Lepton Flavour 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-flavour violating (LFV) processes mu -> e gamma, mu -> eee, and 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 characterise each model, thus providing a powerful framework for experimentally distinguishing between different theories of LFV. Besides the obvious possibility of amplified tree-level generation of mu -> eee and 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 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 polarised mu -> 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 polarised mu -> eee.