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

Vacuum polarization in Yang-Mills theories with Lorentz violation