On calculation of cross sections in Lorentz violating theories

TL;DR

This paper presents a systematic method for calculating scattering cross sections in Lorentz-violating theories, deriving Feynman rules, and applying them to astrophysical processes like photon decay and pair production.

Contribution

It introduces a comprehensive approach to compute cross sections in Lorentz-violating theories, including derivation of Feynman rules for specific operators and their application to astrophysical phenomena.

Findings

Derived Feynman rules for Lorentz-violating operators.

Calculated photon decay and vacuum Cherenkov radiation rates.

Determined cross sections for electron-positron pair production.

Abstract

We develop a systematic approach to the calculation of scattering cross sections in theories with violation of the Lorentz invariance taking into account the whole information about the theory Lagrangian. As an illustration we derive the Feynman rules and formulas for sums over polarizations in spinor electrodynamics with Lorentz violating operators of dimensions four and six. These rules are applied to compute the probabilities of several astrophysically relevant processes. We calculate the rates of photon decay and vacuum Cherenkov radiation along with the cross sections of electron-positron pair production on background radiation and in the Coulomb field. The latter process is essential for detection of photon-induced air showers in the atmosphere.