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hep-ph/9306215 2 Jun 93StudyingminijetsviathepTdependenceoftwo-particlecorrelationinazimuthalangleXin-NianWangNuclearScienceDivision,Mailstop0A-0,LawrenceBerkeleyLaboratoryUniversityofCalifornia,Berkeley,California0yandPhysicsDepartment,DukeUniversity,Durham,NC0. (Received)Followingmypreviousproposalthattwo-particlecorrelationfunctionscanbeusedtoresolvetheminijetcontributiontoparticleproductioninminimumbiasedeventsofhighenergyhadronicinteractions,IstudythepTandenergydependenceofthecorrelation.UsingHIJINGMonteCarlomodel,itisfoundthatthecorrelationc(;)inazimuthalanglebetweentwoparticleswithpT>pcutTresemblesmuchliketwoback-to-backjetsaspcutTincreasesathighcollidingenergiesduetominijetproduction.Itisshownthatc(0;0)c(0;),whichisrelatedtotherelativefractionofparticlesfromminijets,increaseswithenergy.ThebackgroundofthecorrelationforxedpcutTalsogrowswithenergyduetotheincreaseofmultipleminijetproduction.Applicationofthisanalysistothestudyofjetquenchinginultrarelativisticheavyioncollisionsisalsodiscussed...Ce,..Bx,..Qk,..HdTypesetUsingREVTEX

I.INTRODUCTIONMinijetswithpT>fewGeV/carecommonlybelievedtobecomeincreasinglyimportantinhadronicinteractionsforenergiesbeyondtheCERNIntersectingStorageRing(ISR)energyrange.Ithasbeensuggestedbymanyauthorsthattheyareresponsiblefornotonlytheglobalproperties,liketherapidincreaseofthetotalcrosssections[]-[]andtheaveragechargedmultiplicity[,0],butalsothelocalcorrelationanductuations[]-[0]ofmultiparticleproductioninhighenergyppandppcollisions.Theyhavealsobeenestimatedtoplayanimportantroleinultrarelativisticheavyioncollisions[].Anotherparticularlyinterestingfeatureofminijetsisthattheyseemtogiveanaturalexplaination[]totheapparent\ow"eectinhighenergyppcollisions.This\ow"eectistheobservationinexperiments[]atFermilabTevatronColliderenergythattheaveragetransversemomentumofchargedparticlesincreaseswiththetotalmultiplicityoftheeventsandtheincreaseisstrongerforheavyparticlesthanthelightones.However,thisobservationissurprisinglyincoincidentwiththeresultsofanequilibratedquarkgluonplasma(QGP)[]inwhichthecommontransverseowvelocityfromthecollectiveexpansiongivesheavyparticleslargertransversemomentumthanthepions.ThespeculationwasmadeevenmoreplausiblebyLevaiandMuller'snding[]thatthereisnotimeforthebaryonstoequilibratewiththepionsduringtheexpansionofahadronicreball.Othermodelssuchasthestringfusionmodel[]canalsoexplaintheobservedphenomenon.Inordertodierentiatetheminijetpicturefromtheotherscenarios,onemustndawaytoconrmtheinuenceofminijetsonparticleproduction.AlthoughminijetsareanticipatedfromthepredictionofperturbativeQCD(PQCD)andmanyeortshavebeenmadetoinvestigatetheirphenomenologicalconsequences,thereexistslittledirectexperimentalevidenceoftheirpresenceinhadroniccollisions.TheonlyexperimentalattempttondminijetsisbyUAex-periments[]atCERNwherehadronicclusterswithtransverseenergyET>GeVhavebeenidentiedasminijetsandthecrosssectionsarefoundtobeconsistentwiththePQCDprediction.However,thiskindofcluster-ndingmethodevenforinter-mediateETvaluesiscomplicatedbythebackgroundofrandomuctuations[].ForsmallerET,minijetclustersareoverwhelmedbythebackgrounductuation.There-fore,becauseoftheirsmalltransversemomenta,minijetswithrelativelysmallpT>GeV/ccanneverberesolvedasdistinctjetsfromthelargesoftbackgroundinminimumbiasedevents.ToavoidtheexperimentaldicultiesofreconstructingjetswiththehugebackgroundinhighenergyAAcollisions,ithasbeensuggested[]that

