1. 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)
hep-ph/ (to appear in PRD)

2. Realistic QCD phase diagram (Nf=3) Idealized QCD phase diagram (Nf=3)
mu,d ~0 and ms ~200 MeV
beta equilibrium
charge neutral
Realistic QCD phase diagram　(Nf=3) dm
“external fields” μ T
mu,d,s =0
Color superconductor
(CFL)
Idealized QCD phase diagram (Nf=3)
Hadron
QGP μ T
dSC
2SC
QGP
Hadron
mCFL

3. Examples of new phases driven by external fields
system
External field
pairings
New phases
liquid 3He
A phase
magnetic field
A1-A2
electron super
conductor
magnetic impurity
pairing with different moms
Crystalline
Structure
(FFLO)
color super conductor near Tc
m and dm
unequal Fermi moms for
different flavors (u,d,s)
dSC
unequal Fermi moms for ( ) and ( )

4. Color Superconductor (without m, dm )
Entangled pairing
in color-flavor space
(momentum)

5. 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 )
quark mass ms >> mu,d ,
beta equilibrium
d m i= －qi m e (i=u, d, s)
electric neutrality 　
Q＝Qquark +Qelectron= 0
color neutrality
nR＝ nB ＝ nG
major role
minor role

6. Color Superconductor (with m, dm ) near Tc
ms2 μ
Ext. fields: Tc
・ What kind of phase structure near Tc?
・ What are the quark & gluon spectra ?　

7. Ginzburg-Landau free energy
　Near Tc (Δ << Tc)
T<Tc
T>Tc Δ
Corrections from
quark mass &
charge neutrality
color neutrality

8. High density QCD → GL free energy
small external fields
　m=0, dm= Iida & Baym, PRD (`01)

9. m≠0, dm≠0 Iida,Matsuura,Tachibana,&Hatsuda, PRL (2004)
O(Δ2ms2)
Flavor
Flavor dependent shift of the GL free energy

10. shift of critical temperature Larger More stable pairing
averaged Fermi mom.
More stable pairing

11. T New phase : dSC m , dm ≠0 m ,dm =0 normal normal CFL 2SC dSC mCFL
Second order
phase transitions (MFA)
CFL
2SC
dSC
mCFL

12. elementary excitation spectra
Gluons
Quasi fermions
(Nambu-Goldstone bosons)
●Gluons (Meissner masses)
number of
massive gluons
mCFL 8
dSC
2SC 5

13. T unpaired 2 2 5 5 9 paired 2 1 3 4 ● Gapless quasi-fermions
Cf. Alford, Berges & Rajagopal (`99),
M.Huang & I.Shovkovy (`03)
normal phase T
mCFL
dSC
2SC 　
unpaired 2 2 5 5 9
paired 2 1 3 4 p e
Unpaired case
Paired case

14. 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 quarks with different pF
gapless fermion appears at very close to Tc

15. T μ QGP 2SC dSC mCFL Hadron gCFL,g2SC, uSC, CFLK,FFLO, BEC,・・・
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 (2004)
QGP
2SC
dSC
mCFL
Hadron
gCFL,g2SC, uSC, CFLK,FFLO, BEC,・・・ μ

16. back up

17. Ginzburg-Landau (T ~Tc) mA2 >0 (always) QCD
Meissner mass k k
Ginzburg-Landau (T ~Tc)
local coupling to gluons
mA2 >0 (always)
QCD
nonlocal coupling to gluons
δ > ×2πkB T mA82 , κ < 0 unstable to FFLO
δ < ×2πkB T ← our case
mA82 , κ > 0 stable to FFLO 2δ
κ:momentum susceptibility　
Giannakis & Ren (hep-ph/ )

18. T Tc Why color neutrality does not play role ? μe normal μe, μ8 super

19. FFLO　pairing
μu < μd
ku=q + p kd=q – p
“BCS”　pairing (zero free energy condition)
F=E-μN

20. ⇒ dT ~ g2 Tc or gTc >> σTc (at high density)
Order of Δ and δT
~σTc
Δ~　 σTc
dT 　μ　　
Effect of Fluctuation
⇒ dT ~ g2 Tc or gTc >> σTc (at high density) 　

21. T ~0 vs T ~Tc P A
δ<< Tc B C
T ~ difference is important
T ~Tc average is important