405060708090100Events / 2.12 GeV0500010000150002000025000DØ, 9.7 fb)+2 jets, pretagnl®V(DataVVTopV+hfV+lfMultijet 1000)´Signal (=125 GeVHMFigure7.3:MissingTransverseEnergyMissingtransverseenergyfortheelectronandmuonchannelscombined. [GeV]W
TM020406080100120Events / 3 GeV0100002000030000400005000060000DØ, 9.7 fb)+2 jets, pretagnl®V(DataVVTopV+hfV+lfMultijet 1000)´Signal (=125 GeVHMFigure7.4:TransverseMassoftheReconstructedWBosonThetransversemassoftheWbosonasreconstructedbytheleptonand6ETintheelectronandmuonchannelscombined.987.1.2ReconstructingtheHiggsBoson
HiggsbosonswithexoticspinandparityarereconstructedinthesamemannerastheSMHiggsbosonwithJP=0+.Inthefollowing,theterm`Higgsboson'referstothethreeJPstatesconsidered.AtleasttwojetsarerequiredtoreconstructtheHiggsboson.WerequiretwoorthreejetsintheeventwithpT>20GeVtoaccountforpossibleinitial-stateradiation,pile-upevents,ortheunderlyingevent.Jetsarereconstructedinthepseudorapidityregionj´j<2:5.JettransversemomentumdistributionsareshowninFig.7.5.Werequirethatjetsoriginatefromtheprimaryvertex.Thus,selectedjetsmustbematchedtoatleasttwotrackswithpT>0:5GeVwithatleastonehitintheSMTandwithadistanceofclosestapproachwithrespecttotheprimaryvertexoflessthan0.5cminthetransverseplaneandlessthan1cmalongthebeamline. [GeV]TLeading jet p20406080100120140Events / 4.06 GeV0500010000150002000025000300003500040000DØ, 9.7 fb)+2 jets, pretagnl®V(DataVVTopV+hfV+lfMultijet 1000)´Signal (=125 GeVHM [GeV]T Leading jet pnd220304050607080Events / 1.88 GeV0100002000030000400005000060000DØ, 9.7 fb)+2 jets, pretagnl®V(DataVVTopV+hfV+lfMultijet 1000)´Signal (=125 GeVHMFigure7.5:JetpTTransversemomentumdistributionsfortheleadingand2nd-leadingjetsbeforeb-taggingisapplied.Thesedistributionsareforthe2-jetsampleandaresummedoverlepton°avor.JetsfromthedecayoftheHiggsbosoncanbeidenti¯edbytheirbquarkcontentusingtheheavy-°avortaggingmethoddescribedinSection4.4.2.1.Werequireoneortwoofthejets99inaneventtobeb-taggedandde¯nefourb-taggingsamplesbyplacingrequirementsontheoutputoftheb-taggingMVAdiscriminantD.Foreventswithonlyoneb-taggedjeta\tight"requirementofD>0:15mustbemet.Thiscategoryisreferredtoasone-tight-tagor1TT.Eventswithtwob-taggedjetsaredividedintothreecategoriesbasedontheaverageoftheoutputoftheb-taggingMVAforthetwojetswiththehighestMVAoutput.Figure7.6showstheaverage¹D=(Dj1+Dj2)=2foreventswithtwotaggedjets.Thetwo-loose-tag(2LT)categorycorrespondsto0:02<¹D·0:35,thetwo-medium-tag(2MT)categorycorrespondsto0:35<¹D·0:55,andthetwo-tight-tag(2TT)categorycorrespondsto¹D>0:55.TheHiggsbosonisreconstructedfromthetwob-taggedjetsor,inthe1TTcategory,fromtheb-taggedjetandthejetwiththehighestpT.Figure7.7showstheinvariantmassofthetwojetsusedtoreconstructtheHiggsbosonineachb-tagcategory.)/22j
ID+b1j
ID(b00.20.40.60.81Events / 0.05 020040060080010001200140016001800DØ, 9.7 fb)+2 jets, two tagsnl®V(DataVVTopV+hfV+lfMultijet 50)´Signal (=125 GeVHMFigure7.6:Averageb-TaggingMVAOutputAverageb-taggingMVAoutputfortwojetssummedoverlepton°avors.100Dijet mass [GeV]050100150200250300350400Events / 20 GeV010002000300040005000DØ, 9.7 fbnl®V(DataVVTopV+hfV+lfMultijet 200)´Signal (=125 GeVHMDijet mass [GeV]050100150200250300350400Events / 20 GeV020040060080010001200DØ, 9.7 fbnl®V(DataVVTopV+hfV+lfMultijet 200)´Signal (=125 GeVHMDijet mass [GeV]050100150200250300350400Events / 20 GeV050100150200250300350400DØ, 9.7 fbnl®V(DataVVTopV+hfV+lfMultijet 50)´Signal (=125 GeVHMDijet mass [GeV]050100150200250300350400Events / 20 GeV050100150200250300350400DØ, 9.7 fbnl®V(DataVVTopV+hfV+lfMultijet 50)´Signal (=125 GeVHMFigure7.7:DijetInvariantMassDijetinvariantmassforeachb-tagcategoryforthe2-jetsamplecombinedoverlepton°avor.1017.2MultivariateAnalysisTechnique
WeuseaBoostedDecisionTree(BDT)asimplementedintheTMVApackage[51]todis-tinguishtheSMandnon-SMsignalsfromtheSMbackgroundprocesses.Adecisiontreeisaclassi¯erthattakeseventsasinputandsortsthemaccordingtohowsignal-likeorbackground-liketheyappear.Theoutputofthedecisiontreeisdistributedtypicallyfrom¡1to1withbackground-likeeventsoccupyingthelowervaluesandsignal-likeeventsoccupy-ingthehighervalues.Decisiontreesaretrainedoneventsfromknownsignalandbackgroundclasses.Eventsaresplitinto\leaves"bymakingcutsoninputdistributionsthatmaximizesignaltobackgroundseparation.Splittingcontinuesuntiltheresultingleaveshavethede-siredsignalpurityoraminimumleafsizehasbeenreached.Wecombinetheresultsoftreestrainedonrandomsubsetsoftheinputdistributions(referredtoasbagging)toimprovethediscriminatingpower.Aboosteddecisiontreeassignshigherweightstomisclassi¯edeventsonsubsequenttrainingcycles.WetrainaBDTforeachlepton°avor,jetmultiplicity,andb-taggingchannelusingSMWHsignalevents.BecausetheBDTisprimarilysensitivetothemassofthetwobquarksandnottotheanglesbetweentheHiggsbosonandthevectorboson,weexpecttoseelittledi®erenceintheoutputoftheBDTforeithernon-SMJPsignal.Wedonotexpectanysigni¯cantbiasineithertheJP=0¡orJP=2+signalsifwetrainonlyontheSMJPsignal.Figure7.8showstheoutputoftheBDTforeachb-taggingchannelcombinedinlepton°avorandjetmultiplicity.
7.3FinalObservable
BecausethezmomentumoftheneutrinofromthedecayoftheWbosonisnotmeasurable,theobservableweareprimarilyinterestedinisthetransversemassoftheWXsystemde¯ned102BDT Output00.51Events05001000150020002500=9.7 fbintDØ, L80)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2bbnl®WHFigure7.8:BDTOutputBDToutputcombinedinlepton°avor,b-taggingcategory,andjetmultiplicity.asfollows.m2
T=¡EWT+EHT¢2¡¡~pW
T+~pH
T¢2~pW
T=~6ET+~p`
T(7.1)WhenconstructingthepTandEToftheHiggsbosonweconsidereitherthetwob-taggedjetsinthecaseofthetwo-tagcategoriesortheb-taggedjetandthehighest-pTnon-taggedjetinthecaseoftheone-tagcategory.Itisclearfromthetransversemassdistributionsthatthereisasigni¯cantamountofbackgroundevents,particularlyintheregionwheretheSMsignalpeaks.Toimprovesearchsensitivity,wethussplittheeventsintoseparatepurityregionsaccordingtotheoutputoftheBDT.ThemostsensitiveregionwiththehighestsignalpurityrequiresaBDTresponsevalueBDToutabove0:5.Anintermediateregionisde¯nedby0<BDTout·0:5.ThelowestpurityregionaretheeventswithBDTout·0.Thisregionprovidesinsigni¯cantsensitivityinthe¯nalresultrelativetotheothertworegionsandwe103donotincludethisregioninthestatisticalanalysis.TheregionwithaBDToutputabove0:5isreferredtoasthe\high-purity"(HP)channelandtheregionwith0<BDTout·0:5isreferredtoasthe\low-purity"(LP)channel.The¯nalobservables,splitintohigh-andlow-purityregions,aregiveninFigs.7.9and7.10.Thereare32channelsthatenterintothestatisticalanalysisdescribedinChapter8resultingfromsplittingtheeventsbylepton°avor,jetmultiplicity,b-taggingcategory,andpurityregion.104 (GeV)bWb
TM0200400600Events050100150200250=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 1TT HPbbnl®WH (GeV)bWb
TM0200400600Events0102030405060708090100=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2LT HPbbnl®WH (GeV)bWb
TM0200400600Events01020304050=9.7 fbintDØ, L10)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2MT HPbbnl®WH (GeV)bWb
TM0200400600Events0510152025303540=9.7 fbintDØ, L10)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2TT HPbbnl®WHFigure7.9:TransverseMassoftheWXSystem,High-PurityRegionTransversemassoftheWXsystemforeachoftheb-taggingcategoriesinthehigh-puritychannelsummedoverlepton°avorandjetmultiplicity.105 (GeV)bWb
TM0200400600Events01002003004005006007008009001000=9.7 fbintDØ, L100)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 1TT LPbbnl®WH (GeV)bWb
TM0200400600Events020406080100120140160180200=9.7 fbintDØ, L100)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2LT LPbbnl®WH (GeV)bWb
TM0200400600Events020406080100120=9.7 fbintDØ, L50)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2MT LPbbnl®WH (GeV)bWb
TM0200400600Events020406080100120=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2TT LPbbnl®WHFigure7.10:TransverseMassoftheWXSystem,Low-PurityRegionTransversemassoftheWXsystemforeachoftheb-taggingcategoriesinthelow-puritychannelsummedoverlepton°avorandjetmultiplicity.106Chapter8
StatisticalAnalysis
ToanswerthequestionsposedinChapter5wemustdevelopaframeworktodeterminetherelativeagreementofthedatawithourSMandnon-SMHiggsbosonhypotheses.Theprobabilisticnatureofparticleinteractionsleadsustocollectalargedatasampletolookforrareprocessesandtoaccuratelydescribethosewhicharemorecommon.Themostnaturalframeworkisthenastatisticalone.Section8.1describesthehypothesistestandtheteststatisticusedinthisanalysis.Theparticularmethodweuseforinterpretingtheresultsofthehypothesistest,theCLsmethod,isdescribedinSection8.2.Finally,adescriptionofthesystematicuncertaintiespresentinthisanalysisisdescribedinSection8.3.8.1TheHypothesisTest
AsdescribedinChapter7,theresultofasearchforanewphysicsprocessisoneormore¯nalvariabledistributionsmeanttodistinguishbetweenthenewphysicsprocessandthebackgrounds.Inthisanalysisthe¯nalvariableisthetransversemassoftheWHsystem.Wewouldliketode¯neahypothesistestbasedonthisdistributionthatdistinguishesbetweenhavingaHiggsbosonwithSMJPandonewithexoticJP.Thediscriminatingpowerofthetransversemasscomesfromdi®erencesintheshapeofthedistributionfortheSMandnon-SMJPsignals.Toincorporatetheshapeofthedistributioninthestatisticalanalysisweperformacountingexperimentineachbinofthe¯naldistribution.Inthefollowing,the107nullhypothesisH0referstothestandardmodelcase:the¯naldistributionwillcontainallSMbackgroundsandtheSMHiggsbosonsignalwithJP=0+.EachtesthypothesisH1willconsiderallSMbackgroundsandthenon-SMHiggsbosonwithoneoftheexoticJPvalues,JP=0¡orJP=2+.TheNeyman-Pearsonlemmastatesthatthelikelihoodratioisthemostpowerfulhy-pothesistestwhenconsideringhypotheseswhicharefully-speci¯ed.Thelikelihoodratioisde¯nedasQ=L(H1jdata)L(H0jdata)(8.1)whereL(Hjdata)isthelikelihoodofhypothesisHgiventhedata1.Ifweconsidereachbinofthe¯nalvariabledistributionasacountingexperimentwithPoissonstatisticsthenthelikelihoodofhypothesisHgiventhedistributionofthedataistheproductofindividualPoissonlikelihoodfunctionsoverallbins:L(Hjdata)=NbinsYiµpidi¶diedi¡pi(8.2)wherepiisthepredictednumberofeventsanddiisthenumberofdataeventsintheithbin.Thepredictednumberofeventswilldependonthehypothesisconsidered.ForthenullhypothesisthepredictednumberofeventswillbethesumoftheSMHiggsbosonsignal(sSM
i)andbackground(bi)predictions.Forthetesthypothesespiwillbethesumofthenon-SMHiggsbosonsignal(snSM
i)andbackground(bi)predictions.Becausethenaturallogarithmismonotonic,wecanusethemoreconvenientlog-likelihoodratioLLRasourteststatisticwithoutsacri¯cingthepowerofthelikelihoodratiotest.Thischangesthe1Thelikelihoodisnotaprobabilityinthestandardsense;itreferstoeventswithknownoutcomeswheretheprobabilitydealswithfuture(unknown)events.108productinEq.8.2toasimplesummation.Forourpurposeswede¯nethelog-likelihoodratioasLLR=¡2lnQwheretheprefactorischosensuchthatLLR!Â2asthesamplesizeapproachesin¯nity.CombiningEqs.8.1and8.2andperformingsomesimplearithmeticweobtainLLR=2NbinsXi(snSM
i¡sSM
i)¡2NbinsXidilnµsnSM
i+bisSM
i+bi¶:(8.3)Ateststatisticprovidesanorderingrulewithwhichsetsofdatacanbedeterminedasbelongingtoonehypothesisoveranother.MorepositivevaluesoftheLLRde¯nedinEq.8.3indicatethattheobserveddataagreebetterwiththenullhypothesiswhilemorenegativevaluesindicatebetteragreementwiththetesthypothesis.However,withoutcontext,theLLRvaluecalculatedfromthedataisessentiallymeaningless.WecancalculatetheexpectedvaluesoftheLLRbysubstitutingthediinEq.8.3bysSM
i+biorsnSM
i+bibutinordertogaugetheimportanceofanydeviationsweneedtoknowthedistributionofLLRvaluesforeachhypothesis.Thisisdonebysimulatingtheoutcomesofrepeatedexperimentsorpseudo-experiments.Again,toretaintheinformationstoredintheshapeofthe¯nalvariabledistributionweproceedwithaper-bincalculation.IneachbinweassumethatthedatawasdrawnrandomlyfromaPoissonparentdistributionwithameanequaltothepredictednumberofeventspi.Wethengeneratepseudo-databyrandomlydrawingavaluefromthisPoissonparentdistribution.WeiterateoverthetotalnumberofbinsandthevalueoftheLLRiscalculated.ThisprocessisrepeatedmanytimestocreatetwoLLRdistributions:oneassumingthenullhypothesisistrueandoneassumingthetesthypothesisistrue.Acomplicationarisesfromthefactthatthehypothesesweconsiderarenotfully-speci¯ed.Thebackgroundandsignalpredictionsdependonmanyparameterssuchastheintegratedluminosity,selectione±ciencies,andcrosssections.Theseparametersarenotofprimary109interestthemselvesbutmustbetakenintoaccountbecauseoftheirassociateduncertainties.Werefertothemas`nuisanceparameters'.OnemethodofdealingwiththesenuisanceparametersistoassumetheyareGaussian-distributedwithameanequaltothebestestimateofthenuisanceparameterµ0jandastandarddeviation¾jequaltoitsuncertainty.Byvaryingthevaluesofthenuisanceparametersforeachpseudo-experimentwecanincorporatethee®ecttheiruncertaintieshaveontheresults.Changingthevaluesofthenuisanceparameterswillproduceachangeinthenumberofpredictedevents.Foranindividualbin,thenumberofpredictedevents^picanbewrittenintermsofthenominalpredictionpiandadeviationfromthebestestimateforeachnuisanceparameterRj=(µj¡µ0j)=¾jas^pi=pi+NparXjRj±j(8.4)where±jisthefractionalchangeinthenumberofeventsforthenuisanceparameterjandthesumisoverthenumberofnuisanceparameters.ThisGaussianrepresentsourpriorknowledgeofthevaluesofthenuisanceparameters.Beforegeneratingasetofpseudo-datawevarythevaluesofthenuisanceparametersbyrandomlysamplingtheirGaussianpriorsandadjustthepredictednumberofeventsaccordingly.Nextwegeneratethepseudo-databyrandomlydrawingavaluefromthePoissonparentdistributionwithameanequaltothe(adjusted)predictednumberofevents.ThelikelihoodfunctioninEq.8.2ismodi¯edbytheintroductionofaGaussianlikelihoodterm.ThelikelihoodfunctionisthusaproductofaPoissonlikelihoodLPandaGaussianlikelihoodLG:L(Hjdata)=LP£LG=NbinsYiµ^pidi¶diedi¡^pi£NparYje¡R2j=2(8.5)110wherethediarethe(pseudo-)dataandtheproductsgooverthenumberofbinsNbinsandthenumberofnuisanceparametersNpar.Notethatthepredictednumberofevents^piisnowafunctionofthedeviationRj.Thesecondtermre°ectsthedeviationsofthenuisanceparametersasafunctionoftheirpriorwhichtakesintoaccounttherelativeagreementwiththepriorestimate.Theuncertaintiesonthenuisanceparameterscanbelarge,sometimesaslargeas¼30%ofthenominalvalue.Allowingthenuisanceparameterstovaryaccordingtotheiruncertaintiesthereforehastheunfortunatee®ectofdilutingthepowerofthestatisticaltestbybroadeningthewidthoftheLLRdistributionforeachhypothesis.Wemitigatethise®ectbyperforminga\best-¯t"tothedatabymaximizingthelikelihoodfunctioninEq.8.5overtheRj.TheGaussianlikelihoodtermLGservesasapenaltytermforthemaximization.Thee®ectoftheprioristoconstrainthe¯twithintheuncertaintyofthebestestimate.Two¯ts,oneforeachhypothesis,areperformedforeachpseudo-experimentandthedata.The¯nalteststatisticisthelog-likelihoodratioofthemaximizedlikelihoodfunctionsandcanbesummarizedasthefollowing:LLR=¡2lnÃL(H1jdata;^µ)L(H0jdata;^
^µ)!(8.6)wherethe^µ(^
^µ)representthevaluesofthenuisanceparametersthatmaximizethelikelihoodfortheH1(H0)hypothesis.Intheprecedingwehaveimplicitlyassumedonlyonesourceofeventsbutinrealitythereareoftenseveralsourcesofbackgroundsandsignalsthatmustenterintothepredictednumberofevents.ThiscanbeaccomplishedwithadditionalsummationsinEq.8.4.Multiplechannelscanbeincorporatedinasimilarmatter.Theycaneitherrepresentsubdivisionsinthedataoracompletesetof¯nalvariablehistogramswiththeirassociatedpredicted111numberofeventsandnuisanceparameters.
