Quarkonium Feed-Down and Sequential Suppression

arXiv:hep-ph/0106017v211Jun2001June1,2001BI-TP2001/09QuarkoniumFeed-DownandSequentialSuppressionS.Digal,P.PetreczkyandH.SatzFakult¨atf¨urPhysik,Universit¨atBielefeldD-33501Bielefeld,GermanyAbstract:About40-50%ofthequarkoniumgroundstatesJ/ψ(1S)andΥ(1S)producedinhadroniccollisionsoriginatefromthedecayofhigherexcitations.Inahotmedium,thesehigherstatesaredissociatedatlowertemperaturesthanthemoretightlyboundgroundstates,leadingtoasequentialsuppressionpattern.Usingnewfinitetemperaturelatticeresults,wespecifythein-mediumpotentialbetweenheavyquarksanddeterminethedissociationpointsofdifferentquarkoniumstates.OnthebasisofrecentCDFdataonbottomoniumproduction,wethenobtainfirstpredictionsforsequentialΥsuppressioninnuclearcollisions.1.IntroductionThelargevaluesofthecharmandbottomquarkmassespermitpotentialtheorytoprovidearealisticaccountofquarkoniumspectroscopy[1]-[3].Fromthesestudies,itisknownthattheintrinsiclengthscalesofquarkoniaaremuchsmallerthanthoseoftheusualhadrons,withrJ/ψ∼0.2fmandrΥ∼0.1fmfortheradiiofthelowestc¯candb¯bvectormesons,respectively,incontrasttoabout1fmforlightq¯qstateradii.This“short-distance”natureofquarkoniumstatessuggeststhatatleastsomefeaturesoftheirproductioninhadroniccollisionsshouldbeaccessibletoperturbativeQCDcalculations,andthatindeedturnsouttobethecase.Thesimplestandmostgeneralmodelforquarkoniumproduction,thecolorevapora-tionmodel[4],postulatesthatthecross-sectionfortheproductionofagivencharmoniumorbottoniumstateissimplyafixed(energy-independent)fractionofthecorrespondingperturbativelycalculatedc¯corb¯bproductioncross-section.TheresultingpredictionsfortheenergyvariationoftheJ/ψandΥhadroproductioncross-sectionsareexperimentallyverywellconfirmed,fortheΥoverarangefrom√s≃20to1800GeV[5].Theassumedenergyindependenceoftheproductionratiosof2S/1Sand3S/1Sstatesisfoundtoholdoverthesamerange[5].Higherquarkoniumexcitationsdecayintolowerstateswithgenerallyknownbranchingratiosandwidths.Asanexample,theψ′=ψ(2S)decaysintoJ/ψ(1S)+anythingwithabranchingratioof55%,afterameanlife-timeofmorethan103fm.Asaconsequence,J/ψorΥproductioninhadroniccollisionsoccursinpartthroughtheproductionofhigher1excitedstateswhichsubsequentlydecayintothequarkoniumgroundstates.ItisknownexperimentallythatforbothJ/ψandΥabout40-50%ofthehadroproductionrateisduetosuchfeed-downfromhigherexcitations[6]-[10].Quarkoniumproductionthroughfeed-downbecomesparticularlyinterestingwhenquarkoniumstatesareusedtoprobethehotanddensemediumcreatedinhighenergynuclearcollisions.Itwaspredictedthatcolordeconfinement(quark-gluonplasmafor-mation)wouldleadtoJ/ψsuppression,sincesufficientlyhotdeconfinedmediadissolveanyc¯cbinding[11].However,differentquarkoniumexcitationswilldissolveatdiffer-enttemperaturesofthemedium[12],andthroughaloweringoftheopencharm(beauty)thresholdwithtemperature,dissociationbyD¯DorB¯Bdecaybecomespossibleforhigherexcitedstatesevenbelowthedeconfinementpoint[13].Sincethelife-timeoftheexci-tationsismuchlargerthanthatofthemedium,feed-downproductionwillresultinacharacteristicsequentialsuppressionpattern[14,15],withthefractionofJ/ψorΥpro-ducedthroughthedecayofhigherexcitationsbecomingsuppressedatlowertemperaturesthanthedirectlyproducedgroundstates.Tofullypredictthissequentialsuppression,twoprerequisitesareneeded.Wehavetoknowwhatfractionsofthequarkoniumgroundstateproductionoriginatefromwhichhigherexcitations,andwehavetoknowatwhattemperatureorenergydensityofthehotmediumagivenexcitationdissolves.Thefirstcanbedeterminedeitherexperimentallyorthroughaviablemodelforquarkoniumhadroproduction.Thesecondisawell-definedproblemforfinitetemperaturelatticeQCDstudies.Atpresent,neitherproblemiscom-pletelysolved.However,inthecaseofcharmonium,theproductionratesofthehigherexcitationsareexperimentallyknown,andforbottoniumproduction,recentFermilabdata[10,9]providethebasisforfairlyreliableestimates.Thisdeterminesthestructure(i.e.,thesequenceandthedifferentheights)ofthevarioussuppressionstepsforJ/ψandΥproduction,butnottheactualpositionsofthesestepsasfunctionofthetemperatureorenergydensity.Toestimatethese,wemakeuseofrecentlatticestudiescalculatingthetemperaturebehavioroftheheavyquarkpotentialinfullQCD[13,16].Asaresult,weobtainamodifiedJ/ψsuppressionpattern[14,15],includingthedecayofψ′andχcinconfinedmatter[13],andthenfirstquantitativepredictionsforthesequentialΥsuppres-siontobestudiedinforthcomingRHICandLHCexperiments.Thestructureofthispaperisthefollowing.Insection2,wefirstsummarizethehadroproductioncrosssectionsforthedifferentcharmoniumstatesandthendeterminethecorrespondingbottoniumcrosssectionsfromthementionednewCDFdata.Asaresult,wecanfullydescribetheoriginoftheJ/ψandΥproducedinhadroniccollisionsintermsoffeed-downfromhigherexcitedstates.Insection3,weconsiderthetemperaturedependenceoftheheavyquarkpotentialobtainedinrecentlatticeQCDstudies.SolvingthecorrespondingSchr¨odingerequation,wethendetermineinsection4thedissociationparametersforthedifferentstatesinadeconfinedmedium.ThisleadstoquantitativeestimatesofthesequentialJ/ψandΥsuppressionpatterns.2.QuarkoniumProductionandFeed-DownA.CharmoniumStatesI