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 ?
Comments 0
Log in to post a comment