1 heavy quark potentials in full qcd lattice simulations at finite temperature yuu maezawa (the...
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1
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
2
Contents
Motivations Free energy and Potential on lattice Numerical simulations
Summary
Potentials using two-flavor Wilson quarks Screening effect Comparison with Staggered fermion
3
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:
5
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
8
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)
9
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