1. Thermodynamics of QCD in lattice simulation with improved Wilson quark action at finite temperature and density
WHOT-QCD Collaboration
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)
In part published in PRD 75 (2007) and J. Phys. G 34 (2007) S651
INFN, Aug. 6-8, 2007

2. Introduction Full-QCD simulation on lattice at finite T and mq
important from theoretical and experimental veiw
We perform simulations with the Wilson quark action,
because
1, Many properties at T=0 have been well-investigated
RG-improved gauge action + Clover-improved Wilson action
by CP-PACS Collaboration ( )
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
Y. xQCD2007

3. Introduction This talk
Previous studies at T ≠ 0 , mq = 0 with Wilson quark action
(CP-PACS, )
- phase structure, Tc, O(4) scaling, equation of state, etc.
Smaller quark mass (Chiral limit)
Smaller lattice spacing
(continuum limit)
Finite mq
Extension to
This talk
Finite mq using Taylor expansion method
Quark number susceptibility & critical point
Fluctuation at finite mq
Heavy-quark potential in QGP medium
Heavy-quark free energy

4. Numerical Simulations
Two-flavor full QCD simulation
Lattice size:
Action: RG-improved gauge action
+ Clover improved Wilson quark action
Quark mass & Temperature (Line of constant physics)
# of Configurations: confs. ( traj.)
by Hybrid Monte Carlo algorithm
Lattice spacing (a) near Tpc
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5. 1, Heavy-quark free energy
Heavy-quark “potential” in QGP medium
Debye screening mass
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6. Heavy-quark free energy at finite T and mq
Heavy quark free energy in QGP matter
Channel dependence of heavy-quark “potential”
( 1c, 8c, 3c, 6c)
Debye screening mass at finite T
Maezawa et al.
RPD 75 (2007)
Finite density (mq≠ 0)
In Taylor expantion method,
Free energies between Q-Q, and Q-Q at mq > 0 ~
c.f.) Doring et al.
EPJ C46 (2006) 179
in p4-improved
staggered action
Debye mass and
relation to p-QCD at high T

7. Heavy-quark free energy at finite T and mq
Normalized free energy of the quark-antiquark pair
(Q-Q "potential")
Static charged quark
Polyakov loop:
Separation to each channel after Coulomb gauge fixing
Q-Q potential:
Taylor expansion

8. QQ potential at T > Tc
become weak
at mq > 0 ~
1c channel: attractive force
8c channel: repulsive force
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9. QQ potential at T > Tc
become strong
at mq > 0 ~
3c channel: attractive force
6c channel: repulsive force

10. Debye screening effect
Phenomenological potential
Screened
Coulomb form
: Casimir factor
a(T, mq) : effective running coupling
mD(T, mq) : Debye screening mass
Assuming,

11. Debye screening effect
Substituting a and mD to V(r, T, mq)
and comparing to v0(r, T), v1(r, T) … order by order of mq/T
Fitting the potentials of each channel
with ai and mD,i as free parameters.
Debye screening mass (mD,0 , mD,2 ) at finite mq
Y. xQCD2007

12. Debye screening effect
Channel dependence of mD,0(T) and mD,2(T)
These figures are the fitting results of "alpha" and "m_D".
The vertical axis is the "alpha" and "m_D" over T, and the horizontal axis is the T/Tc.
Colors express each channel, black is the singlet channel, ...
These figures show that the channel dependence of "alpha" and "m_D" disappear when the temperature increases.
This implies that at high T, potential of each channel can be written by the same parameters, "alpha" and "m_D".
Channel dependence of mD disappear at T > 2.0Tc ~
Y. xQCD 2007

13. on a lattice vs. perturbative screening mass
2-loop running coupling
Leading order thermal perturbation
Lattice screening mass is not reproduced
by the LO-type screening mass.

14. on a lattice vs. perturbative screening mass
Next-to-leading order perturbation at mq = 0
Rebhan, PRD 48 (1993) 48
Magnetic screening mass:
Quenched results
Nakamura, Saito
and Sakai (2004)
NLO-type screening mass lead to a better agreement with
the lattice screening mass.

15. 2, Fluctuation at finite mq
Quark number susceptivility
Isospin susceptivility
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16. Fluctuation at finite mq
Nf = 2, mq > 0: Crossover PT at mq = 0
Critical point at mq > 0
have been predicted
In numerical simulations
Quark number and isospin susceptibilities
At critical point:
cq has a singularity
cI has no singularity
Hatta and Stephanov,
PRL 91 (2003)
Taylor expansion of quark number susceptibility

17. Susceptibilities at mq = 0
Taylor expansion:
= 2c2
= 2c2I
= 2c2
= 2c2I
RG + Clover Wilson
Susceptibilities (fluctuation) at mq = 0 increase rapidly at Tpc
cI at T <Tpc is related to pion fluctuoation
cI at mp/mr = 0.65 is larger than 0.80

18. Susceptibilities at mq > 0 ~
Taylor expansion:
= 4!c4
= 4!c4I
= 4!c4
= 4!c4I
Dashed Line: 9cq, prediction by hadron resonance gas model
Second derivatives: Large spike for cq near Tpc.
Large enhancement in the fluctuation of baryon number
(not in isospin) around Tpc as mq increases: Critical point?

19. Comparison with Staggered quark results
Quark number (cq) and Isospin (cI) susceptibilities
p4-improved staggered quark , Bielefeld-Swqnsea Collaboration,
Phys. Rev. D71, (2005)
Similar results have been obtained with Staggered quark action
Lattice QCD suggests large fluctuation of cq at mq > 0 ~
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20. Summary 1c, 3c channel: attractive force at mq = 0
We study QCD thermodynamics in lattice simulations
with two flavors of improved Wilson quark action
Heavy-quark free energy
Fluctuation at finite mq
Heavy-quark free energy
QQ potential: become weak
QQ potential: become strong
1c, 3c channel: attractive force
8c, 6c channel: repulsive force
at mq = 0
at mq > 0 ~
Debye screening mass:
Fluctuation at finite mq
Large enhancement in the fluctuation of baryon number
around Tpc as mq increase
Indication of critical point at mq > 0 ?
Y. xQCD2007