8.2CLsMethodAfterobtainingtheLLRdistributionsweusethemtointerpretourobserveddata.Figure8.1illustratesexampleLLRdistributionsforthenullandtesthypothesesandwellasanexampleobservedvalue.Twoimportantp-valuescanbecalculatedfromtheLLRdistributionsandtheobserveddata.Ap-valueisde¯nedastheprobabilityofobtainingaresultatleastasormoreextremethanwhatwasobserved,assumingthehypothesisunderconsiderationistrue.IfweconsiderthatthetesthypothesisistruemoreextremeLLRvaluesthantheobservedLLRvaluelietowardsthenullhypothesisdistribution.Thep-valueforthetesthypothesisptestisthereforetheintegraloftheH1LLRdistributiontotherightoftheobservedvalueLLRobsasindicatedbytheredregioninFig.8.1.Ontheotherhandifweassumethatthenullhypothesisistruemoreextremevalueslietowardsthetesthypothesisdistributionandthep-valuefortheH0hypothesispnullistheintegraloftheH0LLRdistributiontotheleftofLLRobs.ThisisillustratedbytheblueregioninFig.8.1.Weselectasigni¯cancelevel®of5%againstwhichwewilltestourresult.Iftheresultingp-valueislessthanorequalto®werejectthehypothesisatthe1¡®con¯dencelevel(CL).Astrictfrequentistinter-pretationwouldonlyconsiderptestwhendeterminingwhethertorejectthetesthypothesis.However,asdemonstratedintheprevioussection,thenullandtesthypothesesdependonmanyparameterswhichcanresultinpoormodelingofeitherhypothesis.ToprovidesomeprotectionagainstthispoormodelingweusetheCLsmethod[52,53,54].Wede¯neanewquantityCLs:CLs=1¡ptest1¡pnull(8.7)112andusethisindeterminingwhethertorejectthetesthypothesis.IfthevalueofCLsisgreaterthan1¡®werejectthetesthypothesis.Ingeneralthismethodovercoversbutisconsideredacceptableinlightoftheuncertaintyofthemodelingprocess.Figure8.1:ExampleLLRDistributionsExampleLLRdistributionsforthenull(blue)andtest(red)hypotheses.AnexampleobservedLLRvalueisillustratedbytheblackline[55].8.3SystematicUncertainties
Systematicuncertaintiesonthesignalsandbackgroundsareassessedforeachlepton°avor,jetmultiplicity,andb-taggingcategorybyrepeatingtheanalysisindependentlyforeachsourceofuncertaintyvariedby§1standarddeviation.Threetypesofsystematicsarecon-sidered;thosea®ectingthenormalizationofthe¯nalvariable,thosea®ectingtheshapeofthe¯nalvariable,andthosethata®ectbothshapeandrate.Sourcesofsystematicuncertaintiescancomefromtheoreticalpredictions,detectore®ectssuchasobjectreconstruction,andthegenerationofMonteCarloevents.TheuncertaintyontheintegratedluminosityiscalculatedindependentlyinRef.[56]tobe6.1%.Thissystematicisfullycorrelatedacrossallsimu-113latedsamples.Thefollowingsectionsdescribethesourcesofoursystematicuncertaintiesandtheirvaluesinthisanalysis.Table8.1servesasasummary.SystematicValueRateIntegratedluminosity6.1%Topquarkpairproductioncrosssection(¾)7%Singletopquark¾7%Diboson¾6%W+heavy-°avor¾14%W+light-°avor¾4%V+jetsthree-jetscalefactor4%(e)6%(¹)Multijetrateuncertainty4%{20%Shapeb-tagginge±ciency4.0%{4.2%perheavy-°avorjetLight-°avorjetmisidenti¯cation10%perjet
Jetidenti¯cation(ID)e±ciency»3%Jetsmearing,shifting,andremoval1%{4%
Jetenergyresolution1%{4%ShapeandRateMuontriggere±ciency1%{2%LeptonID3%
alpgenmodeling0.3%PartonDistributionFunctions2%
Multijetshapeuncertainty4%{30%Table8.1:SystematicUncertaintiesListofsystematicuncertaintiesa®ectingrateand/orshapeofthe¯nalvariabledistribution.8.3.1ModelingUncertainties
Systematicsrelatedtothemodelingofsimulatedsamplesandthoserelatedtothederivationofthemultijetsamplearedescribedbelow.Ingeneraltheseuncertaintiescana®ectbotheventrateandshape.
alpgenmodeling:Weassessuncertaintiesforall¯vealpgenreweightingfunctionsusedtocorrecttheV+jetssamples.Weadjustthefunctionsbyshiftingtheparameter114thatgivesthelargestshapedi®erenceby§1s.d.Wealsoevaluatethesystematicsrelatedtothejet-to-partonmatchingschemeandtheunderlyingeventmodelingusedbyalpgen.V+jetsthree-jetscalefactors:WhenwesimultaneouslynormalizetheV+jetsandmul-tijetsamplesbyperforminga¯ttothedatawe¯ndthatthescalingfactorsweapplytothe3-jetV+jetssampledi®ersigni¯cantlyfromunity.Wethereforeapplyanaddi-tionaluncertaintyonthe3-jetV+jetssamplethatisuncorrelatedwithlepton°avor.WealsoapplyanormalizationuncertaintyonV+jetseventsthatisanti-correlatedwiththemultijetratesystematic.Multijetrate:Weassignuncertaintiesonthemultijeteventrateof15%intheelectronchanneland20%inthemuonchannel.Thissystematicisuncorrelatedacrosslepton°avor,jetmultiplicity,andb-taggingcategory.Multijetshape:TodeterminetheuncertaintyontheshapeofourmultijetestimatewerelaxthetrianglecutintroducedinSection7.1tomW
T>30¡0:56ETandrepeattheanalysis.Thepositiveandnegativevariationsaretakentobesymmetric.8.3.2TheoreticalUncertainties
Theoreticalsystematice®ectscanenterintotheanalysisfromseveralsourcessuchaspre-dictedcrosssectionsandPDFsets.Thesecana®ectboththeeventrateandshapeofthe¯naldistribution.Wethereforeassessuncertaintiesassociatedwiththeseitems.Crosssectionpredictions:Forsingletopquarkproductionandtopquarkpairproduc-tionthisuncertaintyis7%[57,58]Theuncertaintyonthedibosonproductioncross115sectionis6%[59].TheuncertaintiesonW+hfandW+lfproductionare14%and4%,respectively.TheuncertaintiesonW+hfareestimatedwithmcfm[60,61].PDFsets:Setsofpartondistributionfunctionsarecalculatedfromtheoryandexperimen-talresults.ThechoiceofPDFsetusedinMonteCarloeventgenerationa®ectsthesignalandbackgroundrates.Weassignanuncertaintyof2%toaccountforthis.8.3.3JetSystematics
Thereareseveralsystematicsassociatedwiththepresenceofjetsinthe¯nalstate.Theseuncertaintiescomefromdetectore®ects,objectreconstruction,andb-taggingalgorithms.Jetenergyscale:Theenergywemeasureforajetiscorrectedtoaccountfordetectore®ectssuchasuraniumdecayinthecalorimeter,electronicsnoise,residualenergyfrompreviouscollisions,andinactiveareasofthedetector.ThiscorrectionisreferredtotheJetEnergyScale(JES)correctionanditisappliedtoboththedataandMCevents.TheuncertaintyontheJEScorrectionisassessedbyshiftingtheJESparametersupanddownby1s.d.Jetsmearing,shifting,andremoval:JetsproducedinMCeventsmustbesmearedandshiftedinenergytomatchthecharacteristicsofjetsindata.WeapplytheJetSmear-ingShiftingandRemoval(JSSR)correctiontojetsinMC.Theuncertaintyonthiscorrectionisfoundbyshiftingtheparametersby§1s.d.Jetidenti¯cation:Weassigna2%uncertaintyonthejetidenti¯catione±ciency.bquarkidenti¯cation:Theuncertaintyontheb-tagginge±ciencyisdeterminedbyvary-ingthetaggingratefunctionsupanddown1s.d.insamplescontainingheavy-°avor116jets.Theuncertaintyonthelight-°avormisidenti¯cationrateisdeterminedbyvaryingthelight-°avortagratesby§1s.d.insampleswithnoheavy-°avorjets.8.3.4LeptonSystematics
Thereareseveralsystematicsassociatedwiththepresenceofleptonsinthe¯nalstate.Thesesystematicscana®ectbotheventrateandshape.
Electronidenti¯cation:Weassignanuncertaintyof3%ontheelectronidenti¯catione±ciency.IncludedinthisuncertaintyistheuncertaintyassociatedwiththeEMtrigger.Muonidenti¯cation:Wealsoassignanuncertaintyof3%onthemuonidenti¯catione±ciency.Muontrigger:ThealpgenreweightingsarecalculatedusingtheT¹ORtriggersuiteandappliedtobotheventswithelectronsandeventswithmuons.AdditionalreweightingsareappliedtothemuonchannelwhicharecalculatedfromeventsselectedwithTincl.Toaccountforthedi®erencebetweenthealpgenreweightingsasappliedtotheelectroneventsandmuonseventsweapplyanuncertaintyonthemuontrigger.Itiscalculatedasthedi®erencebetweenapplyingthenominaltriggercorrectionandapplyingatriggercorrectionderivedusingthealpgenreweightingscalculatedusingtheT¹ORtriggersuite.117Chapter9
ResultsandInterpretations
ThestatisticalmethodoutlinedinChapter8canbeusedtoinvestigateseveralquestionsrelatedtothespinandparityoftheparticlediscoveredattheLHC.IsthenewparticlereallytheSMHiggsboson?Atwhatlevelcanweexcludeothernon-SMJPassignments?Istheparticleanadmixtureofdi®erentJPstates?Undertheassumptionthatitis,woulditbepossibletoruleoutanyfractionofnon-SMJPcontent?Toanswerthesequestions,I'vedividedtheresultsintotwocases:1.ThenewparticleexistsasapureJPstateOfprimaryinterestiswhetherornotthenewparticleistheSMHiggsboson.SincetheTevatroncannotmeasurethespinandparityoftheparticledirectlywecanonlyexcludemodelswithexoticJP.Whetherornotweexcludethesemodelsdependsinpartonthetotalpredictedcrosssectionfortheprocess.Unfortunately,thetotalpredictedcrosssectionfortheJP=0¡andJP=2+statesisincalculableandtheexclusionwilldependonanassumedsignalcrosssection.Oneveryreasonablestartingpointwouldbetheobservedrateindata.2.ThenewparticleexistsasanadmixtureofJPstatesAnotherimportantpossibilitytoexcludeiswhetherthediscoveredparticleisapureJPstateoranadmixtureofJPstates.Excludingthispossibilityinitsentiretyrequiresexcludingallpossiblefractionsofnon-SMsignals.Anyexclusionsinthiscasewillagain118dependonanassumedtotalcrosssection.Thisanalysisislimitedtocaseswherethedi®erentJPstatesdonotinterfere.Section9.1de¯nesthehypothesistestsforcases(1)and(2)indetail.TheresultsofthesetestsfortheWX!`ºb¹banalysisarediscussedinSection9.2.DetailsforthecombinationoftheZX!``b¹bandVX!ººb¹banalyseswiththeWX!`ºb¹banalysisarediscussedinSection9.3.ResultsofthecombinationwithinD0andwithCDFarediscussedinthesamesection.
9.1HypothesisConstruction
Inthepreviouschapterwelooselyde¯nedthehypothesistestsforthesakeofsimplicity.Heretheyarede¯nedindetail.ThenullhypothesiswewanttoconsiderforbothcasesisthatthedataisdescribedbythestandardmodelbackgroundsandabosonwithJP=0+.ToinvestigatetheexclusionpotentialforothervaluesofthecrosssectionwenormalizetheSMsignalto¹£¾SM0+where¹isthesignalstrengthand¾SM0+istheHiggsbosonSMcrosssectiontimesbranchingratio.ThenormalizationoftheSMbackgroundprocessesremainsthesameaswhatisdescribedinChapter6.Thetesthypothesisforcase(1)assumesthatthedataisdescribedbytheSMbackgroundsandabosonwithexoticspinandparity,eitherJP=0¡orJP=2+.Forcase(2)theassumptionisthatthedatacontainsanadmixtureoftwodi®erentJPstates{onewithexoticJPandonewithJP=0+.Becausethetesthypothesesareverysimilarwecande¯neageneralhypothesistestthatcanbeappliedinbothcases.ThegeneralhypothesisisthesumoftheSMbackgrounds,theSMsignal,andthenon-SMsignalwithJP=0¡orJP=2+.Likethenullhypothesis,thenormalizationoftheSMbackgroundsremainsasdescribed119previously.Thenormalizationsofthesignalsarede¯nedbasedonthefractionofnon-SMsignalfJP=¾JP=(¾JP+¾0+).Thenon-SMJPsignalisnormalizedto¹tot£¾SM0+£fJPandtheSMJPsignalisnormalizedto¹tot£¾SM0+£(1¡fJP)sothattheoverallnormalizationisequalto¹tot£¾SM0+.Forthecaseassumingapurenon-SMJPstate,fJP=1andthetotalsignalstrength¹totissimplyequaltothenon-SMJPsignalstrength¹JP.Table9.1summarizesthesignalnormalizationsforthenullandtesthypotheses.HypothesisSMsignalnon-SMsignalnormalizationnormalizationNullhypothesisH0¹£¾SM0+{TesthypothesisH1¹tot£¾SM0+£(1¡fJP)¹tot£¾SM0+£fJPTable9.1:SignalNormalizationsSignalnormalizationsforthenullandtesthypotheses.Thefractionofnon-SMJPsignalisdenotedbyfJP.Forthecaseofatesthypothesiswithpurenon-SMJPsignal,fJP=1and¹tot=¹JP.9.2WXAnalysisResultsDiscriminationbetweennon-SMandSMJPassignmentsisachievedbyanalyzingthedis-tributionofthetransversemassoftheWXsystem.ThetransversemassmToftheWXsystemisde¯nedinEq.7.1.Toincreasethesensitivitytheeventsamplehasbeendividedintoorthogonalchannelsbasedonlepton°avor,jetmultiplicity,b-taggingcategory,andsignalpurityregion.Figure9.1showsthetransversemassoftheWXsystemforthetwo-tight-taghigh-puritychannel.PlotsforotherchannelscanbefoundinChapter7.120 (GeV)bWb
TM0200400600Events0510152025303540=9.7 fbintDØ, L10)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2TT HPbbnl®WHFigure9.1:TransverseMassoftheWXSystem,High-PurityRegionTransversemassoftheWXsystemforthetwo-tight-tagb-taggingcategory.OtherplotscanbefoundinChapter7.1219.2.1PureNon-SMJPStatesWe¯rstconsiderthecasewherethesignalisapurenon-SMJPstate.Herethenon-SMJPsignalfractionfJPisoneand¹tot=¹JP.Wearefreetochooseanyvaluesfor¹and¹JP,thesignalstrengthsfortheSMandnon-SMsignalsinthecalculation.Thischoiceisarbitraryandsmallervaluessimplyreducethesensitivityofthetest.OnesimplechoiceistheSMpredictedvalueforHiggsbosonproduction:¹=¹JP=1:0.ThischoiceiswhatweexpectfromtheSMandisaneasypointforcomparisonwithotheranalyses.WeperformthestatisticalanalysiswiththesignalnormalizationslistedinTable9.1fortheJP=0¡andJP=2+signalsindividually.Figures9.2and9.3showthedistributionofthelog-likelihoodratio(LLR)teststatisticcalculatedforeachpseudoexperimentandthedataforJP=0¡andJP=2+,respectively.ByexaminingtheexpectedLLRdistributionswecangetanideaofthediscriminatingpowerofthetransversemassfortheJP=0¡andJP=2+signals.Becausetheteststatisticisanorderingruleweexpectthatthefartherapartthenullandtesthypothesesarethemorediscriminatingpowerthereis.Forexample,ifthenullandtesthypothesesproduceLLRdistributionsthatoverlapcompletelyitwillbeimpossibletodiscriminatebetweenthemnomatterwheretheobservationfalls.ComparingFigs.9.2and9.3weseethatthetwodistributionsareclosertogetherinthecaseofJP=0¡thantheyareforJP=2+.ThissuggeststhatthediscriminatingpowerisstrongerforthecaseofJP=2+thanforJP=0¡.ThisalsoagreeswiththetransversemassdistributioninFig.9.1.TheJP=0¡signalpeakssigni¯cantlyclosertotheSMsignalandbackgroundsthantheJP=2+signal.InadditiontotheexpectedLLRdistributionswecanconsidertheobservedvalue.Inbothcasestheobservedvaluefallsjustinside2standarddeviations(s.d.)fromthemedianexpectedvalue.122Thisindicatesanexcessinthedatafromanupward°uctuation.InFigure9.1someofthisexcessisvisiblein4{5binswhichareinthetailofthedistribution.SincethisplotrepresentsthechannelwiththemostsensitivityintheWX!`ºb¹banalysis,itisnotsurprisingthatweseeanoverallexcess.LLR02040Pseudoexperiments05001000150020002500 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR0Observed LLR = 9.7 fbintDØ, L=1.0mbbnl®VXFigure9.2:Log-likelihoodRatioDistributionsforJP=0¡Thelog-likelihoodratio(LLR)teststatisticcalculatedforeachpseudoexperimentandthedataassuming¹=1:0forJP=0¡.TheLLRdistributionforthenull(test)hypothesisisshowninblue(red)andtheobservedvalueisrepresentedbytheblackverticalline.Thegreenandyellowshadedbandsrepresent1and2standarddeviationsonthemedianexpectationfromthenullhypothesis,respectively.Weproceedtocalculatethep-valuesbyintegratingtheLLRdistributionsforeachhy-pothesisfromtheobservedvalueto§1.Wedenotethep-valueforthenullhypothesisaspnullandthep-valuesforthetesthypothesesasp0¡testandp2+test.ThevalueofCLsiscalculatedas1¡ptest=(1¡pnull).WeinterpretCLsasthecon¯dencelevelatwhichweexcludethenon-SMtesthypothesisinfavoroftheSMprediction.IfCLs¸0:95weexcludethetesthypothesisinfavorofthenullhypothesisatacon¯dencelevel¸95%.Tocalculatetheexpectedp-valuesweinsteadintegratefromthemedianexpectationofthenullhypothesis.Table9.2givestheexpectedandobservedp-valuesaswellasthevalueofCLsassuming123LLR02040Pseudoexperiments02004006008001000120014001600180020002200 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR+2Observed LLR = 9.7 fbintDØ, L=1.0mbbnl®VXFigure9.3:Log-likelihoodRatioDistributionsforJP=2+Thelog-likelihoodratio(LLR)teststatisticcalculatedforeachpseudoexperimentandthedataassuming¹=1:0forJP=2+.TheLLRdistributionforthenull(test)hypothesisisshowninblue(red)andtheobservedvalueisrepresentedbytheblackverticalline.Thegreenandyellowshadedbandsrepresent1and2standarddeviationsonthemedianexpectationfromthenullhypothesis,respectively.
