Phi meson production in relativistic heavy ion collisions

SubrataPal,C.M.Ko,andZi-weiLin

CyclotronInstituteandPhysicsDepartment,TexasA&MUniversity,CollegeStation,Texas77843-3366Withinamultiphasetransportmodelwestudyphimesonproductioninrelativisticheavyioncollisionsfrombothsuperpositionofinitialmultipleproton-protoninteractionsandthesecondarycollisionsintheproducedhadronicmatter.Theyieldofphimesonsisthenreconstructedfromtheirdecayingproductofeitherthekaon-antikaonpairsorthedimuonpairs.Sincethekaon-antikaonpairsatmidrapiditywithlowtransversemomentaarepredominantlyrescatteredorabsorbedinthehadronicmedium,theycannotbeusedtoreconstructthephimesonandleadthustoasmallerreconstructedphimesonyieldthanthatreconstructedfromthedimuonchannel.Within-mediummassmodificationsofkaonsandφmesons,theφyieldfromdimuonsisfurtherenhancedcomparedtothatfromthekaon-antikaonpairs.ThemodelresultiscomparedwiththeexperimentaldataattheCERN/SPSandRHICenergiesanditsimplicationstoquark-gluonplasmaformationarediscussed.

PACSnumbers:24.10.Cn,24.10.Pa,25.75.Dw

I.INTRODUCTION

Oneofthemajorgoalsinrelativisticheavyioncollisionsistostudythepropertiesofhotanddensematterandpossiblytocreateandidentifyanewformofmatter,thequarkgluonplasma(QGP).Itwassuggested[1]thatenhancedstrangenessproductioncouldserveasanimportantsignalforthedeconfinedmatter.Thedominantproductionofss¯pairsviagluon-gluoninteractionmayleadtostrangeness(chemicalandflavor)equilibrationtimescomparabletothelifetimeoftheplasmaandmuchshorterthanthatofathermallyequilibratedhadronicfireball.Thesubsequenthadronizationisthenexpectedtoresultinanenhancedproductionofstrangeandmultistrangeparticlesandantiparticles.Inparticular,ithasbeenarguedthatwiththeformationofquark-gluonplasmanotonlytheproductionofphimesons,whichconsistofss¯,isenhancedbuttheyalsoretaintheinformationontheconditionsofthehotplasmaasitisbelievedthatphimesonsinteractweaklyinthehadronicmatterandthereforefreezeoutquiteearlyfromthesystem[2].

Usingaprotonorsulfurprojectileat200GeV/nucleonandatungstenoruraniumtarget,phimesonproductionhasbeenpreviouslystudiedatCERN/SPSbytheNA38Collaboration[3]andtheHELIOS-3Collaboration[4]viathedimuoninvariantmassspectra.Thedoubleratio(φ/(ω+ρ0))SU(W)/(φ/(ω+ρ0))pWhasbeenmeasuredandwasfoundtohaveavalueof2∼3.Varioustheoreticalattemptshavebeenmadetounderstandthisenhancement.Inparticular,anenhancementofphimesonyieldmaybeasignatureoftheformationofaquarkgluonplasmainthecollisions[2].However,thisenhancementcanalsobeexplainedeitherusinghadronicmodelsifonetakesintoaccountthereducedphimesonmassinnuclearmedium[5]orviathefragmentationofcolorropesthatareformedfromtheinitialstrings[6].

Recently,phimesonproductionhasalsobeenmeasuredincentralPb+Pbcollisionsat158AGeVattheCERN/SPS.TheNA49Collaboration[7]hasidentifiedthephimesonviathedecaychannelφ→K+K−,whiletheNA50Collaboration[8]measureditusingφ→µ+µ−decay.ItwasfoundthattheextractednumberofphimesonfromdimuonchannelexceedsbyafactorbetweentwoandfourfromthatextractedfromtheK+K−channel.ThisdifferencehasbeenattributedtothefactthatnotallphimesonscanbereconstructedfromK+K−resultingfromtheirdecaysduetorescatteringoftheK+andK−inthehadronicmatter.Thesuppressionfactorcanbe40-60%basedontheRQMDmodel[9].Thiseffecthasbeenfurtherstudiedinaschematicmodelbyincludingtheeffectofchangingkaonmassesinthehadronicmedium[10].

