  Perturbation theory for non-Abelian gauge theories at finite temperature is
plagued by infrared divergences caused by magnetic soft modes $\sim g^2T$,
which correspond to the fields of a 3d Yang-Mills theory. We revisit a gauge
invariant resummation scheme to solve this problem by self-consistent mass
generation using an auxiliary scalar field, improving over previous attempts in
two respects. First, we generalise earlier SU(2) treatments to SU(N). Second,
we obtain a gauge independent two-loop gap equation, correcting an error in the
literature. The resulting two-loop approximation to the magnetic mass
represents a $\sim 15%$ correction to the leading one-loop value, indicating a
reasonable convergence of the resummation.

High Energy Physics - Phenomenology;High Energy Physics - Theory