Neutrino Masses in Supersymmetry: R-Parity and Leptogenesis

In the supersymmetric standard model of particle interactions, R-parity nonconservation is often invoked to obtain nonzero neutrino masses. We point out here that such interactions of the supersymmetric particles would erase any pre-existing lepton or baryon asymmetry of the universe before the electroweak phase transition through the $B + L$ violating sphaleron processes. We then show how neutrino masses may be obtained in supersymmetry (assuming R-parity conservation) together with successful leptogenesis and predict the possible existence of new observable particles.