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)

ElectricElectric and and magneticmagnetic screening masses screening masses

from the Polyakov loop correlationsfrom the Polyakov loop correlations

ElectricElectric and and magneticmagnetic screening masses screening masses

from the Polyakov loop correlationsfrom the Polyakov loop correlations

LATTICE2008 @ the College of William and Mary, July 14-19, 2008

IntroductionIntroduction Screening properties in quark-gluon plasma

• Electric (Debye) screening mass (mE)

Heavy-quark bound state (J/, Υ) 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) Screening masses of QCD in 3D-effective field theory (Hart et al. NPB 586 (2000) 443)

Polyakov loop: useful probe to study screening effect on the lattice

)x,(0

)x,/( T1

)x,(4U)x,(tr)x(tr

4

1

0U

tN

Static

quark

Correlation between Polyakov-loops

Potential btw. heavy-quark and heavy-antiquark

Polyakov-loop correlations in full QCD simulation (Nf=2)

Our approach

r

e

NTTrV

rm

c

sc

)y(tr)x(tr/),(exp † 1

Screening properties in QGP

Decomposition of Polyakov-loop operatorDecomposition of Polyakov-loop operatorExtract electric and magnetic sector from Polyakov-loop correlator

Euclidean-time reflection (TE)

)x,()x,(

)x,()x,(

44 AA

AA

)x,()x,( * AA

• Intermediate states between Polyakov loops

Arnold and Yaffe, PRD 52 (1995) 7208

A

A

4 : TE -odd Electric sector

: TE -even Magnetic sector

Charge conjugation (C)

Screening masses with C symmetry for each sector

Decomposition of Polyakov-loop operator

*:

:

C

TE†

)()(

)()(

)()(

)()(

21

21

21

ele,

21

21

21

ele,

21

21

21

mag,

21

21

21

mag,

††

††

††

††

CTE

T aa AtdigP/1

0 4 )x,(exp)x(

Polyakov-loop correlators in gauge invariant (GI) form

Note ,

and correlators are not calculable from PLC in GI form.

0trtr ele, mag,

),(

),(

),(

CTE

)y(tr)x(tr),(

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

ele, ele, ele,

2

mag, mag, mag,

TrC

TrC

GI

GI

Polyakov-loop correlators with gauge fixing (GF)

r

eTTrC

rTm

CTCT

CET

EE

)(

gague,

gague,

gague,

)(),(

Fitting correlation functions by a screening Coulomb form

)y()x(tr),(

)y()x(tr),(

)y()x(tr),(

tr )y()x(tr),(

ele, ele, ele,

ele, ele, ele,

mag, mag, mag,

2

mag, mag, mag,

TrC

TrC

TrC

TrC

GF

GF

GF

GF

),(

),(

),(

),(

),(

CTE

Magnetic sector (TE-even)

Electric sector (TE-odd)

GF mag,

GF mag,

GI mag,

gauge , ,,

E mmmm CT

GF ele,

GF ele,

GI ele,

gauge , ,, mmmm CTE

Magnetic mass

Electric mass

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) (9 0.40.1 :65.0/ pcpc TTTmm ～

Numerical SimulationsNumerical SimulationsPolyakov-loop correlators for each quantum number

),( mag, TrC GF

),( ele, TrC GF

),( mag, TrC GF

),( ele, TrC GF

pcrT

),( mag, TrC GI

),( ele, TrC GI

pcrT

pcrT

TE-even

Magnetic sector

TE-odd

Electric sector

Screening masses for each sector

pc/ TT

Tm

Tm

Tm

/

/

/

GF mag,

GF mag,

GI mag,

Screening massesScreening masses Magnetic sector (TE-even)