Inthepresentpaper,usingamultiphasetransport(AMPT)modelwemakeadetailedandconsistentstudyoftheproductionofphimesonsreconstructedfromtheK+K−andµ+µ−decaychannels.Theeffectsofin-mediummassmodificationtothephimesonyieldandspectraarealsostudiedandarecomparedwiththeexperimentalfindingsbytheNA49and√NA50CollaborationsattheSPSenergies.WealsopresentthephimesonyieldandspectraattheRHICenergyof

II.THEMODEL

A.AMultiphasetransportmodel

Todescribetheheavyioncollisiondynamics,weemployamultiphasetransportmodel(AMPT)thatincludesboththeinitialpartonicandfinalhadronicinteractions.TheAMPTmodel[11]isahybridmodelthatusesasinputtheminijetpartonsfromthehardprocessesandthestringsfromthesoftprocessesintheHIJINGmodel[12].ThedynamicalevolutionofpartonsarethenmodeledbytheZPC[13]partoncascademodel,whilethetransitionfromthepartonicmattertothehadronicmatterisbasedontheLundstringfragmentationmodel[14].Thefinal-statehadronicscatteringsaremodeledbytheARTmodel[15].TheAMPTmodelhasbeenquitesuccessfulindescribingthemeasuredtransversemomentaofpionsandkaons,andtherapiditydistributionsofchargeparticles[16,17]aswellastheparticletoantiparticleratios[18]inheavyioncollisionsatbothSPSandRHIC.Includingmeltingofinitialstringstopartons,themodelcanalsoaccountfortheobservedlargeellipticflow[19]andthemeasuredtwo-pioncorrelationfunction[20]atRHIC.IntheoriginalAMPTmodel,phimesonsareproducedonlyfrominitialstringfragmentation.Inthepresentwork,weextendittoalsoincludephimesonproductionandinteractionsinthehadronicmatter.

B.phimesonproductionandinteractions

ForphimesonproductionfromhadronscatteringsintheARTmodel,weconsiderboththebaryon-baryonin-teractionchannelsBB→φNNandthemeson-baryonchannels(π,ρ)B→φB,whereB≡N,∆,N∗.Thecrosssectionsfortheseprocesseshavebeenevaluatedintheone-boson-exchangemodel[21]andareusedhere.WehavealsoincludedphimesonproductionfromthereactionKΛ→φNwiththecrosssectiontakenfromRef.[5]basedonakaon-exchangemodel.

Phimesoncanbefurtherproducedfromkaon-antikaonscattering.Forakaon-antikaonpairwithinvariantmass

¯→φistakentobeaBreit-WignerformM,thetotalcrosssectionforKK

σKK¯→φ(M)=

3π

22(M2−m2φ)+(mφΓφ)

,(1)

¯isgivenbywherethephimesondecaywidthtoKK

2

gφK¯K

Γφ→KK¯(M)=

6m2φ

,(2)

2

withthecouplingconstantgφK¯/4π≈1.69determinedfromtheempiricalwidthof3.7MeV,correspondingto83%Kofthetotalwidth,atM=mφ.

Forphimesoninteractionswithbaryons,weincludetheabsorptionreactionsgivenbytheinversereactionsofphimesonproductionfrommeson-baryoninteractionsgivenabove.Thecorrespondingcrosssectionsareobtainedusingthedetailedbalancerelations.Thecrosssectionforphimesonelasticscatteringwithanucleonistakentobe0.56mbasextractedfromthedataonphi-mesonphotoproductionusingthevectormesondominancemodel[22].ThesecrosssectionsareshownintheupperleftpanelofFig.1.

