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

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

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

Heavy-Quark Free Energy, Debye Mass, and Spatial String Tension at Finite Temperature in Two Flavor Lattice QCD with Wilson Quark Action

We study Polyakov loop correlations and spatial Wilson loop at finite Temperature in two-flavor QCD simulations with the RG-improved gluon action and the clover-improved Wilson quark action on a $16^3 \times 4$ lattice. From the line of constant physics at $m_{\rm PS}/m_{\rm V}=0.65$ and 0.80, we extract the heavy-quark 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 at high temperature. 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 in terms of $g_{\rm eff}(T)$. We make a comparison between our results with the Wilson quark action and the previous results with the staggered quark action. The spatial string tension is also studied in the high temperature phase and is compared to the next-to-next-leading order prediction in an effective theory with dimensional reduction.Comment: 25 pages, 37 EPS figure

DIRECTION OF ISOMETRIC BALLISTIC FORCE IS RELATED TO ANTAGONISTIC MUSCULE DISCHARGE

The purpose of this study was to investigate the relationship between electromyographic (EMG) activities of human thigh muscles (vastus medialis, vastus lateralis, rectus femoris, biceps femoris and semitendinosus) and the direction of knee extension force during ramp and ballistic contractions. Four subjects exerted isometric knee extension forces at a target force level of 40% of maximum voluntary contraction (MVC) at various speeds. Variations of EMG amplitudes of all thigh muscles during ballistic contraction were much larger than those during ramp contractions. Only biceps femoris was related to the direction of force. These results suggest that EMG activity of biceps femoris muscle is an important factor for deciding direction of isometric ballistic knee extension force

Heavy-quark free energy at finite temperature with 2+1 flavors of improved Wilson quarks in fixed scale approach

The free energy between a static quark and an antiquark is studied by using the color-singlet Polyakov-line correlation at finite temperature. We perform simulations on $32^3 \times 12$, 10, 8, 6, 4 lattices in the high temperature phase with the RG-improved gluon action and 2+1 flavors of the clover-improved Wilson quark action. Since the simulations are based on the fixed scale approach that the temperature can be varied without changing the spatial volume and renormalization factor, it is possible to investigate temperature dependence of the heavy-quark free energy without any adjustment of the overall constant. We find that, the heavy-quark free energies at short distance converge to the heavy-quark potential evaluated from the Wilson-loop operator at zero temperature, in accordance with the expected insensitivity of short distance physics to the temperature. At long distance, the heavy-quark free energies approach to twice the single-quark free energies, implying that the interaction between heavy quarks is screened. The Debye screening mass obtained from the long range behavior of the heavy-quark free energy is compared with results of the thermal perturbation theory and those of $N_f=2$ and $N_f=0$ lattice simulations.Comment: To appear in the proceedigns of 27th International Symposium on Lattice Field Theory (Lattice 2009), Beijing, China, 25-31 July 200