Equation of state in finite-temperature QCD with two flavors of improved Wilson quarks

TL;DR

This study computes the finite-temperature equation of state for QCD with two dynamical Wilson quarks using an RG-improved gluon action and a clover-improved Wilson quark action on lattices with $N_t=4$ and 6. By fixing lines of constant physics via the zero-temperature mass ratio $m_{PS}/m_V$ and determining the associated beta functions, the authors evaluate the pressure and energy density through the integral method along these lines, revealing a weak quark-mass dependence for $m_{PS}/m_V \lesssim 0.8$ and significant lattice artifacts at $N_t=4$ that are reduced at $N_t=6$. The $N_t=6$ results approach the continuum Stefan-Boltzmann limit at high temperature and show EOS behavior in good qualitative agreement with staggered-quark studies, supporting the viability of precise continuum extrapolations with improved Wilson actions. The work provides beta functions for the lattice action, demonstrates path-independent EOS calculations, and outlines a path toward physically relevant, continuum EOS with Wilson-type quarks.

Abstract

We present results of a first study of equation of state in finite-temperature QCD with two flavors of Wilson-type quarks. Simulations are made on lattices with temporal size $N_t=4$ and 6, using an RG-improved action for the gluon sector and a meanfield-improved clover action for the quark sector. The lines of constant physics corresponding to fixed values of the ratio $m_{\rm PS}/m_{\rm V}$ of the pseudo-scalar to vector meson masses at zero temperature are determined, and the beta functions which describe the renormalization-group flow along these lines are calculated. Using these results, the energy density and the pressure are calculated as functions of temperature along the lines of constant physics in the range $m_{\rm PS}/m_{\rm V} = 0.65$--0.95. The quark mass dependence in the equation of state is found to be small for $m_{\rm PS}/m_{\rm V} \simlt 0.8$. Comparison of results for $N_t=4$ and $N_t=6$ lattices show significant scaling violation present in the $N_t=4$ results. At high temperatures the results for $N_t=6$ are quite close to the continuum Stefan-Boltzmann limit, suggesting the possibility of a precise continuum extrapolation of thermodynamic quantities from simulations at $N_t\simgt 6$.

Figures (27)

• Figure 1: Pseudoscalar meson mass squared as a function of $1/K$. Filled symbols are obtained on a $16^4$ lattice. Open symbols are from Ref. CPPACSmq.
• Figure 2: Same as Fig. \ref{['fig:mpi2']}, but for vector meson mass.
• Figure 3: Phase diagram and simulation points on $16^3 \times 4$, $16^3 \times 6$ and $16^4$ lattices.
• Figure 4: Polyakov loop obtained on a $16^3 \times 6$ lattice.
• Figure 5: Polyakov loop susceptibility obtained on a $16^3 \times 6$ lattice.