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Heavy quark Potentials in Full QCD Lattice

Simulations at Finite Temperature

Yuu Maezawa (The Univ. of Tokyo)

Tsukuba-Tokyo collaboration

Univ. of TsukubaS. Aoki

K. KanayaY. Taniguchi

E. EjiriT. HatsudaN. IshiiN. Ukita

The Univ. of Tokyo

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Contents

Motivations Free energy and Potential on lattice Numerical simulations

Summary

Potentials using two-flavor Wilson quarks Screening effect Comparison with Staggered fermion

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Motivations Heavy quark free energy in hot matter

Full-QCD lattice simulation

We use improved Wilson fermion action.

1. Channel dependence of "potential" ( 1c, 8c, 3c, 6c)

2. Effective running coupling at

3. Debye screening mass at

4. Relation to p-QCD at high T

0T

0T

1. not many works

2. Comparison with staggered fermion action

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Free energy and Potential on a lattice

McLerran, Svetitsky, PRD 24 (1981) 450

Free energy of the quark-antiquark pair

)(4 nUtStatic charge

d quark

Quark- antiquark “potential” (normalized free energy)

Polyakov loop:

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Projection operator and

81 PP Nadkarni, PRD 34 (1986) 3904

Quark-quark potential

Separation to each channel after Coulomb gauge fixing

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Numerical simulations

Lattice size:

Gauge action: RG Iwasaki improved action

Fermion action: Clover improved Wilson action (2-flavor)

Quark mass & Temperature

# of Configurations: 500 confs. (5000 traj.)

Gauge fixing: Coulomb gauge

aNTNN

tts

1,41633

points) (6 5.20.1 :80.0/

points) (9 2.30.1 :65.0/

cc

cc

TTTmm

TTTmm

～～

Parameters

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cTr

cT

TrV ),(

1c channel: attractive force8c channel: repulsive force

65.0

m

m

Quark-antiquark potentialDebye

Screening

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cTr

cT

TrV ),(

3c channel: attractive force6c channel: repulsive force

65.0

m

m

Quark-quark potentialDebye

Screening

c.f. Quenched actionNakamura and Saito (2004)

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3

1)6(,

3

2)3(,

6

1)8(,

3

4)1( CCCC

mass screening Debye :)(m

coupling running effective"" :)(

D T

T

M

aa

a ttMC 28

1 1)( : Casimir factor

Fitting the potentials of each channel with and as free parameters.

)( )( TmT D

Screening effectPhenomenological

potential: screened Coulomb potential

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)(T T

TmD )(

cTT

cTT

For T > 2.5Tc, potentials of each channel can be written by the same parameters: and .

)( )( TmT D

Results of and .

)( )( TmT D

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)(4)(eff TTg

Relation between and . )( )( TmT D

cTT

is described by effective running coupling with 10% accuracy.

)(TmD )(eff Tg

Effective running coupling

TTg

TmfN

D

)(1

)(

eff6

TTgTm fND )(1)( eff6 Screening mass?

for 1c potential

10%

12

cTT

T

TmD )(

2

0

12

02 lnlnln)(

SMSM

Tg

MeV 2612 fNSM

)(1)(

loop-26 TgT

Tm fND

Leading order 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.

13

TTgCm mmag )(2Magnetic screening mass:

)(

2

12ln

1

1

2

3)(1)(1

)( 2

6

6 gom

mTgTg

T

Tm

mag

DN

NNLOD

f

f

Next-to-leading order perturbationRebhan, PRD 48 (1993) 48

on a lattice vs. perturbative screening mass

)(TmD

T

TmD )(

cTT

T T2 T3

37.0mC

Lattice screening mass

is well reproduced by the

NLO-type screening mass

at T > 2Tc.

Fitting )2.3( cD TTm

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Comparison with staggered fermion

Kaczmarek and Zantow, PRD 71 (2005) 114510

70.0/,41633 mmNN ts Improved staggered fermion with

)(TT

TmD )(

cTT

cTT

Systematic error due to the difference of actions smaller when )0( aT

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Heavy quark "potential" Lattice QCD simulation using 2-flavor Wilson fermion action

Summary

rTmDer

TMCTrV )()(

)(),(

Screening effect potentials are fitted by

• and are independent on channel.

)( )( TmT D

1c, 3c : attractive force 8c, 6c : repulsive force

TTgTm fND )(1)( eff6 ))(4)(( eff TTg

effective running coupling )(1)(1)( 6 TgCTTgTm NLO

N

Df

2-loop running coupling Systematic error due to the difference

of actions smaller when )0( aT