The fermion mass at next-to-leading order in the HTL effective theory

TL;DR

This paper computes the fermion mass at next-to-leading order in the hard thermal loop effective theory for QED and QCD, addressing a complex problem with limited prior results, and provides explicit formulas with numerical corrections.

Contribution

It presents the first detailed calculation of the fermion mass at next-to-leading order in the HTL effective theory for both QED and QCD.

Findings

QED fermion mass: M=eT/√8 * [1-(1.427 ± 0.02)e/4π]

QCD fermion mass: M=gT/√6 * [1+(1.867 ± 0.02)g/4π]

Addresses a longstanding gap in HTL theory calculations.

Abstract

The calculation of the real part of a quasi-particle dispersion relation at next-to-leading order in the hard thermal loop effective theory is a very difficult problem. Even though the hard thermal loop effective theory is almost 20 years old, there is only one next-to-leading order calculation of the real part of a quasi-particle dispersion relation in the literature. In this paper, we calculate the fermion mass in QED and QCD at next-to-leading order. For QED the result is M=eT/sqrt{8} * [1-(1.427 \pm 0.02)e/4pi] and for QCD with N_f=2 and N_c=3 we obtain M=gT/sqrt{6} * [1+(1.867 \pm 0.02)g/4pi].