Phimesonscanalsobescatteredbymesons.UsingeffectivehadronicLagrangians,wherecouplingconstantsweredeterminedfromexperimentalpartialdecayrates,thetotalcollisionalwidthofφduetothereactionsφπ→KK∗,φρ→KK,φK→φKandφφ→KKwasfoundtobelessthan35MeV[23](whereKdenoteseitherakaonoranantikaonasappropriate).However,recentcalculations[24]basedonaHiddenLocalSymmetryLagrangianshowsthatthecollisionalratesofφwithpseudoscalar(π,K)andvector(ρ,ω,K∗,φ)mesonsareappreciablylarge,especiallyfortheK∗,resultinginamuchsmallermeanfreepath,ofabout2.4fminahadronicmatterattemperatureT>170MeV,comparedtothetypicalhadronicsystemsizeof∼10−15fmcreatedinheavyioncollisions.Wehaveincludedallthesepossibleinteractions,i.e.,φM→(K,K∗)(K,K∗),andφ(K,K∗)→M(K,K∗),whereM≡(π,ρ,ω)withcrosssectionsdeterminedfromthepartialcollisionalwidthsgiveninRef.[24].Specifically,wetakematrixelements

|M|2kf/(kis2),wheresisthec.m.energy

andkiandkfare,respectively,theinitialandfinalc.m.momentaofthecollidinghadrons.Thecrosssectionsfortheinversereactionsoftheaboveprocessesarethenobtainedfromthedetailedbalancerelations.InFig.1,we

2

showthecrosssectionsforphi-pionandphi-rhoscattering(upperrightpanel),phi-kaonscattering(lowerleftpanel),andphi-K∗scattering(lowerrightpanel).Theelasticcrosssectionofphimesonwithothermesonscanbesimilarlyobtainedandisfoundtobeabout2mb. 10φN→KΛφN→πNφN→π∆φN→ρNφM → (K,K*)(K,K*)101: φπ→KK1σ (mb)3σ (mb)1422: φπ→K*K*0.13: φρ→KK4: φρ→K*K*0.0100.20.40.60.81100.20.40.60.81√s − √s0 (GeV)φK → M(K,K*)10πK*ρK*ωK√s − √s0 (GeV)φK* → M(K,K*)ρK*σ (mb)σ (mb)10ρKπK*ρK1ωK*πK00.20.40.60.811πK00.20.40.60.81√s − √s0 (GeV)√s − √s0 (GeV)FIG.1.Phimesonscatteringcrosssectionsbynucleons(upperleftpanel),mesons(upperrightpanel),kaons(lowerleftpanel),andK∗(lowerrightpanel).

C.mediumeffects

Sincethephimesonmassisonly32MeVabovethekaon-antikaonthreshold,itisstronglycoupledtothekaonandantikaondynamics,i.e.,tothestrangenesscontentofthesurroundingmedium.Asmallchangeinthemassesofeitherthephimesonorkaonthuswouldappreciablyaffectthedecaywidthofphimeson.

Studiesbasedonvariousapproaches,suchastherelativisticmean-fieldtheory[25]andthechiraleffectiveLagrangian[26],haveledtoageneralconsensusthatK+feelsaratherweakrepulsivepotentialwhiletheK−feelsarelativelystrongerattractivepotential.Withsuchmodifications,thekaonyieldandspectracouldbesuccessfullyexplainedatSISenergies(1-2AGeV)[27–29]andevenatAGSenergy(∼11AGeV)[30].Inthepresentstudy,weadoptthekaonandantikaonenergiesfromchiraleffectiveLagrangian,i.e.,

󰀇󰀄2

221/2

±bKρ,ωK,K¯=mK+k−aKρS+(bKρ)

(3)

223

wherebK=3fπ/8≈0.333GeVfm3,aK≈0.22GeV2fm3forkaons,andaK¯≈0.45GeVfmforantikaons.The󰀈K+potential,definedbyUK=ωK−

Forthein-mediumphimesonmass,theQCDsumrulestudiesshowthatitdecreasesslightlyinhotdensematter[34–36].UsingtheresultfromRef.[34],wehave

m∗φ

ρ0

,

(4)

whereρ0isthenormalnuclearmatterdensity.

