Perturbative Analysis of CPT-Odd Lorentz-Violating Scalar QCD

TL;DR

This paper conducts a detailed one-loop renormalization analysis of CPT-odd Lorentz-violating scalar QCD, revealing divergence structures and confirming the theory's multiplicative renormalizability.

Contribution

It provides the first explicit one-loop renormalization proof for CPT-odd Lorentz-violating scalar QCD with adjoint scalars, including divergence calculations and beta functions.

Findings

Gauge sector develops Carroll-Field-Jackiw-type divergence, which can vanish in certain gauges.

Scalar sector exhibits CPT-odd single-derivative term proportional to the background vector.

Several Lorentz-violating corrections are ultraviolet finite at one loop.

Abstract

We perform a complete one-loop renormalization analysis of CPT-odd Lorentz-violating scalar quantum chromodynamics with adjoint scalar matter. Working to first order in the preferred background vector and treating the corresponding operators as perturbative insertions, we compute the ultraviolet-divergent parts of the relevant two-, three-, and four-point Green's functions for the gauge, scalar, and ghost fields. We show that the gauge sector develops the expected Carroll-Field-Jackiw-type correction, which generically turns out to be divergent in our theory, although the divergence vanishes in a certain gauge, while the scalar sector displays the corresponding CPT-odd single-derivative term proportional to the background vector. We further demonstrate that several of the Lorentz-violating corrections the three- and four-point function are ultraviolet finite. All one-loop divergences may be absorbed into counterterms already allowed by the classical Lagrangian, providing an explicit proof of the multiplicative renormalizability of the theory at this order. We also obtain the associated renormalization constants and one-loop $\beta$-functions for the gauge coupling, the Lorentz violation parameters, and the scalar self-interaction.