  R-parity violation in the supersymmetric standard model could be the origin
of neutrino masses and mixing accounting for the atmospheric and solar neutrino
oscillations. More interestingly, this hypothesis may be tested in future
colliders by detecting lepton number violating decays of the lightest
supersymmetric particle. Here, we present a comprehensive analysis for the
determination of sneutrino vacuum expectation values from the one-loop
effective scalar potential, and also for the one-loop renormalization of
neutrino masses and mixing. Applying our results to theories with gauge
mediated supersymmetry breaking, we discuss the effects of the one-loop
corrections and how the realistic neutrino mass matrices arise.
