Muonium-antimuonium oscillations and exotic muon decay in brokenR-parity SUSY models

We analyze the process of muonium-antimuonium conversion and the rare decay ${\mu }^{+}\to e^{+}{\overline{\nu }}_e{\nu }_{\mu }$ in the class of low energy $N=1\mathrm{}$ supersymmetric theories containing $R$-parity-breaking terms in the lepton sector. We find that these processes are allowed in those models at the tree level and are controlled by the same combination of coupling strengths. Current experimental constraints on the relevant coupling parameters allow the effective four-fermion couplings for these processes to be as large as $2\times {10}^{-2\mathrm{}}{G}_F$. This is several orders of magnitude larger than many other models allow and just about at the current experimental limits. This result should serve to revitalize experimental searches for these exotic processes.