# On Lorentz violation in $e^{-}\!\!+\!e^{+}\!\rightarrow\!\mu^{-}\!\!+\!\mu^{+}$ scattering at finite temperature

## TL;DR

This paper investigates potential Lorentz and CPT symmetry violations in electron-positron to muon-antimuon scattering at finite temperature, using an extended standard model with non-minimal couplings and Thermo Field Dynamics.

## Contribution

It introduces a CPT-even non-minimal coupling term into the standard model and calculates the scattering cross section at finite temperature to explore symmetry violations.

## Key findings

- Cross section calculations reveal potential Lorentz violation effects.
- Finite temperature influences the magnitude of symmetry-violating contributions.
- The study provides a framework for testing Lorentz and CPT violations in high-energy processes.

## Abstract

Small violation of Lorentz and CPT symmetries may emerge in models unifying gravity with other forces of nature. An extension of the standard model with all possible terms that violate Lorentz and CPT symmetries are included. Here a CPT-even non-minimal coupling term is added to the covariant derivative. This leads to a new interaction term that breaks the Lorentz symmetry. Our main objective is to calculate the cross section for the $e^{-}\!\!+\!e^{+}\!\rightarrow\!\mu^{-}\!\!+\!\mu^{+}$ scattering in order to investigate any violation of Lorentz and/or CPT symmetry at finite temperature. Thermo Field Dynamics formalism is used to consider finite temperature effects.