¹=¹JP=1.Wealsogivethecorrespondingsigni¯canceinunitsofstandarddeviations(s.d.)usingaone-sidedGaussiantailcalculation.Whentestingapurenon-SMJPstateofJP=0¡ourexpectedCLsvalueis0:941andweobserveavalueof0:637.AlthoughwedonotexpecttobeabletoexcludetheJP=0¡hypothesisourobservedvalueismuchlower.Thisisduetoanupwards°uctuationinthedatanearthetailofthetransversemassdistribution.TheWH!`ºb¹bchannelisoneoftheinputstotheSMHiggsbosonsearchatD0thatyieldedanexcessinthedataabovetheSMexpectationconsistentinbothshapeandratetotheHiggsbosondiscoveredattheLHC.WhenwecombineallchannelsinwhichtheHiggsbosondecaystoapairofbquarkswecanmeasurethesignalstrengthofthisexcessbyperformingabest¯ttothedata.Thisgivesavalueof¹=1:23.Bysetting¹=1:23andrepeatingtheanalysiswecanattempttoscalethesignaltomatchwhatwemeasurefrom124JP=0¡vs.JP=0+p0¡testExpected0.030p0¡testObserved0.3511¡pnullExpected0.5001¡pnullObserved0.965CLsExpected0.941(1.56s.d.)CLsObserved0.637(0.35s.d.)JP=2+vs.JP=0+p2+testExpected0.009p2+testObserved0.1141¡pnullExpected0.5001¡pnullObserved0.932CLsExpected0.982(2.09s.d.)CLsObserved0.878(1.16s.d.)Table9.2:D0CLsValuesfor¹=1:0Expectedandobservedp-valuesandCLsvaluesforJP=0¡andJP=2+WXassociatedproduction,assumingsignalcrosssectionsequaltothe125GeVSMHiggsproductioncrosssectionmultipliedby¹=1:0.ThenullhypothesisistakentobethesumoftheSMHiggsbosonsignalandbackgroundproduction.125thebest¯t.However,theWH!`ºb¹bchannelisonlyoneofseveralinputstotheH!b¹bcombinationsothisisonlyanapproximation.Table9.3givesthep-valuesforthecaseof¹=¹JP=1:23forbothJP=0¡andJP=2+states.WeobserveaCLsvalueof0:747withanexpectedvalueof0:975.Again,theobservedvalueismuchlessthantheexpectedvalue.JP=0¡vs.JP=0+p0¡testExpected0.012p0¡testObserved0.2451¡pnullExpected0.5001¡pnullObserved0.971CLsExpected0.975(1.96s.d.)CLsObserved0.747(0.67s.d.)JP=2+vs.JP=0+p2+testExpected0.003p2+testObserved0.0561¡pnullExpected0.5001¡pnullObserved0.937CLsExpected0.995(2.56s.d.)CLsObserved0.941(1.56s.d.)Table9.3:D0CLsValuesfor¹=1:23Expectedandobservedp-valuesandCLsvaluesforJP=0¡andJP=2+WXassociatedproduction,assumingsignalcrosssectionsequaltothe125GeVSMHiggsproductioncrosssectionmultipliedby¹=1:23.9.3CombiningAnalyses
ThemethodfordiscriminatingbetweenSMandnon-SMJPstatesoutlinedinChapter5canbeappliedtoallvectorbosonassociatedHiggsbosonproductionchannels.TheseVHproductionchannelsincludeZH!``b¹b,WH!`ºb¹b,andVH!ººb¹b.Tree-levelFeynmandiagramsfortheseprocessesaregiveninFig.9.4.Ifwecombinetheresultsofthisanalysis126withtheresultsfromsimilaranalysesoftheZH!``b¹bandVH!ººb¹bproductionchannelswewillincreasethesensitivityofthe¯nalresultbeyondanyoftheindividualanalyses.Thestatisticalmethodwe'veusedisamenabletocombiningmanyanalysischannelsandgivesusnoobstacles.Theonlymodi¯cationnecessarywhenincludingtheseadditionalprocessesistheformofthe¯naldiscriminatingdistribution.AsdescribedinChapter5weusethetransversemassoftheWHsystembecausewecannotmeasurethezmomentumoftheneutrinointhe¯nalstate.FortheVH!ººb¹b1channelthisrequiresasmallmodi¯cationtothetransversemass:m2
T=(EVT+EXT)2¡(~pV
T+~pX
T)2;pV
T=6ET:(9.1)Ontheotherhand,fortheZH!``b¹bchannelwedetectbothchargedleptonsandwecanusetheinvariantmassoftheZHsystem:m2=(EZ+EX)2¡(~pZ+~pX)2:(9.2)Toavoiddouble-countingtheeventsamplesforthethreeVHproductionprocessesareorthogonalwithrespecttothenumberofdetectedleptons.SincethestatisticalmethodcancombineanynumberofanalysischannelsweperformthecombinationoftheseprocessesbothwithintheD0experimentandwithintheTevatronasawhole.Section9.4describesbrie°ytheanalysismethodsoftheZH!``b¹bandVH!ººb¹bchannelsattheD0experimentanddiscussestheresultsfromthecombination.ThecombinationwiththeCDFexperimentisdiscussedinSection9.5.1AlthoughthephysicalprocessassociatedwiththisproductionchannelisstrictlyaZbosondecayingtoapairofneutrinos,wemustalsoconsiderthepossibilitythattheproductionisactuallyWH!`ºb¹bandwedonotdetectthechargedlepton.Thisaccountsfor»50%ofthetotalevents.127HqZq'Zb
b`+`HqWq'Wb
b`HqZq'Zb
bFigure9.4:VHAssociatedHiggsBosonProductionTree-levelFeynmandiagramsofvectorbosonassociatedHiggsbosonproduction.9.4D0Combination
TheD0combinationincludestheZH!``b¹b,WH!`ºb¹b,andVH!ººb¹bproductionchannels.ThesechannelsareincludedintheD0SMHiggsbosonsearch[62].Thebest¯ttothedataintheH!b¹bcombinedanalysisforthesignalcrosssectionmultipliedbythebranchingratiois¹=1:23.TheindividualanalysesaredescribedindetailinRef.[39](ZH!``b¹b),Ref.[63](WH!`ºb¹b),andRef.[64](VH!ººb¹b).TheZH!``b¹banalysisselectseventswithatleasttwoisolatedchargedleptonsandatleasttwojets.Thischannelusesakinematic¯ttocorrectthemeasuredjetenergiestotheirbest¯tvalues.Weperformthe¯tbyconstrainingtheinvariantmassoftheleptonpairtobeconsistentwiththemassoftheZbosonandthetotaltransversemomentumoftheleptonsandjetstobeconsistentwithzero.Wedividetheeventsintotwob-taggingcategoriesdependingonthenumberofbquarkjetstaggedintheevent:a\single-tag"category(ST)128anda\double-tag"category(DT).TheSMHiggsbosonsearch[39]usesRandomForestdiscriminantstoproducethe¯naldistributionsforthestatisticalanalysis.OneoftheseRandomForestsprovidesdiscriminationagainsttopquarkpairproductionanddividestheeventsintot¹t-enrichedandt¹t-depletedregions.Forthespinandparityanalysisonlytheeventsinthet¹t-depletedregionareconsidered2.Theinvariantmassisconstructedfromthetwoleptonsandeitherthetwob-taggedjets(DT)oronetaggedjetandtheuntaggedjetwiththehighestpT.Toimprovethediscriminationbetweenthenon-SMsignalsandthebackgroundsweusetheinvariantmassofthedijetsystemMjjtoselecttworegionswithdi®erentpurityregions.TheinvariantmassofthedijetsystemisshowninFig.9.5.Eventswith100·Mjj·150GeVcomprisethe\high-purity"regionwhiletheremainingeventsareinthe\low-purity"region.Figure9.6showstheinvariantmassdistributionoftheZHsystemfortheDTb-taggingcategoryinthehigh-purityregion.AdditionaldistributionsaregiveninAppendixC.Dijet Mass (GeV)0100200300400Events020406080100120140160180200220=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2bllb®ZHDijet Mass (GeV)0100200300400Events0200400600800100012001400=9.5 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2bbnn®ZHFigure9.5:ZH!``b¹bandVH!ººb¹bDijetInvariantMassDijetinvariantmassfortheZH!``b¹bandVH!ººb¹bchannels.2Thisregioncontainsroughly94%ofthesignal.129 (GeV)bZbM0200400600Events0510152025303540=9.7 fbintDØ, L5)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, DT HPbllb®ZHFigure9.6:InvariantMassoftheZHSystemInvariantmassoftheZH!``b¹bsystemfortheDTb-taggingcategoryinthehigh-purityregion.TheSMHiggsbosonsearchintheVH!ººb¹bchannelselectseventswithalarge6ETandexactlytwojets.ThischannelissensitivetoWHassociatedproductionwhenthechargedleptonisnotdetected.Thejetsareclassi¯edintotwob-taggingcategoriesdependingonthesumofthescoresprovidedbythetaggingalgorithm.Thesecategoriesarereferredtoas\medium"(MT)and\tight"(TT).Weuseadedicatedboosteddecisiontreetoprovidesomerejectionofthemultijetbackground.TheSMHiggsbosonsearchusesaboosteddecisiontreediscriminantasthe¯naldistributioninthestatisticalanalysis.ThetransversemassoftheVHsystemisconstructedfromthe6ETandthetwoselectedjets.Weusetheinvariantmassofthedijetsystemtoagaindividetheeventsintohigh-andlow-purityregions.Figure9.5illustratesthedijetinvariantmassfortheVH!ººb¹bchannel.Thischannelde¯nesthehigh-purityregiontoincludethoseeventswith70·Mjj<150GeVwhilethelow-purityregioncontainstheremainingevents.ThetransversemassdistributionfortheTTb-taggingchannelinthehigh-purityregionisshowninFig.9.7.130OtherdistributionscanbefoundinAppendixC. (GeV)bZb
TM0200400Events050100150200250=9.5 fbintDØ, L15)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, TT HPbbnn®ZHFigure9.7:TransverseMassoftheVHSystemTransversemassoftheVH!ººb¹bsystemfortheTTb-taggingcategoryinthehigh-purityregion.
9.4.1D0CombinationResults:PureNon-SMJPStatesAssumingthedataisdescribedbyapurenon-SMJPstateforthetesthypothesiswecalculatetheLLRteststatisticfortwovaluesof¹:¹=1:0correspondingtotheSMpredictionand¹=1:23correspondingtothebest¯tvaluemeasuredinthecombinedD0H!b¹bchannel.TheLLRdistributionsfor¹=1:0aregiveninFig.9.8.Log-likelihoodratioplotsfortheZH!``b¹bandVH!ººb¹bchannelsindividuallyaregiveninAppendixC.FromtheLLRdistributionswecalculatethep-valuesasbefore.Table9.4liststhep-valuesaswellasCLsforeachchannelindividuallyaswellasthecombinationfor¹=1:0.Thecorrespondingtableassuming¹=1:23canbefoundinAppendixC.WeareabletoexcludemodelswithJP=0¡atthe97.6%con¯dencelevel(CL)assuming¹=1:0.Theexpectedexclusionisatthe99.86%CL.WeexcludemodelswithJP=2+atthe99.0%131LLR0204060Pseudoexperiments0200400600800100012001400160018002000 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR0Observed LLR 9.7 fb£ intDØ, L=1.0mbVb®VXLLR0204060Pseudoexperiments02004006008001000120014001600180020002200 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR+2Observed LLR 9.7 fb£ intDØ, L=1.0mbVb®VXFigure9.8:D0CombinationLLRDistributionsfor¹=1:0LLRdistributionsfortheD0combinationoftheZH!``b¹b,WH!`ºb¹b,andVH!ººb¹bchannelsforJP=0¡andJP=2+assuming¹=1:0.TheLLRdistributionassumingthetest(null)hypothesisisshowninred(blue)whiletheobservedLLRvalueisrepresentedbytheblackverticalline.Thegreenandyellowshadedbandsrepresent1and2s.d.ontheexpectationfromthenullhypothesis,respectively.
CLwithanexpectedexclusionof99.94%CL.Assumingasignalstrengthof¹=1:23theexclusionisstronger.WeexcludetheJP=0¡(JP=2+)caseatthe99.5%(99.8%)CLwithanexpectedexclusionof99.98%(99.99%)CL.Byrelaxingtheconstraintthat¹=¹JPwecanexploretheexclusionregionasafunctionofbothsignalstrengths.TodothiswevarytheJP=0+andnon-SMJPsignalstrengthsindependentlyandcalculatethevalueofCLs.IfCLs¸0:95thentheselectedsignalstrengthsareexcluded.Figure9.9illustratestheexpectedexclusionregionandtheobservedexclusionat95%CLasfunctionsoftheSM¹0+andnon-SM¹JPsignalstrengths.Pointsin¹0+-¹JPspaceareexpectedtobeexcludedat¸95%CLiftheyfallintheshadedorhatchedregion.Weexcludepointswhichareabovetheobserved95%CLlinesat>95%CL.Thequotedexclusionfor¹=1:0correspondstothepoint(1.0,1.0)inthis¯gure.132SM+0s / +0s = +0m00.511.522.53SM+0s / PJs = PJm00.20.40.60.81Exp. ExclusionExp. Exclusion=0PJ+=2PJObs. ExclusionObs. Exclusion=0PJ+=2PJ 9.7 fb£ intDØ, L95% CLFigure9.9:D0ObservedandExpectedExclusionRegions,PureJPStatesTheexpectedexclusionregion(greenshadedarea)andobservedexclusion(solidline)asfunctionsoftheJP=0¡andJP=0+signalstrengths.ThehatchedareacorrespondstotheexpectedexclusionregionasafunctionoftheJP=2+andJP=0+signalstrengths.Thedashedlineisthecorrespondingobservedexclusion.133AnalysisZH!``b¹bWH!`ºb¹bZH!ººb¹bCombinedJP=0¡vs.JP=0+p0¡testExpected0.0750.0300.0160.0007p0¡testObserved0.1260.3510.0070.0221¡pnullExpected0.5000.5000.5000.5001¡pnullObserved0.6460.9650.3670.918CLsExpected0.850(1.04s.d.)0.941(1.56s.d.)0.969(1.87s.d.)0.9986(3.00s.d.)CLsObserved0.805(0.86s.d.)0.637(0.35s.d.)0.981(2.07s.d.)0.976(1.98s.d.)JP=2+vs.JP=0+p2+testExpected0.0640.0090.0230.0003p2+testObserved0.1340.1140.0020.0091¡pnullExpected0.5000.5000.5000.5001¡pnullObserved0.7020.9320.1730.906CLsExpected0.872(1.14s.d.)0.982(2.09s.d.)0.953(1.68s.d.)0.9994(3.22s.d.)CLsObserved0.810(0.88s.d.)0.878(1.16s.d.)0.987(2.23s.d.)0.990(2.34s.d.)Table9.4:D0Combinationp-ValuesExpectedandobservedp-valuesandCLsvaluesforJP=0¡andJP=2+VXassociatedproduction,assumingsignalcrosssectionsequaltothe125GeVSMHiggsproductioncrosssectionmultipliedby¹=1:0.9.4.2D0CombinationResults:AdmixturesofJPStatesFortheD0combinationwecanalsoconsiderthepossibilitythatthedataisdescribedbyanadmixtureofSMandnon-SMJPstates.ForthispossibilitywenormalizethesignalsforeachhypothesisasinTable9.1.We¯xthesumoftheSMandnon-SMJPcrosssectionstoaspeci¯cvalueof¹tot£¾SM0+andvarythenon-SMJPsignalfractionfJP.Aspreviously,wechoosevaluesof¹tot=1:0and¹tot=1:23andproceedtocalculatethevalueofCLs.TheobservedandexpectedvaluesofCLsareplottedinFig.9.10asafunctionofthenon-SMJPsignalfractionfor¹tot=1:0.Fractionsareexcludediftheobservedvalueisabovethe95%CL.Assumingatotalsignalstrengthof¹tot=1:0weexcludenon-SMJPsignalfractionsgreaterthan0:80forJP=0¡and0:67forJP=2+atthe95%CL.Theexpectedexclusionsare0:54and0:47,respectively.Foranassumedvalueof¹tot=1:23theexclusionsare134strongerandaresummarizedinTable9.5.Theexclusionregionsasfunctionsofthenon-SMJPsignalfractionfJPandthetotalsignalstrength¹totareillustratedinFig.9.11. Fraction00.10.20.30.40.50.60.70.80.91sCL0.70.80.911.11.21.3 9.7 fb£ intDØ, LSM
Hs=+0s+0s ObservedsCL ExpectedsCL1 s.d.±Expected 2 s.d.±Expected  Fraction+20.10.20.30.40.50.60.70.80.91sCL0.70.80.911.11.21.3 9.7 fb£ intDØ, LSM
Hs=+0s++2s ObservedsCL ExpectedsCL1 s.d.±Expected 2 s.d.±Expected Figure9.10:CLsasaFunctionoftheNon-SMSignalFractionValuesofCLsplottedasafunctionofthenon-SMJPsignalfractionfJPassuming¹tot=1:0.Theobserved(expected)valueisrepresentedbyasolid(dotted)line.Thegreenandyellowshadedbandscorrespondto1and2s.d.ontheexpectationofthenullhypothesis.Thebluehorizontallinecorrespondstothe95%CL.
