Effects of a CPT-even and Lorentz-violating nonminimal coupling on the electron-positron scattering

We propose a new \emph{CPT}-even and Lorentz-violating nonminimal coupling between fermions and Abelian gauge fields involving the CPT-even tensor $(K_F{)}_{\mu \nu \alpha \beta }$ of the standard model extension. We thus investigate its effects on the cross section of the electron-positron scattering by analyzing the process $e^{+}+e^{-}\to {\mu }^{+}+{\mu }^{-}$. Such a study was performed for the parity-odd and parity-even nonbirefringent components of the Lorentz-violating $(K_F{)}_{\mu \nu \alpha \beta }$ tensor. Finally, by using experimental data available in the literature, we have imposed upper bounds as tight as ${10}^{-12}(eV{)}^{-1}$ on the magnitude of the CPT-even and Lorentz-violating parameters while nonminimally coupled.