Probing lepton-number and lepton-flavor violation in semileptonic $\tau$ decays into two mesons

The evaluation, systematic analysis, and numerical study of the semileptonic $\tau$-lepton decays with two mesons in the final state has been made in the frame of the standard model extended by right-handed neutrinos. In the analysis, heavy-neutrino nondecoupling effects, finite quark masses, quark and meson mixings, finite widths of vector mesons, chiral symmetry breakings in vector-meson-pseudoscalar-meson vertices, and effective Higgs-boson-pseudoscalar-meson couplings have been included. Numerical estimates reveal that the decays ${\tau }^{-}\to e^{-}{\pi }^{-}{\pi }^{+}$, ${\tau }^{-}\to e^{-}{K}^{-}{K}^{+}$, and ${\tau }^{-}\to e^{-}{K}^0{\overline{K}}^0$ have branching ratios of the order of ${10}^{-6\mathrm{}}$, close to present-day experimental sensitivities.