Renormalizability of Yang-Mills theory with Lorentz violation and gluon mass generation

We show that pure Yang-Mills theories with Lorentz violation are renormalizable to all orders in perturbation theory. To do this, we employ the algebraic renormalization technique. Specifically, we control the breaking terms with a suitable set of external sources, which eventually attain certain physical values. The Abelian case is also analyzed as a starting point. The main result is that the renormalizability of the usual Maxwell and Yang-Mills sectors are both left unchanged. Furthermore, in contrast to Lorentz-violating QED, the CPT-odd violation sector of Yang-Mills theories renormalizes independently. Moreover, the method induces mass terms for the gauge field in a natural way, while the photon remains massless (at least in the sense of a Proca-like term). The entire analysis is carried out in the Landau gauge.