The equation of state in (2+1)-flavor QCD

TL;DR

This paper calculates the equation of state for (2+1)-flavor QCD across a range of temperatures, providing continuum-extrapolated thermodynamic quantities and an analytic pressure parameterization for phenomenological applications.

Contribution

It offers the first continuum-extrapolated results for thermodynamic quantities in (2+1)-flavor QCD using highly improved staggered quarks and provides an analytic pressure parameterization.

Findings

Thermodynamic quantities reliably extrapolated to continuum limit.

Energy density in the crossover region quantified.

Comparison with perturbation theory at high temperatures.

Abstract

We present results for the equation of state in (2+1)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent $N_{\tau}=6,~8,~10$, and $12$. We show that these data can be reliably extrapolated to the continuum limit and obtain a number of thermodynamic quantities and the speed of sound in the temperature range $(130-400)$ MeV. We compare our results with previous calculations, and provide an analytic parameterization of the pressure, from which other thermodynamic quantities can be calculated, for use in phenomenology. We show that the energy density in the crossover region, $145~ {\rm MeV} \leq T \leq 163$ MeV, defined by the chiral transition, is $\epsilon_c=(0.18-0.5)~{\rm GeV}/{\rm fm}^3$, $i.e.$, $(1.2-3.1)\ \epsilon_{\rm nuclear}$. At high temperatures, we compare our results with resummed and dimensionally reduced perturbation theory calculations. As a byproduct of our analyses, we obtain the values of the scale parameters $r_0$ from the static quark potential and $w_0$ from the gradient flow.