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