# On the photon mass in Very Special Relativity

## TL;DR

This paper investigates the implications of a non-zero photon mass within Very Special Relativity, deriving modified Maxwell equations, Feynman rules, and analyzing effects on electron self-energy and Coulomb scattering, with potential observable signals.

## Contribution

It introduces a gauge invariant photon mass in VSR, derives modified equations and rules, and analyzes its effects on scattering and radiative corrections, highlighting potential experimental signals.

## Key findings

- Photon mass leads to modifications in Maxwell equations and Feynman rules.
- Electron self-energy is computed without infrared divergences.
- A small signal of the privileged direction appears at tree level.

## Abstract

In Very Special Relativity (VSR) a gauge invariant photon mass is allowed. We explore some consequences of keeping this parameter not zero. VSR-Maxwell equations are presented. In addition, we show modifications to the Feynman rules keeping the photon mass and we apply it in the computation of the electron self energy, whose result is free from infrared divergences. A computation of the Coulomb scattering is developed and a small signal of the privileged direction predicted in the theory is present at tree level. Radiative corrections are computed and the photon mass cancels due to soft photon emission as in the standard case.