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格子QCDによるQGP物質の性質の解明

ポリヤコフ・ループの虚部相関によるポリヤコフ・ループの虚部相関によるデバイ遮蔽質量の解析デバイ遮蔽質量の解析

前沢祐前沢祐 （東京大学）（東京大学）

in collaboration within collaboration with

青木慎也、金谷和至、梅田貴士青木慎也、金谷和至、梅田貴士 （筑波大物理）（筑波大物理）

石井理修、浮田尚哉石井理修、浮田尚哉 （筑波大計算セ）（筑波大計算セ）

初田哲男初田哲男 （東京大学）（東京大学）江尻信司江尻信司 （（BNLBNL））

WHOT-QCD CollaborationWHOT-QCD Collaboration

熱場の量子論とその応用熱場の量子論とその応用 @ @ 基研基研, Sep. 5, Sep. 5--7, 20077, 2007

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Definition of Debye screening mass

In QED

In QCD (gauge fixing)

Polyakov loop correlation

?

)(4 nUtStatic

charged Polyakov loop:quark

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True Debye mass?

4A4A

Dm ~One gluonexchange

two gluonexchange

0→grmrm DM ee −− >

4A4A

4A4A+

4A4A 4A

~4A4A A

r

+ ~

rmDe 2−

Tgm

gTm

M

D2~

~

mM becomes dominant at r → ∞

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Exclution of magnetic gluonArnold and Yaffe, PRD 52 (1995) 7208

TC or TE reflection

Operator O which is odd under TE reflection

O( gT ) screening

for example, ○

×

under TE reflection:

Debye mass can be obtained fromIm-Im correlation of Polyakov loop.

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Imaginary correlation for color singlet channel

Separation of Q-Q correlation after Coulomb gauge fixing

Q-Q correlation:

Color-singlet correlation:

Real and Imaginary part of Polyakov loop

TE reflection:

Im-Im correlation for color-singlet channel

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In perturbation theory (weak coupling limit)

~Re-Re and Im-Im correlations

~2~ g

Comparison with “potential” (normalized free energy)

WHOT-QCD Coll. PRD 75 (2007) 074501

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Numerical SimulationsTwo-flavor full QCD simulationTwo-flavor full QCD simulation

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 Tc

41633 ×=× ts NN

points) (12 points) (13

cc

cc

TTTmmTTTmm

0.30.1:80.0/0.40.1:65.0/

～

～

==

==

ρπ

ρπ

fm 25.0~ ,/1 aaNT t=

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Numerical SimulationsColor-singlet correlation

65.0/2.3=

=

ρπ mmTT c

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Results of screening mass

5.182.0 ≤≤ rTFit range

65.0/ =ρπ mm 80.0/ =ρπ mm

There is little discrepancy between V(r) and CIm(r) for mD

Contribution of magnetic gluon is small.

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Results of screening massmM becomes dominant at r → ∞ TgmgTm MD

2~,~

Fit range dependencerTR ≤ini5.182.0 ≤≤ rT

65.0/2.4=

=

ρπ mmTT c

80.0/0.3=

=

ρπ mmTT c

iniR iniR

potential ≠ Im-Im correlation?

large statistics are necessary

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SummaryPolyakov loop correlation

include contribution of magnetic screening mass

Due to TE reflection, A contribution are excludedArnold and Yaffe, PRD 52 (1995) 7208

For color-singlet correlation after Coulomb gauge fixing,

Comparison of mD between potential and Im-Im correlation on lattice

There is no obvious discrepancy.

Contribution of magnetic screening mass is littleat the r and/or T .

Large volumeand/or high T Contribution of magnetic gluon?

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Effective running coupling

Comparison between V(r) and C(r)

)( ∞→T

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Effective running coupling

Comparison between V(r) and C(r)

65.0/ =ρπ mm 80.0/ =ρπ mm

CVL αα ~2 ×

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Comparison with thermal perturbation theory

2-loop running coupling

2

0

1

2

02 lnlnln)( ⎟⎟

⎠

⎞⎜⎜⎝

⎛

Λ+⎟⎟

⎠

⎞⎜⎜⎝

⎛

Λ=−

−SMSM

Tg µββµβloop2

MeV 2612 ≈Λ =fNSM

TTT πππµ 3,2,=

πα

4~)(

2Im gT

65.0/ =ρπ mm 80.0/ =ρπ mm

π3

π

)(4

)(2

Im Tg

T Vp απ

α << −loo2