# One-loop correction to the photon velocity in Lorentz-violating QED

## TL;DR

This paper computes the one-loop momentum-dependent correction to photon velocity in Lorentz-violating QED, revealing how Lorentz violation affects photon dispersion and constraining parameters from observational data.

## Contribution

It provides a nonperturbative calculation of the photon polarization operator in Lorentz-violating QED and derives the modified photon dispersion relation at all orders.

## Key findings

- Photon group velocity is corrected by one-loop effects.
- Constraints on Lorentz-violating parameters from photon timing data.
- Finite, momentum-dependent correction to photon dispersion relation.

## Abstract

We calculate a finite momentum-dependent part of the photon polarization operator in a simple model of Lorentz-violating quantum electrodynamics nonperturbatively at all orders of Lorentz-violating parameters. We sum one-particle reducible diagrams into the modified photon propagator, and determine the physical photon dispersion relation as the location of its pole. The photon dispersion relation, as well as its group velocity, acquires the one-loop momentum-dependent radiative correction. We constrain the Lorentz-violating parameters for heavy charged fermions (muon, $\tau$-lepton, top-quark) from the photon timing observations.