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The WHOT-QCD Collaboration is pushing forward a series of lattice studies of quantum chromodynamics (QCD) at finite temperatures and densities using improved Wilson quarks. Because Wilson-type quarks require more computational resources than the more widely used staggered-type quarks, various theoretical and computational techniques have to be developed and applied. In this paper, we introduce a fixed-scale approach armed with a T-integration method, a Gaussian method based on cumulant expansion, and a histogram method combined with the reweighting technique. Using these methods, we have carried out the first study of finite-density QCD with Wilson-type quarks and the first calculation of the equation of state with 2+1 flavors of Wilson-type quarks. We present the results of these studies and discuss perspectives towards clarification of the properties of 2+1 flavor QCD at the physical point at finite temperatures and densities.

We extend our previous study of the QCD phase structure in the heavy quark region to non-zero chemical potentials. To identify the critical point where the first order deconfining transition terminates, we study an effective potential defined by the probability distribution function of the plaquette and the Polyakov loop. The reweighting technique is shown to be powerful in evaluating the effective potential in a wide range of the plaquette and Polyakov loop expectation values. We adopt the cumulant expansion to overcome the sign problem in the calculation of complex phase of the quark determinant. We find that the method provides us with an intuitive and powerful way to study the phase structure. We estimate the location of the critical point at finite chemical potential in the heavy quark region., The XXIX Internaitonal Symposium on Lattice Field Theory, Lattice2011 July 11-16, 2011 The Village at Squaw Valley, US

We propose a new approach to finite density QCD based on a histogram method with phase quenched simulations at finite chemical potential. Integrating numerically the derivatives of the logarithm of the quark determinant with respect to the chemical potential, we calculate the reweighting factor and the complex phase of the quark determinant. The complex phase is handled with a cumulant expansion to avoid the sign problem. We examine the applicability of this method., The XXIX Internaitonal Symposium on Lattice Field Theory, Lattice2011 July 10-16, 2011 Squaw Lake Tahoe, California

We present a new method to calculate meson spectral functions (SPFs) on the lattice based on a variational method. Because, on a finite volume lattice, the meson SPFs have discrete spectra only, a suitable way to extract such discrete signals is needed. Using a variational method, we can calculate several discrete quantities such as the position and the area of spectral peaks for low-lying states. Moreover data accuracy can be improved by increasing the number of basis functions. In this report, we first confirm our method in the free quark case and show that our method works well. Then, we apply the method to a quenched lattice QCD simulation and calculate the charmonium SPFs for S and P-waves at zero temperature. Our results for the ground state are well consistent with the position and the area of the lowest peaks of charmonium SPFs calculated by the conventional maximum entropy method. For first excited states, the signals may be reliablly extracted with our method because the charmonium mass converges to a value close to the experimental one when the number of basis functions is increased. We also investigate the SPFs for S-wave charmonia at below and above Tc. Our results suggest that J/y and hc may survive up to 1.4Tc., The XXVIII Internaitonal Symposium on Lattice Field Theory, Lattice2010 July 14-19, 2010 Villasimius, Italy

We study the quark mass dependence of the QCD phase transition by an effective potential defined through the distribution function of observables. As a test of the method, we study the first order deconfinement phase transition in the heavy quark mass limit and its fate at lighter quark masses. We confirm that the distribution function for the plaquette has two peaks indicating that the phase transition is of first order in the heavy quark limit. We then study the quark mass dependence of the distribution function by a reweighting method combined with the hopping parameter expansion. We find that the first order transition turns into a crossover as the quark mass decreases. We determine the critical point for the cases of Nf = 1, 2, 3 and 2+1. We find that the probability distribution function provides us with a powerful tool to study the order of transitions., The XXVIII Internaitonal Symposium on Lattice Field Theory, Lattice2010 July 14-19, 2010 Villasimius, Italy

We present the status of our study on the equation of state in 2+1 flavor QCD with nonperturbatively improved Wilson quarks coupled with the RG improved glue. We apply the Tintegration method to non-perturbatively calculate the equation of state by the fixed-scale approach., The XXVIII Internaitonal Symposium on Lattice Field Theory, Lattice2010 July 14-19, 2010 Villasimius, Italy

