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

TL;DR

This paper investigates how scalar leptoquarks could induce lepton flavor-violating tau decays, providing analytical predictions and exploring their detectability in upcoming experiments.

Contribution

It offers the first detailed calculation of one-loop contributions of $R_2$ and $S_1$ leptoquarks to three-body tau decays, including phenomenological analysis at TeV scales.

Findings

Predicted branching ratios can reach future experimental sensitivities.

Constraints from muon anomalous magnetic moment and rare decays limit parameter space.

Lepton-flavor-violating tau decays serve as probes for scalar leptoquark models.

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.