One-Loop Renormalization of QCD with Lorentz Violation

TL;DR

This paper demonstrates that QCD with Lorentz violation remains renormalizable at one-loop order, showing how Lorentz-violating parameters evolve with energy and contrasting their behavior with standard asymptotic freedom.

Contribution

It provides the first explicit proof of one-loop renormalizability of Lorentz-violating QCD and analyzes the energy dependence of Lorentz-violating parameters.

Findings

Lorentz-violating parameters increase with energy scale.

Renormalizability is maintained with consistent counter terms.

CPT-even terms grow with energy, CPT-odd terms behave differently.

Abstract

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 counter terms are consistent with a single re-scaling 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.