9.4.3SummaryofD0Results
TheD0combinationofallthreeVXproductionchannelsincreasedthesensitivityofthespin-paritystudydramaticallywhencomparedtotheWXchannelalone.AssumingasignalcrosssectionmultipliedbybranchingratioconsistentwithmeasurementsatboththeTevatronandtheLHCwewereabletostronglyrejectnon-SMJPpredictionsinfavoroftheSMprediction.Thecombinationalsoallowedustoinvestigatesignaladmixturesandexcludesomenon-SMJPsignalfractions.TheresultsaresummarizedinTable9.5forboth¹=1:0and¹=1:23.ThisresulthasbeenpublishedandmoredetailscanbefoundinRef.[65].135mTotal Signal Scale, 00.511.522.53PJ Fraction, fPJ00.20.40.60.81=0PExp. Exclusion J+=2PExp. Exclusion J=0PObs. Exclusion J+=2PObs. Exclusion J 9.7 fb£ intDØ, L95% CLFigure9.11:D0ObservedandExpectedExclusionRegions,AdmixturesTheexpectedexclusionregion(greenshadedarea)andobservedexclusion(solidline)asfunctionsoftheJP=0¡signalfractionandtotalsignalstrength.Thehatchedareacor-respondstotheexpectedexclusionregionasafunctionoftheJP=2+signalfractionandtotalsignalstrength.Thedashedlineisthecorrespondingobservedexclusion.JPCLs(s.d.)fJP¹=1:0Exp.Obs.Exp.Obs.0¡0.9986(3.00)0.976(1.98)>0.54>0.802+0.9994(3.22)0.990(2.34)>0.47>0.67¹=1:230¡0.9998(3.60)0.995(2.56)>0.45>0.672+0.9999(3.86)0.998(2.91)>0.40>0.56Table9.5:ExpectedandObservedCLsValuesExpectedandobservedCLsvalues(convertedtos.d.inparentheses)andsignalfractionsfor¹=1:0and¹=1:23excludedatthe95%CL.1369.5TevatronCombination
Thestatisticalcombinationofourresultswiththoseofasimilarstudy[66]attheCDFexperimentwillincreasethepotentialexclusionregion.AllthreeVXproductionchannelswerestudiedattheCDFexperimentusingthemethodsuggestedby[38].TheanalysismethodfortheindividualchannelsissimilartowhatwasdoneattheD0experimentandarebrie°ydescribedinthefollowing.Allanalysesusethesamemultivariateclassi¯ertotagbquarkjets.Theclassi¯erdoesnotperformwellonjetswithET>200GeVsob-taggingisnotappliedforthesejetsinallchannels.Forthespin-parityanalysisamultivariateanalysis(MVA)toolwastrainedtodiscriminatebetweentheSMbackgroundsandthenon-SMJPsignal.Eventsthatareclassi¯edasbackgroundarethenclassi¯edusingtheMVAfortheSMHiggsbosonsearchintheWH!`ºb¹bandVH!ººb¹bchannels.DetaileddescriptionsoftheSMHiggsbosonsearchesonwhichthecurrentanalysesarebasedcanbefoundin[67,40,68].ItisinterestingtonotethattheCDFexperimentreported1s.d.and2s.d.de¯citsinthesignalregionsfortheJP=0¡andJP=2+hypotheses,respectively.ThisisincontrasttotheresultsoftheD0studywhichhada2s.d.excess.Thecombinationoftheseresultswillhavethee®ectofbalancingthetwoextremes.ThedetailsoftheTevatroncombinationhavebeenpublishedandmoreinformationcanbefoundinRef.[69].ZH!``b¹bChannel(CDF)Thischannelrequirestwoisolatedleptonsandatleasttwojets.TheCDFanalysisofthischannelrequireseithertwoorthreejets.Eventsaredividedintob-taggingcategoriesbasedontheoutputofamultivariateclassi¯er.FortheZH!``b¹bchanneltheyusethreedouble-b-tagcategoriesandonesingle-b-tagcategory.WH!`ºb¹bChannel(CDF)137CDFrequiresonelepton(eor¹),exactlytwojets,andsigni¯cant6ET.Eventsareclassi¯edaccordingtothequalityoftheselectedlepton.Thesearehigh-qualityleptonsinthecentraldetector,leptonsbasedonisolatedtracks,andelectronsintheforwardregion.Theyde¯ne¯veb-taggingcategories:threedouble-b-tagcategoriesandtwosingle-b-tagcategories.VH!ººb¹bChannel(CDF)TheVH!ººb¹bchannelselectseventswithlarge6ETandtwoorthreejets.Thejetsaredividedintotwodouble-b-tagcategoriesandonesingle-b-tagcategory.ThisanalysisisalsosensitivetoWH!`ºb¹bproductionwheretheleptonisnotidenti¯ed.9.5.1TevatronCombinationResults:PureNon-SMJPStatesFortheTevatroncombinationwe¯rstassumeapurenon-SMJPstateandagaincalculatethevalueofCLsassuming¹=1:0.TheLLRdistributionsforJP=0¡andJP=2+areshowninFig.9.12.Thecalculated1¡CLsvaluesarepresentedinTable9.6.Weexcludemodelswithnon-SMJPsignalswithsigni¯cancesof5:0s.d.and4:9s.d.fortheJP=0¡andJP=2+hypotheses,respectively.Theexpectedsigni¯cancesfortheJP=0¡andJP=2+hypothesesare4:8s.d.and4:6s.d.IntheTevatroncombinationtheobservedsigni¯cancesarehigherthanexpected.Thise®ectisdrivenbyade¯citintheobservednumberofeventsinaregionwithhighnon-SMJPsignalcontentfortheCDFanalyses.ThelargestcontributioncomesfromtheWX!`ºb¹bchannel.138LLR0204060Pseudoexperiments0100200300400500600700SM Higgs68% C.L.SM 95% C.L.SM = 1) m Boson (JP    = 0Observed 10 fb£Tevatron Run II, L bVb®VXLLR0204060Pseudoexperiments0100200300400500600700800900SM Higgs68% C.L.SM 95% C.L.SM = 1) m Boson (+JP    = 2Observed 10 fb£Tevatron Run II, L bVb®VXFigure9.12:LLRDistributionsfortheTevatronCombinationLLRdistributionsfortheTevatroncombinationoftheVXproductionchannelsforJP=0¡andJP=2+assuming¹=1:0.TheLLRdistributionassumingthetest(null)hypothesisisshowninred(blue)whiletheobservedLLRvalueisrepresentedbytheblackverticalline.Thegreenandyellowshadedbandsrepresent1and2s.d.ontheexpectationfromthenullhypothesis,respectively.AnalysisJP=0¡JP=2+1¡CLsExpected9.4£10¡7(4.8s.d.)2.3£10¡6(4.6s.d.)1¡CLsObserved2.6£10¡7(5.0s.d.)5.6£10¡7(4.9s.d.)Table9.6:Tevatron1¡CLsValues1¡CLsvaluesforJP=0¡andJP=2+WXassociatedproduction,assumingsignalcrosssectionsequaltothe125GeVSMHiggsproductioncrosssectionmultipliedby¹=1:0.1399.5.2TevatronCombinationResults:AdmixturesofJPStatesTheTevatroncombinationalsoconsidersthepossibilityofsignaladmixtures.Weexploretheexclusionregionsasfunctionsofthenon-SMJPsignalfractionandthetotalsignalstrength.Figure9.13illustratestheseregions.NotethatmeaningsoftheshadedandhatchedregionsarereversedwhencomparedtothesameplotintheD0combination.Theoverallshapeoftheexclusionregionissimilartotheregionde¯nedbyD0butextendstherangeconsiderably.00.10.20.30.40.50.60.70.80.9100.511.522.5300.10.20.30.40.50.60.70.80.91Total signal scale, mJP fraction, fJPTevatron Run II, L W 10 fb-1Obs. exclusion JP = 0-Obs. exclusion JP = 2+95% C.L.Exp. exclusion JP = 0-Exp. exclusion JP = 2+Figure9.13:TevatronObservedandExpectedExclusionRegions,AdmixturesTheexpectedexclusionregion(greenshadedarea)andobservedexclusion(solidline)asfunctionsoftheJP=2+signalfractionandtotalsignalstrength.Thehatchedareacor-respondstotheexpectedexclusionregionasafunctionoftheJP=0¡signalfractionandtotalsignalstrength.Thedashedlineisthecorrespondingobservedexclusion.140Chapter10
Conclusion
BeginningwiththerecommendationofRef.[38]tostudytheJPcharacteroftheexcessobservedattheTevatronwewereabletoexcludemodelsfortheHiggsbosonwithexoticspinandparitywithhighsigni¯cance.WestudiedWHproductionwheretheWbosondecaysleptonicallyandtheHiggsbosondecaystoapairofbquarksindetail.UsingthetransversemassoftheWHsystemasadiscriminationtoolweinvestigatedtwowell-motivatedJPstates:JP=0¡andJP=2+.Assumingthatthesignalcrosssectionswereequaltothe125GeVSMHiggsbosonproductioncrosssectionmultipliedby¹=1:0wefoundthatwecouldnotexcludethesepossibilitiesatthe95%CL.BycombiningtheothervectorbosonassociatedproductionchannelsatD0wewereabletoexcludetheJP=0¡andJP=2+hypothesesatthe97:6%CLand99:0%CL,respectively.WeconsideredthepossibilitythatthedataisdescribedbyanadmixtureofSMandnon-SMJPstates.WewereabletoexcludeJP=0¡signalfractionsf0¡>0:80andJP=2+signalfractionsf2+>0:67atthe95%CL.WealsocombinedourresultswiththeresultsoftheCDFexperiment.TheJP=0¡andJP=2+hypothesesareexcludedwithsigni¯cancesof5:0s.d.and4:9s.d.,respectively.Thecorrespondingcon¯dencelevelsare>99:9999%.Atthetimeofthiswriting,theseproductionchannelsarenotaccessibletotheexperimentsattheLHCbecauseoftherelativelylowsignal-to-backgroundratio.TheseresultsarethemoststringentexclusionsofmodelsfortheHiggsbosonwithexoticspinandparityinafermionicHiggsbosondecaychannelandwillremainsountiltheLHCacquiresthenecessarysensitivity.141APPENDICES142AppendixA
TheFermilabAcceleratorChain
ThisAppendixprovidesmoredetailontheequipmentusedtoaccelerateprotonsandan-tiprotonsandproducecollisions.TheFermilabacceleratorchainisdescribedindetailbyfollowingthedi®erentpathstakenbyaprotonandanantiprotonbeginningwiththeirpro-ductionandendingwiththeircollisionatacenterofmassenergyof1.96TeV.AlthoughtheFermilabacceleratorchainhasgonethroughmanyupgradesthroughouttheyears(andstillcontinuestodoso!),thefollowingsectionsdescribetheacceleratorchainatthetimeitceasedtooperateasacollidingbeamfacility.SectionA.1describesthepathofaprotonfromthesourcetothe¯nalstageofacceleration.Thecreation,collection,andaccelerationofantiprotonsisdescribedinSectionA.3.
A.1LifeofaProton
A.1.1ThePreaccelerator
AllprotonsatFermilabbegininabottleofhydrogengasatoneoftwopreaccelerators.TherearetwoforredundancyandcanbeconsideredidenticalforthepurposeofthisThesis.Eachpreacceleratorconsistsofanegativehydrogenionsource,aCockcroft-Waltonvoltagegenerator,anelectrostaticacceleratingcolumn,andatransportlineforinjectionintotheLinac.143Tobegin,hydrogengasispumpedintoasurfaceplasmamagnetronsource.Themag-netronsource,Fig.A.1,consistsofaovalshapedcathodesurroundedbyananodeandplacedinamagnetic¯eldparalleltothecathodesurface.TheanodeandcathodeareenergizedFigureA.1:SurfacePlasmaMagnetronSourceDiagramofasurfaceplasmamagnetronsourcelikethoseusedatFermilab.withafewhundredvoltsandhydrogengasispumpedintothespacebetweentheanodeandcathode.Theelectricandmagnetic¯eldscausethecon¯nedelectronstospiralinthegapbetweentheanodeandthecathode,producingadenseplasma.Negativeionsarepro-ducedwhenpositiveionsareattractedto,andstrike,thesurfaceofthecathodeandeithersputtero®negativeionsorgainelectronsthemselves.Todecreasetheenergyrequiredtopullelectronsfromthecathodesurface,cesiumvaporisleakedintothesystemandcoatsthecathodewithaverythinlayer.Onceproduced,thesenegativeionsacceleratefromthecathodethroughthenarrowplasmatotheanode.Whennegativeionsarenearaslitintheanode{theanodeaperture{theyareacceleratedbyanextractorelectrodetoapprox-imately18keV.Toseparatethenegativehydrogenionsfromothernegativespeciesa90±bendingmagnetisusedandguidesthehydrogenionstothe¯rststageofacceleration,theacceleratingcolumn.TheFermilabacceleratingcolumnisanelectrostaticaccelerator.Thehighvoltagedif-ferencerequiredfortheaccelerationisprovidedbyadual-leg,¯vestageCockcroft-Waltongenerator.TheCockcroft-WaltongeneratorisdescribedinSection2.1.1.Asecondlegre-144ducesrippleintheoutputvoltage.TheCockcroft-Waltonprovidesahighvoltageof-750kVfromasourcevoltageof75kV.TheacceleratingcolumnandsourceinstallmentisshowninFig.A.2.Theacceleratingcolumnconsistsofsevendisk-shapedtitaniumelectrodesdesignedtoguidetheionsduringtheiracceleration.Theyareseparatedwithceramicinsulatingdisksandtheinsideiskeptatvacuum.Theentirecolumnisplacedinsideapressurizedglassvesselcontainingtheinsulatinggassulfurhexa°uoridetominimizesparksbetweentheelec-trodeleads.Thehighvoltageisdistributedamongtheelectrodesviaawaterresistorsothevoltagedropbetweenelectrodesisroughlyequal.Theendoftheelectrostaticcolumnisgroundedatthewalloftheenclosure.ReferringtoEq.2.2andconsideringthechargeofthenegativehydrogenionisequaltothatofanelectron,theionsareacceleratedto750keV.Thesourceoperatesinpulsedmodewitharateof15Hzbothtopreservetheintegrityofthesourceandtomatchthe¯xedcycletimeoftheBooster.Apulselastsapproximately80¹s.BetweentheacceleratingcolumnandtheLinacisatransferline,the750keVline,FigureA.2:ProtonSourceandAcceleratingColumnFermilabsourceandacceleratingcolumnassembly.
thatservesseveralfunctions:focusing,selecting,andbunching.Eachtransferlinehassev-eralhorizontalandverticalfocusingquadrupolestokeepthebeamfrombeingdispersed.145Adevicecalledthechopperselectsaportionofthebeam,usuallyapproximately40¹s,tosendtotheLinac.Bunchingthebeamincreasesthecapturee±ciencyoftheLinac.IfacontinuousparticlebeamwereinjectedintotheLinaconlytheparticlesinthestablephaseregionwouldbecapturedandacceleratedwhichwouldamountto35%ofthepulse.Thebuncherisasingle-gapradiofrequencycavitysimilartothecavitiesintheLinac.ItoperatesatthesamefrequencyastheLinacbutwithadi®erentphase.Particlesthatarriveearlyaredeceleratedandparticlesthatarrivelateareaccelerated.Thise®ectivelydecreasestheparticles'widthintimebutincreasestheparticles'momentumspread.Withthebuncher,theLinaccapturerateisapproximately70%.
