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

We present the results of a first study of the equation of state in finite-temperature QCD with two flavors of Wilson-type quarks. The simulations are made on lattices with a temporal size $N_t=4\mathrm{}$ and 6, using a renormalization-group-improved action for the gluon sector and a mean-field-improved clover action for the quark sector. The lines of constant physics corresponding to fixed values of the ratio $m_{\mathrm{PS}}{/m}_{\mathrm{V}}$ of the pseudoscalar 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 $m_{\mathrm{PS}}{/m}_{\mathrm{V}}=0.65\mathrm{}–\mathrm{0.95.}$ The quark mass dependence in the equation of state is found to be small for $m_{\mathrm{PS}}{/m}_{\mathrm{V}}\lesssim \mathrm{0.8.}$ A comparison of the results for $N_t=4\mathrm{}$ and $N_t=6\mathrm{}$ lattices shows a significant scaling violation present in the $N_t=4\mathrm{}$ results. At high temperatures the results for $N_t=6\mathrm{}$ are quite close to the continuum Stefan-Boltzmann limit, suggesting the possibility of a precise continuum extrapolation of thermodynamic quantities from simulations at $N_t\gtrsim 6.$