Abstract
We calculate the Equation of State at high temperatures in 2+1 flavor QCD using the highly improved staggered quark action. We study the lattice spacing dependence of the pressure at high temperatures using lattices with temporal extent $N_{\tau}=6,~8,~10$ and $12$ and perform continuum extrapolations. We also give a continuum estimate for the Equation of State up to temperatures $T=2$ GeV, which are then compared with results of the weak-coupling calculations. We find a reasonably good agreement with the weak-coupling calculations at the highest temperatures.
Highlights
Over the last several years there was a focused effort to calculate the equation of state of strongly interacting matter at net zero baryon density in lattice QCD using physical or nearly physical quark masses and improved staggered action [1,2,3,4,5,6,7,8]
We extended the previous calculation of the equation of state (EoS) with highly improved staggered quark (HISQ) action to higher temperatures
We showed that the quark mass dependence of the trace anomaly is negligible for T > 400 MeV given the statistical error
Summary
Over the last several years there was a focused effort to calculate the equation of state of strongly interacting matter at net zero baryon density in lattice QCD using physical or nearly physical quark masses and improved staggered action [1,2,3,4,5,6,7,8]. For comparison of the lattice QCD results and the weak-coupling results it is advantageous to consider thermodynamic quantities in 2 þ 1 flavor QCD at higher temperatures Such calculations provide a solid reference point for estimating the charm quark contribution to QCD thermodynamics. The understanding of the cutoff dependence of the trace anomaly at high temperature would in principle require a three-loop calculation in lattice perturbation theory. For better understanding of the cutoff dependence of the EoS at high temperatures and a better control of the continuum extrapolation it is desirable to study the cutoff dependence of the pressure directly This may help to understand the difference between the continuumextrapolated results and the results obtained with p4 or asqtad-improved staggered actions and Nτ 1⁄4 6 and 8 at high temperatures [3,4] since cutoff effects here should be small. Some technical aspects of the calculations are presented in the Appendices
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