WHOT-QCD CollaborationWHOT-QCD Collaboration

Yu Maezawa (RIKEN)Yu Maezawa (RIKEN)

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)

MagneticMagnetic and and electricelectric screening masses screening masses

from Polyakov-loop correlationsfrom Polyakov-loop correlations

in two-flavor lattice QCDin two-flavor lattice QCD

MagneticMagnetic and and electricelectric screening masses screening masses

from Polyakov-loop correlationsfrom Polyakov-loop correlations

in two-flavor lattice QCDin two-flavor lattice QCD

Seminar @ Komaba, Todai, May 7, 2008

ContentsContents

Introduction

Decomposition of Polyakov-loop correlator

Numerical simulations in Nf=2 lattice QCD

Summary

• Lattice QCD simulation• Polyakov-loop correlation

Euclidean-time reflection and charge conjugation

Electric and magnetic screening masses

are separately extracted from Polyakov-loop correlators

• Results of screening masses

AdS/CFT correspondence• Comparison with quenched QCD

heavy-quark potential

Big Bang

RHIC

T

q

QGP

nucleusCSC

s-QGP

IntroductionIntroductionStudy of Quark-Gluon Plasma (QGP)

• Early Universe after Big Bang

• Relativistic heavy-ion collision

Theoretical study based on first principle (QCD)

Perturbation theory ・ weak coupling at high T limit

However

Study of strongly-correlated QGP

Lattice QCD simulation at finite (T,q)

・ bulk properties of QGP (p, , Tc, …)

are well investigated at T > 0.

・ internal properties of QGP are

still uncertain.

1) Infrared problem

2) Strong coupling near T ~ Tc /T 4

T / Tpc

Nf = 2, CP-PACS 2001

Tc ~ 170 MeV

IntroductionIntroduction

Polyakov loop: heavy quark at fixed position

Heavy-quark free energy,

inter-quark interaction, screening effects, …

Properties of quarks and gluons in QGP

Heavy-quark potentials

How they are screened?

• Q-Q interaction heavy-meson (J/) correlation

• Q-Q interaction diquark correlation in QGP

• Electric (Debye) screening

• Magnetic screening

)()( 44 yAxA

)()( yAxA ii

IntroductionIntroduction Screening properties in quark-gluon plasma

• Electric (Debye) screening mass (mE)

Heavy-quark bound state (J/, ) in QGP

• Magnetic screening mass (mM)

Spatial confinement in QGP, non-perturbative

)y()x(

)y()x(

ii AA

AA

44

Attempts so far

<> from lattice simulations in quenched approximation (Nakamura et al. PRD 69 (2004) 014506) Supergravity modes in AdS/CFT correspondence (Bak et al. JHEP 0708 (2007) 049)

Polyakov-loop correlations in full lattice simulations (Nf=2)

Our approach

Lattice QCD simulation

Polyakov-loop correlation

Lattice QCD simulation

Polyakov-loop correlation

Basis of lattice QCDBasis of lattice QCD

Gluon action

)()](exp[ c, 3SUxAigaU x

Gluon field

Quark action Wilson-type quark action (Nf = 2)

x c

cg xW

Ng

NS )(Re

11

2

,

112

tr

aNT

t

1Finite temperature

Continuum limit/Thermodynamic limit

a << 1/mD << L

a → 0 and L → ∞

Debye screening mass mD:

Monte Carlo simulations based on importance sampling

Configurations {Ui} proportional to exp(-S(U)) 500-600 confs.

Simulation parameters

pcpcV

PS with TTTm

m0.48.080.0,65.0

Action on lattice

/T 4

T / Tpc

Nf = 2, CP-PACS 2001

MeV200100 qm

Quark mass

Small mq dependence in /T 4

Lattice size

,41633 ts NN

mD/T ~ O(1) a < 1/mD < L

•Iwasaki improved gluon action•Clover-improved Wilson quark action (Nf = 2)

improvement of lattice discretization:

pcTTTFQ /)(

pc/ TT

Static charged quark

Polyakov loopPolyakov loop

Order parameter of confinement-deconfinement PT at Nf = 0

Characterizing rapid crossover transition at Nf = 2

Pseudo-critical temperature Tpc from susceptibility

TdAigP

/1

0 4 ),(exp(x) xtrtr

)x,(0

)x,/( T1

4ATTFQe /)((x)tr

(x)tr

pcT

pc/ TT

Correlation between Polyakov loops

Polyakov-loop correlations

TTrF QQe/),(

)()(ytrxtr †

Free energy between quark (Q) and antiquark (Q)

Separation to each channel after Coulomb gauge fixing

cccc 8133 TFTFTFeee QQ /// 81

9

8

9

1

Free energies between Q and Q

cccc 3633 TFTFTF eee QQ /// *36

3

1

3

2

Normalized free energies (“heavy-quark potential”)

V 1, V

8, V 6, V

3* at T >Tpc: 0),( r

TrV

yx r

WHOT-QCD Coll., PRD 75 (2007) 074501

650./ VPS mm

3

1,

3

2,

6

1,

3

46*381 CCCC

factorCasimir :28

1 1M

aa

aM ttC

mass screening Debye

coupling running effective effeff

:

:4

Dm

g

WHOT-QCD Coll., PRD 75 (2007) 074501

)x(† )y(

4A 4A

effg effg

at at

)()( yxtr †

Single gluon exchange ansatz

rTmM

Der

TCTrV )()(

),( effr

rrV

3

4)(

(T = 0) (T >Tpc)

Heavy-quark potential

Higher order (magnetic) contribution?

