Unitarity implications of ${\tilde{F}}_{\mu \nu }$ and $F_{\mu \nu }$ models with LIV in $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$

Abstract

We studied two different models that included Lorentz Invariance Violation coupling in the scattering processes of $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$. We found that using the model with the dual electromagnetic tensor ${\tilde{F}}_{\mu \nu }$ resulted in violations of unitarity in both vector and axial scenarios. On the other hand, using the model with nonminimal coupling with $F_{\mu \nu }$ preserved unitarity in both vector and axial cases. As a result, this could have significant implications, given that the nonminimal coupling model with the dual electromagnetic tensor ${\tilde{F}}_{\mu \nu }$ appeared to be potentially superior to the electromagnetic tensor $F_{\mu \nu }$. Therefore, we believe that these findings could provide a valuable guide for further exploration into the study of CPT and Lorentz breaking phenomena, with significant implications that are certainly nontrivial.