Supersymmetry with R-parity violation (RPV) provides an interesting framework for naturally accommodating small neutrino masses. Within this framework, we discuss the lepton-flavor violating (LFV) processes $\overrightarrow{\mu }e\gamma ,$ $\overrightarrow{\mu }eee,$ and $\overrightarrow{\mu }e$ conversion in nuclei. We make a detailed study of the observables related to LFV in different RPV models, and compare them to the expectations of R-conserving supersymmetry with heavy right-handed neutrinos. We show that the predictions are vastly different and uniquely characterize each model, thus providing a powerful framework for experimentally distinguishing between different theories of LFV. In addition to the obvious possibility of amplified tree-level generation of $\overrightarrow{\mu }\mathrm{eee}$ and $\overrightarrow{\mu }e$ conversion in nuclei, we find that even in the case where these processes arise at the one-loop level, their rates are comparable to that of $\overrightarrow{\mu }e\gamma ,$ in clear contrast to the predictions of R-conserving models. We conclude that, in order to distinguish between the different models, such a combined study of all the LFV processes is necessary, and that measuring P-odd asymmetries in polarized $\overrightarrow{\mu }\mathrm{eee}$ can play a decisive role. We also comment on the intriguing possibility of RPV models yielding a large T-odd asymmetry in the decay of polarized $\overrightarrow{\mu }\mathrm{eee}.\mathrm{}$

• Received 21 August 2000

DOI:https://doi.org/10.1103/PhysRevD.63.035004