We study scaling behavior of a chiral order parameter performing a simulation of two-flavor QCD with improved Wilson quarks. It has been shown that the scaling behavior of the chiral order parameter defined by a Ward-Takahashi identity agrees with the scaling function of the threedimensional O(4) spin model at zero chemical potential. We extend the scaling study to finite density QCD. Calculating derivatives of the chiral order parameter with respect to the chemical potential in two-flavor QCD, the scaling property of chiral phase transition is discussed in the low density region. We moreover calculate the curvature of the phase boundary of the chirl phase transition in the temperature and chemical potential plane assuming the O(4) scaling relation., The XXVIII Internaitonal Symposium on Lattice Field Theory, Lattice2010 July 14-19, 2010 Villasimius, Sardinia Italy

We report on the status of our study towards the equation of state in 2+1 flavor QCD with improvedWilson quarks. To reduce the computational cost which is quite demanding for Wilson-type quarks, we adopt the fixed scale approach, i.e. the temperature T is varied by Nt at fixed lattice spacing. Since the conventional integral method to obtain the pressure is inapplicable at a fixed scale, we adopt the T-integral method, to calculate the pressure non-perturbatively. Reduction of the computational cost of T = 0 simulations thus achieved is indispensable to study EOS in QCD with dynamical quarks., The XXVII Internaitonal Symposium on Lattice Field Theory - LAT2009 July 26-31, 2009 Peking University, Beijing, China

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 323 £12, 10, 8, 6, 4 lattices in the high temperature phase with the RG-improved gluon action and 2+1 flavors of the clover-improvedWilson 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 Nf = 2 and Nf = 0 lattice simulations., The XXVII Internaitonal Symposium on Lattice Field Theory, July 26-31, 2009 Peking University, Beijing, China

We study thermodynamics of SU(3) gauge theory at xed scales on the lattice, where we vary temperature by changing the temporal lattice size Nt =(Tat )����1. In the xed scale approach, nite temperature simulations are performed on common lattice spacings and spatial volumes. Consequently, we can isolate thermal effects in observables from other uncertainties, such as lattice artifact, renormalization factor, and spatial volume effect. Furthermore, in the EOS calculations, the xed scale approach is able to reduce computational costs for zero temperature subtraction and parameter search to nd lines of constant physics, which are demanding in full QCD simulations. As a test of the approach, we study the thermodynamics of the SU(3) gauge theory on isotropic and anisotropic lattices. In addition to the equation of state, we calculate the critical temperature and the static quark free energy at a xed scale., The XXVI Internaitonal Symposium on Lattice Field Theory July 14-19 2008 Williamsburg, Virginia, USA

Screening properties of the quark gluon plasma are studied from the Polyakov-line correlations in lattice QCD simulations with two flavors of improvedWilson quarks at temperatures T=Tpc '1–4 where Tpc is the pseudocritical temperature. Using the Euclidean-time reflection symmetry and the charge conjugation symmetry, we introduce various types of Polyakov-line correlations and extract screening masses in magnetic and electric sectors. We find that a ratio of the screening masses in the electric sector to the magnetic sector shows qualitative agreement with a prediction from the dimensionally-reduced effective field theory and theN =4 supersymmetric Yang-Mills theory at 1:3 < T=Tpc < 3., The XXVI Internaitonal Symposium on Lattice Field Theory July 14-19 2008 Williamsburg, Virginia, USA

We study the equation of state in two-flavor QCD at finite temperature and density. Simulations are made with the RG-improved gluon action and the clover-improved Wilson quark action. Along the lines of constant physics for mPS/mV = 0.65 and 0.80, we compute the derivatives of the quark determinant with respect to the quark chemical potential μq up to the fourth order at μq = 0. We adopt several improvement techniques in the evaluation. We study thermodynamic quantities and quark number susceptibilities at finite μq using these derivatives. We find enhancement of the quark number susceptibility at finite μq, in accordance with previous observations using staggered-type quarks. This suggests the existence of a nearby critical point., The XXVI Internaitonal Symposium on Lattice Field Theory July 14-19 2008 Williamsburg, Virginia, USA

