from Polyakov-loop correlations in two-flavor lattice QCD

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27 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

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WHOT
-
QCD Collaboration

Yu Maezawa (RIKEN)

in collaboration with

S. Aoki, K. Kanaya, N. Ishii, N. Ukita,

T. Umeda (Univ. of Tsukuba)

T. Hatsuda (Univ. of Tokyo)

S. Ejiri (BNL)

Magnetic

and
electric

screening masses

from Polyakov
-
loop correlations

in two
-
flavor lattice QCD

Seminar @ Komaba, Todai, May 7, 2008

Contents

Introduction


Decomposition of Polyakov
-
loop correlator




Numerical simulations in N
f
=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

m
q

QGP

nucleus

CSC

s
-
QGP

Introduction

Study of
Quark
-
Gluon Plasma (QGP)



Early Universe after Big Bang



Relativistic heavy
-
ion collision

Theoretical study based on first principle (QCD)



Perturbation theory



w敡e coupling

慴ahigh
T

limit


However





Study of
strongly
-
correlated QGP


Lattice QCD simulation at finite (
T
,

m
q
)



bulk p牯p敲瑩敳 of QGP
(
p
,
e

T
c
, …)



are well investigated at

T
> 0.



in瑥牮rl p牯p敲瑩敳 of QGP 慲a


s瑩ll unc敲瑡tn.


Infr慲ad problem


却Song coupling ne慲a
T ~ T
c

e
/
T

4

T
/
T
pc

N
f
= 2
, CP
-
PACS 2001

T
c

~ 170 MeV

Introduction

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
/
y
) correlation



Q
-
Q

interaction diquark correlation in QGP



Electric (Debye) screening



Magnetic screening

Introduction


Screening properties in quark
-
gluon plasma



Electric (Debye) screening mass (
m
E
)




Heavy
-
quark bound state (J/
Y

U
⤠innGm



Magnetic screening mass (
m
M
)



Spatial confinement in QGP, non
-
perturbative


Attempts so far



<
A
m
A
n


牯m慴瑩攠sim慴ansin
q敮eh敤

慰p牯xim慴an


(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 (N
f
=2)


Our approach

Lattice QCD simulation

Polyakov
-
loop correlation

Basis of lattice QCD

Gluon action

Gluon field

Quark action

Wilson
-
type

quark action (
N
f

= 2
)

Finite temperature

Continuum limit/Thermodynamic limit

a

<< 1/
m
D

<<
L

a


0

and

L




Debye screening mass
m
D
:

Monte Carlo simulations based on importance sampling

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


Simulation parameters

Action on lattice

e
/
T

4

T
/
T
pc

N
f
= 2
, CP
-
PACS 2001

Quark mass

Small
m
q

dependence in
e
/
T

4

Lattice size

m
D
/
T

~
O
(1)

a

< 1/
m
D

<
L


Iwasaki improved gluon action


Clover
-
improved Wilson quark action (
N
f
= 2
)

improvement of

lattice discretization

:

Static
charged
quark

Polyakov loop

Polyakov loop

Order parameter of confinement
-
deconfinement PT at
N
f

= 0

Characterizing rapid crossover transition at
N
f

= 2

Pseudo
-
critical temperature
T
pc

from susceptibility

Correlation between Polyakov loops

Polyakov
-
loop correlations

Free energy

between quark
(
Q
)

and antiquark
(
Q
)



Separation to each channel after Coulomb gauge fixing

Free energies between
Q

and
Q

Normalized free energies (“
heavy
-
quark potential
”)

V

1
,
V

8
,
V

6
,
V

3*

at

T

>
T
pc
:

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

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

Single gluon exchange ansatz

(
T

= 0)

(
T

>
T
pc
)

Heavy
-
quark potential

Higher order (magnetic) contribution?

~ + +

: Screened Coulomb form

: Single electric gluon exchange


Heavy
-
quark “potential”

with gauge fixing



m
E

(
A
4
)

: electric mass



m
M

(
A
)


: magnetic mass

~ + +



m
E

(
A
4
)

: electric mass



m
M

(
A
)


: magnetic mass

Leading
-
order in
g

from electric sector

Higher
-
order in
g

from magnetic sector


Heavy
-
quark “potential”

with gauge fixing

~ + +



m
E

<
2
m
M

: electric dominance



m
E

>
2
m
M

: magnetic dominance

Inequality

between
m
E

and
m
M

is important

Which term is dominant at long distance?

c.f. perturbative
-
QCD


m
E
~
O
(
gT
)

>>

m
M

~
O
(
g
2
T
)

at high
T

limit

Magnetic

dominance

What about the magnitude of
m
E

and
m
M


at
T

~

(1
-
4)

T
c
?


