Equation of state in 2+1 flavor QCD with improved Wilson quarks by the fixed scale approach

We study the equation of state in 2+1 flavor QCD with nonperturbatively improved Wilson quarks coupled with the RG-improved Iwasaki glue. We apply the $T$-integration method to nonperturbatively calculate the equation of state by the fixed-scale approach. With the fixed-scale approach, we can purely vary the temperature on a line of constant physics without changing the system size and renormalization constants. Unlike the conventional fixed-$N_t$ approach, it is easy to keep scaling violations small at low temperature in the fixed scale approach. We study 2+1 flavor QCD at light quark mass corresponding to $m_\pi/m_\rho \simeq 0.63$, while the strange quark mass is chosen around the physical point. Although the light quark masses are heavier than the physical values yet, our equation of state is roughly consistent with recent results with highly improved staggered quarks at large $N_t$.Comment: 14 pages, 12 figures, v2: Table I and Figure 3 are corrected, reference updated. Main discussions and conclusions are unchanged, v3: version to appear in PRD, v4: reference adde

Three-dimensional physics and the pressure of hot QCD

We update Monte Carlo simulations of the three-dimensional SU(3) + adjoint Higgs theory, by extrapolating carefully to the infinite volume and continuum limits, in order to estimate the contribution of the infrared modes to the pressure of hot QCD. The sum of infrared contributions beyond the known 4-loop order turns out to be a smooth function, of a reasonable magnitude and specific sign. Unfortunately, adding this function to the known 4-loop terms does not improve the match to four-dimensional lattice data, in spite of the fact that other quantities, such as correlation lengths, spatial string tension, or quark number susceptibilities, work well within the same setup. We outline possible ways to reduce the mismatch.Comment: 14 page

Finite temperature phase transition of two-flavor QCD with an improved Wilson quark action

We study the phase structure of QCD at finite temperatures with two flavors of dynamical quarks on a lattice with the size $N_s^3 \times N_t=16^3 \times 4$, using a renormalization group improved gauge action and a clover improved Wilson quark action. The simulations are made along the lines of constant physics determined in terms of $m_{\rm PS}/m_{\rm V}$ at zero-temperature. We show preliminary results for the spatial string tension in the high temperature phase.Comment: 7 pages, 7 figures, talk presented at Lattice 2006 (high temperature and density

Static quark free energies at finite temperature with two flavors of improved Wilson quarks

Polyakov loop correlations at finite temperature in two-flavor QCD are studied in lattice simulations with the RG-improved gluon action and the clover-improved Wilson quark action. From the simulations on a $16^3 \times 4$ lattice, we extract the free energies, the effective running coupling $g_{\rm eff}(T)$ and the Debye screening mass $m_D(T)$ for various color channels of heavy quark--quark and quark--anti-quark pairs above the critical temperature. The free energies are well approximated by the screened Coulomb form with the appropriate Casimir factors. The magnitude and the temperature dependence of the Debye mass are compared to those of the next-to-leading order thermal perturbation theory and to a phenomenological formula given in terms of $g_{\rm eff}(T)$. Also we made a comparison between our results with the Wilson quark and those with the staggered quark previously reported.Comment: 7 pages, 9 figures, talk given at Lattice 2006 (high temperature and density

Application of fixed scale approach to static quark free energies in quenched and 2+1 flavor lattice QCD with improved Wilson quark action

Free energies between static quarks and Debye screening masses in the quark-gluon plasma are studied on the basis of Polyakov-line correlations in lattice simulations of 2+1 flavors QCD with the renormalization-group improved gluon action and the $O(a)$-improved Wilson quark action. We perform simulations at $m_{\rm PS}/m_{\rm V} = 0.63$ (0.74) for light (strange) flavors with lattice sizes of $32^3 \times N_t$ with $N_t=4$--12. We adopt the fixed-scale approach, where temperature can be varied without changing the spatial volume and renormalization factor. We find that, at short distance, the free energies of static quarks in color-singlet channel converge to the static-quark potential evaluated from the Wilson-loop at zero-temperature, in accordance with the expected insensitivity of short distance physics to the temperature. At long distance, the free energies of static quarks approach to twice the single-quark free energies, implying that the interaction between static quarks is fully screened. The screening properties can be well described by the screened Coulomb form with appropriate Casimir factor at high temperature. We also discuss a limitation of the fixed-scale approach at high temperature.Comment: 16 pages, 14 figure

An effective thermodynamic potential from the instanton with Polyakov-loop contributions

We derive an effective thermodynamic potential (Omega_eff) at finite temperature (T>0) and zero quark-chemical potential (mu_R=0), using the singular-gauge instanton solution and Matsubara formula for N_c=3 and N_f=2 in the chiral limit. The momentum-dependent constituent-quark mass is also obtained as a function of T, employing the Harrington-Shepard caloron solution in the large-N_c limit. In addition, we take into account the imaginary quark chemical potential mu_I = A_4, translated as the traced Polayakov-loop (Phi) as an order parameter for the Z(N_c) symmsetry, characterizing the confinement (intact) and deconfinement (spontaneously broken) phases. As a result, we observe the crossover of the chiral (chi) order parameter sigma^2 and Phi. It also turns out that the critical temperature for the deconfinment phase transition, T^Z_c is lowered by about (5-10)% in comparison to the case with a constant constituent-quark mass. This behavior can be understood by considerable effects from the partial chiral restoration and nontrivial QCD vacuum on Phi. Numerical calculations show that the crossover transitions occur at (T^chi_c,T^Z_c) ~ (216,227) MeV.Comment: 15 pages, 7 figure

Thermodynamics and heavy-quark free energies at finite temperature and density with two flavors of improved Wilson quarks

Thermodynamics of two-flavor QCD at finite temperature and density is studied on a $16^3 \times 4$ lattice, using a renormalization group improved gauge action and the clover improved Wilson quark action. In the simulations along lines of constant $m_{\rm PS}/m_{\rm V}$, we calculate the Taylor expansion coefficients of the heavy-quark free energy with respect to the quark chemical potential ($\mu_q$) up to the second order. By comparing the expansion coefficients of the free energies between quark($Q$)and antiquark($\bar{Q}$), and between $Q$ and $Q$, we find a characteristic difference at finite $\mu_q$ due to the first order coefficient of the Taylor expansion. We also calculate the quark number and isospin susceptibilities, and find that the second order coefficient of the quark number susceptibility shows enhancement around the pseudo-critical temperature.Comment: Talk given at the XXV International Symposium on Lattice Field Theory (Lattice 2007), July 30 - August 4, 2007, Regensburg, German

Fixed Scale Approach to Equation of State in Lattice QCD

A new approach to study the equation of state in finite-temperature QCD is proposed on the lattice. Unlike the conventional method in which the temporal lattice size $N_t$ is fixed, the temperature $T$ is varied by changing $N_t$ at fixed lattice scale. The pressure of the hot QCD plasma is calculated by the integration of the trace anomaly with respect to $T$ at fixed lattice scale. This "$T$-integral method" is tested in quenched QCD on isotropic and anisotropic lattices and is shown to give reliable results especially at intermediate and low temperatures.Comment: 5 pages, ReVTeX, 4 figures, version to appear in PR