Thermal phase transition of

1
Thermal phase transition of color
superconductivity with Ginzburg-Landau effective
action on the lattice
M. Ohtani ( RIKEN ) with S. Digal
(Univ. of Tokyo) T. Hatsuda (Univ. of
Tokyo)

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

XQCD, Aug 2 _at_ Swansea
2
Introduction
T
RHIC
Quark-Gluon Plasma
170MeV
Hadrons
Color Superconductivity
? ? ?qq ? ? 0
N ? Cores
µ
400MeV
Non-perturbative analysis of colorsuper
transition
3
Ginzburg-Landau effective action
? Iida Baym PRD 65 (2002) 014022
? GL action in terms of the quark pair field Ffc
(x) gauge field
4
mean field without gluon
? Iida Baym PRD 63 (2001) 074018
mean field (ungauged)
l2
normal ? CFL
D F D
D
as T
l1
F 0
normal ? 2SC
unbound
_at_ Tc(MF)
0 F 0
D
2nd order transition
5
weak gauge coupling limit
? Matsuura,Hatsuda,Iida,Baym PRD 69 (2004) 074012
mean field (ungauged)
perturbative analysis
l2
Normal ? CFL
gluonic fluctuation
l1
F 3 term
normal ? 2SC
unbound
2nd order transition
6
Phase diagram in weak gauge coupling
CFL
2SC
normal
1-T/Tc(MF) k
l2
unbound
l1
7
Phase diagram in weak gauge coupling
8
Analytic results for large ?
mean field (ungauged)
perturbative analysis
l2
Normal ? CFL
gluonic fluctuation
l1
normal ? 2SC
unbound
2nd order transition
1st order transition
9
Setup for Monte-Carlo simulation
parameters
b 5.1 ? 0.7 ? bc in pure YM

take several pairs of (l1, l2 ), scanning k
Lattice size
Lt 2 , Ls 12, 16, 24, 32, 40
with 3,000-60,000 configurations
update
pseudo heat-bath method for gauge field
generalized update-algorithm of SU(2) Higgs-field
? Bunk, NP(Proc.Suppl) 42 (95), 556
_at_ RIKEN Super Combined Cluster
10
broken phase
plateau jump _at_ kc
? Phase identification
Tr FxFx
(Tr FF )1/2
update step
large order param. ? broken phase
11
identifying the phases by eigenvalues of FyF
matrix elements of FF
12
Phase diagram with li fixed
k
CFL
Color Superconducting state
? Similar trends with SU(2) Higgs ?
no clear signal of end points as li
0.16
2SC
normal
(Quark-Gluon Plasma)
0.08
l1 l2 .0005
Hadron
b
5.6
5.1
4.8
3.6
13
1st order transition Hysteresis boundary shift
initial config. a thermalized config.
with slightly
different k
CFL
2SC
Polyakov loop
normal
k
14
Phase diagram with b fixed
lattice simulation
l2
CFL
CFL w/ metastable 2SC
2SC ?CFL
metastable 2SC 2SC observed in hysteresis
disappeared in boundary shift test
2SC
l1
1st order transition
15
Free energy by perturbation
? Iida,Matsuura,Tachibana,Hatsuda PRD 71 (2005)
054003
D1 D2
2
D1 FF D1
D3
CFL
normal
2SC
D3
16
Summary and outlook

• ? GL approach with quark pair field F gauge on
  lattice
• ? SU(3) Higgs model
• eigenvalues of FF 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-m,