Thermal phase transitions in realistic dense quark matter
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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).

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Thermal phase transitions in realistic dense quark matter

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)


Realistic QCD phase diagram(Nf=3)

Idealized QCD phase diagram (Nf=3)

mu,d ~0 and ms ~200 MeV

beta equilibrium

charge neutral

“external fields”

T

T

dm

mu,d,s =0

QGP

QGP

2SC

dSC

mCFL

Hadron

Hadron

Color superconductor

(CFL)

μ

μ


Examples of new phases driven by external fields

unequal Fermi moms for ( ) and ( )


Color Superconductor (without m, dm )

Entangled pairing

in color-flavor space

(momentum)


  • quark mass ms >> mu,d 0,

  • beta equilibrium

    d m i= -qime (i=u, d, s)

  • electric neutrality

    Q=Qquark +Qelectron=0

  • color neutrality

    nR= nB= nG

major role

minor role

Realistic quark matter at T~Tc

Why we consider T~Tc ? Effect of the ext. field (m, dm )prominent

Ginzburg-Landau expansion possible (Δ<< Tc )


Tc

ms2

μ

Color Superconductor (with m, dm ) near Tc

Ext. fields:

・ What kind of phase structure near Tc?

・ What are the quark & gluon spectra ?


Δ

Δ

T>Tc

T<Tc

Corrections from

quark mass &

charge neutrality

Corrections from

color neutrality

Ginzburg-Landau free energy

Near Tc (Δ << Tc)


High density QCD → GL free energy

small external fields

  • m=0, dm=0Iida & Baym, PRD (`01)


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

O(Δ2ms2)

Flavor

Flavor dependent shift of the GL free energy


shift of

critical temperature

Larger

averaged Fermi mom.

More stable pairing


New phase : dSC

m , dm ≠0

m ,dm =0

T

normal

normal

Second order

phase transitions (MFA)

CFL

2SC

dSC

mCFL


elementary excitation spectra

  • Gluons

  • Quasi fermions

  • (Nambu-Goldstone bosons)

●Gluons (Meissner masses)


e

e

Unpaired case

Paired case

p

p

● Gapless quasi-fermions

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

M.Huang & I.Shovkovy (`03)

normal phase

T

mCFL

dSC

2SC

unpaired

0

0

2

2

5

5

9

paired

0

2

1

3

0

4

0


summary

We studied the phase structure near CSC ⇔ QGP boundary

with strange quark mass and charge neutrality

using Ginzburg-Landau theory

m and dm lead to

Flavor dependent pF

Pairing occur between quarkswith different pF

gapless fermion appearsat very close to Tc


thermal phase structure in the mean-field approx. (MFA)

& new dSC phase (this work)

T

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

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

QGP

2SC

dSC

mCFL

Hadron

gCFL,g2SC, uSC,CFLK,FFLO, BEC,・・・

μ



k

k

Meissner mass

Ginzburg-Landau (T ~Tc)

local coupling to gluons

mA2 >0 (always)

QCD

nonlocal coupling to gluons

δ > 0.3041 ×2πkB T mA82 , κ < 0 unstable to FFLO

δ < 0.3041 ×2πkB T ← our case

mA82 , κ > 0 stable to FFLO

κ:momentum susceptibility

Giannakis & Ren (hep-ph/0412015)


Why color neutrality does not play role ?

T

μe

normal

Tc

μe,μ8

super

μ8


“BCS”pairing(zero free energy condition)

F=E-μN

FFLOpairing

μu <μd

ku=q + pkd=q – p


Δ~σTc

dT μ

~σTc

Order of Δ and δT

Effect of Fluctuation

⇒ dT ~ g2 Tc or gTc>>σTc(at high density)


T ~0 vs T ~Tc

P

A

δ<< Tc

B

C

T ~0 difference is important

T ~Tc average is important


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