•Lightest screening mass

•At high T,

GI mag, m : Magnetic mass

GF mag,

GF mag,

GI mag, ~~ mmm

In weak coupling expansion,

2/1

0 421

mag 1~T

Adig

Polyakov-loop correlators in magnetic sector (TE-even) become,

mreAAgTrC 224

24

4mag ~)y()x(~),(

Two gluon exchanges

Tm

Tm

Tm

m CTE

/

/

/

GI mag,

GF mag,

GF mag,

gauge,

pc/ TT

GF ele,

GF ele,

GI ele,

m

m

m

Screening massesScreening masses Electric sector (TE-odd)

Tm

Tm

Tm

m CTE

/

/

/

GF ele,

GF ele,

GI ele,

gauge,

In weak coupling expansion,

3/1

0 4!31

/1

0 4ele ~TT

AdigAdig

Polyakov-loop correlators in electric sector (TE-odd ) become,

mrGI

mrGF

eAAgTrC

eAAgTrC33

434

6ele

442

ele

~)y()x(~),(

~)y()x(~),(

: one gluon ex.

: three gluon ex.

•Lightest screening mass

•At T > 1.5Tpc ,

GF ele,

GF ele, ~ mm

Electric mass

GI

ele,GF

ele,GF

ele, ~ mmm

Relation to gluon correlatorsRelation to gluon correlators

r

eAA

r

eAA

rm

Mii

rm

E

M

E

)y()x(

)y()x( 44Assuming that electric and magnetic

screening masses are defined as,

r yx Electric mass

TE-odd PLC with gauge fixing

Magnetic mass

TE-even PLC in gauge invariant form

r

eTAAgTrC

rTmGF

E )(

442

ele, )()y()x(~),(

)y()x(~),( 24

24

4 mag, AAgTrC GI

…Two electric and magnetic exchanges

•TE-even PLC in gauge invariant form22

mag, ),(

r

e

r

eTrC

rmrmGI

ME

rmccTrC

TrCEGF

GI

) (2exp)),((

),(212

ele,

mag,

Mm

Magnetic mass can be extracted from

pc/ TT

Mass inequality: mM < mE

For T > 2Tpc, both mM and mE

decreases as T increases.

For Tpc < T < 2Tpc, mM and mE

behaves differently.

Fit results of mE and mM

Comparison with quenched calculationComparison with quenched calculation

For T > 1.5Tpc, qualitative behavior (mM < mE) is the same.

For T < 1.5Tpc,

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 ?Violation of two-gluon exchange assumption?

From Polyakov-loops in Nf=2 QCD this work

pc/ TT

Comparison with other calculationsComparison with other calculations Screening masses from GI correlator in Nf=2 lattice QCD (this work)

Supergravity modes in AdS/CFT correspondence (Bak et al. JHEP 0708 (2007) 049)

Screening masses of QCD in 3D-effective field theory (Hart et al. NPB 586 (2000) 443)

TTmTTm GIGI 1410~,64~ ele, mag,

TmTJm CPTE 1.16~)0(,34.7~)0( Assuming: PJ ,0

agreement at T > 1.3Tpc

Screening ratioGI

mag,GI

ele, / mm

TmTJm CPTE 26.6~)0(,60.3~)0( at Nf=2, T=2MS

Difference of D.o.F

Magnitude of masses

Electric and magnetic screening masses in QGP from Polyakov-loop correlator with gauge fixing

Using Euclidean-time reflection TE and charge conjugation C,

the Polyakov-loop correlator can be decomposed:

Fitting by a screened Coulomb form

Relation to gluon correlators obtained mM and mE

Temperature dependence: mM < mE

Comparison with quenched results from <AA> qualitative agreement at T > 1.5Tpc

Comparison with AdS/CFT and 3D-EFT agreement of screening ratio at T > 1.3Tpc

SummarySummary

• Electric sector (TE-odd):

• Magnetic sector (TE-even):GF

mag,GF

mag,GI

mag, ,, mmm

GF ele,

GF ele,

GI ele,

gauge , ,, mmmm CTE

described by weak coupling expansion

• Electric mass:

• Magnetic mass:

GF ele,

GF ele, ~ mmGI

mag, m