Three-loop HTL QCD thermodynamics

TL;DR

This paper applies three-loop hard-thermal-loop perturbation theory to compute quark-gluon plasma thermodynamics, achieving high-order accuracy and good agreement with lattice data at accessible temperatures.

Contribution

It advances HTL perturbation theory to three-loop order for QCD thermodynamics, the highest order feasible before infrared issues dominate.

Findings

Three-loop results match lattice data well for T ≥ 2-3 T_c.

Renormalization effectively removes divergences at this order.

The approach extends the applicability of perturbative QCD to relevant experimental temperatures.

Abstract

The hard-thermal-loop perturbation theory (HTLpt) framework is used to calculate the thermodynamic functions of a quark-gluon plasma to three-loop order. This is the highest order accessible by finite temperature perturbation theory applied to a non-Abelian gauge theory before the high-temperature infrared catastrophe. All ultraviolet divergences are eliminated by renormalization of the vacuum, the HTL mass parameters, and the strong coupling constant. After choosing a prescription for the mass parameters, the three-loop results for the pressure and trace anomaly are found to be in very good agreement with recent lattice data down to $T \sim 2-3\,T_c$, which are temperatures accessible by current and forthcoming heavy-ion collision experiments.