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

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.