Collider Probes of Four-Lepton Final States in Maximally Flavor-Violating $U(1)_{L_{\mu}-L_{\tau}}$ Model

Abstract

We investigate the collider signatures of the maximally flavor-violating $U(1)_{L_\mu-L_\tau}$ model, where a new gauge boson $Z^\prime$ and scalar triplets induce lepton flavor-changing interactions in the $\mu$-$\tau$ sector. Focusing on four-lepton final states at multi-TeV lepton colliders, we conduct a detailed analysis of cross sections, asymmetries, and polarization effects. We show that the signal cross section is highly sensitive to $m_{Z^\prime}$ and the effective parameters $\tilde{g}/m_{Z^\prime}$, while remaining largely insensitive to the triplet Yukawa couplings within the phenomenologically allowed region. The forward-backward asymmetry exhibits a characteristic monotonic dependence on $m_{Z^\prime}$, and beam polarization can significantly suppress Standard Model backgrounds while enhancing new physics contributions. We find that over the phenomenologically allowed parameter space, the predicted observables remain highly sensitive to the underlying model parameters. These results demonstrate that multi-lepton final states are powerful probes of the $U(1)_{L\mu - L_\tau}$ framework and offer valuable guidance for future searches at muon and electron-positron colliders.