Thein-mediumdecaywidthofphimesontokaon-antikaonpairisthengivenby

Γ∗¯(M)φ→KK

=

2

gφK¯K

56m∗φ

Althoughthephimesonmassdecreasesinthemedium,thelargerreductionoftheoverallkaon-antikaonmasswith

increasingdensityresultsinanincreaseofphimesonwidthΓ∗¯inthemedium.Atdensityρ=2ρ0,thephiφ→KKmesonin-mediumwidthisabout45MeV.

III.RECONSTRUCTIONOFPHIMESONS

󰀂󰀇󰀂󰀌∗2󰀄󰀌∗2

∗∗23/2∗2

.(m−(m−m)(mφ−(m∗+m)¯¯φKKKK

(5)

Sincephimesonisunstable,itcanonlybedetectedfromitsdecayproductofeitherthekaon-antikaonpairorthe

leptonpair.Thekaon-antikaonpairdecayingfromaphimesonis,however,likelytoundergoappreciablerescatteringinthemedium,andthiswouldleadtoareconstructedinvariantmasssituatedoutsidetheoriginalphimesonpeak.Infact,themomentumtransfertoakaonsufferingonecollisionwithapionatT=150MeVcanbeestimatedtobeabout45MeVwhichismuchlargerthanthetotalphimesonwidthofΓφ=4.45MeV.Hencephimesonsdecayinginthedensemediumisdifficulttobeidentifiedviareconstructedkaon-antikaonpairs.Incontrast,dileptonshavenegligiblefinal-stateinteractionswiththesurroundinghadronicmediumandthereforeescapeessentiallyunscathedduringtheentireevolutionofthesystem.Dileptonsarethusconsideredtocarryusefulinformationabouthadronpropertiesinhotanddensehadronicmatter[37],whichareexpectedtobedifferentfromthoseinfreespace.

A.dileptons

Todetectaphimesonfromitsdimuondecay,weneedthedecaywidthforφ→µ+µ−[38],whichinthemediumis

Γ∗φ→µ+µ−(M)

=Cµ+µ−

4

m∗φ

M2

󰀃1/2󰀁

1+

2m2µ

Γφ

,(7)

whereNφ(t)denotesthenumberofphimesonattimet.Intheabove,thefirsttermcorrespondstodimuonproduction

beforethefreeze-outtimeoftf=35fm/cconsideredinourcalculation,whilethesecondtermreferstodimuonemissionafterfreeze-out.Thereconstructedphimesonnumberisobtainedbydividingtheaboveexpressionbythedimuonbranchingratioinfree-spaceofΓφ→µ+µ−/Γφ=3.7×10−4.Sincemostpreviousstudies[9,10]haveneglectedthephimesonannihilationandproductionchannelsviabaryonsandespeciallybypseudoscalarandvectormesons,thephimesonlifetimeinthesestudiesisthuscomparabletothelifetimeofthesystem.Consequently,phimesonsfromdimuonchannelgetsignificantcontributionsonlyafterfreeze-out.

B.kaons

Thenumberofkaon-antikaonpairstemmingfromphimesondecaycanbesimilarlyexpressedasEq.(7)fordimuonproduction,i.e.,

4

NKK¯=

󰀉

tf

0

dtNφ(t)Γ∗¯(M)+Nφ(tf)φ→KK

Γφ→KK¯

652dN/dt (c/fm)1.54φ ↔ KK+−Nφ(t)321005101520253010.50051015202530t (fm/c)654t (fm/c)dN/dt (c/fm)4dN/dt (c/fm)φ+M ↔ (K,K*)+(K,K*)φ+K* ↔ M+(K,K*)321φ+K ↔ M+(K,K*)200510152000510t (fm/c)t (fm/c)FIG.2.Upperleftpanel:Timeevolutionofmidrapidity(|y|<0.5)phimesonfromPb+PbcollisionsattheSPSenergyof158AGeVatanimpactparameterofb≤3.5fmintheAMPTmodel.Theresultsareforwithout(solidcurve)andwith(dashedcurve)in-mediummassmodifications,andwithfurtherincreaseofphimesonnumberbytwointheHIJINGmodel(dottedcurve).Thephimesonyieldobtainedfrompurelyhadronicrescatteringwithoutanymediumeffectsisshownbydash-dottedcurve.Upperrightpanel:Thephimesonproduction(solidcurves)anddecayrates(dashedcurves)fortheprocessφ↔K+K−.Thethincurvesarewithoutin-mediummassmodificationwhilethethickonesincludemediummassmodification.Lowerpanels:φproduction(solidcurves)andabsorptionrates(dashedcurves)fordifferentchannelswithoutanymassmodifications;whereM≡π,ρ,ω.

