Novel constraints on ΔL=1 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 ΔL=1 superpotential operators λ _ijkL_iL_jE_k^c and λ_ijk′L_iQ_jD_k ^c, and the ΔL=1 soft terms A_ijkL̃ _iL̃_jẼ_k^c and A _ijk′L̃_iQ̃_jD̃ _k^c. The two-loop contributions analyzed are those induced by the radiatively generated mass splitting between the CP-even and CP-odd sneutrino states. It is shown how the constraints on the couplings λ_ijk and λ_ijk′ 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 λ_i33 and λ _i33′ that are rather difficult to escape. The two-loop analysis yields also constraints on A_i33 and A_i33′, which are not bounded at the one-loop level. More freedom remains for the couplings λ_ijk, λ_ijk′, and A_ijk, A_ijk′, when j and k are first- or second-generation indices.