Thermodynamics of QCD Thermodynamics of QCD in lattice simulation in lattice simulation

with improved Wilson quark action with improved Wilson quark action at finite temperature and density at finite temperature and density

Yu Maezawa (Univ. of Tokyo)Yu Maezawa (Univ. of Tokyo)

in collaboration within collaboration with

S. Aoki, K. Kanaya, N. Ishii, N. Ukita, S. Aoki, K. Kanaya, N. Ishii, N. Ukita, T. Umeda (Univ. of Tsukuba)T. Umeda (Univ. of Tsukuba)T. Hatsuda (Univ. of Tokyo)T. Hatsuda (Univ. of Tokyo)

S. Ejiri (BNL)S. Ejiri (BNL)

WHOT-QCD CollaborationWHOT-QCD Collaboration

xQCD @ INFN, Aug. 6-8, 2007

In part published in PRD 75 (2007) 074501 and J. Phys. G 34 (2007) S651

Y. Maezawa @ xQCD2007 2

1, Many properties at T=0 have been well-investigated RG-improved gauge action + Clover-improved Wilson action by CP-PACS Collaboration (2000-2001)

Accurate study at T≠0 are practicable

2, Most of studies at T≠0 have been done with Staggered quark action Studies by Wilson quark action are important

IntroductionFull-QCD simulation on lattice at finite T and q

important from theoretical and experimental veiw

We perform simulations with the Wilson quark action, because

3

Previous studies at T ≠ 0 , q = 0 with Wilson quark action (CP-PACS, 1999-2001)

- phase structure, Tc, O(4) scaling, equation of state, etc.

Previous studies at T ≠ 0 , q = 0 with Wilson quark action (CP-PACS, 1999-2001)

- phase structure, Tc, O(4) scaling, equation of state, etc.

Introduction

This talk Finite q using Taylor expansion method

Quark number susceptibility & critical point

Fluctuation at finite q

Heavy-quark potential in QGP medium

Heavy-quark free energy

Y. Maezawa @ xQCD2007 4

Lattice size:

Action: RG-improved gauge action + Clover improved Wilson quark action

Quark mass & Temperature (Line of constant physics)

# of Configurations: 500-600 confs. (5000-6000 traj.) by Hybrid Monte Carlo algorithm

Lattice spacing (a) near Tpc

fm 25.0~ ,/1 aaNT t

Two-flavor full QCD simulationTwo-flavor full QCD simulation

Numerical Simulations

41633 ts NN

points) (12 0.376.0 :80.0/

points) (13 0.482.0 :65.0/

cc

cc

TTTmm

TTTmm

～

～

Y. Maezawa @ xQCD2007 5

1, Heavy-quark free energy1, Heavy-quark free energyHeavy-quark “potential” in QGP mediumDebye screening mass

6

Debye mass and

relation to p-QCD at high T

Heavy-quark free energy at finite T and q Heavy-quark free energy at finite T and q

Heavy quark free energy in QGP matter Channel dependence of heavy-quark “potential”

( 1c, 8c, 3c, 6c) Debye screening mass at finite T

Finite density (q≠ 0)

Maezawa et al.RPD 75 (2007) 074501

In Taylor expantion method,

c.f.) Doring et al.EPJ C46 (2006) 179

in p4-improved staggered action

Free energies between Q-Q, and Q-Q at q > 0 ~

7

)(4 nUt

Static charged quark

Polyakov loop:

Separation to each channel after Coulomb gauge fixing

Taylor expansion

Normalized free energy of the quark-antiquark pair (Q-Q "potential")

Q-Q potential:

Q-Q potential:

Heavy-quark free energy at finite T and q

Y. Maezawa @ xQCD2007 8

QQ potential at QQ potential at T > TcQQ potential at QQ potential at T > Tc

1c channel: attractive force

8c channel: repulsive force

become weakat q > 0~

9

QQ potential QQ potential at at T > TcQQ potential QQ potential at at T > Tc

3c channel: attractive force6c channel: repulsive force

become strongat q > 0~

10

Debye screening effectDebye screening effectDebye screening effectDebye screening effectPhenomenological

potential Screened Coulomb form

: Casimir factor

(T, q) : effective running coupling

mD(T, q) : Debye screening mass

Assuming, 2210 ))(()()(),(

TT

TTTT qq

q

220 ))(()(),( ,, T

TmTmTm qDDqD

Y. Maezawa @ xQCD2007 11

Substituting and mD to V(r, T,q)

and comparing to v0(r, T), v1(r, T) … order by order ofq/T

Debye screening effectDebye screening effectDebye screening effectDebye screening effect

Debye screening mass (mD,0 , mD,2 ) at finite q

Fitting the potentials of each channel

with i and mD,i as free parameters.