22

r

e

r

e

r

e rmrmrm MEE

)y()x(tr † cN

1~ + +

: Screened Coulomb form

: Single electric gluon exchange

Heavy-quark “potential” with gauge fixing

• mE (A4) : electric mass

• mM (A) : magnetic mass

22

r

e

r

e

r

e rmrmrm MEE

)y()x(tr † cN

1~ + +

• mE (A4) : electric mass

• mM (A) : magnetic mass

Leading-order in gfrom electric sector

Higher-order in gfrom magnetic sector

Heavy-quark “potential” with gauge fixing

22

r

e

r

e

r

e rmrmrm MEE

)y()x(tr † cN

1~ + +

• mE < 2mM : electric dominance

• mE > 2mM : magnetic dominance

Inequality between mE and mM is important

Which term is dominant at long distance?

c.f. perturbative-QCD

mE ~ O(gT) >> mM ~ O(g2T) at high T limitMagneticdominance

What about the magnitude of mE and mM

at T ~ (1-4) Tc?

Heavy-quark “potential” with gauge fixing

Decomposition of Polyakov-loop correlatorDecomposition of Polyakov-loop correlatorExtract electric and magnetic sector from Polyakov-loop correlator

Euclidean-time reflection (TE)

Charge conjugation (C)

)x,()x,(

)x,()x,(

44 AA

AA

)x,()x,( * AA

C

T

AA

E

4

Intermediate states in z-direction

Magnetic and electric gluons btw. Polyakov-loops

Arnold and Yaffe,PRD 52 (1995) 7208

z

Decomposition of Polyakov-loop operator

)y()x(tr)y()x(tr

)y()x(tr)y()x(tr )y()x(tr

ooooc

oeoec

eoeoc

eeeec

†

c

NN

NNN

11

111

*:

:

C

TE†

)()(

)()(

oo

ee

††

††

21

21

21

21

21

21

CTE

Polyakov-loop correlator four parts

Polyakov-loop correlator four parts

Decomposition of Polyakov-loop operator

*:

:

C

TE†

)()(

)()(

oo

ee

††

††

21

21

21

21

21

21

CTE

)y()x(tr),( ooooc

oo N

TrC1

Electric sector

○ |A4>

× |Ai>, |Ai Ai > rT

eTrC

rmE

),(oo

),(oo TrC × ×

)y()x(tr)y()x(tr

)y()x(tr)y()x(tr )y()x(tr

ooooc

oeoec

eoeoc

eeeec

†

c

NN

NNN

11

111

211 tr)y()x(tr),(

ceeee

c

ee

NNTrC

rmccTrC

TrCE ) (exp

)),((

),(oo

ee

2212 Mm

Evaluate mE and mM in lattice simulation of Nf=2 QCD

Magnetic sector

22

r

e

r

eTrC

rmrm ME

),(ee○ |Ai Ai >, |A4 A4 >

× |Ai>, |A4>

),(ee TrC ×

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.)

Lattice spacing (a) near Tpc

Gauge fixing: Coulomb gauge

fm 25.0~ ,/1 aaNT t

Two-flavor full QCD simulationTwo-flavor full QCD simulation

Numerical SimulationsNumerical Simulations

41633 ts NN

points) (7 .. :./

points) (9 .. :./

pcpc

pcpc

TTTmm

TTTmm

0301800

0401650

～

～

),(ee TrC

),(oo TrC

),(eo TrC

),(oe TrC

pcrT pcrT

Numerical SimulationsNumerical Simulations

650./ mm

Correlation functions between Polyakov-loops (heavy-quark potential)

Coo(r,T) electric screening mass

Cee(r,T) magnetic screening mass

)y()x(tr)y()x(tr

)y()x(tr)y()x(tr )y()x(tr

ooooc

oeoec

eoeoc

eeeec

†

c

NN

NNN

11

111

Screening massesScreening masses

Mass inequality: mM < mE

For T > 2Tpc, both mM and mE decreases as T increases.

For Tpc < T < 2Tpc, mM and mE behaves differently.

mE well approximated by the NLO formula

650./ mm 800./ mm

pc/ TT pc/ TT

)(ln),(),(/)(NLO 2212

43

23

34 1 gOTgTgTTm

M

E

mm

E Rebhan, PRD 48 3967

Screening massesScreening masses

Mass inequality: mM < mE

For T > 2Tpc, both mM and mE decreases as T increases.

