Supersymmetric neutrino masses and mixing with R-parity violation

In the context of the minimal supersymmetric standard model, non-zero neutrino masses and mixing can be generated through renormalizable lepton number (and thus R-parity) violating operators. It is examined whether neutrino mass matrices from tree and one-loop contributions can account for two mass-squared differences and mixing angles that explain current experimental data. By accommodating, in particular, the solar and atmospheric neutrino data, we find interesting restrictions not only on the free parameters of the theory, such as lepton number violating couplings and soft parameters, but also on the oscillation parameters of atmospheric neutrinos.