Y. Maezawa @ xQCD 2007 12

• Channel dependence of mD disappear at T > 2.0Tc

cTT

Debye screening effectDebye screening effectDebye screening effectDebye screening effect

cTT

~

Channel dependence of mD,0(T) and mD,2(T)

13

cTT

2

0

12

02 lnlnln)(

SMSM

Tg

MeV 2612 fNSM

2

2

26

2loop-2

221)()( q

NN

Dff TTgTm

Leading order thermal perturbation

2-loop running coupling on a lattice vs. perturbative screening mass

)(TmD

TTT 3,2,

T T2 T3

Lattice screening mass is not reproduced

by the LO-type screening mass.

cTT

14

TTgCm mmag )(2Magnetic screening mass:

)(ln)()(

)(, 2

6

60

2

12

1

1

2

311 go

m

mTgTg

T

Tm

mag

DN

NNLOD

f

f

Next-to-leading order perturbation at q = 0

Rebhan, PRD 48 (1993) 48

on a lattice vs. perturbative screening mass

)(TmD

482.0mC Quenched resultsNakamura, Saito and Sakai (2004)NLO-type screening

mass lead to a better agreement

with the lattice screening mass.

cTT

T T2 T3

?,NLO

2Dm

Y. Maezawa @ xQCD2007 15

2, Fluctuation at finite 2, Fluctuation at finite q

Quark number susceptivilityIsospin susceptivility

16

Fluctuation at finite q

Critical point at q > 0 have been predicted

T

hadron

QGP

CSCIn numerical simulations

Quark number and isospin susceptibilities

2I

2

I

2q

2

32q

2

q

ln1

p

Z

VT

p

2

2

duI

duq

• q has a singularity

• I has no singularity

At critical point:

Hatta and Stephanov, PRL 91 (2003) 102003

Taylor expansion of quark number susceptibility

2

q422

42

2

q 122T

ccT

Tp

T q

Nf = 2, mq > 0: Crossover PT at q = 0

17

Susceptibilities at q = 0

• Susceptibilities (fluctuation) at q = 0 increase rapidly at Tpc

• I at T <Tpc is related to pion fluctuoation

2

q422

42

2122

Tcc

T

Tp

T q

q

Taylor expansion:Taylor expansion:

RG + Clover Wilson RG + Clover Wilson

I at m/m = 0.65 is larger than 0.80

65.0/ mm 80.0/ mm

= 2c2

= 2c2

I

= 2c2

= 2c2

I

18

Susceptibilities at q > 0

• Second derivatives: Large spike for q near Tpc.

Dashed Line: 9q, prediction by hadron resonance gas model

2

q422

42

2122

Tcc

T

Tp

T q

q

Taylor expansion:Taylor expansion:

= 4!c4

= 4!c4

I

Large enhancement in the fluctuation of baryon number (not in isospin) around Tpc as q increases: Critical point?

~

65.0/ mm 80.0/ mm

= 4!c4

= 4!c4

I

Y. Maezawa @ xQCD 2007 19

Comparison with Staggered quark resultsComparison with Staggered quark resultsQuark number (q) and Isospin (I) susceptibilities

p4-improved staggered quark , Bielefeld-Swqnsea Collaboration, Phys. Rev. D71, 054508 (2005)

• Similar results have been obtained with Staggered quark action

Lattice QCD suggests large fluctuation of q at q > 0~

Y. Maezawa @ xQCD2007 20

SummarySummarySummarySummaryWe study QCD thermodynamics in lattice simulations with two flavors of improved Wilson quark action

Heavy-quark free energy Fluctuation at finite q

Heavy-quark free energy

QQ potential: become weakQQ potential: become strong

1c, 3c channel: attractive force8c, 6c channel: repulsive force

at q = 0

at q > 0~

LO2,2,

NLO0,0, ,~ DDDD mmmm Debye screening mass:

?NLO2,Dm

Fluctuation at finite q

Large enhancement in the fluctuation of baryon number

around Tpc as q increaseIndication of critical point at q > 0 ?