More onR−parity- and lepton-family-number-violating couplings from muon(ium) conversion, andτandπ0decays

We present a new class of constraints to the lepton-family-number- and $R$-parity-violating couplings from muonium conversion ${\mu }^{-}{+}_{22}^{48}\mathrm{Ti}\to e^{-}{+}_{22}^{48}\mathrm{Ti}$, a class of $\tau$ decays $\tau \to l+$ (light meson) with $l=\mu \hspace{0.5em}or\hspace{0.5em}e$, and $J/\psi$ and ${\pi }^0$ decays into a lepton pair. We find that ${\mu }^{-}{+}_{22}^{48}\mathrm{Ti}\to e^{-}{+}_{22}^{48}\mathrm{Ti}$ provides one of the strongest constraints along with $\Delta m_K,\Delta m_B,$ $\mu \to e\gamma$, and the neutrinoless double $\beta$ decay. The search for these lepton-family-number-violating decays forbidden in the standard model is clearly warranted in various low-energy experiments such as $\tau$-charm factories and PSI, etc.