Acker and co-workers have recently proposed an economical solution to the solar and atmospheric neutrino deficits, in which both are explained by large-angle ${\nu }_e-{\nu }_{\mu }$ oscillations, supplemented by ${\nu }_e$ decays. We show how to embed their phenomenological model into an electroweak framework in which global electron and muon numbers, [$\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_e\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{\mu }$], spontaneously break at a scale of 1 ke V. Despite such a low scale, our model is technically natural. The naturalness requirement, together with nucleosynthesis constraints, point to the existence of relatively light, largely sterile neutrinos with masses in the MeV range. We find a number of potentially interesting experimental implications of these models, one of which is an explanation of the excess events that have been found near the end points in the double-$\beta$ decay of several elements. One formulation of our model involves a novel realization of supersymmetry, for which the new light particles and their superpartners are split by very small amounts in comparison with the weak scale.

• Received 10 June 1993

DOI:https://doi.org/10.1103/PhysRevD.48.4326