Equation of state in 2+1 flavor QCD at high temperatures

Abstract

We calculate the Equation of State at high temperatures in 2+1 flavor QCD using the highly improved staggered quark (HISQ) action. We study the lattice spacing dependence of the pressure at high temperatures using lattices with temporal extent Nτ = 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.

Determination of the QCD coupling from the static energy and the free energy

“…For the given reasons the new result is more precise at short distances and has a better estimate of the errors. It supersedes the previous calculation [2,6].…”

“…The tunneling between different topological sectors is suppressed for these gauge ensembles. Nevertheless, no statistically significant difference has been observed for bulk observables other than the light quark condensate [2] in different topological sectors.…”

“…see Refs. [2,6] for the details. Here, and in the following E(r) denotes the QCD static energy calculated on the lattice.…”

“…We use the value r 1 = 0.3106 (17) fm determined from the pion decay constant. Since the quark mass dependence of r 1 /a is small, the m l = m s /20 and m l = m s /5 results can be combined to produce a parametrization of r 1 /a as a function of the bare lattice gauge coupling β [2]. The tunneling between different topological sectors is suppressed for these gauge ensembles.…”

“…We used one, two and five levels of HYP smearings [9] in our calculations. In the studies of the Equation of State [2,6], the static energy was extracted from two-exponential fits to the Wilson line correlators using a fixed range of Euclidean time τ /a that the mean and statistical error of the effective mass. Although, we can usually identify an unambiguous plateau in the window 7 ≤ τ /a ≤ 11, we have to restrict the fit to narrower windows in multiple cases that are similar to those shown above.…”