Color plasma oscillation in strangelets(6)

The dispersion relation and damping rate of longitudinal color plasmons in finite strange quark matter (strangelets) are evaluated in the limits of weak coupling, low temperature, and long wavelength. The property of the QCD vacuum surrounding a strangelet

InFig.2,wehaveshownΓRPA/ωpasafunctionofRforvariousvaluesofηs.Forω≤µ+mi,whichissatis edat

(vp)(¯qq)(0)(so)ω=ωp,ImΠ00cancelsoutImΠ00.Ontheotherhand,thecontributionsofImΠ00andImΠ00,thelatterbeingsuppressedbyonepowerαswithrespecttotheformer,leadtothedampingofwhichtheratebehavesas～c/R

[16].SuchcontributionsmayberegardedasLandaudamping,i.e.,adecayofthecollectivemodebyexcitingasinglerealparticle-holepair.Inthiscase,thesurfaceofthestrangelet,whichactsasaboundaryconditiondeterminingthediscretequarklevelsratherthanasascatterer,rendersΓRPAnonzeroquantummechanicallyandindependentofαsintheweak-couplinglimit.AscanbeobservedfromFig.2,ΓRPAhasonlyaslightdependenceonms.In(0)thenonrelativisticlimit,onlythepartImΠ00remainsuptoO(1/kF,iR),stillyieldingΓRPA∝R 1.WeremarkinpassingthatforastrangeletwithradiusR<～3fm,whichhasabaryonnumberoflessthan～30,higher-orderterms 1in(kF,iR)asignoredheremaywellhaveconsequencetothefrequencyanddampingrateofthecolorplasmons.Wenextconsiderthedampingofthelongitudinalcolorplasmonsduetocollisions[17]betweenquarksintheweak-couplingregime.Thesecollisions,bycolorexchange,disrupttheself-consistent eldsresponsiblefortheplasmonsandaddΓcoltotheRPAresultΓRPA.IfoneattemptstocalculateΓcolinperturbationtheory,onemeetsaninfrareddivergencethatarisesfromthecolormagneticinteractionsmediatedbytransversegluons.Atleastfor nitetemperature[18],suchadivergencecannotberemovedevenbydynamicalscreening[19]ofthemagneticinteractions

[20].ThisindicatesthatcalculationsofΓcoluptoleadingorderinαsrequirenonperturbativefeaturesoftherelativisticquark-gluonplasmawhichmaypossiblydevelopamagneticmassmmagandtherebyprovideane ectivecuto [21].Forathermal,masslessplasmaatzerobaryondensity,wheremmag～αsT,onethusobtainsΓcol～αsln(1/αs)Tfromkinetictheory[17].Thisratearisesfromthecollisionintegralassociatedwithone-gluonexchangeinthebulkplasma; nite-sizecorrectionsofO(1/kF,iR)tosuchabulkresultforΓcolshouldbeofhigherorderinαsthanΓRPA,whichremainsintheabsenceofthecollisionintegral.Atthenonzerostrangequarkmass,baryondensity,andtemperatureofinteresthere,however,thevaluesofmmagandhenceofΓcolareessentiallyunknown.Therefore,allwecanmentionisthatsuchacollisionaldampingortheLandaudampingduetoindividualexcitationsofquarkparticle-holepairs1dominatesthetotaldampingrateΓtot=ΓRPA+Γcol,accordingtowhetherthemeanfreepathofthequarks～Γ colissmallorlargecomparedwithR.Here,itisinstructivetonotethatnodampingoftheplasmonsduetogluonradiationoccursintheabsenceofthesurfacecolorcharge.

V.CONCLUDINGREMARKS

Wehavecalculatedthedispersionrelationanddampingrateofthelongitudinalcolorplasmaoscillationsinastrangeletintheregimesofweakcoupling,lowtemperature,andlongwavelength.ForkF,iR 1,wehavefoundthatthefrequencyofsuchoscillationsisalmostaslargeasthatofbulkcolorplasmonsandthattheLandaudampingyieldsalifetimeproportionaltoR.However,thepresentanalysisisaccompaniedbyseveraluncertainties.Wehavecon nedourselvestothecaseoflow|q|andT.Withincreasing|q|,multipoleplasmonexcitationsshoulddevelop.At nitetemperature,furthermore,gluonicexcitationsintheintermediatestatecontributetotheproperpolarizationΠ00;withintheone-loopapproximation,suchacontributionissimplyaddedtothequark-loopcontributionwithoutinterference[8].Astudyallowingforthoseexcitationshasyettobedone.Shelle ectsinstrangeletsalsoremaintobetakenintoaccount;suche ectsarepredictedtomanifestthemselvesremarkablyforA<～100[6,22].Itisexpectedfromtheanalogywiththecaseofcollectiveexcitationsinnormalnucleithatwhetherstrangeletsareinthevicinityofclosedshellsornotplaysaroleinthepropertiesofthecolorplasmaoscillations.Third,itistobenotedthatthepresentanalysisisrestrictedtotheweak-couplingregime(αs 1).Inthestronglyinteractingnonperturbativeregime(αs～1),morerelevanttoarealsystem,thedampingrateofthecolorplasmonscouldbegreatlymodi ed.Thesenonperturbativee ectsshouldhaveprimarysigni cancetothecollisionaldamping.

Toconclude,webrie yaddresswhattypeoftracesastrangelet,ifformedinheavy-ioncollisionexperiments[23]performedatabeamenergyoforder200GeVpernucleonona xedtarget,couldleaveviaexcitationsofthelongitudinalcolorplasmons.Immediatelyaftercentralnucleus-nucleuscollisionsatsuchenergies,itisexpectedthataquark-gluonplasmawouldbeproducedintheresultingmatterofsu cientlyhighenergydensity.Then,thequark-gluonplasmamightdevelopintostrangeletsviapre-freeze-outevaporationofpions,K+,andK0whichcarryawayentropyandantistrangenessfromthesystem.Thisstrangenessdistillationmechanism,suggestedbyGreineretal.

[24],wouldworkaslongasstrangeletsarestableagainststrongdecay.Notethatthefreezeouttemperature～100–200MeV[25]iscomparablewiththefrequencyωpforrealisticvaluesofαsintherange～0.4–1.Longitudinalcolorplasmaoscillationswouldthusbethermallyexcitedinstrangeletsuntilthetemperaturefullydrops.Onatimescale1oforderΓ tot,theexcitedcolorplasmonswoulddecayintoquarkparticle-holepairs,leadingtoemissionofphotonsandleptonpairsviaelectromagneticinteractions.Theseelectromagneticsignals,havingenergyoforderorlessthan～ωp,mightbeobservedinthehighlyenergeticheavy-ioncollisionsatCERN’sSPSexperiments[23].Inordertosupportthepicturementionedabove,however,estimatesallowingforrelaxationprocessesoccurringinsuchacooledand