Heavy
-
quark “potential”

with gauge fixing

Decomposition of Polyakov
-
loop correlator

Extract electric and magnetic sector from Polyakov
-
loop correlator

Euclidean
-
time reflection (
T
E
)





Charge conjugation (
C
)


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

Polyakov
-
loop correlator


four parts

Polyakov
-
loop correlator


four parts

Decomposition of Polyakov
-
loop operator




Electric sector



|
A
4
>

×

|
A
i
>, |
A
i
A
i
>

×

×




Evaluate
m
E

and
m
M

in lattice simulation of N
f
=2 QCD

Magnetic sector



|
A
i
A
i
>, |
A
4
A
4
>

×

|
A
i
>, |
A
4
>

×



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
T
pc



Gauge fixing: Coulomb gauge

Two
-
flavor full QCD simulation

Numerical Simulations

Numerical Simulations

Correlation functions between Polyakov
-
loops


(heavy
-
quark potential)

C
oo
(
r
,
T
)

electric screening mass

C
ee
(
r
,
T
)

magnetic screening mass

Screening masses



Mass inequality:
m
M

<
m
E




For
T >
2
T
pc
, both
m
M

and
m
E

decreases as
T

increases.



For
T
pc

< T <
2
T
pc
,
m
M

and
m
E

behaves differently.



m
E

well approximated by the NLO formula

Rebhan, PRD 48 3967

Screening masses



Mass inequality:
m
M

<
m
E




For
T >
2
T
pc
, both
m
M

and
m
E

decreases as T increases.



For
T
pc

< T <
2
T
pc
,
m
M

and
m
E

behaves differently.



m
E

well approximated by the NLO formula

Rebhan, PRD 48 3967

Screening ratio



m
E

<
2
m
M

: electric dominance



m
E

>
2
m
M

: magnetic dominance

Heavy
-
quark potential in color
-
singlet channel

Heavy
-
quark potential is


Electrically dominated

Inequality
m
M

<
m
E

<
2
m
M

is satisfied at
1.3
T
pc
<
T

<
4
T
pc

Comparison with AdS/CFT

Screening masses in N=4 supersymmetric Yang
-
Mills matter

Bak et al.

JHEP 0708 (2007) 049

Good agreement at
T

>

1.5
T
pc

Spectra of supergravity modes



Lightest
T
E
-
odd

mode (electric sector)




Lightest
T
E
-
even

mode (magnetic sector)

Screening ratio

D.O.F btw. SYM and QCD different

Comparison with quenched calculation



For
T

>

1.2
T
pc
, qualitative behavior (
m
M

<
m
E
) is the same.



For
T

<

1.2
T
pc
,

as
T


T
pc



m
E

decreases



m
M

increases

Quench



m
E

increases



m
M

decreases

N
f
=2 QCD

From <
AA
> in Quenched QCD

Nakamura et al, PRD69 (2004) 014506

Order of the phase transition responsible ?

From Polyakov
-
loops in

N
f
=2 QCD


this work

Comparison with heavy
-
quark potential

Inequality
m
E

<
2
m
M
is satisfied at
1.3
T
pc
<
T

<
4
T
pc

Heavy
-
quark potential


is dominated by electric screening.



Heavy
-
quark potential of color
-
singlet channel









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

m
E



2
m
M

m
E



m
M

Comparison with heavy
-
quark potential

m
1
eff

(V
1
)

~

m
E
(C
oo
) V
1
(
r
,
T
)

is electrically dominated


m
av
eff

(V
av
)

~

m
M
(C
ee
) V
av
(
r
,
T
)

is magnetically dominated

m
M
<

m
E

<
2
m
M

is confirmed.

Summary

Electric 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
m
E

and
m
M

in lattice simulations of N
f
=2 QCD

Temperature dependence:
m
M

<
m
E

<
2
m
M


Heavy
-
quark potential is
electrically dominated.

Comparison with AdS/CFT correspondence


Good agreement of screening ratio at
T

>

1.5
T
pc

Comparison with quenched QCD


Qualitative agreement at
T

>

1.2
T
pc


Different behavior at
T

<

1.2
T
pc




C
oo
(
r
,
T
)

couples to
|
A
4
>


electric mass (
m
E
)



C
ee
(
r
,
T
)

couples to
|
A
i
A
i
>, |
A
4
A
4
>

magnetic mass (
m
M
)

Summary

Comparison with heavy
-
quark potential


color
-
singlet channel is
electrically

dominated.


color
-
averaged channel is
magnetically

dominated.

m
M
<

m
E

<
2
m
M

is confirmed.

Notice at high temperature!

m
E
~
O
(
gT
)

>>

m
M

~
O
(
g
2
T
)

Future



Chiral & continuum limit




Single magnetic
-
gluon exchange in Polyakov
-
loop correlation?

Large statistics

Single magnetic
-
gluon exchanges

C
eo
(
r
,
T
)

couples to single magnetic gluon

|
A
i
>


However, signal of
C
eo

is very small

Comparison btw.
C
eo
(
r
,
T
)

and
m
M

obtaind from
C
ee
/(
C
oo
)
2

C
eo

will become good probe of
m
M

with high statistics.

Buck up slides

Comparison with thermal perturbation theory

Rebhan, PRD 48 (1993) 48

at
1.5
T
pc

<
T

< 4.0
T
pc

~ ~

Non
-
perturbative contributions

in NLO: magnetic mass
m
M



Next
-
to
-
leading order

PRD 73 (2006) 014513



2
-
loop running coupling

Leading order

Next
-
to
-
leading order