Color plasma oscillation in strangelets(2)

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

statesinsideastrangelet.Theresultingdispersionrelationanddampingrateofthelongitudinalcolorplasmaoscil-lationaredescribedinSecs.IIIandIV,respectively.ConcludingremarksaregiveninSec.V.

II.POLARIZATION

WeconsiderasphericalstrangeletofradiusRandbaryonnumberA,composedofanearlynoninteractinganduniformgasofu,d,andsquarksandembeddedintheQCDvacuum.Thechemicalpotentialµiofquarksof avori,includingtherestmassmi,isassumedtobeindependentofi.Suchindependenceensures avorequilibriumamongthequarks,sincenormallyleptonshaveavanishinglysmallchemicalpotentialinthestrangelet[6].Weworkinunitsinwhichh¯=c=kB=1.Wesetµi≡µ=300MeV,mu=md=0,andms=0–300MeV.ThetemperatureTofthesystemistakentobeintherange0≤T µ.Thezero-temperaturemodelforquarkmatterwillthusbeadoptedbelow.

Letusnowexaminethepropertiesoflongitudinalcoloroscillationmodesinastrangeletbycalculatingthecor-respondingproperpolarizationΠ00intheRPA(one-looporder).AtT=0,Π00canbeexpressedintermsofthe0correlationfunctionofthetimecomponentofthequarkcurrentJα(α=1,...,8)as

Π00(q)=

withi2 200 [Jα(x),Jα(y)] θ(x0 y0),(1)

00¯Jα(x)=λαabψai(x)γψbi(x),

whereq=(ω,q)isthefour-momentumtransfer,V=4πR3/3isthevolumeofthestrangelet,gistherenormalizedcolorcouplingconstant,ψaiisthequark eldofcoloraand avori,λαabaretheSU(3)generators,and ··· denotestheexpectationvalueinthegroundstate.Theright-handsideofEq.(1)isnotsummedoverαandisinvariantunderchangeinα.InthelimitV→∞,thisformofΠ00(q)reducestotheusualformwrittenforbulkuniformmatter.Hereafter,weassumethatthemomentumtransfer|q|isfarsmallerthanR 1.

Theessentialpartofthepresentstudyistoincorporatethediscretequarklevelsintotheone-loopordercalculationsofΠ00.Forsuchcalculations,we rstwritethequark eldintheformofamodeexpansion

0(+)( )0iωkix0ψai(x,x)=[cξκaiΨξκai(x)e iωkix+d Ψ(x)e],(2)ξκaiξκai

ξκ

whereΨξκaiandcξκaiarethespinorandtheannihilationoperatorforthequarkeigenstateofenergyωki=(+)