R-parity Violation and Neutrino Masses

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.