singleinclusivespectraofproducedparticlescanbeusedtostudythepropertiesofjetproduction.Similarly,Ihaveproposedinapreviouspaper[0]thattwoparticlecorrelationfunctionsisusefultostudythecontentofminijetsinminimumbiasedeventsofhadronicinteractions.Inthispaper,IreportthedetailedstudyofthepTandenergydependenceofthetwo-particlecorrelationintheazimuthalangleandtheinuenceofniterapiditycuts.Sinceparticlesfromjetfragmentationarecorrelatedinbothdirectionsoftheminijets,theyhavebeenfound[]todominateboththeshortandforward-backwardtwo-particlecorrelationsinpseudorapidity.Fortwo-particlecorrelationintheaz-imuthalangle,contributionfromback-to-backminijetsshouldbestronglypeakedatbothforward(=0)andbackward(=)directions.Ifwecalculatethesamecorrelation,butforsomeselectedparticleswhosetransversemomentaarelargerthanacertainpTcut,thetwopeaksshouldbemoreprominentbecausetheseparticlesaremorelikelytocomefromminijets.TheenergyandpTdependenceofsuchcorrelationsofchargedparticlesmustdependontherelativefractionofminijeteventsandmini-jetmultiplicity,thussheddingsomelightonminijetcontentintheseevents.Onthecontrary,particlesfromsoftproductionoffusedstringsoranexpandingquarkgluonplasmaareisotropicalinthetransverseplaneandwouldonlyhavesomenominalcorrelationinthebackwarddirectionduetomomentumconservation.Theexperimentalstudyofthetwo-particlecorrelationsisimportanttoclarifythecontroversialissuewhethertheobservedavordependenceofthecorrelationbetweenthemultiplicityandaveragetransversemomentumatFermilabTevatronenergy[]isduetominijetproduction[],orstringinteraction[],ortheformationofaquarkgluonplasma[].Ontheotherhand,itcanalsoprovideconstraintsontheoreticalmodelsashowtocombinePQCDhardscatteringswithnonperturbativesoftinteractions,howtoparametrizethesoftprocesses,andwhatistheappropriatefragmentationschemeofmultipleminijets.Inthelightofthestudyonintermittencyinparticleproduction[],italsohelpsustohaveabetterunderstandingoftheintermittentuctuationsinhadroniccollisionsatcolliderenergiesasparticlesfromjetfragmentationindeedhavebeenshowntohavestrongintermittentbehavior[].ThisstudyisbasedontheMonteCarlomodel,HIJING[],whichcombinesasimpletwo-stringphenomenologyforlowpTprocessestogetherwithPQCDforhighpTprocesses.SinceHIJINGisamodelwithaveryspecicschemeofminijetfrag-mentation,theresultswegetareonlyaqualitativeestimateoftheeectsofminijetsonthetwo-particlecorrelationfunctions.Thoughthecorrelationsinpseudorapidityandazimuthalanglearebothimportant,welimitourdiscussionsonlytothe

