Thermal phase transitions in realistic dense quark matter

Taeko Matsuura (Tokyo)

K. Iida (RIKEN BNL)

M. Tachibana (RIKEN)

T. Hatsuda (Tokyo)

Physical Review Letters 93 (2004) 132001

hep-ph/0411356 (to appear in PRD)

μ

T mu,d,s =0

Color superconductor (CFL)

Idealized QCD phase diagram (Nf=3)Idealized QCD phase diagram (Nf=3)

Hadron

QGP

mu,d ~0 and ms ~200 MeV beta equilibriumcharge neutral

Realistic QCD phase diagram 　 (Nf=3)Realistic QCD phase diagram 　 (Nf=3)

““external fields”external fields”

μ

T

dSC2SC

QGP

Hadron mCFL

system External field pairings New phases

liquid 3He

A phase

magnetic field A1-A2

electron super

conductor

magneticimpurity

pairing with different moms

Crystalline

Structure

(FFLO)

color super conductor near Tc

m and unequal Fermi moms for

different flavors (u,d,s)

dSC

unequal Fermi moms for ( ) and ( )

Examples of new phases driven by external fields Examples of new phases driven by external fields

Color Superconductor (without m, ) Color Superconductor (without m, )

Entangled pairing in color-flavor space

PJ 0 Color antisym

Flavor antisym

ab a bij i 5 jq C q (m

omen

tum

)

Realistic quark matter at T~TcRealistic quark matter at T~Tc

quark mass ms >> mu,d 0,

beta equilibrium

i= － qi e (i=u, d, s)

electric neutrality 　

Q ＝ Qquark +Qelectron= 0

color neutrality

nR ＝ nB ＝ nG

major role

minor role

Why we consider T~Tc ? Effect of the ext. field (m, ) prominent Ginzburg-Landau expansion possible (Δ<< Tc )

Color Superconductor (with m, ) near TcColor Superconductor (with m, ) near Tc

・ ・ What kind of phase structure near TWhat kind of phase structure near Tcc? ?

・ ・ What are the quark & gluon spectra ?What are the quark & gluon spectra ? 　　

2

4sm

2

2sm

2

2sm

2

4sm

Tc

Ext. fields:0

0 =u

d

s s

m

m

ms2

μ

Ginzburg-Landau free energyGinzburg-Landau free energy

　 Near Tc (Δ << Tc)

2 4 6S( ) +O( ) , 0C

C

T -Ta b a b

T

Corrections fromquark mass &charge neutrality

Corrections fromcolor neutrality

T<TcT>Tc

ΔΔ

　 m=0, =0 Iida & Baym, PRD (`01)

3E 0

0

QCD at finite temperature & density

1S ( ( ) )

4a ad d r iD m F F

small external fields

22 2 21

4 4 42

ud ds su

ud ds su

β

β

2 2 2Cud ds su

C

T -T

T 2

4

( )

( )

O

O

22

1 2 =4 , ( / )2 cT

High density QCD → GL free energyHigh density QCD → GL free energy

m≠0, ≠0 　　　　 Iida,Matsuura,Tachibana,&Hatsuda, PRL (2004)

2lnFij

ijij C

p

T

2

F Fi jF

ij

p pp

2lnFijC

ijij C C

pT -T

T T

Flavor dependent shift of the GL free energy

O(Δ2ms2)

Flavor

1 lnFijijc

c c

pT

T T

Larger averaged Fermi mom.

ud ds suF F Fp p p ud ds su

c c cT T T

shift of shift of critical temperaturecritical temperature

More stable pairing

22

2

3

8 2sm

g

New phase : dSCNew phase : dSC

T

dSC

2 cT

3 cT

mCFL

2SCCFL

normal normal

m ,=0 m , ≠0

Second order phase transitions (MFA)

elementary excitation spectraelementary excitation spectra

Gluons Quasi fermions (Nambu-Goldstone bosons)

●Gluons (Meissner masses)

number of

massive gluons

mCFL 8

dSC 8

2SC 5

2 2 2A1,2

2 2 2A4,5

2 2 2A6,7

2 2 2 2 2 22

A 2 28

4 4 2 22

2 2A

γ g ( + )

γ g ( + )

γ g ( + )

4γ g

3 +

+4γ g

3 +

ds us

ds ud

us ud

ds us ds ud us ud

ds us

ds us ds us

ds us

m

m

m

m

m

2( / )cT

● Gapless quasi-fermions

T

normal phase

2SC 　mCFL dSC

Cf. Alford, Berges & Rajagopal (`99),

M.Huang & I.Shovkovy (`03)

p p

Unpaired case Paired case

0 2 0 4 0 3 1paired 9 5 5 2 2 0 0unpaired

2

smonly

summarysummary

We studied the phase structure near CSC ⇔ QGP boundary with strange quark mass and charge neutrality using Ginzburg-Landau theory

　　　　m and lead to Flavor dependent pF

Pairing occur between quarkswith different pF

ij ij

c FT p

gapless fermion appearsat very close to Tc

μ

T

dSC2SC

QGP

Hadron mCFL

gCFL,g2SC, uSC,CFLK,FFLO, BEC, ・・・

thermal phase structure in the mean-field approx. (MFA)& new dSC phase (this work)

Order of the phase transition may change. (beyond MFA)

Matsuura, Iida, Hatsuda, and Baym, PRD 074012(2004)

back up

Ginzburg-Landau (T ~Tc) local coupling to gluons mA

2 >0 (always)

QCD nonlocal coupling to gluons

k k

Giannakis & Ren (hep-ph/0412015)

2δ

δ > 0.3041 ×2πkB T mA8

2 , κ < 0 unstable to FFLO δ < 0.3041 ×2πkB T ← our case mA8

2 , κ > 0 stable to FFLO

κ:momentum susceptibility　

Meissner mass

Why color neutrality does not play role ?

T normal

super

μe, μ8

μe

μ8

2( )O

(1)O

Tc

FFLO　 pairing

“BCS”　 pairing(zero free energy condition) F=E-μN

μu < μd

ku=q + pkd=q – p

22

2

3

8 2sm

g

Order of Δ and δT

~σTc

Δ~ 　 σTc

T 　 μ　　Effect of Fluctuation

⇒ T ~ g2 Tc or gTc

>> σTc

(at high density)

　

T ~0 vs T ~Tc

ACB

P

T ~0 difference is important

T ~Tc average is important

δ<< Tc