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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)
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-…