Quark Pair Production in the Chiral Phase Transition

The production of quarks and antiquarks during a sudden restoration of chiral symmetry, as it might occur in very energetic heavy ion collisions, is considered. If gluons are already present they can assist additively to the overall production: real gluons

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aQuarkPairProductionInTheChiralPhaseTransitionCarstenGreinerDepartmentofPhysics,DukeUniversity,DurhamNC27708-0305(February7,2008)AbstractTheproductionofquarksandantiquarksduringasuddenrestorationofchiralsymmetry,asitmightoccurinveryenergeticheavyioncollisions,isconsidered.Ifgluonsarealreadypresenttheycanassistadditivelytotheoverallproduction:realgluonsarepartiallydecayingduringsuchachiraltransition.Thetotalnumberofproducedquarksiscalculatedandfoundtobequitesizeable.Itisspeculatedthatsuchaphenomenoncouldgiverisetoasigni cantcontributiontotheoverallquarkpaircreationinthepreequilibriumstageoftheheavyioncollision.25.75.+r,11.10.Qr,12.38.Bx,24.85.+p

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The production of quarks and antiquarks during a sudden restoration of chiral symmetry, as it might occur in very energetic heavy ion collisions, is considered. If gluons are already present they can assist additively to the overall production: real gluons

OneprimarygoalintheupcomingrelativisticheavyioncollisionexperimentsattheBrookhavenRelativisticHeavyIonCollider(RHIC)andtheCERNLargeHadronCollider(LHC)isthetemporaryformationandpotentialobservationofanewformofmatter,thequarkgluonplasma,adecon nedphaseofQCD[1].Itisexpectedthatthisphaseisalsoaccompaniedbyarestorationofchiralsymmetry[2].Athighenoughtemperaturesthemas-siveandcon nedquasiparticles,theconstituentquarks,becomebare,undressedquarkswithcurrentquarkmassesbeingmuchlighterthantheconstituentquarkmasses.Suchaphysicalpictureisrealizedinmodeldescriptionsoflow-energy,e ectiveQCDlagrangiansliketheNambuandJona-Lasinio(NJL)model[3,4]:Atlargeenoughcouplingchiralsymmetryofthevacuumisspontaneouslybrokenandexhibitsanonvanishingscalarquarkcondensate q¯q (250MeV)3.AsimilarbehaviourisexperiencedinlatticeQCDcalculations[5].Thescalarcondensateattributesascalarsel nteractiontothefermionpropagatorresultinginthepresenceofconstituentquarksatlowenergies,inlinewithexperiencefromhadronicspectroscopy.Forhighertemperatures,however,thecondensatebecomesweakerandvan-ishesatsu cientlylargetemperatures(ontheorderofT～200MeV)[6,3],whichisalsofoundinrecentQCDcalculations[7].

Relativisticheavyioncollisionso ertheonlypossiblewaytogainmoreinsightintothephasestructureofnuclearmatteratsuchhightemperatures(anddensities).However,fromtheonsetthereactionduringanysuchacollisionproceedsfaro equilibrium,sothatathermalquarkgluonplasmamaybereachedonlyaftersome nitetime.Accordingtotheresultsofthepartoncascademodel[8]thequarkswillreach,ifatall,achemicalsaturationonlyeventuallyinacentralrelativisticheavyioncollisionatcolliderenergieswhereasthegluonssaturateonasigni cantlysmallertimescale(inabouthalfafm/c)[9,10].This‘hotglue’scenariowasproposedbyShuryak[9].Thereasonforthisparticularbehaviourliesinthefactthatthequarksareonlyproducedinsecondorderbygluonannihilationandtherateforthisprocessissmallcomparedtothecorrespondingoneforgluonproduction.Thedecayofasinglegluonintoaquarkandantiquarkis,ofcourse,kinematicallynotallowed,aslongasallpartonsaretreatedase ectiveon-shellparticles.Inthisworkwewanttoproposethat

The production of quarks and antiquarks during a sudden restoration of chiral symmetry, as it might occur in very energetic heavy ion collisions, is considered. If gluons are already present they can assist additively to the overall production: real gluons

theoccurrenceofachiralphasetransitioncanhavesomeprofoundin uenceonthequarkpairproduction,iftherestorationwillhappenonaveryshorttimescale.Theideaisthatifindeedadecon nedstate(equilibratedornot)willbeformedinthereactionofaheavyioncollision,the‘undressing’ofthequarksshouldalreadyhaveoccurred.Beingprobablystillfarfromequilibriumthischiralrestorationmaythushappenratherspontaneously.Weassumethatthescalarquarkcondensateσ～ q¯q wouldmeltonatimescalesmallerthananyscalesetbythedynamics.Thedecayofthevacuuminducesaspontaneouscreationofquarkandantiquarkpairs.Duringthechiralrestorationtransitionthequarksarenolongeron-shellparticles,theirspectralfunctioncontainsawideo -shellspectrum,thuspermittingalsothedecayofasinglegluonintoaquark-antiquarkpair.Thedecayofboththevacuumandasubstantialfractionofenergeticgluonswouldacceleratethechemicalsaturationofthequarkphasespace.

Todescribethee ectonquarkpairproductionweconstructasimplemodelforfermionicmatter.Denotingthetimeofchiralrestorationatt=0,thelightquarkmassesthenarefunctionsoftime mc

Weassumethatnofurtherresidualinteractionsactamongthequarks.Whileansatz(1)

mayappearquitearti cial,itcapturestheessentialspiritofwhatonewouldnaivelycall‘atransitiontothephasewithrestoredchiralsymmetry’.TheconstituentvacuumbecomesunstablesothatduringtherestorationofthemassesoccupiedstatesofthenegativeDiraccontinuumarepartiallytransferredintothepositivecontinuum.TheamplitudeforthisisobtainedinastraightforwardwaywithintheIn/Outformalism.AparticlewithmomentumpsittinginthenegativeDiracseaisdescribedbytheincoming(constituent)wavefunctionψ↓(In)m(t)= ～350MeVfort≤0.(1)mb～10MeVfort>0≡ p↓= p↓(x,t)(thearrow‘↓’denotesaDirac-stateinthenegativecontinuum,

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