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

TL;DR

This paper compares two Lorentz invariance violation models in electron-positron to muon-antimuon scattering, finding that the model with the electromagnetic tensor $F_{}$ preserves unitarity, unlike the one with the dual tensor $ ilde{F}_{}$.

Contribution

It demonstrates that the nonminimal coupling model with $F_{}$ maintains unitarity, providing a better framework for studying CPT and Lorentz breaking effects.

Findings

The $ ilde{F}_{}$ model violates unitarity in both vector and axial cases.

The $F_{}$ model preserves unitarity in both cases.

Implications for future CPT and Lorentz violation research.

Abstract

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.