Cool quark matter with perturbative quark masses

TL;DR

This paper introduces an approximation scheme for perturbative thermal QCD calculations involving light quark masses, simplifying computations while maintaining high accuracy, and applies it to obtain analytic results consistent with numerical data.

Contribution

The authors develop a simplified approximation method for thermal QCD with light quark masses, achieving analytic results accurate to $O(g^5)$ and validating it against numerical calculations.

Findings

Approximation scheme simplifies calculations with minimal accuracy loss.

Analytic results agree well with numerical non-approximated results.

Conditions for validity are satisfied for the three lightest quarks in relevant regimes.

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.