Color plasma oscillation in strangelets(3)

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=(+)

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