A brief overview of hard-thermal-loop perturbation theory

TL;DR

This paper reviews the development of hard-thermal-loop perturbation theory (HTLpt) as a method to improve the convergence of thermal QCD calculations, demonstrating its effectiveness through thermodynamic computations up to three-loop order.

Contribution

It introduces HTLpt as a systematic resummation scheme for thermal QCD, showing its application to various theories and its potential for accurate calculations at LHC temperatures.

Findings

HTLpt improves convergence of thermal QCD calculations.

HTLpt provides consistent results up to three-loop order.

Applicable to static and dynamic quantities at high temperatures.

Abstract

The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades. Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence. The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion, and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic calculations for QED, pure-glue QCD, and QCD with N_f=3 up to three-loop order. The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.