lattercase.Theremainingofthispaperisorganizedasfollows.InSec.IIwebrieyreviewtheHIJINGmodelasdiscussedindetailedinRef.[].InSec.IIIwestudythepTdependenceofthetwo-particlecorrelationsinandtheirresemblancetolargepTjetproles.Specialemphasisisgiventotheeectsofminijetsontheback-to-backdierencesofthecorrelation,c(0;0)c(0;).InSec.IV,theenergydependenceofthebackgroundofthecorrelationanditsimplicationonmultipleminijetproductionarediscussed.Theeectofniterapiditycutisalsodiscussed.Finally,Sec.Vconcludeswithasummaryandremarks.II.THEHIJINGMODELTheHIJINGmodel[]hasbeendevelopedmainlyformultiplejetandparticleproductioninpp,pA,andAAcollisionsatenergiesps>AGeV.TheformulationofHIJINGwasguidedbythesuccessfulimplementationofPQCDinthePYTHIAmodel[]andtheneedtoincorporateaconsistentmodelofsoftprocesses.Itthusprovidesalinkbetweenthedominantnonperturbativefragmentationphysicsatinter-mediateenergiesandtheperturbativephysicsathighercolliderenergies.AdetaileddescriptionoftheHIJINGmodelcanbefoundinRef. [].ItincludesmultiplejetproductionwithinitialandnalstateradiationalongthelinesofthePYTHIAmodel[]andsoftbeamjetsaremodeledbyquark-diquarkstringswithgluonkinksalongthelinesoftheDPM[]andFRITIOF[]models.Fornucleusinducedreac-tions,nuclearshadowingofpartonstructurefunctionsandnalstateinteractionofproducedjetsarealsoconsidered[].Intheeikonalformalism,theinelasticcrosssectionofpporppcollisionsisgivenbyin=Zdb[e(soft+jet)TN(b;s)];()whereTN(b;s)isthepartonicoverlapfunctionbetweentwonucleonsatimpactpa-rameterb,jet(p0;s)isthetotalinclusivejetcrosssectioncalculatedfromPQCDwithpT>p0,andsoft(s)isthecorrespondingphenomenologicalinclusivecrosssectionofsoftinteractions.Thecrosssectionsfornoandjnumberofhardorsemihardpartonscatteringsare,0=Zdb[esoftTN(b;s)]ejetTN(b;s);()j=Zdb[jetTN(b;s)]jj!ejetTN(b;s);()withtheirsumgivingrisetothetotalinelasticcrosssection,in.Followingtheabove

formulas,thecrosssectionwithatleastonehardpartonscattering,denedashard,isthenhard=Zdb[ejetTN(b;s)]esoftTN(b;s);()andtheaveragenumberofpartonscatteringsperinelasticeventishnjeti=jet(p0;s)=in:()ShowninFig.aretheenergydependenceofhnjetiandthefractionalcrosssectionofhardprocesses,hard=inforp0=GeV/candsoft=mb.Weseethatasenergyincreasesinelasticeventscontainmoreandmorehardprocessesandnallyaredominatedbyminijetproduction.TheprobabilitiesformultipleminijetproductionalsobecomeprominentatenergiesaboveTeVashnjeti>.Onceagain,weemphasizeherethatp0andsoftinHIJINGmodelarephe-nomenologicalandmodeldependentparametersseparatingPQCDathighpTfromthenonperturbativelowpTregime.Ourguidelineforchoosingthevalueofp0isthatitshouldbemuchlargerthanQCD00MeV/cinordertoapplyPQCDbutlowenoughtopermitthesimplestpossiblemodelforthenonperturbativedynamics.Choosingp0=GeV/callowsustouseaconstantsoft=mbtoreproducetheobservedenergydependenceofthetotal,elasticandinelasticcrosssectionsinppandppcollisions[0,].Withtheseparameters,ithasbeenshown[]thatasimpletwo-stringmodelsucestoaccountforthesoftdynamics.AcompletetestoftheHIJINGmodelhasbeenreportedinRef. [].Themodelhasbeensuccessfultoprovideaconsistentexplanationofnotonlytheenergydependenceofpseudorapiditydistributions,moderatepTinclusivespectra,andtheviolationofKoba-Nielsen-Olesen(KNO)scaling,butalsotheavorandmultiplicitydependenceoftheaveragetrans-versemomentum[]inppandppcollisionsinawideenergyrangeps=0{00GeV.Inaddition,itisalsoconsistentwiththeavailabledataonpAandAAcollisionsatmoderateenergiesps<0AGeV[].III.TWO-PARTICLECORRELATIONExperimentalstudyofparticlesfromthefragmentationofhighpTjetshasshownthatparticleswithlargeraveragetransversemomentaaremuchconcentratedinbothdirectionsoftheback-to-backjets.ThewidthsofthesejetprolesareaboutinbothpseudorapidityandazimuthalangleashasbeendeterminedfromthecalorimetricstudyofhighpTjets.Itisapparentthatsimilartrendsshouldalsoholdforparticlesfromminijetsandtheymustinuencethetwo-particlecorrelationfunctions.Ithas

