Vacuum polarization in Yang-Mills theories with Lorentz violation

The renormalizable extension of a pure Yang-Mills theory with Lorentz violation is characterized by the CPT-Even $(k_F)_{\mu \nu \lambda \rho}$ and the CPT-Odd $(k_{AF})_\mu$ constant Lorentz coefficients. In this paper, the one-loop structure of the theory up to second order in these Lorentz violating coefficients is studied using the BFM-gauge. Results for the diverse beta functions are derived and contrasted with those given in the literature at first order in these parameters. Special emphasis is putted on the beta function $\beta(g)$, which is studied in both mass-independent and mass-dependent renormalization schemes. It is found that in a mass-independent scheme the $(k_{AF})_\mu$ Lorentz coefficient does not contribute to the $\beta(g)$ function, but it does in a mass-dependent scheme with contributions that are gauge-dependent and IR divergent.