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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Yu Maezawa (Univ. of Tokyo) In collaboration with

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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


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

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


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 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

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

  • Tc from r-meson mass mr

  • Tc from Sommer scale r0


Pade-type ansatz

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.


Wilson quark

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

Quark number susceptibility

Isospin susceptibility


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 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


Taylor expansion:

= 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 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


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

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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