One-loop renormalization of QCD with Lorentz violation

The explicit one-loop renormalizability of the gluon sector of QCD with Lorentz violation is demonstrated. The result is consistent with multiplicative renormalization, as the required counterterms are consistent with a single rescaling of the Lorentz-violation parameters. In addition, the resulting beta functions indicate that the CPT-even Lorentz-violating terms increase with energy scale in opposition to the asymptotically free gauge coupling and CPT-odd terms. The calculations are performed at lowest order in the Lorentz-violating terms, as they are assumed small.