curveintheupperleftpanelofFig.2,thisleadstoasuppressedpeakinthetimeevolutionofphimesonabundancebutdoesnotchangemuchthephimesonnumberatlatertimes,whencomparedtothatinthecaseofincludingtheinitialphimesonsfromstringdecays.

2.rapiditydistribution

TherapiditydistributionofphimesonsreconstructedfromK+K−andµ+µ−channelsincentralPb+Pbcollisionat158AGeVisshowninFig.3.Inabsenceofanymediumeffects,theresultsforphimesonsfromthetheK+K−channel(thinsolidcurve)areingoodagreementwiththeNA49experimentaldata[7](solidcircles).Withfree-spacedecaywidthofphimeson,therapiditydistributionofallphimesonsfromtheK+K−,neglectingtheirscattering,isidenticaltothatreconstructedfromtheµ+µ−channel(thindashedcurve).Duetorescatteringorabsorptionofthekaonpairs,∼30%ofallφmesonsarelostinthereconstruction,ofwhichabout40%ofthedecayingkaonshaveatleastone(anti)kaonthatsufferelasticscattering.ThemaximumdepletionofphimesonsfromtheK+K−channeloccursatmidrapiditywherekaon-antikaonpairsundergoappreciablescatteringinthedensehadronicmedium.Notethataroundy=0,phimesonfromdimuonchannelisaboutafactor1.7largerthanfromthekaon-antikaonchannel,whichissmallerthanthefactorof2-4enhancementobservedintheNA50data[8].

6

7Pb(158A GeV) + Pb6543210 dN/dY−4−2024YFIG.3.RapiditydistributionofphimesonreconstructedfromK+K−pairs(solidcurves)andfromµ+µ−channel(dashedcurves)forPb+Pbcollisionsat158AGeVatanimpactparameterofb≤3.5fmintheAMPTmodel.Theresultsareforwithout(thincurves)andwith(thickcurves)in-mediummassmodifications.Thedottedcurvecorrespondstophimesonsfromthedimuonchannelwithin-mediummassesandwiththephimesonnumberfromHIJINGincreasedbyafactoroftwo.ThesolidcirclesaretheNA49experimentaldata[7]fromtheK+K−channel.

3.transversemassspectrum

InFig.4,weshowthetransversemassspectraatmidrapidityforphimesonfromkaon-antikaon(solidsquares)anddimuon(opensquares)channelwithoutmediumeffects.ItisseenthatatlowmTthephimesonfromK+K−channelissuppressedduetorescattering.Sincethetransversemomentumofaparticleincreasesduetoincreasingnumberofscatteringandduetopressurebuild-upinsidethesystem,thedecayedkaonsattheearlystages,whicharepredominantlyscattered,thushavelowtransversemomenta.Thetransversemassspectracanbeapproximatelyfittedbyexp(−mT/T).TheinverseslopeparameterTreportedbyNA50[8]fromtheµ+µ−channelfor1.74.In-mediumeffect

ModificationofphimesonandkaonmassesisexpectedtoenhancetheproductionanddecayofphimesoninthemediumandtoleadtoapossiblefurtherincreaseofthesuppressionfactorR(mT).Theabundanceofphimesonasafunctionoftimeofthecollidingsystemwithin-mediummassmodificationisshownintheupperleftpanelofFig.2(dashedcurve).Theabundanceexhibits20%increaseatthepeak,anditfinallymergeswiththefree-spacevalueatlargetimeswhenmediumeffectsarenegligibleandchemicalequilibriuminallchannelssetsin.ThisenhancementcanbemainlyattributedtotheincreaseintheK+K−→φproductionrateduetolargerwidthΓ∗¯inthedenseφ→KKmedium,asshownbythickcurvesintheupperrightpanelofFig.2.

