with improved Wilson quark action at finite temperature and density

bronzekerplunkMechanics

Oct 27, 2013 (3 years and 5 months ago)

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Thermodynamics of QCD

in lattice simulation

with improved Wilson quark action

at finite temperature and density

Yu Maezawa (Univ. of Tokyo)

in collaboration with

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

T. Umeda (Univ. of Tsukuba)

T. Hatsuda (Univ. of Tokyo)

S. Ejiri (BNL)

WHOT
-
QCD Collaboration

xQCD @ INFN, Aug. 6
-
8, 2007

In part published in PRD 75 (2007) 074501 and J. Phys. G 34 (2007) S651

Y. Maezawa @ xQCD2007

2

1, Many properties at T=0 have been well
-
investigated


RG
-
improved gauge action + Clover
-
improved Wilson action


by CP
-
PACS Collaboration (2000
-
2001)


Accurate study at T≠0 are practicable

2, Most of studies at T≠0 have been done with
Staggered quark


action


Studies by Wilson quark action are important

Introduction

Full
-
QCD simulation on lattice at finite
T

and
m
q

important from theoretical and experimental veiw

We perform simulations with the
Wilson quark action
,


because

3

Previous studies at
T

≠ 0

,
m
q

= 0

with Wilson quark action


(CP
-
PACS, 1999
-
2001)

-

phase structure,
T
c
, O(4) scaling, equation of state, etc.


Smaller quark mass (Chiral limit)


Smaller lattice spacing


(continuum limit)


Finite
m
q

Extension to

Introduction

This talk

Finite
m
q

using
Taylor expansion method

Quark number susceptibility & critical point



Fluctuation at finite
m
q

Heavy
-
quark potential in QGP medium



Heavy
-
quark free energy

Y. Maezawa @ xQCD2007

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.)


by Hybrid Monte Carlo algorithm



Lattice spacing (
a
) near
T
pc

Two
-
flavor full QCD simulation

Numerical Simulations

Y. Maezawa @ xQCD2007

5

1, Heavy
-
quark free energy

Heavy
-
quark

potential


in QGP medium

Debye screening mass

6

Debye mass and


relation to p
-
QCD at high
T

Heavy
-
quark free energy at finite
T

and
m
q




Heavy quark free energy in QGP matter



Channel dependence of heavy
-
quark “potential”


( 1
c
, 8
c
, 3
c
, 6
c
)



Debye screening mass at
finite
T

Finite density
(
m
q


0
)

Maezawa et al.

RPD 75 (2007) 074501

In Taylor expantion method,

c.f.) Doring et al.

EPJ C46 (2006) 179

in p4
-
improved

staggered action

Free energies between
Q
-
Q
, and
Q
-
Q

at
m
q

> 0


~

7

Static
charged
quark

Polyakov loop:



Separation to each channel after
Coulomb gauge fixing

9

Taylor expansion



Normalized free energy of the quark
-
antiquark pair


(
Q
-
Q

"potential")

9

Q
-
Q

potential:



Q
-
Q

potential:

Heavy
-
quark free energy at finite
T

and
m
q


Y. Maezawa @ xQCD2007

8

QQ potential at
T > T
c

1
c

channel:
attractive force

8
c

channel:
repulsive force

become
weak

at
m
q

> 0

~

9

QQ potential
at
T > T
c

3
c

channel:
attractive force

6
c

channel:
repulsive force

become
strong

at
m
q

> 0

~

10

Debye screening effect

Phenomenological potential

Screened

Coulomb form

: Casimir factor

a
(
T
,
m
q
)
: effective running coupling

m
D
(
T
,
m
q
)

: Debye screening mass

Assuming,

Y. Maezawa @ xQCD2007

11

Substituting
a

慮搠
m
D

to
V
(
r
,
T
,

m
q
)


and comparing to
v
0
(
r
,
T
)
,
v
1
(
r
,
T
)



order by order of

m
q
/
T

Debye screening effect

Debye screening mass (
m
D,
0

,
m
D,
2

) at finite
m
q

Fitting the potentials of each channel


with
a
i

and
m
D,
i

as free parameters.

Y. Maezawa @ xQCD 2007

12



Channel dependence
of

m
D

disappear at
T

> 2.0
T
c

Debye screening effect

~

Channel dependence of
m
D,
0
(T)

and
m
D,
2
(T)


13



Leading order thermal perturbation



2
-
loop running coupling


on a lattice vs. perturbative screening mass

Lattice screening mass is
not

reproduced

by the LO
-
type screening mass.

14

Magnetic screening mass:



Next
-
to
-
leading order perturbation at
m
q

= 0


Rebhan, PRD 48 (1993) 48


on a lattice vs. perturbative screening mass

Quenched results

Nakamura, Saito

and Sakai (2004)

NLO
-
type

screening mass
lead to a better agreement
with

the lattice screening mass.

Y. Maezawa @ xQCD2007

15

2, Fluctuation at finite
m
q

Quark number susceptivility

Isospin susceptivility

16

Fluctuation at finite
m
q


Critical point at
m
q
> 0

have been predicted

In numerical simulations



Quark number

and
isospin

susceptibilities




q

has a singularity




I

has no singularity

At critical point:

Hatta and Stephanov,

PRL 91 (2003) 102003

Taylor expansion of quark number susceptibility

N
f
= 2,
m
q
> 0
: Crossover PT at
m
q
= 0

17

Susceptibilities at
m
q

= 0




Susceptibilities (fluctuation) at

m
q
= 0
increase rapidly at

T
pc




I

at
T

<
T
pc

is related to
pion
fluctuoation

Taylor expansion
:

RG + Clover Wilson


I

at
m

/
m


= 0.65

is larger than
0.80

= 2c
2

= 2c
2
I

= 2c
2

= 2c
2
I

18

Susceptibilities at
m
q

> 0




Second derivatives:
Large spike for


q

near
T
pc
.

Dashed Line: 9

q
,
prediction by
hadron resonance
gas model

Taylor expansion
:

= 4!c
4

= 4!c
4
I

Large
enhancement

in the
fluctuation of baryon number


(not in isospin) around

T
pc

as

m
q

increases:
Critical point?

~

= 4!c
4

= 4!c
4
I

Y. Maezawa @ xQCD 2007

19

Comparison with Staggered quark results

Quark number (

q
) and Isospin (

I
) susceptibilities

p4
-
improved staggered quark ,
Bielefeld
-
Swqnsea Collaboration,


Phys. Rev. D71, 054508 (2005)



Similar results have been obtained with Staggered quark action

Lattice QCD suggests
large fluctuation of

q

at
m
q

> 0

~

Y. Maezawa @ xQCD2007

20

Summary

We study QCD thermodynamics in lattice simulations

with two flavors of improved Wilson quark action



Heavy
-
quark free energy



Fluctuation at finite
m
q

Heavy
-
quark free energy

QQ potential: become
weak

QQ potential: become
strong

1
c
, 3
c

channel:
attractive force

8
c
, 6
c

channel:
repulsive force

at
m
q

= 0

at
m
q

> 0

~

Debye screening mass:

Fluctuation at finite
m
q

Large enhancement

in the fluctuation of
baryon number

around
T
pc

as
m
q

increase

Indication of
critical point

at
m
q

> 0 ?