Yu Maezawa (Univ. of Tokyo) In collaboration with

1. 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

2. 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

3. 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

4. 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.

5. 1, Critical temperature • Tc from r-meson mass mr • Tc from Sommer scale r0

6. 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.

7. 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).

8. 2, Fluctuations at finite m Quark number susceptibility Isospin susceptibility

9. 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

10. 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?

11. 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

12. 3, Heavy quark free energy and Debye screening mass in QGP medium Today's poster session by Y. Maezawa

13. 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.

14. 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.