Neutrino masses in the supersymmetric Majoran model

A class of supersymmetric SU(2)xU(1) models in which the lepton number symmetry is spontaneously broken is studied with regard to the issue of neutrino masses. We find that (I) if the explicit supersymmetry breaking terms include trilinear boson couplings and Majorana masses for the gauge fermions, then one neutrino species acquires a Majorana mass at the tree level while the rest acquire their Majorana mass radiatively and (II) if the supersymmetry breaking terms only include mass terms for the scalar bosons, then one neutrino acquires a small Dirac mass at the two-loop level while the rest remain massless to all orders. (orig.)