alreadybeenshowninRef.[]thatminijetsarethedominantmechanismunderlyingboththeenhancedshortrangeandforward-backwardcorrelationsin.InthispaperIdemonstratethattheenergyandpTdependenceoftwo-particlecorrelationsintheazimuthalanglecanbeusedtostudyminijetsinminimumbiasedevents.OnecanexpectthatwithhigherpcutT,thecorrelationmustlooksimilartothehighpTjetproles.Moreover,theenergydependenceofthecorrelationforxedpcutTshouldberelatedtotheincreaseofthefractionofminijeteventsandtheaveragenumberofminijetsasshowninFig..Thenormalizedtwo-particlecorrelationfunctionsaredenedas,c(;)(;)()();()where()istheaveragedparticledensityinand(;)isthetwo-particledensitywhichisproportionaltotheprobabilityofjointparticleproductionatand.Both()and(;)areintegratedoverthewholerapidityrange.Thelimitationofarestrictedrapidityrangewillbediscussedinthenextsection.Inactualcalculations,onedirectioninthetransverseplaneisrandomlyselectedas=0foralltheeventsandthenboththeaveragedsingleinclusivedensity()andthetwo-particlejointdensity(0;)arecalculated.Becausethecollisionsaresymmetricalinthetransverseplaneperpendiculartothebeamdirection,()shouldbeaconstantequaltothetotalaveragedmultiplicityoftheselectedparticlesdividedby.Similarly,(0;)isalsoindependentofthedirectionwhichischosenas=0.Infact,onecanevenchoosethedirectionofeachparticleas=0tocalculatec(0;)andthenaverageitoverallparticlesineachevent.Inthiscaseonecangetbetterstatisticsforalimitednumberofevents.SinceIhavetheluxurytoproducemanyeventsthroughtheMonteCarlosimulation,IinsteadtrytoaverageoverasmanyeventsaswecantoachievethebeststatisticspossibleoverglobalquantitiessuchasthenumberofjetspereventwithrelativelargepT.ShowninFigs.{arecalculatedresultsontwo-particlecorrelationfunctionsinppandppcollisionsatdierentenergies.TostudythepTdependence,thecor-relationsareobtainedforselectedparticleswithdierenttransversemomentumcutpT>pcutT=0(long-dash-short-dashedhistograms),0.(dottedhistograms),.0(solidhistograms),.(short-dashedhistograms),and.0(dot-dashedhistograms).Atlowenergyps=0GeV(Fig. )whereminijetproductionisnotveryimportantasseenfromFig.,thereisverylittlecorrelationbetweentwoparticleswith<=ex-ceptsomesmallincreaseat0forthecaseofpT>:0GeV/c.Thecorrelationatistotallyduetothemomentumconservationwhichincreaseswithlarger

