Thermodynamics%20of%20QCD%20in%20lattice%20simulation%20with%20improved%20Wilson%20quark%20action%20at%20finite%20temperature%20and%20density

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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) 074501 and J.
Phys. G 34 (2007) S651
xQCD _at_ INFN, Aug. 6-8, 2007
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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 T0 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
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Introduction
Previous studies at T ? 0 , mq 0 with Wilson
quark action
(CP-PACS,
1999-2001) - phase structure, Tc, O(4) scaling,
equation of state, etc.
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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 500-600 confs. (5000-6000
  traj.)
• by
  Hybrid Monte Carlo algorithm
• Lattice spacing (a) near Tpc

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1, Heavy-quark free energy

• Heavy-quark potential in QGP medium
• Debye screening mass

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Heavy-quark free energy at finite T and mq

• Heavy quark free energy in QGP matter

Maezawa et al. RPD 75 (2007) 074501
Finite density (mq? 0)
In Taylor expantion method,
c.f.) Doring et al. EPJ C46 (2006) 179 in
p4-improved staggered action
Debye mass and relation to p-QCD at
high T
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Heavy-quark free energy at finite T and mq

• Normalized free energy of the quark-antiquark
  pair
• 
  (Q-Q "potential")

Static charged quark

• Separation to each channel after Coulomb gauge
  fixing

• Taylor expansion

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QQ potential at T gt Tc
1c channel attractive force 8c channel
repulsive force
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QQ potential at T gt Tc
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Debye screening effect
Phenomenological potential
Screened Coulomb form
a(T, mq) effective running coupling mD(T, mq)
Debye screening mass
Assuming,
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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
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Debye screening effect
Channel dependence of mD,0(T) and mD,2(T)

• Channel dependence of mD disappear at T gt 2.0Tc

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• 2-loop running coupling

• Leading order thermal perturbation

Lattice screening mass is not reproduced by the
LO-type screening mass.
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• Next-to-leading order perturbation at mq 0

Rebhan, PRD 48 (1993) 48
Quenched results Nakamura, Saito and Sakai (2004)
NLO-type screening mass lead to a better
agreement with the lattice screening mass.
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2, Fluctuation at finite mq

• Quark number susceptivility
• Isospin susceptivility

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Fluctuation at finite mq
Nf 2, mq gt 0 Crossover PT at mq 0
Critical point at mq gt 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) 102003
Taylor expansion of quark number susceptibility
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Susceptibilities at mq 0
2c2 2c2I
2c2 2c2I
RG Clover Wilson

• Susceptibilities (fluctuation) at mq 0
  increase rapidly at Tpc
• cI at T ltTpc is related to pion fluctuoation

cI at mp/mr 0.65 is larger than 0.80
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Susceptibilities at mq gt 0

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?
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Comparison with Staggered quark results
Quark number (cq) and Isospin (cI)
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 cq at
mq gt 0

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Summary
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