Free Energies of Heavy Quarks in Full-QCD Lattice Simulations with Wilson-Type Quark Action WHOT-QCD Collaboration Yu Maezawa (RIKEN) in collaboration with S. Aoki, K. Kanaya, N. Ishii, H. Ohno (Univ. of Tsukuba) S. Ejiri (BNL) T. Hatsuda (Univ. of Tokyo) T. Umeda (YITP) QUARK MATTER2009 @ Knoxville, Mar. 31, 2009

Introduction To remove theoretical uncertainties in heavy-ion experiments First principle calculations by Lattice QCD at finite (T, m): important Purpose of WHOT-QCD Collaboration Investigation of QCD thermodynamics in lattice simulations with Wilson quark action e.g.) critical temperature, phase structure, equation of state, charmonium spectra, heavy-quark free energy, Debye mass,… Why Wilson quark action? Basic properties at T = 0 well investigated by CP-PACS&JLQCD Coll.: Iwasaki (RG) improved gauge action + Clover improved Wilson quark action Precise set of the lattice spacing and quark mass is applicable at finite T based on the fixed scale approach. talk by Kanaya on Friday Topics of this talk Heavy-quark free energy Relation of inter-quark interaction between zero and finite T Debye screening effect in QGP perturbative Debye mass and flavor dependence

Operator similar to the Wilson-loop Heavy-quark free energy To characterize an interaction b/w static quarks, T = 0 Heavy-quark potential Wilson-loop operator T > 0 Heavy-quark free energy Nadkarni (1986) Polyakov-line : static quark at x Correlation b/w Polyakov-lines projected to a color singlet channel in the Coulomb gauge Operator similar to the Wilson-loop at finite T Heavy-quark free energy may behave in QGP as: short r: F 1(r,T ) ~ V(r) (no effect from thermal medium) mid r : screened by plasma long r : two static-quark free energies w/o interactions

Approaches of lattice simulations at finite T To vary temperature on the lattice, a: lattice spacing Nt: lattice size in E-time direction Fixed Nt approach Fixed scale approach WHOT-QCD, PRD 79 (2009) 051501. talk by Kanaya on Friday Changing a (controlled by the gauge coupling (b = 6/g2)), fixing Nt Advantages: T can be varied arbitrarily, because b is an input parameter. Changing Nt , fixing a Advantages: investigation of T dependence w/o changing spatial volume possible. renormalization factor dose not change when T changes.

Results of numerical simulations Heavy-quark potential at T = 0 from Wilson-loop operator Heavy-quark free energy at T > 0 from Polyakov-line correlator Properties of Debye screening mass

Simulation details Nf = 2+1 full QCD simulations Lattice size: Ns3 x Nt = 323 x 12, 10, 8, 6, 4 Temperature: T ~ 200-700 MeV (5 points) Lattice spacing: a = 0.07 fm Light quark mass*: mp/mr = 0.6337(38) Strange quark mass*: mK/mK* = 0.7377(28) Scale setting: Sommer scale, r0 = 0.5 fm *CP-PACS & JLQCD Coll., PRD78 (2008) 011502.

Heavy-quark potential at T = 0 Data calculated by CP-PACS & JLQCD Coll. on a 283 x 58 lattice Phenomenological potential Our fit results = Coulomb term at short r + Linear term at long r + const. term

Heavy-quark free energy at T > 0 At short distance F 1(r,T ) at any T converges to V(r) = F 1(r,T=0 ). Short distance physics is insensitive to T. Note: In the fixed Nt approach, this property is used to adjust the constant term of F 1(r,T ). In our fixed scale approach, because the renormalization is common to all T. no further adjustment of the constant term is necessary. We can confirm the expected insensitivity!

Heavy-quark free energy at T > 0 At short distance F 1(r,T ) at any T converges to V(r) = F 1(r,T=0 ). Short distance physics is insensitive to T. T ~ 200 MeV: F 1 ~ V up to 0.3--0.4 fm T ~ 700 MeV: F 1 = V even at 0.1 fm Range of thermal effect is T-dependent.

Heavy-quark free energy at T > 0 2FQ evaluated from Polyakov-line operator Long distance F 1(r,T ) becomes flat and has no increase linealy. Confinement is destroyed due to a thermal medium effect. At large r, correlation b/w Polyakov-lines will disappear, F 1 converges to 2x(static quark free energy) at long distance

Derivative of heavy-quark free energy Derivative screening effect in QGP at mid distance No screening effect const. + increasing Screening effect decreasing exponentially with r Screening effect appears obviously extract the Debye mass by fitting F 1 to screened Coulomb form

Debye screening mass in QGP Temperature dependence of mD mD is proportional to T. c.f.) prediction in perturbation theory

Debye screening mass in QGP NLO LO Perturbative screening mass LO NLO Rebhan, PRD 48 (1993) 48 Lattice screening mass is not reproduced by LO-type screening mass. Contribution of NLO-type corrects the LO-type screening mass.

Debye screening mass in QGP Flavor dependence of Debye mass Nf = 2: fixed Nt ap. 163x4, mp/mr = 0.65 WHOT, PRD75 (2007) 074501 Nf = 0: fixed scale ap. 203x(26-8) WHOT, in preparation c.f.) Staggered-type quark action Tc (Nf=2) Tc (Nf=0) Magnitude of Debye mass RBC-Bielefeld collaboration Fixed Nt ap., mp ~ 220 MeV Dynamical quark effects are important for Debye mass.

Summary Dynamical quark effects are important for mD. We report the current status of our study of QCD thermodynamics. Full-QCD lattice simulations with Wilson-type quark action in fixed scale approach Heavy-quark free energy F 1(r,T ) Correlation b/w Polyakov-lines projected to the color-singlet channel in Coulomb gauge At short distance F 1 at any T converges to heavy-quark potential at T = 0 Short distance physics is insensitive to T. At long distance F 1 becomes flat and has no increase linearly. Correlation b/w Polyakov-lines disappears and F 1 converges to 2FQ Debye screening mass in QGP at mid distance mD is proportional to T well reproduced by perturbative mD in NLO. Dynamical quark effects are important for mD.