  We have shown recently that the resummation of soft photon contributions
leads to a non-exponential decay of the fermion excitations in hot QED plasmas.
The retarded propagator of a massless fermion was found to behave as $S_R(t >>
1/gT) \sim \exp{-\alpha T t [\ln(\omega_p t) + C]}$, where $\omega_p=gT/3$ is
the plasma frequency, $\alpha=g^2/4\pi$, and $C$ is a constant, independent of
$g$, which was left undefined. This term is computed in this paper. In gauges
with unphysical degrees of freedom, it is gauge-fixing independent provided an
infrared regulator is introduced in the gauge sector. We also extend our
analysis to hot QCD and express the quark and gluon propagators in the form of
three-dimensional Euclidean functional integrals which may be evaluated on the
lattice.
