Cherenkov Radiation with Massive, CPT-violating Photons

TL;DR

This paper explores Cherenkov radiation in a modified photon theory with CPT violation and a small photon mass, addressing theoretical issues and calculating radiation rates for timelike CPT-violating backgrounds.

Contribution

It constructs a covariant polarization basis for CPT-violating photons with mass and computes Cherenkov radiation rates, extending the understanding of Lorentz- and CPT-violating electrodynamics.

Findings

Cherenkov radiation rate at high energies includes a mass-independent contribution.

A covariant polarization basis for massive CPT-violating photons is explicitly constructed.

The theory remains consistent with a tiny photon mass below experimental bounds.

Abstract

The source of CPT-violation in the photon sector of the Standard Model Extension arises from a Chern-Simons-like contribution that involves a coupling to a fixed background vector field $k_{AF}^\mu$. These Lorentz- and CPT-violating photons have well-known theoretical issues that arise from missing states at low momenta when $k_{AF}^\mu$ is timelike. In order to make the theory consistent, a tiny mass for the photon can be introduced, well below current experimental bounds. The implementation of canonical quantization can then be implemented as in the CPT-preserving case by using the St\"uckelberg mechanism. We explicitly construct a covariant basis of properly-normalized polarization vectors at fixed three-momentum satisfying the momentum space field equations, in terms of which the vector field can be expanded. As an application of the theory, we calculate the Cherenkov radiation rate for the case of purely timelike $k_{AF}^\mu$, and find a radiation rate at high energies that has a contribution that does not depend on the mass used to regulate the photons.