Thermodynamics of two-flavor lattice QCD with an improved Wilson quark action at
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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.

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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


Introduction

1. Set the Wilson quark action at 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

Introduction

To 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


Why qcd thermodynamics with wilson quark action

Extension to Wilson quark action at

  • 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 T0 have been done using Staggered-type quark actions.

Studies by a Wilson-type quark action are necessary.

Previous studies at T0, 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
Simulation details Wilson quark action at

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.


1 critical temperature

1, Critical temperature Wilson quark action at

  • Tc from r-meson mass mr

  • Tc from Sommer scale r0


Critical temperature from polyakov loop susceptibility

Pade-type ansatz Wilson quark action at

Quench limit Chiral limit

Critical temperature from Polyakov loop susceptibility

Chiral 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.


Comparison with staggered quark results

Wilson quark Wilson quark action at

Staggered quark

Comparison with staggered quark results

Tc 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).


2 fluctuations at finite m

2, Fluctuations at finite Wilson quark action at m

Quark number susceptibility

Isospin susceptibility


Fluctuations at finite Wilson quark action at m

  • cq has a singularity

  • cI has no singularity

At critical point:

Confirmation by a Wilson-type quark action

Critical point at m0

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


Susceptibilities at m 0

Taylor expansion: Wilson quark action at

= 4!c4

= 4!c4I

= 2c2

= 2c2I

~

Susceptibilities at m > 0

Dashed 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 results1
Comparison with Staggered quark results Wilson quark action at

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


3 heavy quark free energy and debye screening mass in qgp medium

3, Heavy quark free energy Wilson quark action at and Debye screening mass in QGP medium

Today's poster session by Y. Maezawa


Debye screening mass Wilson quark action at 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 Wilson quark action at

  • 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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