7

Pb(158A GeV)+PbR(mT)10.80.60.40.2101 dN/(mT dmT dy)010000.51mT−m0 (GeV/c)21.510−110−200.20.40.60.811.21.41.61.82mT − m0 (GeV/c)FIG.4.Transversemassspectraformidrapidity(|y|<1)phimesonsreconstructedfromK+K−pairs(solidsymbols)andfromµ+µ−channel(opensymbols)forPb+Pbcollisionsat158AGeVatanimpactparameterofb≤3.5fmintheAMPTmodel.Theresultsareforwithout(squares)andwith(triangles)in-mediummassmodifications.ThesolidcirclesaretheNA49data[7]forφ→K+K−decay,andtheopencirclesaretheNA50data[40]forφ→µ+µ−.IntheinsetisshownasafunctionofmTtheratioR(mT)forphimesonsdecayingtokaon-antikaonpairsthatarenotscatteredtothosedeterminedfromthedimuonchannel.Theresultsareforwithout(squares)andwith(triangles)in-mediummassmodification,andwithafurtherincreaseofphimesonnumberbytwointheHIJINGmodel(circles).

TherapiditydistributionofφfromkaonpairsthathavenotsufferedanycollisionisshowninFig.3within-mediummasses(thicksolidcurve),whichisfoundtoliewithintheerrorbarsoftheNA49data.Sincefree-spacebranchingratioisusedtodeterminethephimesonabundancefromthekaonchannel,itisevidentfromEq.(8)thatlargein-mediumwidthΓ∗¯leadstoappreciableproductionandsimultaneousdecayofphimeson,resultinginφ→KK

dN/dy≈7.1aty≈0forallthesekaonpairs.Incontrast,sincethebranchingratioforφ→µ+µ−islargelyunalteredinthemedium,thedN/dyofthereconstructedphimesonsaty≈0is4.5andthusabout1.9timeslargerthanthatfromthekaonchannel.

Thetransversemassspectrainthekaonicchannelwithmediumeffects(solidtrianglesinFig.4)revealsnearlyidenticalslopeasforthebaremasses.Ontheotherhand,thelargenumberofdimuonproductionatlowmTintheearlystageofcollisionswithin-mediummassesleadstoaslightlysteepermassspectrawithaslopeparameterofT=220MeV.ThisisclearlyseenintheinsetofFig.4(triangles)fortheratioR(mT)wherethesuppressionatlowmTis≃33%.

5.discussions

OurresultsonthephimesonyieldreconstructedfromkaonanddimuonchannelsdiffersatmostbyaboutafactoroftwointheAMPTmodel,whichcorrespondsonlytothelowerboundtothedifferencesfoundintheNA49andNA50data.ForasystematiccomparisonwiththeoryitisinstructivetoundertakeanexperimentwhereboththekaonandmuonpairsfromphimesonsaredeterminedinthesamemTandyrange.IfdifferencesaslargeasafactoroffourcorrespondingtotheupperboundoftheNA49andNA50dataisindeedobservedinthesameexperiment,thismaythensuggestthatothermechanisms,suchasformationofcolorrope[6]orquark-gluonplasma[2],areneededforphimesonproduction.IntheQGPscenario,becauseofcopiousproductionofss¯pair,itssubsequenthadronizationmayresultinadramaticincreaseofphimesonabundanceinexcessofthatproducedpurelybyhadronicrescatterings[2].Thephimesonproducedattheinitialstageshouldcontributeprimarilytothedimuonchannel.TomimictheeffectofenhancedphimesonproductioninQGP,wemakeanadhocincreaseinthephimesonnumberbyafactoroftwointheHIJINGmodel.ThetimeevolutionofNφisillustratedinFig.2(dottedcurve)wherethephimesonyield,insteadofexhibitingapeak,rapidlydecreasestoitsequilibriumvaluewhichcorroboratesthefindingsofRef.[24].Includingalsothemediumeffect,therapiditydistributionfromnon-scatteredkaonisincreasedbyanother∼8%,

8

whereastheyieldfromµ+µ−channelisconsiderablyenhanced(dottedcurveinFig.3).TheresultingsuppressionfactorR(mT)atlowmTis≈21%asisevidentfromtheinsetofFig.4(circles).

