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) 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 Introduction To remove theoretical uncertainties in heavy-ion experiments, First principle calculations by Lattice QCD at finite (T,  ): important Many interesting results have been obtained, e.g. critical temperature, phase structure, equation of state, heavy quark free energies, Debye mass... 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 1. Set the lattice spacing and quark mass precisely 2. Understand uncertainties from lattice formulations 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 Comparison between different fermion formulations is necessary. e.g. Wilson quark action and Staggered quark action

3 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. 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,  q =0 with this action ( ) : phase structure, Tc, O(4) scaling, equation of state, etc. Three topics covered in this talk Smaller quark mass (Chiral limit) Smaller lattice spacing (continuum limit) Finite  Smaller quark mass (Chiral limit) Smaller lattice spacing (continuum limit) Finite  Extension to Poster session by Y. Maezawa Critical temperature T c Fluctuations at  q > 0 (Quark number susceptibility) Heavy quark free energies and Debye mass in QGP medium Critical temperature T c Fluctuations at  q > 0 (Quark number susceptibility) Heavy quark free energies and Debye mass in QGP medium

4 Lattice spacing ( a ) near T c. Scale setting:  meson mass (m  ) Lattice spacing ( a ) near T c. Scale setting:  meson mass (m  ) Simulation details Critical temperature Lattice size: Ns 3 x Nt = 16 3 x 4 and 16 3 x 6, m  /m  = 0.5 ~ 0.98 Quark number susceptibilities (fluctuations) Lattice size: Ns 3 x Nt = 16 3 x 4, m  /m  = 0.8, T/T pc = 0.76 ~ 2.5 Heavy quark free energies and Debye mass Lattice size: Ns 3 x Nt = 16 3 x 4, m  /m  = 0.65, 0.8, T/T pc = 1.0 ~ 4.0 Critical temperature Lattice size: Ns 3 x Nt = 16 3 x 4 and 16 3 x 6, m  /m  = 0.5 ~ 0.98 Quark number susceptibilities (fluctuations) Lattice size: Ns 3 x Nt = 16 3 x 4, m  /m  = 0.8, T/T pc = 0.76 ~ 2.5 Heavy quark free energies and Debye mass Lattice size: Ns 3 x Nt = 16 3 x 4, m  /m  = 0.65, 0.8, T/T pc = 1.0 ~ 4.0 e.g. Two-flavor full QCD simulation

5 1, Critical temperature T c from  -meson mass m  T c from Sommer scale r 0 T c from  -meson mass m  T c from Sommer scale r 0

6 Critical temperature from Polyakov loop susceptibility TcTc TcTc Chiral extrapolation Ambiguity by the fit ansatz: for the case, T c becomes 4 MeV higher. Further simulations with smaller mass are in progress. Ambiguity by the fit ansatz: for the case, T c becomes 4 MeV higher. Further simulations with smaller mass are in progress. Pade-type ansatz Quench limit Chiral limit T pc /m 

7 Comparison with staggered quark results Ambiguity of Sommer scale ( r 0 ): 10% difference r 0 = 0.469(7) fm : A. Gray et al., Phys. Rev. D72, (2005) Asqtad improved staggered quark action + Symanzik improved gauge action r 0 = 0.516(21) fm : CP-PACS & JLQCD, hep-lat/ Clover improved Wilson quark action + Iwasaki improved gauge action Studies at T = 0 are also very important for the determination of T c. RBC-Bielefeld, hep-lat/ p4-improved staggered quark action RBC-Bielefeld, hep-lat/ p4-improved staggered quark action Both results seem to approach the same line in the continuum limit (large Nt). T c in Sommer scale unit Wilson quark Staggered quark

8 2, Fluctuations at finite  Quark number susceptibility Isospin susceptibility

9 Fluctuations at finite  Critical point at  0 In numerical simulations Quark number and isospin susceptibilities In numerical simulations Quark number and isospin susceptibilities Bielefeld-Swansea Collab. (2003) using improved staggered quark action, Enhancement in the fluctuation of quark number at  q > 0 near T c by Taylor expansion method Bielefeld-Swansea Collab. (2003) using improved staggered quark action, Enhancement in the fluctuation of quark number at  q > 0 near T c by Taylor expansion method Confirmation by a Wilson-type quark action  q has a singularity  I has no singularity  q has a singularity  I has no singularity At critical point: Event by event fluctuations in heavy ion collisions Hatta and Stephanov, PRL 91 (2003)

10 Susceptibilities at  > 0 Susceptibilities (fluctuation) at  q =0 increase rapidly at T pc Second derivatives: Large spike for  q near T pc. Susceptibilities (fluctuation) at  q =0 increase rapidly at T pc Second derivatives: Large spike for  q near T pc. Dashed Line: 9  q, prediction by hadron resonance gas model ~ Taylor expansion: = 2c 2 = 2c 2 I = 2c 2 = 2c 2 I = 4!c 4 = 4!c 4 I = 4!c 4 = 4!c 4 I RG + Clover Wilson (m  /m  =0.8,  q =0) RG + Clover Wilson (m  /m  =0.8,  q =0) Large enhancement in the fluctuation of baryon number (not in isospin) around T pc as  q increases: Critical point?

11 Comparison with Staggered quark results Quark number (  q ) and Isospin (  I ) susceptibilities p4-improved staggered quark, Bielefeld-Swqnsea Collab., Phys. Rev. D71, (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 Lattice screening mass is not reproduced by LO-type screening mass. Contribution of NLO-type corrects the LO-type screening mass. Lattice screening mass is not reproduced by LO-type screening mass. Contribution of NLO-type corrects the LO-type screening mass. LO NLO

14 Summary We report the current status of our study of QCD thermodynamics lattice simulation with Wilson-type quark action. Critical temperature Fluctuation and quark number susceptibility at finite  q Indication of critical point at  > 0? Chiral extrapolation with Nt=4, 6 Heavy quark free energies and Debye mass in QGP LO-type perturbation is not enough to reproduce the lattice Debye mass. (Poster session of Y. Maezawa) Simulation with smaller mass and lattice spacing are in progress Large enhancement in the fluctuation of baryon number around T pc as  increase