NNLO hard-thermal-loop thermodynamics for QCD

TL;DR

This paper computes the thermodynamic properties of quark-gluon plasma at three-loop order using hard-thermal-loop perturbation theory, showing good agreement with lattice data for temperatures above twice the critical temperature.

Contribution

It provides a three-loop order calculation of QCD thermodynamics using HTL perturbation theory, extending previous lower-order results.

Findings

Pressure and trace anomaly match lattice data well for T ≥ 2T_c

Ultraviolet divergences are renormalized at three loops

Method applicable for general N_c and N_f

Abstract

We calculate the thermodynamic functions of a quark-gluon plasma for general N_c and N_f to three-loop order using hard-thermal-loop perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum, the HTL mass parameters, and the strong coupling constant.We show that at three loops, the results for the pressure and trace anomaly are in very good agreement with recent lattice data down to temperatures T~2T_c.