Simple radiative neutrino mass matrix for solar and atmospheric oscillations.

A simple 3× 3 neutrino Majorana mass matrix is proposed to accommodate both the solar and atmospheric neutrino deficits. This scenario can be realized naturally by a radiative mechanism for the generation of neutrino masses. It also goes together naturally with electroweak baryogenesis and cold dark matter in a specific model. There is now a good deal of evidence from different experiments that there exists a solar neutrino deficit[1, 2, 3, 4] as well as mounting evidence for an atmospheric neutrino deficit.[5, 6] In terms of neutrino oscillations, the former (latter) is an indication that νe (νμ) is not a mass eigenstate.[7, 8] A popular approach to the neutrino-mass problem is the seesaw mechanism,[9] in which case mνl is naively expected to be proportional to m 2 l , where l = e, μ, τ , and the mixing angles are assumed to be small, in analogy with what is observed in the quark sector. However, that is not the only, nor necessarily the most natural, possibility. In this paper, a very different form of the neutrino mass matrix will be proposed. It is simple and can be realized naturally by a radiative mechanism for the generation of Majorana neutrino masses. It also fits very well into the framework of a recently proposed doublet Majoron model[10, 11] which allows for the generation of baryon number during the electroweak phase transition as well as having ντ as the late decaying particle for a consistent interpretation that the missing mass of the Universe is all cold dark matter. Consider the following 3× 3 Majorana mass matrix for the states νe, νμ, and ντ (or νS, a hypothetical singlet neutrino):