Masslessness of ghosts in equivariantly gauge-fixed Yang--Mills theories

We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang--Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang--Mills theory is needed in order to obtain this result.