Color plasma oscillation in strangelets

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

Colorplasmaoscillationinstrangelets

KeiIida

DepartmentofPhysics,UniversityofTokyo,7-3-1Hongo,Bunkyo,Tokyo113-0033,Japan

(February9,2008)

Thedispersionrelationanddampingrateoflongitudinalcolorplasmonsin nitestrangequark

matter(strangelets)areevaluatedinthelimitsofweakcoupling,lowtemperature,andlongwave-

length.ThepropertyoftheQCDvacuumsurroundingastrangeletmakesthefrequencyofthe

plasmonsnearlythesameasthecolorplasmafrequencyofbulkmatter.Theplasmonsaredamped

bytheircouplingwithindividualexcitationsofparticle-holepairsofquarks,ofwhichtheenergy

levelsarediscretizedbytheboundary.Forstrangeletsofmacroscopicsize,thelifetimeoftheplas-

monsisfoundtobeproportionaltothesize,asinthecaseoftheusualplasmaoscillationsinmetal

nanoparticles.

arXiv:nucl-th/9907039v1 9 Jul 1999PACSnumbers:12.38.Mh,25.75.-qI.INTRODUCTIONAtextremelyhightemperatureand/orbaryondensity,quark-gluonplasmas[1]areconsideredtobeenergeticallyfavorableascomparedwithhadronicmatter.Suchextremeconditionspreventusfromcon rmingthepresenceofquark-gluonplasmas,althoughitisexpectedininteriorsofneutronstarsandinultrarelativisticheavy-ioncollisions.Theintriguingpossibilitythatstrangequarkmatter,composedofu,d,andsquarks,mightbethegroundstateofthestronginteractionwaspointedoutbyWitten[2].Ifthisiscorrect, nitestrangequarkmatter,whichisusuallyreferredtoasstrangelets,wouldbeamorestableself-boundsystemthana56Fenucleus.Then,disruptionofneutronstarsandhighlyenergeticheavy-ioncollisionscouldleavebehindmanystrangelets.Thismightallowustodetectquark-gluonplasmasintheformofstrangeletsundervariousexperimentalsituationsTheground-statepropertiesofstrangeletsweredescribedbyFarhiandJa e[6]withintheMITbagmodel; nite-sizee ectssuchassurface,Coulomb,andshelle ectsweretakenintoaccount.Inultrarelativisticheavy-ioncollisions,however,thepossiblyformedstrangeletsshouldbeaccompaniedbythermallyexcitedstates.Amongvariousexci-tations,wetakenoteofspin-and avor-symmetric,longitudinalcolorplasmons[7,8]thatrepresentcollectivecoun-teroscillationsofdi erentcolordegreesoffreedom.Inastrangelet,theseplasmonsareexpectednotonlytoexhibitadispersionrelationdependentonthecolordielectricpropertyofthemedium,butalsotoundergoasize-dependentdampingasinthecaseofanopticallyexcitedmetalclusterornanoparticle.Whenthenanoparticleissmallenoughfortheelectronstobenearlycollisionlessandfortheelectricdipoleradiationtobeoflittlesigni cancebutistoolargefortheshellstructuretotakee ect,thesurfaceplasmonexcitationsaredampedinatimeproportionaltothesizeTheirenergyisresonantlyabsorbedbyindividualexcitationsofparticle-holepairsoftheelectronshavingdiscreteenergylevelsduetothepresenceoftheboundary.Noticethatthequark-gluonplasmainastrangeletisfully

relativisticincontrasttotheelectrongasinananoparticle.Consequently,newfeaturesshouldarisefromspin-orbitinteractionsandfromexcitationsinvolvingantiquarks,bothofwhichmaya ectthelifetimesofthecolorplasmons.Longitudinalcolorplasmaoscillationsinrelativisticanddegeneratebulkmatterofu,d,andsquarkswereinves-tigated[7,8]bycalculatingthecurrent-currentcorrelationfunctionwithintherandom-phaseapproximation(RPA)whichisvalidintheweak-couplingThedispersionlawanddampingfortheseoscillationsareessentiallythesameasthoseexaminedbyJancovici[11]forelectromagneticplasmaoscillationsinarelativisticanddegenerateelec-trongas.Ineithercase,themodepropertiesarecharacterizedbythecorrespondingplasmafrequencyandLandaudampingasinanonrelativisticplasma.Inthispaper,weestimatethelong-wavelength,low-temperaturepropertiesoflongitudinalcoloroscillationmodesinastrangeletofmacroscopicsize,surroundedbytheQCDvacuum,byin-corporatingthediscreteenergylevelsofquarksintothecurrent-currentcorrelationfunctionwithintheRPA.Thevanishingcolordielectricconstantofthevacuumleadstotheabsenceofthesurfacecolorcharge;ifpresent,itwouldmodifythee ectivecolorelectric eldinsidethestrangeletaccordingtoaMie-typeformula.Wethus ndthatthefrequencyofthelongitudinalcolorplasmonsinthestrangeletisalmostthesameasthatinbulkquarkmatter.ThelifetimeoftheplasmonsisdeterminedbythedipoletransitionsfromaquarkstateintheFermiseatoanunoccupiedone.Itisshownthatthequarkparticle-holepairsinvolveddamptheplasmonsatarateinverselyproportionaltothestrangeletsize.BeyondtheRPA,however,theplasmonsarefurtherdampedbycollisionsbetweenquarks.

InSec.II,thelongitudinalpolarizationfunctioniscalculateduptoone-looporder,allowingforthediscretequark