pTcuts.AswaspointedoutinRef.[],minijetcontributiontoparticleproductionatthehighestCERNISRenergiesps0GeVisjustbeginningtoemerge.Thisisagainillustratedherebytheslightincreaseofthecorrelationat0forparticleswithpT>:0GeV/c.AswecanseefromFig.,minijetproductionincreasesveryfastwithenergyandbecomesasignicantpartofthehadronicinteractionsaboveps>00GeV.Therefore,thetwo-particlecorrelationfunctionsinFig.forps=00GeVareverydierentfromthoseatps=0GeVinFig..WeobservethatthereisapparentlystrongcorrelationbetweentwoparticleswithpT>0:GeV/catboth0andformingavalleyat=.ThisfeatureisverysimilartothehighpTjetprolesasfunctionsofrelativetothetriggeredjetaxis[].However,duetotherelativelargefractionofparticlesfromsoftinteractionswheremomentumconservationdictatesthetwo-particlecorrelationat,theresultantc(0;)atisstilllargerthanat0.WhereasinhighpTjetproles,thepeakofparticleowtowardthetriggeredjet(=0)isalwaysnarrowerbuttheheightisaboutthesameasinthebackwarddirection(=).ThedominanceofparticlesfromsoftinteractionsatthisenergyisclearlydemonstratedinthecaseofpcutT=0wherec(0;)monotonicallyincreasesfrom0.at=0to0.at=.Asweincreasetheenergyto.andTeV(Figs.,),thecorrelationfunctionswithnopTcutbecomeatteroverthewholeangularrangeduetotheincreasingfractionofparticlesfromminijetsrelativetothesoftprocesses.ThecorrelationfunctionswithhigherpTcutslookmoreandmoresimilartothehighpTjetproleswithc(0;0)c(0;)andnarrowerpeaksat0.WeknowfromFig.thatparticlesfromsoftproductionhavesomestrongcorrelationonlyatduetomomentumconservationwhileparticlesfromminijets,ontheotherhand,haveenhancedcorrelationbothat0and.Theactualshapeofthecorrelationfunctionthendependsontherelativefractionsofparticlesfromminijetsandsoftprocesses.LookingthroughFigs. {,wecanclearlyseethattheheightofthecorrelationfunctionsatgraduallybecomesequaltothatat0asshowninFig.bytheincreaseofthedierencec(0;0)c(0;)withenergy.ItapproacheszeroforanyxedpcutTathigherenergies.Thisenergydependenceofc(0;0)c(0;)isadirectconsequenceoftheincreaseofminijetproductionwithenergyinppandppcollisions.Thus,ithasbeendemonstratedthatthestudyoftheenergyandpTdependenceoftwo-particlecorrelationfunctionc(0;)canprovideuswithinformationabouttheminijetcontentinminimumbiasedevents.

IV.EFFECTSOFMULTIPLEMINIJETSANDFINITERAPIDITYCUTWhentheaveragenumberofproducedminijetsislargerthanone(Fig.)athighcollidingenergies,multipleminijetproductionbecomesimportant[0,].Sincetheseminijetsareindependentlyproduced,theyshouldincreasethebackgroundtothetwo-particlecorrelation.Theveryextremecasesarecentraleventsofhighenergyheavyioncollisionswherehundredsofminijetsareproduced.Thetwo-particlecorrelationwillbecompletelyatwhenthevalleysweseeinFigs. {forppandppcollisionsarelledupbytheincreasedbackground.Inhadroniccollisionsthisrarelyhappensandtheincreaseofthebackgroundcanbeconsideredasanimplicationofmultipleminijetproduction.PlottedinFig.isthedierencec(0;0)c(0;=)betweenthecorrelationat=0andthebackgroundinthevalley==foreachxedpcutTasafunctionofps.Itgrowsrstwithenergyduetotheincreaseofminijeteventsandtherelativesmallnumberofminijetsperevent.However,astheprobabilitiesofmultipleminijetproductionbecomeincreasinglyimportant,thedierencethendecreaseswithenergy.ThelargerthepcutT,thesoonerthedecreasebegins.UnlikehighpTback-to-backjetswhicharebothkinematicallyboundedtothecentralrapidityregion,apairofminijetscanbeeasilyproducedwithlargerapiditygapbetweenthem.Whenwetriggeroneminijetinalimitedrapiditywindow,theotheronewhichisproducedinthesamepartonscatteringoftenfallsoutsidetherapiditywindow.Therefore,ifwecalculatetwo-particlecorrelationforparticlesinalimitedrapidityrange,minijetcontributiontothebackwardcorrelation(=)willmostlydropoutwhilethecontributiontoforwardcorrelation(=0)stillremains.Indeed,asshowninFig.,theforwardcorrelationat=0forparticlesinjj.V.SUMMARYANDREMARKSItisdemonstratedindetailinthispaperthattwo-particlecorrelationfunctionsintheazimuthalangleareusefulforthestudyofminijetsandtheircontributiontoparticleproductionintheminimumbiasedeventsofhadronicinteractions.Because