A.1.2TheLinac
TheFermilabLinaciscomposedoftwodi®erentmachinesthatworkintandemtoacceleratethebeamto400MeV.The¯rstmachineisanAlvarezdrifttubelinac(DTL).Itconsistsof¯vecylindricaloxygen-freehighconductivity(OFHC)coppercladsteeltanks.Eachtankispoweredbyitsown5MWpowersourceandresonatesat201.24MHz.Eachcavityhasseveralresonantcellsextendingfromthecenterofonedrifttubetothenextwiththecelllengthranginginlengthfrom6.04cmto67.9cm.Thephaseshiftbetweenadjacentacceleratingcellsiszeroandeachradiofrequency(RF)bucketcontainsaparticlebunch.Theaverageaxialelectric¯eldrangesfrom1.6MV/mto2.6MV/m.ThisportionoftheLinacacceleratesthenegativehydrogenionsto116MeV.AfteraccelerationintheDTLtheH¡ionsmoveintothesecondportionoftheLinac,theside-coupledlinac(SCL).InsteadofonecavitycontainingmultipleacceleratingcellsasintheDTL,eachcavityisonecellintheSCL.TheSCLconsistsofsevenmoduleswhicharedividedintofoursectionswithsixteenacceleratingcellsand¯fteencouplingcells.Eachcell146hasa¼=2phaseshiftfromeachadjacentcell,givingaphaseshiftof¼betweenacceleratingcells.Individualmodulesarepoweredwithasingle12MWpowersourceandresonateat804.96MHz.BecausethedrivingfrequencyisfourtimesthatoftheDTLandthephaseshiftbetweenacceleratingcellsisdi®erentby¼,thebunchestraveleightacceleratingcellsapartintheSCL.Thepowerisdistributedfromoneindependentacceleratingcelltothenextthroughthecouplingcells.Ananalogoussystemwouldbeasetofmassesconnectedinserieswithsprings.Ifonemassissettooscillatetheotherswillcometooscillateatthesamefrequencythroughthecouplingofthesprings.Anexamplesectionofaside-coupledlinacisshowninFig.A.3.Inadditiontocouplingcavities,eachsectionisconnectedviaaFigureA.3:Side-CoupledLinacSectionAnexamplesectionofaside-coupledlinac.bridgecouplerthatisthelengthofthreecouplingcells.Thisallowsfortheplacementoffocusingquadrupolesandbeamdiagnostics.TheRFpowerisimportedatthemiddlebridgecouplertoequalizethepowerdroopateitherend.Oneofthemainbene¯tsoftheSCListhenose-coneshapeoftheacceleratingcavities.FigureA.4showstheelectric¯eldintheacceleratingcavityduetothenose-cones.Theelec-tric¯eldishighlyconcentratedinthecenteroftheacceleratinggapwhichproducesamoree±cientacceleration.Theaverageaxial¯eldineachmoduleisapproximately7.5MV/m,147aboutthreetimesthatoftheDTL.Afterthe66msLinaccyclethebeamhasanenergyof400MeV.FigureA.4:Nose-ConeFieldTheelectric¯eldofanose-cone.Noticetheconcentrated¯eldinthecenteroftheacceleratingregion.BetweentheLinacandtheBoosterisatransferline,the400MeVline,thatthathasasimilarfunctiontothelinebetweenthePreacceleratorandtheLinac.Aportionofthepulse,thechop,fromtheLinacisselectedtobesenttotheBooster.ThelengthdeterminestheresultingintensityofthebeamintheBooster.AcartoonofthechoppingprocessisshowninFig.A.5.First,theplatesofthechopperarechargeduptoapproximately60kVandbeamgoesthroughunde°ected.Ittravelsthroughthecenterofafocusing(inthehorizontaldirection)quadrupoleandstraightthroughtheLambertsonseptummagnettowardsthebeamdump.Atthestartofthechopthelowerplateisgroundedandthebeamisde°ectedupwards.Itentersthequadrupoleo®-centerandgetsfurtherde°ectedintothe¯eldregionoftheLambertson.TheLambertsongivesthebeamahorizontalbendofapproximately11±.Attheendofthechopthetopchopperplateisgroundedandtheremainingbeamisagainunde°ectedandissenttothebeamdump.Afterthechopisselecteditissentdown¯fteenfeettotheBoosteratanangleofapproximately13±.AfterbeingkickedoutoftheSCL,148FigureA.5:400MeVChopperCartoonofthechoppersectioninthe400MeVlinefromtheLinactotheBooster.thebeampassesthroughadebuncherwhichhelpsremovethe804.96MHzRFstructurefromtheSCLandreducethemomentumspreadinthebeam.Inadditiontofocusingandsteeringmagnets,the400MeVlinemustalsomatchthelatticeoftheSCLtothelatticeoftheBoosterfore±cienttransfer.
A.1.3TheBooster
TheBoosteristhe¯rstinaseriesofthreesynchrotronsintheFermilabacceleratorchain.Itisafast-cyclingmachinethatcompletesacyclefrominjectiontoextractioninroughly66ms.Ithasacircumferenceof468mandconsistsof96combinedfunctionmagnetsarrangedinaFOFDOODlattice:focusingquadrupole,shortdriftlength,focusingquadrupole,defo-cusingquadrupole,longdriftlength,andanotherdefocusingquadrupole.Ithasseventeenacceleratingcavitieslocatedinthelongdriftsections.149Attheinjectionenergyof400MeVoneturnintheBoostertakes2.22¹s.Withachoplengthofapproximately40¹s,thebeamfromtheLinaccouldwraparoundtheBoostereighteentimes!Itisherethatthebene¯tofstartingwithnegativehydrogenionsisapparent.Ifthesourceproducedprotonsitwouldonlybepossibleto¯lluponeturnoftheBooster.Inthiswaytheintensityofthebeamislimitedandalargeamountofbeamiswasted.AcleverroutewastakentosolvethisproblemandisshowninFig.A.6.Uponinjection,theFigureA.6:ChargeExchangeInjectionTwosetsofdipolemagnetsproduceabumpintheorbitofthecirculatingprotonsandinjectednegativehydrogenionswhichputstheminthepathofastrippingfoilwhichremoveselectrons.
circulatingprotonsarebumpedfromtheirnominalorbitandsentwiththenegativehydrogenionsthroughastrippingfoilwhichremoveselectronsfromthenegativeions.Aftergoingthroughthestrippingfoilthebeamissentbacktoitsnominalorbitwithnewlyacquiredprotons.Thenegativeandneutralproductsareabsorbed.InnormaloperationtheBoosterisabletoaccept¯veturnsofbeamfromtheLinac.AfterthebeamhasbeeninjectedandtheRFstructureoftheLinachasdecayedaway,thebeamiscapturedbytheBooster's38MHZRFsysteminto84RFbuckets.Earlyinthecycle,thelastthreebunchesinthebunchtrainareejectedandthecorrespondingbuckets150clearedtoallowtimefortheejectionkickermagnetstoturnon.Duringacceleration,theRFfrequencyincreasesfrom37.8MHzto52.8MHztomatchtheincreasingkineticenergyofthebeam.Attheendoftheaccelerationcycletheprotonshaveakineticenergyof8GeVandarereadytobedeliveredtotheMainInjector.The8GeVtransferlinebetweentheBoosterandtheMainInjectormuststeerthebeamdown11feettotheleveloftheMainInjectorandaroundobstacles(suchastheAntiprotonSource)allwhilemaintaininghorizontalandverticalfocus.Becausethetransferlinehasitsownlatticestructure,therearetwolatticematchesthatneedtobedonebeforeinjectionintotheMainInjector:matchingtheBoosterlatticetothetransferlinelatticeandmatchingthetransferlinelatticetotheMainInjectorlattice.BecausetheextractionfrequencyoftheBoosterandtheinjectionfrequencyoftheMainInjectorareequal,theBoosterphase-lockswiththeMainInjectorandperformsabucket-to-buckettransferofbeam.A.2TheMainInjector
TheMainInjectoristhesecondsynchrotronandistherealworkhorseoftheFermilabacceleratorchain.Itservesmanyfunctionsintheacceleratorchain;deliveringprotonsandantiprotonstotheTevatronforacceleration,deliveringprotonstotheAntiprotonSource,transferringantiprotonstoandfromtheAccumulatorandRecycler,anddeliveringbeamto¯xedtargetandneutrinoexperiments.TheMainInjectorhasacircumferenceof3319mandiscomposedof344dipoleand208quadrupolemagnetsarrangedinaFODOlatticewithmostofthedipolesplacedinthedrift(O)spaces.Itiscapableofacceleratingprotonsandantiprotonsupto150GeV.IthaseighteenRFcavitiesoperatingfrom52.8MHzto53.1MHzdividedintotwoindependentsystems.Thisisrequiredforslip-stacking,amethod151ofincreasingtheintensityofthebeamthatinvolveslettingtwoBoosterbatcheswithslightlydi®erentRF(andhencemomentum)slippasteachotherintheringuntiltheyarealignedandthenrecapturingthebunchesinasingleRFbucket.TheMainInjectorcanalsocoalesceprotonandantiprotonbunchesbyrotatingseveralbunchesviasynchrotronoscillationsina2.5MHzRFbucketandthenrecapturingthemina53MHzbucket.ApartialbatchfromBoosterofapproximatelysevenbunchesarepassedtoMainInjectorandacceleratedto150GeVwhentheyarecoalescedintoasinglebunchandinjectedintotheTevatron.Atotalof36ofthesesuperbunchesareinjectedintotheTevatronforcollisions.A.2.1TheTevatron
TheTevatronisthethirdsynchrotronand¯nalacceleratorinthechain.Itisasuper-conductingsynchrotronthatis6.3kmincircumference.OverathousandsuperconductingmagnetscooledtoliquidheliumtemperaturesmakeuptheFODOlatticeoftheTevatron.Unliketheothermachineswhichserveavarietyofpurposesthroughoutthecomplex,theTevatronhasonemodeofoperation:collidermode.Itsjobistoacceleratecounter-rotatingprotonsandantiprotonstotheir¯nalenergyof980GeVandthencollidethemattwo¯xedpointsaroundthering.Oncetheaccelerationiscomplete,itfunctionsasastorageringwherestablebeamscollideforhoursonend.Thereareeightacceleratingcavitieswhichresonatefrom53.103MHzto53.104MHzduringacceleration.Theaccelerationofbothpro-tonsandantiprotonsinthismachinerequirestwoindependentRFsystemstoallowfor¯necontrolovertherelativepositionsofthebeams.Theeightacceleratingcavitiesaredividedintotwogroups:onethatacceleratestheprotonsandonethatacceleratestheantiprotons.TheTevatronnowhas36coalescedbunchesofprotonscirculatingattheinjectionenergyof150GeV.WewillreturntotheTevatronlaterwhendiscussingantiprotons.152A.3LifeofanAntiproton
Antiprotonsaremoredi±culttomakeandmanyaspectsoftheacceleratorchainre°ectthis.Togetanideaofhowdi±cultitistoproduceantiprotonsconsiderthatforevery105protonsthatbombardthetargetonlyabouttwoantiprotonsareproduced.TheFermilabAntiprotonSourceconsistsoftheTargetVault,twotriangularsynchrotrons:theDebuncherandtheAccumulator,andapermanent-magnetstorageringcalledtheRecycler.TheMainInjectorandtheTevatronarealsodirectlyinvolvedintheaccelerationandtransportoftheantiprotons.Tobegin,BoostersendstwobatchesofprotonstoMainInjectorwheretheyareslip-stackedandacceleratedto120GeV.MainInjectorthenrotatesthebunchesinlongitudinalphasespace,creatingbuncheswhichhavealargemomentumspreadbutasmallspreadintime.ThebunchesarethenextractedfromtheMainInjectorandsenttotheTargetVault.
A.3.1TargetVault
Upstreamofthetargetisasweepermagnet,arotatingdipolewhichde°ectstheprotonbeaminacircletoreduceheatingofthetarget.TheprotonsimpingeonanInconel(anickel-ironalloy)targetwhichproducesasprayofsecondaryparticlessomeofwhichareantiprotons.Thetargetiscylindricalinshapeandrotatesonanaxisperpendiculartotheincomingbeamtoreducetargetheatinganddegradation.Immediatelyafterthetargetisalithiumlenswhichfocusesthesecondariesinbothtransverseplanes.Lithiumisusedbecauseitistheleastdensesolidconductor;scatteringandabsorptionoftherareantiprotonsisminimized.Acoppercollimatorwithaholeboredinthecenterforthebeamtotravelthroughprotectsthenextelement,apulseddipolemagnet.Thismagnetselectsnegatively-charged8GeV153secondariesandsendsthemtotheDebuncher.
A.3.2TheDebuncher
TheDebuncherisaroundedtrianglesynchrotronwithatraditionalFODOlattice.Itoper-atesata¯xedenergyof8GeV,thepeakenergyoftheBoosterandclosetotheantiprotonproductionpeak.Asthenameimplies,itsfunctionistodebunchtheincomingantiprotons.DuringthetransitfromtheTargetVaultmostofthesecondariesthatwerenotantiprotonsdecayedawayandtherestwillbelostduringthe¯rstfewtripsaroundtheDebuncher.TheantiprotonsthatarelefthaveretainedthebunchstructureoftheprotonsthatlefttheMainInjector.ThemainRFsystemintheDebuncherisa53.1MHzsystemthatisresponsibleforrotatingthebeamofantiprotonsinlongitudinalphasespacetorecreatebunchesthathavealargespreadintimeandasmallmomentumspread.Itisalsoresponsiblefordebunchingthebeam.AsecondaryRFsystemmaintainsagapbetweentheheadandtailofthebunchtrainsothetrain¯tsaroundthesmallerAccumulatorring.TheDebuncherusesstochas-ticcoolingofthebeamtodecreasethetransverseandlongitudinalemittanceresultinginadenserparticlebeam.Stochasticcoolingusessetsofpick-upsandkickerstodetectandcorrecterrorsinthebeamenergyandtransversedisplacement.
A.3.3TheAccumulator
TheAccumulatorisan8GeV¯xed-energysynchrotronintheshapeofatrianglewith°at-tenedcorners.ItliesontheinsideradiusinthesametunnelastheDebuncherandhasasimilarFODOlattice.TheAccumulatorcollectssuccessiveantiprotonbatchesfromtheDebuncheroverseveralhours.Itperformsmomentumstackingwherenewlyinjectedbeam154iscooledanddeceleratedtowardsacoremomentumvalue.FigureA.7showstheradialdistributionofantiprotons,collectivelycalledthestack,intheAccumulator.Antiprotonsoflowerenergyoccupyasmallerradiusinthemachine.Thereisadi®erenceinenergyof150MeVfromthestackcoretotheinjectionorbit.ThisisaccomplishedintheAccumulator¯rstthroughRFmanipulationsandthenthroughstochasticcooling.BeamfromtheDe-FigureA.7:AccumulatorStackPro¯leRadialantiprotondistributionintheAccumulator.Particlesontherightinthediagramarelowerinmomentumandhaveasmallerorbitalradius.
buncherisacontinuousribbonandiscapturedinto53MHzbucketsanddecelerated60MeVanddepositedattheedgeofthestacktail.TheRFvoltageisloweredslowlytoallowthebeamtodebunch.Stacktailcoolingsystemsaremomentumcoolingsystemswithpick-ups155inhighdispersionsections.Thesecoolingsystemsdeceleratethebeamtothecoreregioninapproximatelytwentyminutes.Onceinthecoreregion,momentumcoolingsystemskeepthebeamcontainedinthecorebydeceleratinghighermomentumparticlesandacceleratinglowermomentumparticlestokeeptheminsidethemachine.Transversecoolingpickupsforthecorearelocatedinlowdispersionsectionsandareusedtocontrolthetransverseemittance.Onceastackofsuitableintensityisreached,partofthecoreisextractedfromtheAccumulatorandtransferredtotheRecyclerbytheMainInjector.A2.52MHzRFsystemcreatesfourbunchesfromthecoreandslowlyacceleratesthemthroughtherestofthestackandallthewaytotheextractionorbit.TheyarethenkickedoutoftheAccumulatorwithoutdisturbingtherestofthestackandtransferredbytheMainInjectortotheRecycler.A.3.4TheRecycler
TheRecyclerisan8GeVstoragering.ItconsistsofpermanentcombinedfunctionmagnetsarrangedinaFODOlattice.ItresidesabovetheMainInjectorinthesametunnel.LiketheAccumulatoritsjobistoaccumulateandstoreantiprotons.ItacceptsseveralbatchesofantiprotonsfromtheAccumulatorandiscapableofstoringthemforhours.IntheRecyclertheaccumulatedantiprotonsarereferredtoasthestashtodi®erentiatefromtheAccumulator'sstack.LiketheAccumulatorandDebuncher,theRecyclerusesstochasticcoolingtocontrolboththetransverseandlongitudinalemittance.Unlikethesemachines,theRecycleralsouseselectroncoolingtodecreasethemomentumspread.Inthisschemeanelectrongunproducesahighlycollimatedandnearlymonochromaticelectronbeamwhichisacceleratedtomatchtheaveragevelocityofthecirculatingantiprotons.Thiselectronbeamisthen156allowedtotravelalongsidetheantiprotonbeamforashortdistance.Alongtheway,energyfromthe`hot'antiprotonsistransferredtothe`cold'electrons.Theelectronsarethenreturnedtothesourcetakingtheenergygainedwiththem.Sofarwe'veseenbeamstoredintwodi®erentways:inbunchesorinacontinuousribbon.TheRecyclerstoresitsbeaminadi®erentmanner.InsteadofusingaresonantRFcavityitusesawide-bandRFcavitythatiscapableofproducingamultitudeof(non-resonant)waveforms.ThemostusedwaveformintheRecyclerisarectangularpulse.Beamisstoredlongitudinallybetweenanegativeandapositivevoltagepulsecalledabarrierbucket.Allothermanipulationsofthebeamaredoneusingadditionalrectangularpulses.Duringinjection,thefourbunchesofantiprotonsfromtheMainInjectorarecapturedbya2.5MHzsinusoidalwaveformwhichiscontainedinsideabarrierbucket.Thegainonthewaveformisreducedandthebeamisallowedtodebunchinsidethebarrierbucket.Thisbarrierbucketisthenmovedtowardsthestashandthebarriersbetweenthemareremoved.WhentheRecyclerintensityisgreatenoughandtheTevatronisreadytostartanewstoretheantiprotonsarelongitudinally`momentum-mined'.AnothersetofRFmanipulationscreatesnineparcelsoflowmomentumspread.TheseparcelsaremovedonebyonetotheextractionregionwheretheyaremadeintofourbunchesandsenttotheMainInjectorforacceleration.
A.3.5TheMainInjector:AnAntiproton'sPointofView
Afterinjecting36coalescedprotonbunchesintotheTevatrononeatatime,MainInjectorcanbeginacceptingantiprotonsfromtheRecycler.Becauseantiprotonshavethesamemassbutoppositechargeastheprotons,thelatticeoftheMainInjectoralsoworkstoaccelerate157antiprotonsaslongastheirdirectionoftravelisoppositethatoftheprotons.1TheMainInjectoracceptsfourbunchesfromtheRecyclerequaltooneparcelor1=9ofthestash.Itacceleratesthesefourbunchesto150GeVanddepositsthemintheTevatron.ToacceptanotherfourbunchesfromtheRecycleritreturnsbackto8GeV.Nineofthesetransfersaremadeforatotalof36antiprotonbunches.
