Unitarity implications of \(\tilde{F}_{\mu \nu }\) and \(F_{\mu \nu }\) models with Lorentz invariance violation in \(e^{+}e^{-} \rightarrow \mu ^{+}\mu ^{-}\)

We studied two different models that included Lorentz Invariance Violation coupling in the scattering processes of \(e^+e^- \rightarrow \mu ^+\mu ^-\). 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.