particlesfromjetfragmentationaremoreconcentratedalongthejetaxes,theyresultinenhancedtwo-particlecorrelationinboththetriggered(=0)andthebackward(=)direction.Ontheotherhand,particlesfromisotropicsoftproductiononlyhavesomenominalcorrelationinthebackwarddirectionduetomomentumconser-vation.Therefore,theenergydependenceoftherelativeheightc(0;0)c(0;)ofthecorrelationinthetwooppositedirectionsisdirectlyrelatedtotheminijetcontentintheparticleproductionandincreaseswiththecollidingenergy.Furthermore,mul-tipleminijetproductionbecomesimportantathighenergiesandtheyincreasethebackgroundrelativetotheenhancedcorrelationat=0and.ItisimportanttokeepinmindthattheresultsweobtainedviaHIJINGareonlyintendedtoshowqualitativelytheeectsofmultipleminijetsontheenergyandpTdependenceoftwo-particlecorrelationin.Thequantitativemagnitudesofthecorrelationsmustdependonthespecicschemeofminijetfragmentationandthecolorowofmultipleminijets[]inHIJING.Itisimportanttostudyinthefuturethesensativityoftwo-particlecorrelationfunctionstotheschemesofminijetfragmentationandthecolorowstructureofmultipleminijets.ThenalschemeswhichsurvivethetestsonsingleinclusivespectrahavealsotobeconstrainedbytheexperimentalmeasurementsoftheenergyandpTdependenceoftwo-particlecorrelationfunctions.IhaveemphasizedtheimplicationsoftheenergyandpTdependenceofthetwo-particlecorrelationfunctionsonminijetproduction.Forexperimentsataxeden-ergy,onecanalsoinvestigatethecontributionofminijetstothetwo-particlecorrela-tionfunctionbycomparingthedirectmeasurementstothecalculationfromthesamedatasamplebutwithrandomizedazimuthalangleforeachparticle.Duetothisrandomizationof,thecorrelationcalculatedfromthemanipulateddatashouldbemuchatterthantherealoneforanygivenpcutT.ItisalsoimportantandinterestingtostudythepTdependenceoftwo-particlecorrelationfunctionsinpseudorapidityandthecorrelationrelativetoatriggeredparticlewhichhasthehighestpTineachevent[0].AsdiscussedinSec.IV,thetwo-particlecorrelationininultrarelativisticheavyioncollisionsshouldbemuchatterthaninppandppcollisionsforanyxedpcutTduetothehugenumberofminijetproduction.However,ifweincreasepcutTtoamuchlargervalue(e.g. {GeV/c),thebackgroundtothecorrelationbecomessmallerduetosmallcrosssectionsoflargepTjets.SincethesingleinclusivespectrumatlargeandmoderatepThasbeenshowntobesensativetojetquenching[],two-particlecorrelationisapparentlymorerelevanttothestudyofjetquenchingandthe

implicationonenergylossmechanismitconveys.ACKNOWLEDGMENTSIwouldliketothankA.Goshaw,M.Gyulassy,B.Muller,andS.Ohfortheirhelpfulcommentsandencouragingdiscussions.ThisworkwassupportedbytheDirector,OceofEnergyResearch,DivisionofNuclearPhysicsoftheOceofHighEnergyandNuclearPhysicsoftheU.S.DepartmentofEnergyunderContractNo.DE-AC0-SF000andDE-FG0-0ER0.0

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FIGURESFIG..Fractionalcrosssectionhard=inforatleastonehardscatteringandaveragenumberofminijetproductionhnjetipereventasfunctionsofps.FIG..Thecorrelationfunctionsc(0;)betweentwoparticleswithxedpTcutovsinppcollisionsatps=0GeV.FIG..ThesameasFig.,exceptforppcollisionsatps=00GeV.FIG..ThesameasFig.,exceptforppcollisionsatps=:TeV.FIG..ThesameasFig.,exceptforps=TeV.FIG..Theenergydependenceofthedierencec(0;0)c(0;)betweenthecorrela-tionat=0andforeachxedpTcuto.FIG..Theenergydependenceofthedierencec(0;0)c(0;=)betweenthecor-relationat=0andthebackgroundat=foreachxedpTcuto.FIG..ThesameasFig.,exceptforchargedparticlesinalimitedrapidityrangeofjj<.

출처: arXiv:9306.215 • 원문 보기