  We determine the next-to-leading order dispersion laws for slow-moving quarks
in hard-thermal-loop perturbation of high-temperature QCD where weak coupling
is assumed. Real-time formalism is used. The next-to-leading order quark
self-energy is written in terms of three and four HTL-dressed vertex functions.
The hard thermal loops contributing to these vertex functions are calculated ab
initio and expressed using the Feynman parametrization which allows the
calculation of the solid-angle integrals involved. We use a prototype of the
resulting integrals to indicate how finite results are obtained in the limit of
vanishing regularizer.
