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 $M=eT/\sqrt{8}(1\ensuremath{-}(1.427\ifmmode\pm\else\textpm\fi{}0.02)e/4\ensuremath{\pi})$ and for QCD with ${N}_{f}=2$ and ${N}_{c}=3$ we obtain $M=gT/\sqrt{6}(1+(1.867\ifmmode\pm\else\textpm\fi{}0.02)g/4\ensuremath{\pi})$.