Novel constraints on [Formula Presented] interactions from neutrino masses

We reanalyze the constraints imposed on lepton-number violating interactions by radiative contributions to neutrino masses at the one- and two-loop levels in supersymmetric models without R parity. The interactions considered are the (Formula presented) superpotential operators (Formula presented) and (Formula presented) and the (Formula presented) soft terms (Formula presented) and (Formula presented) The two-loop contributions analyzed are those induced by the radiatively generated mass splitting between the (Formula presented)-even and (Formula presented)-odd sneutrino states. It is shown how the constraints on the couplings (Formula presented) and (Formula presented) coming from the one-loop analysis can be evaded. In such a case, the two-loop contributions to neutrino masses become important. The combined one- and two-loop analysis yields constraints on the couplings (Formula presented) and (Formula presented) that are rather difficult to escape. The two-loop analysis yields also constraints on (Formula presented) and (Formula presented) which are not bounded at the one-loop level. More freedom remains for the couplings (Formula presented) (Formula presented) and (Formula presented) (Formula presented) when j and k are first- or second-generation indices.