# Photon splitting constraint on Lorentz Invariance Violation from Crab Nebula spectrum

## TL;DR

This paper derives a new, more stringent constraint on Lorentz invariance violation by analyzing photon splitting effects in the Crab Nebula spectrum, impacting high-energy astrophysics theories.

## Contribution

It calculates photon splitting decay width in Lorentz-violating QED and uses astrophysical data to set the tightest bounds yet on Lorentz violation for photons.

## Key findings

- Established a 95% CL bound on Lorentz violating photon mass scale.
- Improved previous constraints by over an order of magnitude.
- Demonstrated astrophysical spectra can probe fundamental physics.

## Abstract

We calculate the decay width of the photon splitting into three photons in a model of quantum electrodynamics with broken Lorentz invariance. We show that this process can lead to a cut-off in the very-high-energy part of a photon spectra of astrophysical sources. We obtain the 95\% CL bound on the Lorentz violating mass scale for photons from the analysis of the very-high-energy part of the Crab Nebula spectrum, obtained by HEGRA. This bound improves previous constraints by more than an order of magnitude.