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 background field method 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 put 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.

Automated summary

This paper studies the renormalizable extension of a pure Yang-Mills theory with Lorentz violation, focusing on the one-loop structure up to second order in the Lorentz violating coefficients. The beta functions are derived and compared with the first-order results given in the literature. Special attention is given to the beta function beta(g), which is studied in both mass-independent and mass-dependent renormalization schemes. It is found that the Lorentz coefficient (k(AF))(mu) contributes to the beta(g) function only in the mass-dependent scheme, with contributions that are gauge dependent and IR divergent.