Neutrino masses and sneutrino mixing in R-parity violating supersymmetry

R-parity-violating supersymmetry with a conserved baryon number $B$ provides a framework for particle physics with lepton number ($L$) violating interactions. Two important probes of the $L$-violating physics are neutrino masses and sneutrino-antisneutrino mass-splittings. We evaluate these quantities in the context of the most general CP-conserving, R-parity-violating $B$-conserving extension of the minimal supersymmetric standard model. In generic three-generation models, three sneutrino-antisneutrino mass splittings are generated at tree-level. In contrast, only one neutrino mass is generated at tree-level; the other two neutrinos acquire masses at one-loop. In many models, the dominant contribution to the radiative neutrino masses is induced by the non-zero sneutrino-antisneutrino mass splitting