Comment on "Vacuum Photon Splitting in Lorentz-Violating Quantum Electrodynamics"

TL;DR

This paper critically examines claims of observable photon triple splitting in Lorentz-violating QED, clarifying that such on-shell processes are strictly forbidden at the considered order, thus challenging prior predictions.

Contribution

It refutes previous claims by demonstrating that on-shell photon triple splitting probability is zero at the examined order in Lorentz-violating QED.

Findings

On-shell photon triple splitting probability is zero at the considered order.

The analogy with collinear parametric down-conversion is misleading.

Observable photon splitting effects are not expected in the studied framework.

Abstract

It has been argued in hep-ph/0212382 that there may be observable effects from photon triple splitting in an extended version of quantum electrodynamics with Lorentz violation in the fermion sector. The argument is based on an analogy with photon splitting via collinear parametric down-conversion in optically active crystals. In this Comment, we point out that the analogy is misleading and that, at the order considered, the probability of on-shell photon triple splitting is strictly zero.