The observation of charged lepton flavor violation would be a clear signal of new physics. In this work, we study flavor-violating three-body $\tau$ decays induced by the scalar leptoquarks $R_2$ and $S_1$. We consider a parameter space constrained by the radiative processes $\Delta a_\mu$ and $\ell_i \to \ell_n \gamma$, focusing on flavor structures where only the top or charm quark contributes. We compute the one-loop contributions to the processes $\tau\rightarrow\ell_n\ell_n\ell_m^c$ and provide analytical expressions for the corresponding branching ratios in the $R_2$ and $S_1$ representations. We then analyze the phenomenology of these channels, comparing the roles of the top- and charm-quark sectors in the parameter space. Our results show that, within the considered scenarios, the scalar leptoquarks $R_2$ and $S_1$ can lead to sizable branching ratios consistent with the imposed coupling constraints.

juan.hoyos@cinvestav.mx

Juan Pablo Hoyos Daza.