The reweighting method is widely used in numerical studies of QCD, in particular, for the cases in which the conventional Monte-Carlo method cannot be applied directly, e.g., finite density QCD. However, the application range of the reweighing method is restricted due to several problems. One of the most severe problems here is the overlap problem. To solve it, we examine a multipoint reweighting method in which simulations at several simulation points are combined in the data analyses. We systematically study the applicability and limitation of the multipoint reweighting method in two-flavor QCD at zero density. Measuring histograms of physical quantities at a series of simulation points, we apply the multipoint reweighting method to calculate the meson masses as continuous functions of the gauge coupling $\beta$ and the hopping parameters $\kappa$. We then determine lines of constant physics and beta functions, which are needed in a calculation of the equation of state at finite temperature., Comment: 16 pages, 25 figures. arXiv admin note: text overlap with arXiv:1501.06331

We study the quark mass dependence of the finite temperature QCD phase transition in the heavy quark region using an effective potential defined through the probability distribution function of the average plaquette. Performing a simulation of SU(3) pure gauge theory, we first confirm that the distribution function has two peaks indicating that the phase transition is of first order in the heavy quark limit, while the first order transition turns into a crossover as the quark mass decreases from infinity, where the mass dependence of the distribution function is evaluated by the reweighting method combined with the hopping parameter expansion. We determine the endpoint of the first order transition region for N_f=1, 2, 3 and 2+1 cases. The quark mass dependence of the latent heat is also evaluated in the first order transition region., Comment: 13 pages, 17 figures, 3 tables

We study the equation of state in 2+1 flavor QCD with nonperturbatively improved Wilson quarks coupled with the renormalization group-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-Nt 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 mπ/mρ≃0.63, while the strange quark mass is chosen around the physical point. Although the light quark masses are still heavier than the physical values, our equation of state is roughly consistent with recent results with highly improved staggered quarks at large Nt.

We propose a method to evaluate spectral functions on the lattice based on a variational method. On a lattice with a finite spatial extent, spectral functions consist of discrete spectra only. Adopting a variational method, we calculate the locations and the heights of spectral functions at low-lying discrete spectra. We first test the method in the case of analytically solvable free Wilson quarks at zero and finite temperatures and confirm that the method well reproduces the analytic results for low-lying spectra. We find that we can systematically improve the results by increasing the number of trial states. We then apply the method to calculate the charmonium spectral functions for S and P-wave states at zero-temperature in quenched QCD and compare the results with those obtained using the conventional maximum entropy method (MEM). The results for the ground state are consistent with the location and the area of the first peak in spectral functions from the MEM, while the variational method leads to a mass which is closer to the experimental value for the first excited state. We also investigate the temperature dependence of the spectral functions for S-wave states below and above $T_c$. We obtain no clear evidences for dissociation of $J/\psi$ and $\eta_c$ up to 1.4$T_c$., Comment: 13 pages, 23 figures

Screenings of the quark-gluon plasma in electric and magnetic sectors are studied on the basis of generalized Polyakov-line correlation functions in lattice QCD simulations with two flavors of improved Wilson quarks. Using the Euclidean-time reflection (R) and the charge conjugation (C), electric and magnetic screening masses are extracted in a gauge-invariant manner. Long distance behavior of the standard Polyakov-line correlation in the quark-gluon plasma is found to be dictated by the magnetic screening. Also, the ratio of the two screening masses agrees with that obtained from the dimensionally-reduced effective field theory and the N=4 supersymmetric Yang-Mills theory.

Dissociation of charmonia in hot QCD is studied on a quenched anisotropic lattice using standard plaquette gauge action and O(a) improved Wilson fermion action. Simulations are carried out at temperatures in the range 0.88 TC to 2.3 TC. We calculate effective masses and Bethe–Salpeter wavefunctions for the ground state (1S, 1P) and some excited states (2S, 2P) with variational analysis. To distinguish between bound states and scattering states, we apply two methods: first, we compare effective masses for charmonium correlation functions under different spatial boundary conditions. Because the scattering states are sensitive to the boundary conditions, finite volume effects are expected when a charmonium dissociates. Second, we study if the wavefunctions show a sign of scattering states which will be characterized by a broad wavefunction. We find no clear evidence of dissociation for the charmonium states up to 2.3 TC so far.