Lepton flavor violating $\tau^- \to \ell_i^- \ell_i^- \ell_j^+$ ($\ell_i\neq \ell_j$) decays induced by $S_1$ and $R_2$ scalar leptoquarks

Abstract

Charged lepton flavor violation provides a clear experimental signature in the search for physics beyond the Standard Model. In this work, we study the flavor-violating three-body tau decays $\tau^- \to \ell_i^- \ell_i^- \ell_j^+$ ($\ell_i \neq \ell_j$) induced by the scalar leptoquarks $R_2$ and $S_1$, focusing on flavor structures dominated by top- or charm-quark contributions. We compute the one-loop contributions to these processes and derive analytical expressions for the corresponding branching ratios. The phenomenological implications are analyzed for leptoquark masses at the TeV scale, taking into account current constraints from the anomalous magnetic moment of the muon, radiative lepton-flavor-violating decays, and the process $\mu^-\to e^-e^-e^+$. Within the allowed parameter space, the predicted branching ratios for $\tau^- \to \ell_i^- \ell_i^- \ell_j^+$ can approach the sensitivities expected in near-future experiments. These results highlight the potential of three-body $\tau$ decays as probes of lepton-flavor violation and as complementary tests of scalar leptoquark scenarios.