Temperature effects for $e^-+e^+\rightarrow \mu^-+\mu^+$ scattering in very special relativity

TL;DR

This paper explores how very special relativity (VSR) modifies electron-positron scattering cross-sections at finite temperature, revealing combined effects of VSR and thermal environment, with implications for experimental parameter estimation.

Contribution

It introduces a calculation of electron-positron scattering cross-section in VSR at finite temperature using Thermo Field Dynamics, highlighting the combined impact of VSR and thermal effects.

Findings

Cross-section is affected by VSR modifications.

Temperature influences scattering cross-section.

Estimated VSR parameter from experimental data.

Abstract

The electron-positron scattering process is investigated in the context of very special relativity (VSR). This theory assumes that the true symmetry of nature is not the full Lorentz group, but some of its subgroups, such as the subgroups $SIM(2)$ and $HOM(2)$. In this context, the cross-section for electron-positron scattering at finite temperature is calculated. The effects of temperature are introduced using the Thermo Field Dynamics (TFD) formalism. Our result shows that the cross-section is changed due to both effects, the VSR contributions and temperature effects. An estimated value for the VSR parameter using experimental data available in the literature is discussed.