For Tpc < T < 2Tpc, mM and mE behaves differently.

mE well approximated by the NLO formula )(ln),(),(/)(NLO 2212

43

23

34 1 gOTgTgTTm

M

E

mm

E

650./ mm 800./ mm

pc/ TT pc/ TT

Rebhan, PRD 48 3967

Screening ratioScreening ratio

221

r

e

r

e

r

e

N

rmrmrm

c

MEE

)y()x(tr †

• mE < 2mM : electric dominance

• mE > 2mM : magnetic dominance

Heavy-quark potential in color-singlet channel

Heavy-quark potential is Electrically dominated

Inequality mM < mE < 2mM

is satisfied at 1.3Tpc < T < 4Tpc

pc/ TT

ME mm /

Comparison with AdS/CFTComparison with AdS/CFTScreening masses in N=4 supersymmetric Yang-Mills matter

Bak et al. JHEP 0708 (2007) 049

Good agreement at T > 1.5Tpc

Spectra of supergravity modes

• Lightest TE-odd mode (electric sector)

• Lightest TE-even mode (magnetic sector)

TmD 40413.

Tm 33612.gap

461.)(

)(

gap

E

ED

Tm

Tm

Screening ratio

D.O.F btw. SYM and QCD different

pc/ TT

ME mm /

Comparison with quenched calculationComparison with quenched calculation

For T > 1.2Tpc, qualitative behavior (mM < mE) is the same.

For T < 1.2Tpc,

as T → Tpc

• mE decreases

• mM increases

Quench

• mE increases

• mM decreases

Nf=2 QCD

From <AA> in Quenched QCDNakamura et al, PRD69 (2004) 014506

c/ TT

650./ mm

pc/ TT

Order of the phase transition responsible ?

From Polyakov-loops in Nf=2 QCD this work

Comparison with heavy-quark potentialComparison with heavy-quark potential

Inequality mE < 2mM is satisfied at 1.3Tpc < T < 4Tpc

Heavy-quark potential is dominated by electric screening.

• Heavy-quark potential of color-singlet channel

• Heavy-quark potential of color-averaged channel (gauge invariant)

r

ee

rmTTrV

1eff

11

†/),( )y()x(Tr

2

r

ee

rmTTrV

aveff

avav

†/),( )y(Tr)x(Tr

mE ⇔ 2mM

mE ⇔ mM

pc/ TT650./ mm

Comparison with heavy-quark potentialComparison with heavy-quark potential

m1eff (V1) ~ mE (C

oo) V1(r,T) is electrically dominated

maveff (Vav) ~ mM (C

ee) Vav(r,T) is magnetically dominated

22

r

e

r

e

r

e rmrmrm MEE

22

r

e

r

e rmrm ME

mM < mE < 2mM is confirmed.

SummarySummaryElectric and magnetic screening masses in QGP

from Polyakov-loop correlator

Using Euclidean-time reflection and charge conjugation,

the Polyakov-loop correlator can be decomposed:

Calculate mE and mM in lattice simulations of Nf=2 QCD

Temperature dependence: mM < mE < 2mM

Heavy-quark potential is electrically dominated.

Comparison with AdS/CFT correspondence

Good agreement of screening ratio at T > 1.5Tpc

Comparison with quenched QCD

Qualitative agreement at T > 1.2Tpc

Different behavior at T < 1.2Tpc

• Coo(r,T) couples to |A4> electric mass (mE)

• Cee(r,T) couples to |AiAi>, |A4A4> magnetic mass (mM)

SummarySummaryComparison with heavy-quark potential

color-singlet channel is electrically dominated.

color-averaged channel is magnetically dominated.

mM < mE < 2mM is confirmed.

Notice at high temperature!

mE ~ O(gT) >> mM ~ O(g2T)

Future

• Chiral & continuum limit

• Single magnetic-gluon exchange in Polyakov-loop correlation?

Large statistics

Single magnetic-gluon exchangesSingle magnetic-gluon exchanges

C

T

AA

E

4

Ceo(r,T) couples to single magnetic gluon |Ai>

However, signal of Ceo is very small

Comparison btw. Ceo(r,T) and mM obtaind from Cee/(Coo)2

Ceo will become good probe of mM with high statistics.

Buck up slides

Comparison with thermal perturbation theoryComparison with thermal perturbation theory

)(

2

12ln

1

1

2

3)(1)(1

)( 2

6

6 gOm

mTgTg

T

Tm

M

DN

ND

f

f

NLO

Rebhan, PRD 48 (1993) 48

461./ MD mm at 1.5Tpc < T < 4.0Tpc~ ~

Non-perturbative contributions in NLO: magnetic mass mM

Next-to-leading order

2

0

1

2

02 lnlnln)(

SMSM

Tg

MeV 2612 fNSM

TTT 32 ,,

PRD 73 (2006) 014513

2-loop running coupling

Leading order Next-to-leading order

rmccTrC

TrCE ) (exp

)),((

),(oo

ee

2212 Mm