Thermal phase transition of Thermal phase transition of color superconductivity with color superconductivity with

Ginzburg-Landau effective action on the Ginzburg-Landau effective action on the latticelattice

M. Ohtani ( RIKEN )

with S. Digal (Univ. of

Tokyo) T. Hatsuda (Univ. of Tokyo)

XQCD, Aug 2 @ Swansea

• Introduction • GL effective action• Phase diagram in weak gauge coupling • Phase transition on the lattice• Summary

Δ ~ 100MeVΔ ~ 100MeVTTcc ~ 60MeV ~ 60MeV

IntroductionIntroduction

Non-perturbative analysis of colorsuper transition

Ｔ

μ

Hadrons

Quark-Gluon Plasma

Color Superconductivity

RHICRHIC

170MeV170MeV

~400~400MeVMeV

N ☆ Cores

qq qq 00

¶ no sign problem bosonic T-dependence: m, i , ,g

(

Ginzburg-Landau effective actionGinzburg-Landau effective action

GL action in terms of the quark pair field fc (x) & gauge field

Iida & Baym PRD 65 (2002) 014022

{discretize & rescale

SUf (3) SUc(3) Higgs on Lattice

2 couplings for quartic terms

○○○

mean field without gluonmean field without gluon Iida & Baym PRD 63 (2001) 074018

mean field (ungauged)

normal CFL

normal 2SC

unbound

2nd order transition

as T

@ Tc(MF)

1 = 2

in weak coupling

weak gauge coupling limitweak gauge coupling limit

mean field (ungauged) perturbative analysis

Matsuura,Hatsuda,Iida,Baym PRD 69 (2004) 074012

Normal CFL

normal 2SC

unbound

2nd order transition

gluonicfluctuation

||3 term

1st order transition

normal 2SC

normal2SCCFLunbound

norm

al

CFL

normal

unbound

Phase diagram in weak gauge couplingPhase diagram in weak gauge coupling

CFL

2SC

T/Tc(MF)

Phase diagram in weak gauge couplingPhase diagram in weak gauge coupling

Analytic results for large Analytic results for large

mean field (ungauged) perturbative analysis

Normal CFL

normal 2SC

unbound

2nd order transition

gluonicfluctuation

1st order transition

normal 2SC

normal2SCCFLunbound

norm

al

CFL

parameters

Setup for Monte-Carlo simulationSetup for Monte-Carlo simulation

Lattice size Lt = 2 , Ls = 12, 16, 24, 32, 40

@ RIKEN Super Combined Cluster

pseudo heat-bath method for gauge field generalized update-algorithm of SU(2) Higgs-field

= 5.1 0.7 c in pure YM

take several pairs of (1, 2 ), scanning {

with 3,000 － 60,000 configurations

Bunk, NP(Proc.Suppl) 42 (‘95), 556

update

broken phasebroken phase

Phase identification

(Tr †)1/2

large order param.⇔ broken phase

plateau jump @ c

update step

phase transition to ‘color super’

Tr

x† x

¶ Tr x†x 0 even in sym. phasethermal fluctuation

identifying the phases by eigenvalues of identifying the phases by eigenvalues of yy

diagonalization

matrix elements of †† ・・・ CFL

a † b ・・・ 2SC b

¶ †: gauge invariant

Hadron

(Quark-Gluon Plasma)

Color Superconducting state

5.14.8 5.6

0.08

0.16

Phase diagram with Phase diagram with ii fixed fixed

3.6

CFL

2SC

normal

● Similar trends with SU(2) Higgs

● no clear signal of end points as i

1 = 2 =.0005

2SC

CFL

11stst order transition: Hysteresis & boundary shift order transition: Hysteresis & boundary shift

initial config. = a thermalized config. with slightly different Hysteresis :

different configs. with same

Put 3 configs in

spatial sub-domain

Thermalize it

with fixed

Poly

akov

loop

normal

CFL

2SC

Phase diagram with Phase diagram with fixed fixed

1

2

CFL

2SC

1st order transition

CFL w/ metastable 2SC

2SC CFL

lattice simulation

metastable 2SC: 2SC observed in hysteresis & disappeared in boundary shift test

perturbative analysis

2SC

2SCCFL

unbound

CFL

0 1 2 3 4 5 6 7

0

1

2

3

4

5

Free energy by perturbationFree energy by perturbation

=

normal

CFL

†

2SC

Iida,Matsuura,Tachibana,Hatsuda PRD 71 (2005) 054003

● largest barrier btw normal &CFL

● metastable 2SC

Summary and outlookSummary and outlook

GL approach with quark pair field & gauge on lattice SU(3) Higgs model

eigenvalues of †to identify the phases 1st order trans. to CFL & 2SC phases in coupling space

We observed hysteresis. transition points boundary shift with mixed domain config.

metastable 2SC state in transition from normal to CFL, which is consistent with perturbative analysis

charge neutrality, quark mass effects, correction to scaling, phase diagram in T-…