Cool quark matter with perturbative quark masses

Abstract

In perturbative thermal calculations, introducing nonzero quark masses causes considerable complications. In this article we describe an approximation scheme valid for sufficiently light masses which significantly simplifies the relevant calculations with only a small loss in accuracy. We apply the scheme to Quantum Chromodynamics, with two massless and one massive flavor, obtaining analytic results which are in excellent agreement with numerical non-approximated results. Our results are accurate to $O(g^5)$ in the strong coupling parameter $g$, as long as either the chemical potential $\mu$ of the quark species with nonzero mass $m$ satisfies $m = O(g \mu)$ or if the temperature $T$ satisfies $m = O(g T)$. We find that these conditions are always satisfied for the three lightest quarks for the values of $\mu$, $T$ where Quantum Chromodynamics is perturbatively convergent.