Yu Maezawa (Univ. of Tokyo) in collaboration with S. Aoki, K. Kanaya, N. Ishii, N. Ukita,

1. 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 @ INFN, Aug. 6-8, 2007

2. 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 T=0 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 Y. Maezawa @ xQCD2007

3. This talk Finite mqusing Taylor expansion method Extension to • Fluctuation at finite mq • Smaller quark mass (Chiral limit) • Smaller lattice spacing • (continuum limit) • Finite mq Quark number susceptibility & critical point • Heavy-quark free energy Heavy-quark potential in QGP medium 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.

4. 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 Y. Maezawa @ xQCD2007

5. 1, Heavy-quark free energy • Heavy-quark “potential” in QGP medium • Debye screening mass Y. Maezawa @ xQCD2007

6. Channel dependence of heavy-quark “potential” ( 1c, 8c, 3c, 6c) • Debye screening mass at finite T 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, Free energies between Q-Q, and Q-Q at mq> 0 ~ c.f.) Doring et al. EPJ C46 (2006) 179 in p4-improved staggered action Debye mass and relation to p-QCD at high T

7. Polyakov loop: • Q-Qpotential: • Q-Q potential: 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

8. QQ potential at T > Tc become weak at mq > 0 ~ 1c channel: attractive force 8c channel: repulsive force Y. Maezawa @ xQCD2007

9. QQ potential at T > Tc 3c channel: attractive force 6c channel: repulsive force become strong at mq > 0 ~

10. : Casimir factor Debye screening effect Phenomenological potential Screened Coulomb form a(T, mq) : effective running coupling mD(T, mq) : Debye screening mass Assuming,

11. 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 aiand mD,i as free parameters. Debye screening mass (mD,0 , mD,2 ) at finite mq Y. Maezawa @ xQCD2007

12. Debye screening effect Channel dependence of mD,0(T) and mD,2(T) • Channel dependence ofmDdisappear at T > 2.0Tc ~ Y. Maezawa @ xQCD 2007

13. on a lattice vs. perturbative screening mass • 2-loop running coupling • Leading order thermal perturbation Lattice screening mass is not reproduced by the LO-type screening mass.

14. on a lattice vs. perturbative screening mass Magnetic screening mass: • 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.

15. 2, Fluctuation at finite mq • Quark number susceptivility • Isospin susceptivility Y. Maezawa @ xQCD2007

16. Fluctuation at finite mq Nf = 2, mq > 0: Crossover PT at mq = 0 Critical point at mq > 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

17. Taylor expansion: Susceptibilities at mq = 0 = 2c2 = 2c2I = 2c2 = 2c2I RG + Clover Wilson • Susceptibilities (fluctuation) atmq = 0 increase rapidly atTpc • cIat T <Tpc is related to pion fluctuoation cI at mp/mr= 0.65 is larger than 0.80

18. Taylor expansion: Susceptibilities at mq > 0 ~ = 4!c4 = 4!c4I = 4!c4 = 4!c4I Dashed Line: 9cq, prediction by hadron resonance gas model • Second derivatives: Large spike forcqnear Tpc. Large enhancement in the fluctuation of baryon number (not in isospin) aroundTpcasmqincreases: Critical point?

19. 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 > 0 ~ Y. Maezawa @ xQCD 2007

20. Summary 1c, 3c channel: attractive force 8c, 6c channel: repulsive force at mq= 0 QQ potential: become weak QQ potential: become strong at mq> 0 ~ Debye screening mass: Fluctuation at finite mq Large enhancement in the fluctuation of baryon number around Tpc as mq increase Indication of critical point at mq > 0 ? 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 Y. Maezawa @ xQCD2007