Virtual Color Superconductivity--Status and Perspective
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arXiv:hep-ph/0003001v2 15 Mar 2000VirtualColorSuperconductivity–StatusandPerspectivea
S.YingDepartmentofPhysics,FudanUniversity,Shanghai200433,ChinaE-mail:sqying@fudan.edu.cn
Abstract
Thestatusofourunderstandingofthepropertiesandmanifestationsofcolorsuperconductivityatzeroandlowdensityisbrieflyreviewed.Futurepossibilityishighlighted.
1Introduction
QCDatfinitetemperatureandzerodensityconditionisrelativelywellun-
derstoodcomparedthefinitedensitysituation.Thetechnicalreasonsarewell
known.Physically,quantumdecoherenceincreasesastemperaturegetshigh
makingthebehaviourofthesystemessentiallyclassical.Ontheotherhand,
densityeffectsdonotreducequantumcoherence.Onehastodealwiththe
quantumeffects.Abriefreviewisgivenhereaboutthecurrentstatusofour
understandingoftheroleplayedbythecolorsuperconductingphaseinthe
stronginteractiongroundstateclosetozerodensityandinhadronstructure.
2HighDensityLimit
ThegroundstateofQCDathighenoughdensityismostlikelytobeinacolor
superconductingphase.ThisisbecausequarksonahighFermisurfacecarry
highmomentumandproducelargemomentumtransferinscattering,sothat
thetwoquarkinteractionkernelincolortripletchannelcanbeapproximated
wellbyanattractiveonegluonexchangeterm.Theattractiveinteraction
generatestheBCSinstabilitythatcreatesagapoforder∆BCS∼e−c/gwith
caconstant.Thepropertiesofthecolorsuperconductingphaseareactively
studiedintherecentliteraturebaseonvariousapproachesliketheinstanton
model,theonegluonexchangeapproximationimprovedbyrenormalization
grouptreatmentandthecontact4-fermioninteractionmodel.
Nomatterwhatmodelsareadoptedforthediscussion,thefactthatcolor
superconductingphaseshouldbethegroundstateofthehighdensityquark
matterisquiteclearaccordingtowellestablishedBCStheoryforsupercon-
ductivityinnon-relativisticcondensedmattersystems.Agapoforderofafew100MeVisguaranteedatnotsohighdensitysincethenaturalscaleof
theproblemisoforder1GeVandthecouplingbetweenquarksisoforder1.
Otherwise,finetuningisrequired.
Thegeneralconsensusonthepropertiesofthecolorsuperconductingphase
ofquarkmatteratasymptoticallyhighdensityandzerotemperatureisthat
thegroundstateisinacolorflavorlockedstateinvolvingup,downandstrange
quarks.Asthedensityislowered,thecolorflavorlockedstateceasestobe
thetruegroundstateofthesystem,thetruegroundstateisinacolorsu-
perconductingphaseinvolvesonlytheupanddownquarks.Suchacolor
superconductingphaseisagaindisfavouredasthedensityisfurtherlowered
tosomecriticaldensityρc.Thecolorsuperconductingphasestopstomanifest
atamacroscopicscalewhenρ≤ρc.Thecurrentestimateofρcissohighthat
thephysicaleffectsofthecolorsuperconductingphasecanonlybepossibleto
manifestinaneutronstarintheconventionalunderstandingoftheproblem
basedmainlyonthephysicalpicturegainedinthestudyofnon-relativistic
manybodysystems.
Sincetherearealreadyreviewsonthissubject1athighdensity,Ishall
mainlyconcentrateonabriefreviewofmyowneffortsinthepast10years
(1989-1999),whichactuallystartedthestudyofvacuumcolorsuperconduc-
tivity.Ihoweverlookedattheproblemwithadifferentperspective.
3ThePossibleRoleoftheColorSuperconductingPhaseatLow
orZeroDensity
Whatisthefateofthecolorsuperconductingphaseatlowdensitythen?One
thingisquiteclearthattheattractionbetweenquarkpairsinacolortriplet
statestillexist.Itisevidencedbytheexistenceofbaryonswhicharemadeup
ofthreequarks.Oneofthereasonsbesidesconfinementforthecolorsuper-
conductingphasetodisappearatlowdensityisduetothecompetitionfrom
thequark–antiquarkpairing.Sinceasthedensityislowered,theantiquark
excitationduetointeractionbecomeslesssuppressed.Asufficientnumberof
theinteractiongeneratedantiquarksbegintopairwiththequarksofthesys-
temtocondenseinthegroundstate,whichcausethewellknowspontaneous
breakingofthechiralsymmetry.
Inordertostudythephaseandtheneighbourhoodofthestronginteraction
vacuumstate,thepresentframeworkoffinitedensitytheorybasedonnon-
relativisticspace-timeisfoundtobeinadequate.Inconsistenciesinthelogic
flowofphysicalargumentationandunphysicalsolutionoccurwhenonegoes
beyondthequasi-particlepicture.Thusnotonlythekinematicsofindividual
particleshastoberelativistic,butalsothecovariancerelatedtotherelativistic
2space-timetransformationforthewholesystematthequantumfieldlevelhas
tobeimplementedinawaythatisconsistenttoquantummechanics.
Theresultsoftheeffortsinclude:1)themodelbuildingandstudyingfor
vector2,3andscalar4diquarkcondensationandmanyofthetechnicaldevelopment3
2)theintroductionofan8–componentrealrepresentationforfermions2,3,5,6,7,
whichisnotidenticaltotheconventional4-componentrepresentationatfi-
nitedensity5,7.Theadvantageofusingthe8–componenttheorytostudythe
vacuumpropertiesisdiscussed.Italsoenablemetoisolatesomeofthedif-
ferencesnearzerodensitybetweenmyworkandthelatercommonlyadopted
ones8whichcontainacontinuousmixingbetweenthecolorsuperconducting