Lepton-flavor violation in supersymmetric models with trilinear R- parity violation

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 mu to e gamma , mu to eee, and mu to 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 mu to eee and mu to 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 mu to 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 mu to 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 mu to eee. (38 refs).