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

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

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

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

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

Heavy-quark free energy at finite T and mq Heavy quark free energy in QGP matter Channel dependence of heavy-quark “potential” ( 1c, 8c, 3c, 6c) Debye screening mass at finite T 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

Heavy-quark free energy at finite T and mq Normalized free energy of the quark-antiquark pair (Q-Q "potential") Static charged quark Polyakov loop: Separation to each channel after Coulomb gauge fixing Q-Q potential: Taylor expansion

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

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

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

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

Debye screening effect Channel dependence of mD,0(T) and mD,2(T) These figures are the fitting results of "alpha" and "m_D". The vertical axis is the "alpha" and "m_D" over T, and the horizontal axis is the T/Tc. Colors express each channel, black is the singlet channel, ... These figures show that the channel dependence of "alpha" and "m_D" disappear when the temperature increases. This implies that at high T, potential of each channel can be written by the same parameters, "alpha" and "m_D". Channel dependence of mD disappear at T > 2.0Tc ~ Y. Maezawa @ xQCD 2007

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.

on a lattice vs. perturbative screening mass Next-to-leading order perturbation at mq = 0 Rebhan, PRD 48 (1993) 48 Magnetic screening mass: Quenched results Nakamura, Saito and Sakai (2004) NLO-type screening mass lead to a better agreement with the lattice screening mass.

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

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

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

Susceptibilities at mq > 0 ~ Taylor expansion: = 4!c4 = 4!c4I = 4!c4 = 4!c4I Dashed Line: 9cq, prediction by hadron resonance gas model Second derivatives: Large spike for cq near 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 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

Summary 1c, 3c channel: attractive force 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 QQ potential: become weak QQ potential: become strong 1c, 3c channel: attractive force 8c, 6c channel: repulsive force at mq = 0 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 ? Y. Maezawa @ xQCD2007