重离子碰撞中冻结的几何和动力学方面的可观测意义Observableimplicationsofgeo

Observableimplicationsofgeometricalanddynamicalaspectsoffreeze-outinheavyioncollisionsFabriceRetière1andMichaelAnnanLisa21LawrenceBerkeleyNationalLaboratory,Berkeley,California94720,USA2PhysicsDepartment,TheOhioStateUniversity,Columbus,Ohio43210,USA(Received30January2004;published29October2004)Usingananalyticalparametrizationofhadronicfreeze-outinrelativisticheavyioncollisions,wepresentadetailedstudyoftheconnectionsbetweenfeaturesofthefreeze-outconfigurationandphysicalobservables.Wefocusespeciallyonanisotropicfreeze-outconfigurations(expectedingeneralforcollisionsatfiniteimpactparameter),azimuthallysensitiveHanburry-Brown-Twissinterferometry,andfinal-stateinteractionsbetweennonidenticalparticles.ModelcalculationsarecomparedwithdatatakeninthefirstyearofrunningatRHIC;whilenotperfect,goodagreementisfound,raisingthehopethataconsistentunderstandingofthefullfreeze-outscenarioatRHICispossible,animportantfirststeptowardsunderstandingthephysicsofthesystempriortofreeze-out.DOI:10.1103/PhysRevC.70.044907PACSnumber(s):25.75.Ld,25.75.Gz,24.10.NzI.INTRODUCTIONThefirstdatafromcollisionsbetweenheavynucleiattheRelativisticHeavyIonCollider(RHIC)havegeneratedin-tensetheoreticaleffortstounderstandthehot,densemattergeneratedintheearlystageofthecollision[1].Testingthesetheoreticalideasreliesoncomparisontoexperimentalob-servables.Leptonic[2]orelectromagnetic[3]observablesarebelievedtoprobedirectlytheearly,densestageofthecollision.MostoftheearlydatafromRHIC,however,havebeenonhadronicobservables.MeasurementsofhadronsathightransversemomentumspTd[4]havegeneratedmuchexcitement,astheymayprovideusefulprobesofthedensemediumproducedatRHIC[5].However,themediumitselfdecayslargelyintothesoft(low-pT)hadronicsector.Softhadronicobservablesmeasuredirectlythefinal“freeze-out”stageofthecollision,whenhadronsdecouplefromthebulkandfree-streamtothedetectors.Freeze-outmaycorrespondtoacomplexconfigurationinthecombinedcoordinate-momentumspace,withcollectivecomponents(oftencalled“flow”)generatingspace-momentumcorrela-tions,aswellasgeometricalanddynamical(flow)anisotro-pies.Adetailedexperimentallydrivenunderstandingofthefreeze-outconfigurationisthecrucialfirststepinunder-standingthesystem’spriorevolutionandthephysicsofhotcoloredmatter.Inthispaper,weexploreindetailananalyticparametri-zationofthefreeze-outconfiguration,whichincludesnon-trivialcorrelationsbetweencoordinate-andmomentum-spacevariables.Wediscusstheconnectionsbetweenthephysicalparametersofthemodelandobservablequantities.Ifthemodel,withcorrectchoiceofphysicalmodelparam-eters,canadequatelyreproduceseveralindependentmea-suredquantities,thenitmightbeclaimedthatthis“crucialfirststep,”mentionedabove,hasbeenperformed.Aconsistentreproductionofalllow-pTobservationsatRHICisnotachievedinmostphysicalmodelswhichaimtodescribetheevolutionofthecollision.Inparticular,itisdifficulttoreproducemomentum-spacemeasurementswhilesimultaneouslydescribingthefreeze-outcoordinate-spacedistributionprobedbytwo-particleintensityinterferometrymeasurements[6][alsoknownasHanburry-Brown-Twiss(HBT)[7]measurements].Hadroniccascademodelspredictatooweakmomentumazimuthalanisotropyandtoolargesourcesizes[8].Hydrodynamictransportmodelsdescribesuccessfullytransversemassspectraandellipticflowbutfailatdescribingpionsourceradii[9];somehydrodynamicmod-elshavesuccessfullyreproducedpionsourceradii[10],butonlywithdifferentmodelparametersthanthoseusedtore-producespectraandellipticflow[11].Similarly,sophisti-catedhybridtransportmodels(e.g.,AMPT[12])requiredif-ferentmodelparameters[13]toreproducedataonellipticflow[15]andHBTmeasurements[16].Goodreproductionofobservedvalueshasbeenacheivedinmodelswhichadjustparameterstofitdatawithinagivenfreeze-outscenario,suchasintheBuda-Lundhydroapproach[17].Theworkpre-sentedherefallsintothislattercategory.Theparametrizationusedinthispaper(“blast-wavepa-rametrization”)issimilarinformtothefreeze-outconfigu-rationobtainedfromhydrodynamiccalculations[18],butwetreatthephysicalparametersoftheconfiguration(e.g.,tem-perature)asfreeparameters.Ourmaingoalissimplytoquantifythedrivingphysicalparametersoffreeze-outatRHICandthedependenceofobservablesontheseparam-eters.Furthermotivationforexploringfreeze-outconfigurationsofthetypediscussedhereisthattheyimplicitlyassumea“bulk”systemwhichmaybedescribedbyglobalparameters(temperature,flowstrength,etc.)Discussionsofa“newphaseofmatter”andits“equationofstate”areonlysensibleifindeedsuchassumptionshold.Comparisonofblast-wavecalculationswithseveralindependentmeasurements,then,isacrucialconsistencycheckoftheseassumptions(though,ofcourse,asuccessfulcomparisonstillwouldnotconstituteaproofoftheirvalidity).Intransportmodels,whethertheconstituentsarehadrons[19,20],partons[21,22],orfluidelements[9,23–25],iftheyreinteractsubstantially,pressuregradientsaregenerated,PHYSICALREVIEWC70,044907(2004)0556-2813/2004/70(4)/044907(33)/$22.50©2004TheAmericanPhysicalSociety70044907-1leadingtocollectivevelocityfields(“flow”),pushingthematterawayfromthehotcenterofthecollisionandintothesurroundingvacuum.Evidenceofcollectiveflow,generatedbyfin