Quantum properties of a non-Abelian gauge invariant action with a mass parameter

We continue the study of a local, gauge invariant Yang-Mills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator $F_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent Becchi-Rouet-Stora-Tyutin (BRST) symmetry. Although our action contains extra (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories. The full theory is renormalized explicitly at two loops in the $\overline{\mathrm{MS}}$ scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.