A.3.6TheTevatron:AnAntiproton'sPointofView
Onceall36protonbunchesareloadedsatisfactorily,theTevatronpreparestoreceivean-tiprotonsfromtheMainInjector.Tominimizethee®ectsofhavingtwoseparatebeamsinthesamebeampipeelectrostaticseparatorsareturnedongivingakicktotheprotonsinbothtransverseplanes.Thiscausestheprotonstoperformbetatronoscillationsaroundtheidealpathresultinginaspiralpath.Whenantiprotonsareinjected,theyfeelanequalandoppositeforceandalsofollowaspiraltrajectory.Theresultlookslikeadoublehelix.Once36bunchesofantiprotonsareinthemachinetheyareacceleratedto980GeV.Next,thehelicaldisplacementisremovednearthecollisionpointsandbeamissqueezedintoasmallcross-sectionalareaforcollisions.Afterunboundparticleswhichcandamagesensitivematerialinthedetectorsareremoved,astoreisdeclaredandphysicsdata-takingbegins.Thestorelastsforhoursandendswhentheluminosityhasfallenbelowapredeterminedvalueand/ortheRecyclerhasaccumulatedalargeenoughstashtobeginanotherstore.1InMainInjector'scase,protonstravelcounterclockwiseandantiprotonstravelclockwise.ThisisoppositetotherotationalsenseintheTevatron.158AppendixB
TheD0DetectorinDetail
ThisAppendixdescribestheD0detectoringreaterdetailthanwhatwaspresentedinthemaintext.Forreference,thecross-sectionalviewoftheD0detectorfromChapter4isreproducedhere.FigureB.1:D0DetectorCutawayviewoftheD0detectorshowingtheonionskinlayeringofthedetectorsub-components.159B.1TrackingSystem
Theprimarypurposeofthetrackingsystemistorecordthetracksleftbychargedparticlesoriginatingfromthecollisionsoftheprotonandantiprotonbeams.Muchinformationcanbegainedaboutthecollisioneventfromtheserecordedtracks.Placingthetrackingvol-umeinsidethemagnetic¯eldofasolenoidmakesadditionalmeasurementspossible.Threeimportantfunctionsofthetrackingsystemarebasedontheinformationprovidedbytherecordedtracks.Onesuchimportantfunctionofthetrackingsystemisvertexing.Byex-trapolatingtracksbacktowardsthebeam,theprimaryinteractionvertexfortheeventcanbefoundwithgoodprecision.Secondaryverticescausedbylong-livedparticlestravelingashortdistancebeforedecayingcanalsobedetected.Thisplaysamajorroleindetectinglong-livedbquarkhadrons.Anotherimportantfunctionisparticleidenti¯cation.Trackscanbematchedtoparticleshowersseeninthecalorimeterstohelpdeterminetheparticletype.Determiningthedirectionofcurvatureoftheparticle'strajectoryinthemagnetic¯eldgivesameasurementofthesignofitscharge.The¯nalfunctionofthetrackingsystemisobtainingamomentummeasurementoftheparticlestraversingthedetector.Thisisdonebymeasuringthecurvatureofthetrackinthemagnetic¯eld.Manyofthesefunctions,particularlymomentummeasurementsandvertexing,requirethetrackingsystemtobetheclosestdetectorsubsystemtotheinteractionpoint.Directlyoutsidethebeampipe,itoccupiestheradialspacebetween1.6cmand52cmfromthecenterofthebeampipeandis2.5minextent.Sincethedirectionandpositionofthesetracksisimportantinreconstructingthecollisionevent,caremustbetakentominimizescatteringoftheparticleso®activedetectormaterialandsupportstructures.Particlespassingthroughthetrackingsystemshouldnotloseanyappreciableamountofenergyorbedivertedfrom160theiroriginalpath.ThetrackingsystemconsistsoflowatomicnumberZmaterialstominimizethenumberofradiationlengths.Thetrackingsystemconsistsoftwodetectors:theSiliconMicrostripTrackerandtheCentralFiberTrackerdescribedinSectionB.1.2andSectionB.1.3,respectively.BecausethemagnetsystemisanessentialpartofthetrackingsystemitwillbedescribedinSectionB.1.1.B.1.1Magnets
Themagnetic¯eldwhichaidsintrackingparticlesisprovidedbythecombinationoftwomagnets:asolenoidandatoroid.Theentiretrackingsystemisinsidetheboreofthesolenoidmagnetorientedparalleltothebeamaxis.Thesolenoidmagnetalongwiththerestofthedetector(withtheexceptionofsomeofthemuonsystem)isinsidethetoroidmagnet.Thecentral¯eldofthesolenoidis2Twhilethe¯eldinthetoroidis1.9T.Aprojectionoftheresultingmagnetic¯eldinthey-zplaneisshowninFig.B.2.Themagnetic¯eldissymmetricaboutthex-zdiagonal.Themagnets'polarityisperiodicallyreversedanddataistakenineachofthefourcon¯gurations.
B.1.1.1Solenoid
Thesolenoidisasuperconductingmagnetthatis2.54mlongand1.22mindiameter.ThesuperconductingcablesaremadefromeighteenCu:NbTistrandsstabilizedinaluminum.Thecablesarewoundintwolayersinsideasupportingcylinder.Thecablesarecooledwithliquidheliumandoperateinthesuperconductingregime.Acurrentof4749Athroughthecoilsgivesacentral¯eldof2T.161FigureB.2:D0MagneticFieldPlottedistheprojectionofthemagnetic¯eldinthey-zplanewiththesolenoidandtoroidatfullcurrent.Notethatthemagnetic¯eldpossessesx-zsymmetry;¯eldlinesatthepoints(y,§z)di®erbyasmuchas2.5minx.Valuesaregiveninunitsofkilogauss(kG).162B.1.1.2Toroid
ThetoroidisconsideredpartofthemuonsystemdiscussedinSectionB.4andalsoservesasthereturnforsomeofthe¯eldlinesofthesolenoid.Unlikethesolenoid,thetoroidoperatesintheclassicalregime.Themagnetismadefromironwindingsaroundasteelyokeandhasthreesections:twoendtoroidsandonecentraltoroid.Thecentraltoroidisasquareannulusabout1mthickand7.6mlong.Itiswoundwithtwentycoilsoftenturnseach.Thetwoendtoroidsaresquarewitha1.8msquareholetoaccommodatethebeamline.Eachendtoroidiswoundwitheightcoilsofeightturnseachandiswiredinserieswiththecentraltoroid.Thecurrentthroughthetoroidis1500Agivinga¯eldinsidetheyokeof1.8Tinthecentraltoroidand1.9Tintheendtoroids.
B.1.2SiliconMicrostripTracker
TheSiliconMicrostripTracker(SMT)isasolidstatesemiconductordetector.Sensorsaremadefrombulkn-type1siliconandareeithersingle-ordouble-sided.Single-sidedsensorsaremadebyimplantingp-type2siliconinstripsononesideofthen-typebulksilicon.Double-sidedsensorsaremadebyimplantingstripsofn-typesiliconwithalargerfractionofdonorimpuritiesthanthebulkmaterialontheothersideofsingle-sidedsensors.Voltageisappliedacrossthestripssuchthatthep-typeimplantssitatanegativevoltagecomparedtothen-typebulkorn-typestrips.Thiscreatesalargeregionwheretherearenofreechargecarriersastheholes(electrons)inthep-type(n-type)materialareattractedtothecathode(anode).Thisregionisreferredtoasthedepletionregionandistheactiveareaof1N-typesemiconductorshavemajoritychargecarriers(electrons)thatarenegativeandareproducedbyaddingimpuritiesthatdonateelectronstothemateriallattice.2P-typesemiconductorshavemajoritychargecarriers(holes)thatarepositiveandareproducedbyaddingimpuritiesthatacceptelectronstothemateriallattice.163thedetector.Whenachargedparticlepassesthroughthesensoritionizesthematerialinthedepletionregioncreatingelectron-holepairs.Thesemigratetothestripsandthechargeisreadout.Thedetectoriscomposedofmanyofthesesensorsarrangedinbarrelsanddisks.AnisometricviewoftheSMTisshowninFig.B.3.Thebarrelsprovideameasurementofther-Áforthetracksinthecentral(smallj´j)regionofthedetector.Disksmeasurether-zcoordinateaswellasther-Ácoordinateintheforward(highj´j)regions.TherearesixbarrelsintotalcappedatthehighjzjendbyadiskcomposedofwedgedetectorscalledanF-disk.EachendofthebarrelregioniscappedbythreeadditionalF-disks.Onelargediameterdisk,calledanH-disk,islocatedinthefar-forwardregions.AseparatesystemcalledLayer0isinstalledinsidetheinnerdiameterofthebarrelsanddisks.B.1.2.1Barrels
Eachofthesixbarrelshasfourlayerswitheachlayercomposedoftwosublayers.Thebarrelsiliconmodule,calledaladder,consistsofa12cmlongsensorregionandfront-endelectronicsnecessarytoreadoutthesensoronaberylliumsubstrate.LaddersinthesublayersarearrangedsuchthattheyprovideanoverlapinÁasinFig.B.3.Eachbarrelcontains72ladderswithsensorsofvaryingwidths.Thesecondandfourthlayerofallbarrelshaveladderswithdouble-sidedsiliconsensors.Thep-sidehasstripsorientedparalleltothebeampipewithastrip-to-stripdistance(pitch)of50¹m.Stripsonthen-sideareorientedatanangleof2±withrespecttotheaxialstripsandhaveapitchof62.5¹m.The¯rstandthirdlayersofthetwoouterbarrelshavesingle-sidedladderswithastrippitchof50¹morientedparalleltothebeampipe.Fortheinnerfourbarrels,the¯rstandthirdlayershavedouble-sidedladderswitha90±stereoangle.Thep-sidestripsarealignedparalleltothe164FigureB.3:D0SiliconMicrostripTrackerAnisometricviewoftheD0SMT.Notethatthetwofar-forwardH-diskswereremovedtoinstallLayer0(notshown).
beampipeasinthesingle-sideddeviceswhilethen-sidestripsareperpendicular.B.1.2.2F-disks
Thereare12F-disksinall:oneatthehighjzjendofeachofthesixbarrelsandthreeateachendofthebarrelassembly.EachF-diskismadein12sectionswithonedouble-sidedsensorpersection.Thesensorsareisoscelestrapezoidswithstripsoneithersidealignedwithalongedgeofthetrapezoid,givinga30±stereoangle.Thesectionsarejoinedwithalternatingp-andn-sidesfacingthecenterofthedetector.Thestrippitchforthep-andn-sidesareequaltothoseofthedouble-sided2±barrelsensors.Theactivelengthofthebarrel/diskstructureandtheendF-disksisapproximately1066mm.B.1.2.3H-disks
TherearecurrentlytwoH-disksintheD0detector,thoughtherewerefouratthebeginningofRunII.Theyarelocatedatz¼§100cm.Twenty-fourtrapezoidalsensorscomprise165eachH-disk.Eachsensorisformedbygluingtwosingle-sidedsensorsback-to-back.LiketheF-disks,stripsarealignedwithalongedgeofthetrapezoid,givingane®ectivestereoangleof15±.Thestrippitchforthesedetectorsis40¹m.B.1.2.4Layer0
Layer0wasinstalledalongwithanewberylliumbeampipein2006.Itresidesinthespacebetweenthebeampipeandthe¯rstlayersofthebarrels.Thewholedeviceisapproximately1660mmlongwiththesensorscoveringz·j380jmm.Thereare48single-sidedsensorsinallwithstrippitchesof71¹mand81¹m.Theyarearrangedonahexagonalcarbon¯bersupporttubewitharowofeightsensorsoneachface.Rowsalternatebetween16.1mmand17.6mmfromthebeamaxis.The71(81)¹mstrippitchsensorsarelocated16.1(17.6)mmfromthebeam.
B.1.3CentralFiberTracker
TheCentralFiberTracker(CFT)isascintillating¯berdetector.Thepassageofchargedparticlesthroughthe¯bersproducesphotonsfromionizationandexcitationevents.Becausethenumberofphotonsproducedinscintillating¯berforanionization/excitationeventissmall,itisimportantthatthedevicedetectingthesephotonsisextremelysensitive.Weusevisuallightphotoncounters(VLPCs)whichproduceanelectricalsignalinresponsetophotonsandarecapableofdetectingsinglephotons.Fibersweremadebyextrudingpolystyrenedopedwithtwo°uorescentdyes.Theprimary°uorescentdye(about1%byweight)israpidlyexcitedbytheneighboringexcitedpolystyrenethroughanon-radiativenear-¯eldinteraction.Theprimary°uorescentrapidlyrelaxesandemitsashortwavelength(¼340nm)photon.Becausethisphotondoesnottravelfarinpolystyrene,theseconddye,166awavelength-shifter,isnecessary.Theseconddye(presentatabout1500ppm)absorbsthisphotonandre-emitsitat¼530nm,whichistransmittedwellbypolystyrene.Withtwocladdingsofdecreasingindexofrefractiontheattenuationlengthinthesescintillating¯bersisapproximately5m.OnceoutoftheactivevolumeoftheCFT,thelighttravelsinlight-shieldedclear¯berswhicharechemicallysimilartothescintillating¯bersallthewaytotheVLPCsatthebottomofthedetector.
B.1.3.1FiberArrangement
Thescintillating¯bersintheCFTare835¹mindiameterandare1.66mor2.52minlength.Theyaregroupedintoribbonsof256¯berseachintworowsof128.The¯berspacingrangesfrom928¹mto990¹manddependsontheradiusatwhichthe¯bersarelocated.Thesecondrowof¯bersiso®setfromthe¯rstbyhalfthisdistance.Theseribbonsarebondedtotheoutsideofcarbon¯bersupportcylindersintwolayers:anaxiallayerandastereolayer.Intheaxiallayerthe¯bersareorientedparalleltothebeamaxis.Thestereolayerhas¯bersorientedata§3±anglewithrespecttotheaxiallayer.Thesignoftheanglealternatesbetweencylinders.Thereareeightcylinderstotaloccupyingtheradialspacefrom20cmto52cm.
B.2PreshowerDetectors
Directlyoutsidethesolenoidbeforethecalorimeterarethepreshowerdetectors.Theycanbeconsideredpartofboththetrackingsystemandthecalorimetry;theymarkthebeginningofelectromagneticshoweringandareusedtomatchtrackstoshowersseeninthecalorimeter.LiketheCFT,thepreshowerdetectorsusescintillationlighttodetectthepassageofcharged167particles.Insteadofsingle¯bersthepreshowerdetectorsusepolystyrenestripswithatriangularcrosssection.Thestripsaredopedwith°uorescentdyeandawavelength-shifting¯berisplacedinthecenter.Thelightiscollectedbythecenter¯berandtransferredtoVLPCsforread-outviaclear¯ber.Therearethreepreshowerdetectors:theCentralPreshowerdetector(CPS)andtwoForwardPreshowerdetectors(FPS).Allthreeusethesametypeofscintillatingstripsbutthestripsarearrangeddi®erentlyfortheCPSandFPS.B.2.1CPS
TheCPSsitsbetweenthesolenoidandthecalorimeter.Directlyoutsidethesolenoidisaleadradiatorcoveredwithsteel.Thisradiatorandthesolenoidprovideabouttworadiationlengthstoparticleswithnormalincidence.Atlargeranglesthisincreasestoaboutfourradiationlengths.ScintillatorstripsintheCPSarenestedtogethertoformsinglelayersthatareapproximately7mmtall,slightlytallerthanthestripsthemselves.TheCPSconsistsofthreesuchlayersofscintillator:oneaxiallayerandtwostereolayerswithanglesof¼§24±.B.2.2FPS
TherearetwoFPSdetectors,oneoneitherendoftheD0detector.Theyaremountedontheendcalorimetercryostats(seeSectionB.3).ScintillatorstripsintheFPSarenestedtogethersuchthatalayerofscintillatorisaboutastallasastrip:about5mm.Therearefoursuper-layersseparatedinzineachFPSdetector.Eachsuper-layerconsistsofeightactiveÁ=22:5±modulesseparatedbyeightinactiveregions.Thesecondandfourthsuper-layersarerotatedby22.5±withrespecttothe¯rstandthirdsuper-layers,creatingtwoactive168e®ectivelayersineach22.5±wedge.Eachlayerconsistsoftwosublayersofscintillatorstripswitha22.5±stereoanglebetweenthem.Theinnerlayerisshorterthantheouterlayerandmainlydetectsminimallyionizingparticles.Betweentheinnerandouterlayerisashortpieceoflead/steelabsorberwhichaddstworadiationlengthsinthepathoftheparticlesproducingelectromagneticshowersintheouterlayer.Thesolenoidprovidesuptothreeradiationlengthsforparticlestravelingintheouterareaoftheouterlayerwherethereisnoabsorber.
B.3Calorimeters
TheprimarypurposeofthecalorimeteristomakeameasurementoftheenergyofparticlesproducedintheD0detector.Unlikethetrackingsystemwhichisdesignedtomeasurethepassageofparticleswithminimaldisturbance,thecalorimeterisdesignedtostopparticlescompletely.Inthiswayparticlesmakeacompletedepositoftheirenergy.TheD0detectorusesasamplingcalorimeterthathasalternatinglayersofabsorberandactivematerial.ParticlestravelingthroughtheabsorbercreateshowersofsecondaryparticlesthatareeitherelectromagneticorhadronicinnatureasdescribedinSection2.3.1.Thesesecondaryparticlesionizetheactivematerialandthechargeiscollectedandmeasured.TheD0calorimeterisacompensatingcombinedelectromagnetic(EM)andhadroniccalorimeter;ithasanequalresponsetoelectromagneticandhadronicparticleswiththesameenergy.BecauseEMandhadronicshowergenerationisgovernedbytwodi®erentlengthscales{theradiationlength(X0)andthenuclearinteractionlength(¸A){thecalorimeterhasvaryingabsorberthicknessesandmaterialstocapturebothtypesofshowers.InhighZmaterialsX0ismuchsmallerthan¸AsoEMshowersoccurclosertotheinteractionregionthanhadronicshowers.169TheD0calorimeterhasthreeshoweringlayers:theEMlayer,the¯nehadroniclayer,andthecoarsehadroniclayer.TheactivematerialintheD0calorimeterisliquidargon.ForFigureB.4:CalorimeterCellSchematicofatypicalcalorimetercell.accessibility,thecalorimeterisdividedintothreeseparatecryostats,acentralcryostatandtwoendcryostats.Dependingonthelayerandcryostattheabsorberiseitherdepleteduranium,auranium-niobiumalloy,copper,orsteel.AtypicalcalorimetercellisshowninFig.B.4.Sensorpadsinterleavedbetweensheetsofabsorberarepatternedforsegmentedreadout.Cellswhosecenterslieatthesame´andÁaregangedtogetherindepthtocreatereadouttowersasshowninFig.B.5.FigureB.5:CalorimeterReadoutTowersShownaretheD0calorimeterreadouttowers.Calorimetercellslyingatthesame´andÁaregangedtogethertoformtowersforreadout.170B.3.1CentralCalorimeter
Thecentralcalorimeter(CC)coverstheregionj´j.1.TheEMsectionismadefrom3mm-thickabsorberplatesofnearlypuredepleteduranium.Ithasfourseparatedepthlayers,organgings,thatare1.4,2.0,6.8,and9.8X0thick.Thetotalnumberofradiationlengthsfrommaterialbetweenthecalorimeterandtheinteractionregionisaboutfourat´=0.The¯nehadronicsectionismadefrom6mm-thickplatesofauranium-niobiumalloy.Ithasthreegangingsthatare1.3,1.0,and0.76¸Athick.Thereisonlyonecoarsehadroniclayermadefrom46.5mm-thickplatesofcopperthatis3.2¸Athick.B.3.2EndCalorimeters
Theendcalorimeters(EC)extendthecoverageofthecalorimetertoj´j.4.Thematerialbetweentheinteractionregionandthe¯rstactivegapintheECprovidesapproximately4.4X0ofmaterialat´=2.LiketheCC,theEChasfourdepthlayersintheEMsectionthatareapproximately1.6,2.6,7.9,and9.3X0thick.TheEMsectionisadiskmadefromplatesofnearlypuredepleteduranium4mmthick.ThehadronicsectionsoftheECaredividedintothreeregionsfromthebeamline:theinnerhadronic,middlehadronic,andouterhadronicregions.Theinnerandmiddlehadronicregionshaveboth¯neandcoarsehadronicsections.Finehadronicsectionsaremadefrom6mm-thickuranium-niobiumplatesandhavefourgangings1.1(0.9)¸Athickintheinner(middle)hadronicsections.Thereisonlyonedepthlayerfortheinner(middle)coarsehadronicsectionthatismadefrom46.5mm-thicksteelplateswithatotalthicknessof4.1(4.4)¸A.Theouterhadronicregionhasonlyonecoarsehadronicgangingmadefromthesamesteelplateswithatotalmaximumthicknessof6.0¸A.Theseplatesareinclinedatanangleofapproximately60±withrespecttothebeam171axistoavoidcracks.
