Gauge invariant electromagnetic properties of fermions induced by CPT violation in the Standard Model Extension

TL;DR

This paper investigates how CPT-violating Lorentz-violating effects in the Standard Model Extension modify the electromagnetic vertex of fermions, revealing new structures and setting bounds on Lorentz violation through magnetic moment measurements.

Contribution

It provides a detailed one-loop analysis of CPT-violating effects on the fermion-photon vertex, including gauge invariance proof and new physics contributions at different orders of Lorentz violation.

Findings

Vertex function has additional Lorentz structures.

Gauge invariance maintained via nonrenormalizable operators.

Derived bounds on Lorentz violation from fermion magnetic moments.

Abstract

Low-energy Lorentz-invariant quantities could receive contributions from a fundamental theory producing small Lorentz-violating effects. Within the Lorentz-violating extension of quantum electrodynamics, we investigate, perturbatively, the contributions to the one-loop $ff\gamma$ vertex from the $CPT$-violating axial coupling of a vector background field to fermions. We find that the resulting vertex function has a larger set of Lorentz structures than the one characterizing the usual, Lorentz invariant, parametrization of the $ff\gamma$ vertex. We prove gauge invariance of the resulting one-loop expression through a set of gauge invariant nonrenormalizable operators introducing new-physics effects at the first and second orders in Lorentz violation, and which generate tree-level contributions to the $ff\gamma$ vertex. Whereas loop contributions involving parameters that violate Lorentz invariance at the first order are $CPT$-odd, those arising at the second order are $CPT$-even, so that contributions to low-energy physics are restricted to emerge for the first time at the second order. In this context, we derive a contribution to anomalous magnetic moment of fermions, which we use to set a bound on Lorentz violation.