Soft supersymmetry breaking as the sole origin of neutrino masses and lepton number violation

We discuss a scenario in which the supergravity induced soft terms, conventionally used for breaking supersymmetry, also lead to non-zero Majorana neutrino masses. The soft terms lead to the spontaneous violation of the lepton number at the gravitino mass scale m 3 / 2 which in turn leads to (i) the Majorana masses of 𝒪 ( m 3 / 2 ) for the right-handed neutrinos and (ii) the R -parity breaking at the same scale. The former contributes to light neutrino masses through the type I seesaw mechanism, while the latter adds to it through neutrino-neutralino mixing. Both contributions can scale inversely with respect to m 3 / 2 given that gaugino and Higgsino masses are also of order m 3 / 2 . Together, these two contributions adequately explain observed neutrino masses and mixing. One realization of the scenario also naturally leads to a μ parameter of 𝒪 ( m 3 / 2 ). Despite the lepton number symmetry breaking close to the weak scale, the Majoron in the model exhibits very weak coupling to leptons, satisfying existing constraints on Majoron-lepton interactions. The right-handed neutrinos in the model have a large coupling to Higgsinos. This coupling and the relatively large heavy-light neutrino mixing induced through the seesaw mechanism may lead to the observable signals at colliders in terms of displaced vertices.