B.4MuonSystem
Becauseoftheirhighermass,muonsdonotradiateasmuchenergyviabremmstrahlungaselectrons.Theydon'tproduceparticleshowersandleavethedetectorwithmostoftheirenergyintact.Theydohoweverleaveionizationtracksinthedetector.Themuonsystemsitsontheveryouterfacesofthedetectorandexiststomakemeasurementsofmuonsastheyexitthedetector.ThetoroidmagnetdiscussedinSectionB.1.1isanessentialpartofthemuonsystem.Ameasurementofthemuonmomentumcanbemadebymeasuringthepositionoftracksbeforeandaftertraversingthetoroid.Tracksinthemuonsystemcanalsobematchedtotracksinthetrackingportionofthedetectorformuonidenti¯cation.Usingquickresponsescintillationmaterialthemuonsystemcanassociateamuontrackwiththecorrectbunchcrossing.Thisscintillatorisalsoimportantineventtriggering,aprocesswhichselectseventsforrecordingbasedondesirableeventfeatures,suchasaneventwithanassociatedmuons.MoreinformationoneventtriggeringcanbefoundinSectionB.7.Itisalsopossibletorejectcosmicraybackgroundswhichoriginateoutsidethedetectorandtraversethedetectoratlargeangles.Inadditiontothefastresponsescintillator,themuonsystemuseswiredrifttubestotrackmuons.Thedrifttubescollectthechargeleftwhenpassingparticlesionizethesurroundinggas.
B.4.1WideAngleMuonSystem
TheWideAngleMuonSystem(WAMUS)coversthej´j.1region.Itconsistsofthecentraltoroidmagnet(SectionB.1.1),threelayersofproportionaldrifttubes(PDTs),thecosmic172capandbottomscintillationcounters,andtheAÁscintillationcounters.B.4.1.1ProportionalDriftTubes
TherearethreelayersofPDTsinWAMUSdenotedA,B,andC.TheA-layerresidesbetweenthecalorimeterandthecentraltoroidmagnetwhiletheB-andC-layerslieoutsidethecentraltoroid.EachlayerconsistsofeitherthreeorfourstacksofPDTs.Each10.1cmPDTcellismadefromalongrectangularaluminumtubewithananodewireinthecenterandacathodepadaboveandbelowtheanodewire.Thetubeis¯lledwith84%argonand8%CH4=CF4thatgivesamaximumelectrondrifttimeof500ns.Twoanodewiresaregangedtogetherandarereadoutatoneendofeachcell.PositioninformationalongthePDTisgatheredfromthetimingdi®erencebetweenthesignalattheendofthestruckwireandthesignalattheendofitspartner'swire.Thepositionresolutionusingthismethodcanbeanywherefrom10cm-50cmdependingonwherethehitoccurred.Informationabouttheamountofchargedepositedonthecathodepadscanbringtheresolutiondowntoabout5mm.AscanbeseenintheexplodedviewoftheD0muonwirechambersinFig.B.6,thePDTcoverageonthebottomissparseduetothecalorimetersupports.Still,approximately55%ofthecentralregioniscoveredbythreelayersofPDTsandcloseto90%oftheregioniscoveredbyatleasttwolayersofPDTs.
B.4.1.2CosmicCapandBottom
ThecosmiccapandbottomscintillationcounterscovertheouterlayerofthecentralmuonPDTs.ThecosmiccapreferstothecounterscoveringthetopandsidesofthecentralmuonC-layerPDTswhilethecosmicbottomreferstocounterscoveringthebottomB-andC-layercentralmuonPDTs.Bothprovidefasttiminginformationthatisusedtoassociateahitin173aPDTwiththeappropriatebunchcrossingandtorejectthecosmicraybackground.Thereare240cosmiccapscintillationcounters.Eachcounterismadefrom0.5in-thickplasticscintillator25inwideand81.5in-113inlong.TheyareorientedwiththeirlengthalongÁandtheirwidthalongz.Lightfromchargedparticleinteractionsisgatheredbywavelengthshifting¯bersthataregluedintogroovesalongthelengthofthescintillatorfromeachendtojustpastthecenter.Fibersarecollectedinthecenterintotwobundlesandthelightisdetectedbytwophotomultipliertubes(PMTs)mounteddirectlyonthecounter.Thereare132countersinthecosmicbottomontheoutsideoftheBandCPDTlayers.RefertoFig.B.7fortheplacementofthecounters.Incontrasttothecosmiccapcounters,thecosmicbottomcountersareplacedwiththeirwidthalongÁandtheirlengthalongz.Therearetwotypesofcountersemployedinthecosmicbottom;botharesimilarindesigntothecosmiccapcounters.Forty-eightcountersinthecenterbottomB-layerareidenticaltothecosmiccapcounterswithminorimprovementsinedge¯berplacement.TherearesixteentotalcounterslocatedonthebottomsidesoftheB-layerPDTs.Theremaining68countersonthebottomB-andC-layerPDTshavefewertotal¯bersthatareplacedinverticalratherthanhorizontalgrooveslikethoseinthecosmiccap.Thelightyieldinthisarrangementissimilartothatinthecosmiccap.Likethecosmiccap,lightisdetectedbyPMTsmounteddirectlyonthecounter.
B.4.1.3AÁScintillationCountersInadditiontothescintillatorontheouterlayersofcentralmuonPDTsthereisanotherlayerofscintillatorontheoutsideoftheA-layerPDTsgenerallyreferredtoastheAÁscintillationcounters.Thesecountersareusedforidentifyingandtriggeringonmuons,rejectingbackscatteringfromtheforwarddirection,andprovidingatimestamponlowpT174muonsthatmaynotreachthecosmiccapandbottomcounters.Thecountersaremadefromscintillatorplasticwithwavelengthshifting¯bersembeddedinverticalgroovesinamannersimilartothesecondtypeofcosmicbottomcounter.Likethecosmiccapandbottom,thelightisdetectedbyaPMTmounteddirectlytothecountercase.TheAÁcountersare33.25inlongandareusedinthreewidths:14.46in,10.84in,and9.09in.Theuseofthreedi®erentwidthsallowsforarelativelyconstant4.5±segmentationinÁthatmatchesthesegmentationoftheCFT.CountersarealignedwiththeirlengthsalongzandtheirwidthsalongÁwiththewidestcounterslocatedatthecornersofthedetectorandthethinnestnearthecenterline.Agapofapproximately2.5monthecenterbottomaccommodatesthecalorimetersupport.Ninecountersbuttedend-to-endmakeupthelengthofthedetectorforatotalof630counters.FigureB.6:D0MuonWireChambersExplodedviewoftheD0muonwirechambers.175FigureB.7:D0MuonScintillatorExplodedviewoftheD0muonscintillator.B.4.2ForwardAngleMuonSystem
TheForwardAngleMuonSystem(FAMUS)coverstheregion1.j´j.2.Itconsistsoftheendfacesofthetoroidmagnet(SectionB.1.1),threelayersofminidrifttubes(MDTs),threelayersofscintillationcounters,andasigni¯cantamountofshielding.Theshieldingnearlyeliminatesthetwomainsourcesofnon-muonbackgroundfromprotonandantiprotonremnants:i)theirinteractionswiththeendofthecalorimeterandbeampipeinsidethedetectorandii)theirinteractionswiththeTevatronquadrupolesjustoutsidethedetector.Theshieldingsurroundsthebeampipefromtheendcalorimetercryostat,throughtheendtoroidmagnet,tothewallofthecollisionhallwhereitpartiallysurroundstheTevatronquadrupolemagnets.Itismadefromlayersoflead,polyethylene,andirontoabsorbgammarays,neutrons,andelectromagneticandhadronicparticlesrespectively.176B.4.2.1MiniDriftTubes
Muonmomentummeasurementsintheforwardregionusearraysofminidrifttubes(MDTs).IdenticalinoperatingprincipletothePDTs,thesearesmallerandhencehaveamuchsmallermaximumdrifttimeofabout60ns.Therearethreelayersarrangedinsidethetoroid(layerA)andoutsidethetoroid(layersBandC).EachlayerhaseitherthreeorfourstacksofMDTsmountedalongthemagnetic¯eldlinesoftheendfacetoroids.EachMDTiscomposedofeightrectangularaluminumcellswithaninternalcrosssectionof9:4£9:4mm2andaW-Auanodewiredownthecenter.Thewireisgroundedattheelectronicsandthecathodeisheldataconstantnegativehighvoltage.Cellsare¯lledwithaCF4-CH4(90%-10%)gasmixture.ThecoordinateresolutionfortheMDTswhentakingintoaccountthetimingelectronicsisapproximately0.7mmperhit.
B.4.2.2ForwardScintillatorCounters
Theforwardscintillatorcountersareprimarilyusedfortriggeringoneventsthatcontainmuons.Theyarearrangedinthreelayersinside(layerA)andoutsidethetoroid(layersBandC).Eachlayeriscomposedof0.5inplasticscintillatortilescutintotrapezoidsandarrangedina¯shscalepatternaroundthebeampipeasshowninFig.B.8.ThesegmentationinÁisapproximately4.5±tomatchthesegmentationintheCFTfortriggeringpurposes.Segmentationin´is0.12fortheinnerninelayersand0.07fortheouterthreelayers.TheouterC-layercountersarethelargestat60£110cm2.Eachtilehaswavelength-shiftingbarsontwoadjacentedgestocollectandtransmitlighttothePMTattachedtothetile.177FigureB.8:ForwardMuonScintillatorB.5ForwardProtonDetector
Asubdetector,calledtheForwardProtonDetector(FPD),designedtomeasurescatteredprotonsandantiprotonsthatdonotimpingeonthemaindetectorislocatedoneithersideofthedetectorinsidetheTevatrontunnel.Itisprimarilyusedtotagdi®ractiveeventswhereoneorbothincidentprotonssurvivetheinteractionintact3andarescatteredatverysmallangleswithrespecttothebeam.TheFPDisamomentumspectrometerthatusesmagnetsintheacceleratorlatticeandpositiondetectorswhichcanbemovedveryclosetothebeam.Therearenineindependentspectrometers:oneontheoutgoingantiprotonsideoftheD0detectordownstreamfromthebendingdipolemagnetandfouroneachsideoftheD0detectordownstreamfromthelow¯quadrupoles.Therearetwohorizontal(inandout)andtwovertical(upanddown)spectrometerstoeithersideoftheD0detector.Thespectrometerdownstreamfromthe3Contrarytoelasticscattering,additionalparticlesareproducedinthescatteringeventeveninthecasewherebothprotonsareintact.178bendingdipoleistotheinsideofthebend.Eachspectrometerhasanupstreamandadownstreampositiondetector.ThepositiondetectorsarehousedinmovablestainlesssteelcontainerscalledRomanpotswhichallowthemtooperateoutsidetheultra-highvacuumofthebeampipeandberetractedduringsuboptimalbeamconditions.Romanpotsaregroupedintocastles:fourcastleswithfourRomanpotseachservingtheupstreamanddownstreampositiondetectorsoftheeightspectrometersnearesttheD0detectorandtwocastleswithoneRomanpoteachservingthespectrometerdownstreamfromthebendingdipole.Thepositiondetectorsaremadefromsixstacksofscintillating¯berribbonsarrangedwiththeedgesoftheribbonsintheplaneperpendiculartothebeam.Stacksareorientedatanglesof§45±and90±withrespecttothebottomofthedetector.Therearetwostacksineachorientationthatareo®setby2=3ofthe¯berwidth.Scatteredprotonsandantiprotonstravelthroughathinsteelwindowandimpingeonthescintillator.Fibersarereadoutbymulti-anodephotomultipliertubesandintegratedintotheCFTelectronics.Betweenthe90±and¡45±layersisasolidpieceofscintillatingplasticreadoutbyafastphotomultipliertubethatisusedfortriggeringpurposes(SeeSectionB.7).
B.6LuminosityMonitor
MeasuringtheinstantaneousluminositybeingprovidedtoD0bytheTevatronisanim-portantprocessbothforonlineoperationando®-linedataanalysis.Theinstantaneousluminositydictatesthetriggersetusedatagiventimeduringoperationandthereforede-terminesthephysicsprocessesbeingrecordedforlateranalysis.O®-lineanalysesrequireanaccurateluminositymeasurementforpropereventyieldpredictionsofspeci¯cprocesses.179TheD0subdetectorresponsibleformeasuringtheinstantaneousluminosityistheLuminos-ityMonitor(LM).Additionally,theLMprovidesafastmeasurementofthezcoordinateoftheinteractionvertexandameasurementofthebeamhalo.Thesemeasurementsaredonebydetectinginelasticproton-antiprotoncollisionsthroughscintillationlight.Twoarraysofplasticscintillationcounterslocatedatz=§140cmcomprisetheLM.Eacharraycontains24countersdividedintotwoenclosuresattachedtothesphericalheadoftheendcalorimeters.At15cmlong,theyoccupytheradialspacebetweenthebeampipeandtheFPSdetectoroverthepseudorapidityrange2:7<j´j<4:4.Theirlocationintheforwardregionclosetotheinteractionpointnecessitatestheuseofradiation-hardPMTsforreadout.Signalsfromeacharrayarecollectedandatimingpulseiscreatedforeacharray.Thedi®erenceinthetimingpulsesdeterminesthezcoordinateoftheinteractionvertexzvtxtowithin6cm.Toselectonlythoseinteractionswhichoriginatefrombeam-beamcollisions,acutisplacedonthezcoordinateoftheinteractionvertexsuchthatjzvtxj<100cm.Thisencompassesnearlyalloftheproton-antiprotoncollisionsproducedbytheTevatron.Anybeamhaloparticlestravelingparalleltothebeamandnotparticipatinginthebeam-beamcollisionswillhaveazvtxofapproximately§140cmandbeexcludedbythecut.TheinstantaneousluminosityLisdeterminedbythebunchcrossingfrequencyfoftheTevatron,theaveragenumberofinelasticproton-antiprotoncollisionspercrossing¹NLMasmeasuredbytheLM,andthee®ective4inelasticp¹pcrosssectionintotheLM¾LMgivenbyEq.B.1.L=f¹NLM¾LM(B.1)4Thecrosssectionisane®ectiveone;ithasfactorswhichaccountfortheacceptanceande±ciencyoftheLM.TheacceptanceisrelatedtotheprobabilitythataninteractionwillhaveparticlesinthegeometriccoverageoftheLM.GiventhatparticlesareintheacceptanceoftheLM,thee±ciencyisrelatedtotheprobabilitythattheeventwillberecordedbythedetector.180Thee®ectiveinelasticp¹pcrosssection¾LMiscalculatedtobe46§3mb.Ingeneral¹NLMisgreaterthanoneandmustbedeterminedbycountingthefractionofbeamcrossingswithouteventsandapplyingPoissonstatistics.
B.7TriggeringSystem
With36bunchesofprotonsandantiprotonstravelingaroundtheTevatron48thousandtimespersecond,thereareapproximately1.7millionpossibleinteractionspersecond.Recordingalloftheseinteractionsisnotfeasible.Fortunately,alargefractionoftheseeventsareuninterestingforthepurposesoftheD0experiment.Byhavinganideaofwhatinterestingeventslookliketothedetector,wecanuseaprocesscalledtriggeringtolookforandrecordonlytheeventswe¯ndinteresting.D0usesathree-tieredtriggeringsystembasedinbothhardwareandsoftwaretoaccomplishthis.Thelevelsaredesignedtoactasa¯lteringsystemwitheachstepincreasingincomplexity.TheLevel1(L1)triggerconsistsofhardwareelementswithanacceptrateofapproximately2kHz.EventsthatpassaresenttotheLevel2(L2)systemwhichconsistsofhardwareandmicroprocessorsassociatedwitheachsubdetectorandaglobalprocessorthatmakestriggerdecisionsnotonlybasedonindividualphysicsobjectsbutobjectcorrelationsaswell.TheacceptrateofL2isapproximately1kHz.IfaneventispassedbyL2itissenttothefarmofabout250computernodesthatmakeupLevel3(L3).Level3passeseventsatarateofabout50Hz.Thoseeventsarerecordedforlatero²inereconstruction.181B.7.1Level1
Level1isimplementedinhardwaredeviceswhichoriginateinfourdetectorsubsystems:thescintillating¯bertrackingsystem,thecalorimeter,themuonsystem,andtheforwardprotondetector.Everyeventisexaminedandeachsubsystemsubmitseventinformationtothetriggerframework(TFW).TheTFWconstructsphysicstriggersfromthetriggerscon-structedbytheL1systemsusingAND/ORlogicaloperators.InadditiontotheconstructionofphysicstriggerstheTFWmanagescommunicationwiththefront-endelectronicsandthetriggercontrolcomputer,appliesprescalingtotriggers,andcoordinatesreadoutuponaL2accept.ThelogicalORofthephysicstriggersiswhatdetermineswhethertheeventisselectedforadditionalprocessinginLevel2.
