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### 1, Critical temperature

### 3, Heavy quark free energy and Debye screening mass in QGP medium

Thermodynamics of two-flavor lattice QCD with an improved Wilson quark action at non-zero temperature and density

Yu Maezawa (Univ. of Tokyo)

In collaboration with

S. Aoki, K. Kanaya, N. Ishii, N Ukita (Univ. of Tsukuba)

T. Hatsuda (Univ. of Tokyo)

S. Ejiri (BNL)

WHOT-QCD Collaboration

1. Set the lattice spacing and quark mass precisely

2. Understand uncertainties from lattice formulations

Accurate calculation of physical quantities at T = 0

Comparison between different fermion formulations is necessary.

e.g. Wilson quark action and Staggered quark action

IntroductionTo remove theoretical uncertainties in heavy-ion experiments,

First principle calculations by Lattice QCD at finite (T, m): important

- Many interesting results have been obtained,
- e.g. critical temperature, phase structure, equation of state, heavy quark free energies, Debye mass ...

Two key issues for precision lattice study

Extension to

- Smaller quark mass (Chiral limit)
- Smaller lattice spacing (continuum limit)
- Finite m

Poster session by Y. Maezawa

Why QCD thermodynamics with Wilson quark action?1, A well-improved lattice action available:

Basic properties at T = 0 well-investigated

Iwasaki (RG) improved gauge action+ Clover improved Wilson action

Systematic studies have been done by CP-PACS Collaboration (1996~).

Large stock of data at T = 0

2, Most of studies at T0 have been done using Staggered-type quark actions.

Studies by a Wilson-type quark action are necessary.

Previous studies at T0, mq=0 with this action (1999-2001) : phase structure, Tc, O(4) scaling, equation of state, etc.

Three topics covered in this talk

- Critical temperature Tc
- Fluctuations at mq> 0 (Quark number susceptibility)
- Heavy quark free energies and Debye mass in QGP medium

Simulation details

Two-flavor full QCD simulation

- Critical temperature
- Lattice size: Ns3 x Nt = 163 x 4 and 163 x 6, mp/mr = 0.5 ~ 0.98
- Quark number susceptibilities (fluctuations)
- Lattice size: Ns3 x Nt = 163 x 4, mp/mr = 0.8, T/Tpc = 0.76 ~ 2.5
- Heavy quark free energies and Debye mass
- Lattice size: Ns3 x Nt = 163 x 4, mp/mr = 0.65, 0.8, T/Tpc = 1.0 ~ 4.0

- Lattice spacing (a) near Tc.
- Scale setting: r meson mass (mr)

e.g.

- Tc from r-meson mass mr
- Tc from Sommer scale r0

Pade-type ansatz

Quench limit Chiral limit

Critical temperature from Polyakov loop susceptibilityChiral extrapolation

Tc

Tpc/mr

- Ambiguity by the fit ansatz:for the case , Tc becomes 4 MeV higher.
- Further simulations with smaller mass are in progress.

Wilson quark

Staggered quark

Comparison with staggered quark resultsTc in Sommer scale unit

- RBC-Bielefeld, hep-lat/0608013
- p4-improved staggered quark action

Ambiguity of Sommer scale (r0): 10% difference

- r0 = 0.469(7) fm : A. Gray et al., Phys. Rev. D72, 094507 (2005)
- Asqtad improved staggered quark action + Symanzik improved gauge action
- r0 = 0.516(21) fm : CP-PACS & JLQCD, hep-lat/0610050
- Clover improved Wilson quark action + Iwasaki improved gauge action

Studies at T = 0 are also very important for the determination of Tc.

Both results seem to approach the same line in the continuum limit (large Nt).

Fluctuations at finite m

- cq has a singularity
- cI has no singularity

At critical point:

Confirmation by a Wilson-type quark action

Critical point at m0

Event by event fluctuations in heavy ion collisions

In numerical simulations

Quark number and isospin susceptibilities

Hatta and Stephanov, PRL 91 (2003) 102003

Bielefeld-Swansea Collab. (2003) using improved staggered quark action,

Enhancement in the fluctuation of quark number at mq > 0 near Tc

by Taylor expansion method

Taylor expansion:

= 4!c4

= 4!c4I

= 2c2

= 2c2I

~

Susceptibilities at m > 0Dashed Line: 9cq, prediction by hadron resonance gas model

RG + Clover Wilson

(mp/mr=0.8, mq=0)

- Susceptibilities (fluctuation) at mq=0 increase rapidly at Tpc
- Second derivatives: Large spike for cqnear Tpc.

Large enhancement in the fluctuation of baryon number (not in isospin) around Tpc as mq increases: Critical point?

Comparison with Staggered quark results

Quark number (cq) and Isospin (cI) susceptibilities

p4-improved staggered quark , Bielefeld-Swqnsea Collab., Phys. Rev. D71, 054508 (2005)

- Similar to the results of Staggered-type quarks

Today's poster session by Y. Maezawa

Debye screening mass from Polyakov loop correlation

- Leading order thermal perturbation

NLO

LO

- Lattice screening mass is not reproduced by LO-type screening mass.
- Contribution of NLO-typecorrects the LO-type screening mass.

Summary

- We report the current status of our study of QCD thermodynamics lattice simulation with Wilson-type quark action.

Critical temperature

Chiral extrapolation with Nt=4, 6

Simulation with smaller mass and lattice spacing are in progress

Fluctuation and quark number susceptibility at finite mq

Large enhancement in the fluctuation of baryon number around Tpc as m increase

Indication of critical point at m > 0?

Heavy quark free energies and Debye mass in QGP

(Poster session of Y. Maezawa)

- LO-type perturbation is not enough to reproduce the lattice Debye mass.

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