Fermion mass at next-to-leading order in the hard thermal loop effective theory

Abstract

The calculation of the real part of a quasiparticle 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 quasiparticle dispersion relation in the literature [H. Schulz, Nucl. Phys. B413, 353 (1994)]. In this paper, we calculate the fermion mass in QED and QCD at next-to-leading order. For QED the result is $M=eT/\sqrt{8}(1-(1.427\pm 0.02)e/4\pi )$ and for QCD with $N_f=2$ and $N_c=3$ we obtain $M=gT/\sqrt{6}(1+(1.867\pm 0.02)g/4\pi )$.