B.7.1.1L1Tracking
Thescintillating¯bersystemswhichparticipateintheLevel1triggerdecisionaretheFPSandCFT/CPSaxialsystems,collectivelyreferredtoastheCentralTrackTrigger(L1CTT).BydesignthesesystemsprovidetriggersforchargedparticleswithatransversemomentumpTgreaterthan1.5GeV.Findingtracks,¯ndingenergyclustersoriginatinginthepreshowerdetectors,andmatchingtrackstoclustersarethemainfunctionsofthescintillating¯bersystemsinL1.Signi¯cantprocessingresourcesarereservedfor¯ndingandtriggeringonisolatedchargedparticletracks.Inaddition,listsoftracksaresenttotheL1muonsystemtobeusedasseeds.
B.7.1.2L1Calorimeter
Thecalorimetergroupsreadouttowerstwobytwoin´andÁintotriggertowers.TransverseenergyETthresholdsaresetforthesumtotalofalltriggertowersandforeachtriggertower182individually.Inaddition,thresholdscanbede¯nedforthetotalunbalancedor\missing"transverseenergy6ET.Thepartialsumsnecessaryforthecalculationcanbeusedtotriggeronjetswhicharemuchlargerthanthetriggertowers.
B.7.1.3L1Muon
TheLevel1muonsystemlooksforhitpatternsconsistentwiththepassageofamuonusingthemuonscintillatorandwirechambersandtheseedtracksfromtheL1CTTsystem.Triggersareformedinthescintillatorby1)matchingL1CTTtrackstohitsineithertheA-layerortheA-andB-layerand2)requiringhitsineithertheA-layerortheA-andB-layerwithoutamatchedtrack.Additionally,hitsinthemuonwirechambersareusedtocon¯rmscintillatorhitsineachlayer.Thesecon¯rmedhitsareusedtoformtriggers3)ineithertheA-layerortheA-andB-layerscintillator.
B.7.1.4L1FPD
TheForwardProtonDetectoralsotakespartintheLevel1trigger.ItselectseventsinwhichbeamparticlesleavetheinteractionregionintactandhitoneormoreFPDspectrometers.Wecreateapixelgridfromthestacksofscintillatingribboninthepositiondetectorsandcomparepixelhitstodetectorpixelhitpatternsstoredinhardware.Timinginformationisobtainedfromthetriggerscintillatorusingfastphotomultipliertubes.TheFPDtriggersystemusesthistiminginformationtolookforcoincidencesbetweenhitsignalsofbothpositiondetectorsforanyoftheninespectrometerssignalingthepassageofanintactbeamparticle.Coincidencesbetweenspectrometersoneithersideoftheinteractionregionareindicativeofaneventwherebothbeamparticlesleavetheinteractionregionintact.183B.7.2Level2
FollowingaLevel1acceptfromtheTFW,theeventbeginsprocessingatL2.Level2consistsofadetector-speci¯cpreprocessingstageandaglobalprocessingstage.ThepreprocessingstagecollectsinformationfromtheL1triggersystemandthedetectorfront-endstoformphysicsobjects.Atthegloballevel,datafromdi®erentpartsofthedetectorcanbecom-binedtoformhigher-qualityphysicsobjectsthanthoseavailableatthepreprocessingstage.Inaddition,correlationsbetweenobjectsacrossthewholedetectorcanbeexamined.AlldetectorsubsystemsparticipatinginLevel1alsoparticipateinLevel2withtheexceptionoftheForwardProtonDetector.AlsoparticipatinginL2istheSiliconMicrostripTracker.The¯nerspatialresolutionoftheSMTwithrespecttotheCFTallowsforamoreprecisetrackreconstructionandanimprovedmomentummeasurement.TheL2globalprocessingstagerunsalgorithmsonthedatareceivedfromthepreprocessorsbasedonwhattriggers¯redatLevel1.TheL2globaldecisionisreturnedtotheTFW.
B.7.3Level3
EventswhichpassLevel2aresenttotheLevel3trigger.Level3isafullyprogrammablesoftwaretriggerwhichhasaccesstothefulldetectorinformation.Itperformsalimitedreconstructionofthefulleventandmakesitsdecisionbasedoncompletephysicsobjectsandtheirrelationships.Thesoftwareresidesonabout250commercialcomputersrunningtheLinuxoperatingsystem.Eventfragmentsfromdi®erentpartsofthedetectorareroutedtoasingleL3nodewheretheeventisbuiltandmadeavailabletoL3processes.EventsselectedbyL3aredestinedforstorageontapeandfullo²inereconstruction.184AppendixC
AdditionalDistributions
Thisappendixcontainsadditionalplotsandtablesnotincludedinthemaintext.C.1AdditionalVXDistributionsPlotsoftheinvariant(transverse)massareincludedforallVHanalysesforeachb-taggingchannelandpurityregion.Thehigh-purityplotsfortheWHanalysisarereproducedhereforcomparison.185 (GeV)bZbM0200400600Events020406080100120=9.7 fbintDØ, L20)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, ST HPbllb®ZH(a) (GeV)bZbM0200400600Events0510152025303540=9.7 fbintDØ, L5)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, DT HPbllb®ZH(b) (GeV)bZbM0200400600Events050100150200250=9.7 fbintDØ, L100)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, ST LPbllb®ZH(c) (GeV)bZbM0200400600Events010203040506070=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, DT LPbllb®ZH(d)FigureC.1:InvariantMassofthe``b¹bSystemInvariantmassofthe``b¹bsystemintheZH!``b¹banalysisforeventsinthe(a)single-taghigh-purity(STHP),(b)double-taghigh-purity(DTHP),(c)single-taglow-purity(STLP),and(d)double-taglow-purity(DTLP)channels.TheJP=2+andJP=0¡samplesarenormalizedtotheproductoftheSMcrosssectionandbranchingfractionmultipliedbyanadditionalfactor.Heavy-andlight-°avorquarkjetsaredenotedbylfandhf,respectively.Over°oweventsareincludedinthelastbin.Forallsignals,amassof125GeVfortheHorXbosonisassumed.186 (GeV)bWb
TM0200400600Events050100150200250=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 1TT HPbbnl®WH(a) (GeV)bWb
TM0200400600Events0102030405060708090100=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2LT HPbbnl®WH(b) (GeV)bWb
TM0200400600Events01020304050=9.7 fbintDØ, L10)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2MT HPbbnl®WH(c) (GeV)bWb
TM0200400600Events0510152025303540=9.7 fbintDØ, L10)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2TT HPbbnl®WH(d)FigureC.2:TransverseMassofthe`ºb¹bSystem,High-PurityRegionTransversemassofthe`ºb¹bsystemintheWH!`ºb¹banalysisinthehigh-purity(HP)regionfor(a)1tight-tag(1TT),(b)2loose-tags(2LT),(c)2medium-tags(2MT),and(d)2tight-tags(2TT)channels.TheJP=2+andJP=0¡samplesarenormalizedtotheproductoftheSMcrosssectionandbranchingfractionmultipliedbyanadditionalfactor.Heavy-andlight-°avorquarkjetsaredenotedbylfandhf,respectively.Over°oweventsareincludedinthelastbin.Forallsignals,amassof125GeVfortheHorXbosonisassumed.187 (GeV)bWb
TM0200400600Events01002003004005006007008009001000=9.7 fbintDØ, L100)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 1TT LPbbnl®WH(a) (GeV)bWb
TM0200400600Events020406080100120140160180200=9.7 fbintDØ, L100)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2LT LPbbnl®WH(b) (GeV)bWb
TM0200400600Events020406080100120=9.7 fbintDØ, L50)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2MT LPbbnl®WH(c) (GeV)bWb
TM0200400600Events020406080100120=9.7 fbintDØ, L30)´(Signals DataMultijetV+lfV+hfttsingle tVV Signal+0 Signal0 Signal+2, 2TT LPbbnl®WH(d)FigureC.3:TransverseMassofthe`ºb¹bSystem,Low-PurityRegionTransversemassofthe`ºb¹bsystemintheWH!`ºb¹banalysisinthelowpurity(LP)regionfor(a)1-tight-tag(1TT),(b)2-loose-tags(2LT),(c)2-medium-tags(2MT),and(d)2-tight-tags(2TT)channels.TheJP=2+andJP=0¡samplesarenormalizedtotheproductoftheSMcrosssectionandbranchingfractionmultipliedbyanadditionalfactor.Heavy-andlight-°avorquarkjetsaredenotedbylfandhf,respectively.Over°oweventsareincludedinthelastbin.Forallsignals,amassof125GeVfortheHorXbosonisassumed.188 (GeV)bZb
TM0200400Events0200400600800100012001400=9.5 fbintDØ, L60)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, MT HPbbnn®ZH(a) (GeV)bZb
TM0200400Events050100150200250=9.5 fbintDØ, L15)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, TT HPbbnn®ZH(b) (GeV)bZb
TM0200400Events0100200300400500600700800=9.5 fbintDØ, L300)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, MT LPbbnn®ZH(c) (GeV)bZb
TM0200400Events020406080100120140160=9.5 fbintDØ, L150)´(Signals DataMultijetV+lfV+hfttVV Signal+0 Signal0 Signal+2, TT LPbbnn®ZH(d)FigureC.4:TransverseMassoftheººb¹bSystemTransversemassoftheººb¹bsystemintheVH!ººb¹banalysisforeventsinthe(a)medium-taghigh-purity(MTHP),(b)tight-taghigh-purity(TTHP),(c)medium-taglow-purity(MTLP),and(d)tight-taglow-purity(TTLP)channels.TheJP=2+andJP=0¡samplesarenormalizedtotheproductoftheSMcrosssectionandbranchingfractionmultipliedbyanadditionalfactor.Heavy-andlight-°avorquarkjetsaredenotedbylfandhf,respectively.Over°oweventsareincludedinthelastbin.Forallsignals,amassof125GeVfortheHorXbosonisassumed.189C.2AdditionalLLRDistributionsThissectioncontainsLLRdistributionsforeachVHanalysisandallanalysescombinedfor¹=1:0.LLR01020Pseudoexperiments050010001500200025003000 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR0Observed LLR = 9.7 fbintDØ, L=1.0mbllb®VX(a)LLR02040Pseudoexperiments05001000150020002500 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR0Observed LLR = 9.7 fbintDØ, L=1.0mbbnl®VX(b)LLR02040Pseudoexperiments0200400600800100012001400160018002000 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR0Observed LLR = 9.5 fbintDØ, L=1.0mbbnn®VX(c)LLR0204060Pseudoexperiments0200400600800100012001400160018002000 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR0Observed LLR 9.7 fb£ intDØ, L=1.0mbVb®VX(d)FigureC.5:D0LLRDistributionsfortheJP=0¡HypothesisLLRdistributionscomparingtheJP=0+andtheJP=0¡hypothesesforthe(a)ZH!``b¹banalysis,(b)WH!`ºb¹banalysis,(c)VH!ººb¹banalysis,and(d)theircombination.TheJP=0+andJP=0¡samplesarenormalizedtotheproductoftheSMcrosssectionandbranchingfractionmultipliedby¹=1:0.TheverticalsolidlinerepresentstheobservedLLRvalue,whilethedarkandlightshadedareasrepresent1s.d.and2s.d.ontheexpectationfromthenullhypothesisH0,respectively.HereH0istheSMJP=0+signalplusbackgrounds.Forallsignals,amassof125GeVfortheHorXbosonisassumed.190LLR01020Pseudoexperiments050010001500200025003000350040004500 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR+2Observed LLR = 9.7 fbintDØ, L=1.0mbllb®VX(a)LLR02040Pseudoexperiments02004006008001000120014001600180020002200 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR+2Observed LLR = 9.7 fbintDØ, L=1.0mbbnl®VX(b)LLR02040Pseudoexperiments02004006008001000120014001600180020002200 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR+2Observed LLR = 9.5 fbintDØ, L=1.0mbbnn®VX(c)LLR0204060Pseudoexperiments02004006008001000120014001600180020002200 LLR+01 s.d.± LLR +02 s.d.± LLR +0 LLR+2Observed LLR 9.7 fb£ intDØ, L=1.0mbVb®VX(d)FigureC.6:LLRDistributionsfortheJP=2+HypothesisLLRdistributionscomparingtheJP=0+andtheJP=2+hypothesesforthe(a)ZH!``b¹banalysis,(b)WH!`ºb¹banalysis,(c)VH!ººb¹banalysis,and(d)theircombination.TheJP=0+andJP=2+samplesarenormalizedtotheproductoftheSMcrosssectionandbranchingfractionmultipliedby¹=1:0.TheverticalsolidlinerepresentstheobservedLLRvalue,whilethedarkandlightshadedareasrepresent1s.d.and2s.d.ontheexpectationfromthenullhypothesisH0,respectively.HereH0istheSMJP=0+signalplusbackgrounds.Forallsignals,amassof125GeVfortheHorXbosonisassumed.191C.3ExpectedandObservedp-valuesfor¹=1:23AnalysisZH!``b¹bWH!`ºb¹bZH!ººb¹bCombinedJP=0¡vs.JP=0+p0¡testExpected0.0460.0120.005<0.0001p0¡testObserved0.0720.2450.00060.0051¡pnullExpected0.5000.5000.5000.5001¡pnullObserved0.6150.9710.2150.922CLsExpected0.908(1.33s.d.)0.975(1.96s.d.)0.989(2.31s.d.)0.9998(3.60s.d.)CLsObserved0.883(1.19s.d.)0.747(0.67s.d.)0.997(2.78s.d.)0.995(2.56s.d.)JP=2+vs.JP=0+p2+testExpected0.0370.0030.009<0.0001p2+testObserved0.0780.0560.0030.0021¡pnullExpected0.5000.5000.5000.5001¡pnullObserved0.6790.9370.3630.911CLsExpected0.925(1.44s.d.)0.995(2.56s.d.)0.983(2.11s.d.)0.9999(3.86s.d.)CLsObserved0.885(1.20s.d.)0.941(1.56s.d.)0.991(2.35s.d.)0.998(2.91s.d.)TableC.1:ExpectedandObservedp-Valuesfor¹=1:23Expectedandobservedp-valuesandCLsvaluesforJP=0¡andJP=2+VXassociatedproduction,assumingsignalcrosssectionsequaltothe125GeVSMHiggsproductioncrosssectionmultipliedby¹=1:23.ThenullhypothesisistakentobethesumoftheSMHiggsbosonsignalandbackgroundproduction.192REFERENCES193REFERENCES[1]E.W.Weisstein,Cylindricalcoordinates,FromMathWorld{AWolframWebResource.[2]E.W.Weisstein,Sphericalcoordinates,FromMathWorld{AWolframWebResource.[3]O.Chamberlain,E.Segrµe,C.Wiegand,andT.Ypsilantis,Phys.Rev.100,947(1955).[4]K.A.Oliveetal.,[ParticleDataGroup],ChinesePhysicsC38,090001(2014).[5]H.D.Politzer,Phys.Rev.Lett.30,146(1973).[6]D.J.GrossandF.Wilczek,Phys.Rev.Lett.30,1343(1973).[7]S.L.Glashow,Nucl.Phys.22,579(1961).[8]S.Weinberg,Phys.Rev.Lett.19,1264(1967).[9]A.Salam,OriginallyprintedinSvartholm:ElementaryParticleTheory,ProceedingsOfTheNobelSymposiumHeld1968AtLerum,Sweden,Stockholm1968,367-377.[10]P.W.Higgs,Phys.Rev.Lett.13,508(1964).[11]F.EnglertandR.Brout,Phys.Rev.Lett.13,321(1964).[12]G.S.Guralnik,C.R.Hagen,andT.W.B.Kibble,Phys.Rev.Lett.13,585(1964).[13]L.¶Alvarez-Gaum¶eandJ.Ellis,Nat.Phys.7,2(2011).[14]M.Baaketal.,TheEuropeanPhysicalJournalC74(2014).[15]G.Abbiendietal.,[ALEPH,DELPHI,L3,andOPALCollaborations,theLEPWorkingGroupforHiggsBosonSearches],Phys.Lett.B565,61(2003).[16]S.Heinemeyer,C.Mariotti,G.Passarino,andR.Tanaka(Eds.),[LHCHiggsCrossSectionWorkingGroup],CERN-2013-004(2013).194[17]T.Aaltonenetal.,[CDFandD0Collaborations],Phys.Rev.D88,052014(2013).[18]T.Aaltonenetal.,[CDFandD0Collaborations],Phys.Rev.Lett.109,071804(2012).[19]G.Aadetal.,[ATLASCollaboration],Phys.Lett.B716,1(2012).[20]S.Chatrchyanetal.,[CMSCollaboration],Phys.Lett.B716,30(2012).[21]S.DimopoulosandH.Georgi,Nucl.Phys.B193.[22]H.Murayama,UCB-PTH-00/05(2000),PedagogicalreviewSUSYreviewgivenat1999ICTPSummerSchool.[23]G.Brancoetal.,Phys.Rep.516,1(2012).[24]A.Djouadi,Phys.Rep.459,1(2008).[25]L.RandallandR.Sundrum,Phys.Rev.Lett.83,3370(1999).[26]L.RandallandR.Sundrum,Phys.Rev.Lett.83,4690(1999).[27]F.Abeetal.,[CDFCollaboration],Phys.Rev.Lett.74,2626(1995).[28]S.Abachietal.,[D0Collaboration],Phys.Rev.Lett.74,2422(1995).[29]S.Abachietal.,Nucl.Instrum.MethodsPhys.Res.A338,185(1994).[30]V.Abazovetal.,Nucl.Instrum.MethodsPhys.Res.A565,463(2006).[31]R.Angstadtetal.,Nucl.Instrum.MethodsPhys.Res.A622,298(2010).[32]S.Chatrchyanetal.,[CMSCollaboration],Phys.Rev.D89,092007(2014).[33]G.Aadetal.,[ATLASCollaboration],Phys.Lett.B726,120(2013).[34]A.Martin,W.Stirling,R.Thorne,andG.Watt,TheEuropeanPhysicalJournalC63,189(2009).[35]W.J.Stirling,privatecommunication.195[36]D.Miller,S.Choi,B.Eberle,M.Mhlleitner,andP.Zerwas,Phys.Lett.B505,149(2001).[37]J.D.Richman,CALT-68-1148(1984).
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