Theimportanceofinitialphimesonstothedimuonyieldisalsoseeninthescenarioofneglectingphimesonsfromtheinitialstringdecays.Inthiscase,wefindthatthephinumberobtainedfromtheK+K−channelisessentiallyunaffectedduetochemicalequilibrationviathehadronicscatterings,butthephimesonreconstructedfromdimuonsis,however,significantlysuppressed.

B.RHIC

108 dN/dY6420101−6−4−2Y02461/(2πmT) dN/(dmT dy) 10010−110−200.20.40.60.8121.21.4mT − m0 (GeV/c)FIG.5.Therapiditydistribution(toppanel)andthetransversemassspectra(bottompanel)formidrapidity(|y|<0.5)phimesonsreconstructedfromK+K−pairs(solidcurves)andfromµ+µ−channel(dashedcurves)forAu+Aucollisionsat

√

RHICenergyof

s=130A

GeV.Ofthetotalphimesonyieldof37perevent,about24%ofthesearelostinthekaonicchannelbyhadronicrescatteringandabsorption.NotethatinspiteofenhancedphimesonproductionintheearlystagesofthecollisionascomparedtotheSPSenergy,itsabundanceaty≈0isonlyaboutafactorof1.5largeinthedimuonchannel.ThismaybeattributedtofewerkaonslostbyrescatteringatRHICastheycanescaperapidlyoutofthecollisionzoneunperturbedduetooftheirlargeenergies.ItisseenthatphimesonmultiplicitiesreconstructedfromK+K−pairsatmidrapidityintheAMPTmodelisconsistentwiththeSTARdata[41].

ThetransversemassspectraofφmesonfromthetwochannelsareshowninthebottompanelofFig.5,andcomparedwiththeSTARdata[41]fortheK+K−channel.ComparedtoaslopeparameterofT=379±50MeVinthedata,theAMPTmodelpredictsasmallervalueofT=335MeVinthekaonicchannelintherange09

largeellipticflowobservedinAu+Aucollisionsat

√

s=130AGeV,theAMPTmodelgivestheyieldandslopeparameterofphimesonsfromthe

KKchannelthatareinreasonableagreementwiththeSTARdata.SimilartotheresultsforheavyioncollisionsatSPS,thephimesonyieldfromthedimuonchannelisabout1.5timeslargerthanthatfromtheK+K−channelintheabsenceofadditionalphimesonproductionduetotheformationoftheinitialpartonicstage.Thisnumberisexpectedtoincreasesignificantlyifweincludesuchenhancedproductionofinitialphimesons.IndeedatRHIC,largeenergydensitiesareexpectedtobereached,andapartonicmatterwithalongerlifetimeandoccupyingalargervolumecouldbeformed.ComparedtoSPSenergy,largerss¯productioninthepartonicstageanditssubsequenthadronizationwouldthereforeresultinanenhancedphimesonabundance,especiallyattheearlystages.Thesephimesonsshouldcontributedominantlyinthedimuonchannelwhilemostofthemwillescapedetectioninthekaonicchannel.ItisthusofgreatinteresttohaveexperimentaldataonphimesonsfromthedimuonmeasurementattheRHICenergy.

+

−

VI.ACKNOWLEDGMENT

ThispaperisbasedonworksupportedbytheNationalScienceFoundationunderGrantNos.PHY-9870038andPHY-0098805,theWelchFoundationunderGrantNo.A-1358,andtheTexasAdvancedResearchProgramunderGrantNo.FY99-010366-0081.

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