Three inequivalent mass-degenerate Majorana neutrinos and a scenario of their splitting for neutrino oscillations

Abstract

The mass matrix of three Majorana neutrinos of equal mass is not necessarily proportional to the identity matrix, but expressible in terms of two angles and one phase. We discuss how such a mass matrix may be stable or unstable against radiative corrections. We then propose a scenario with additional explicit breaking of the threefold degeneracy to account for the atmospheric neutrino data, while the radiative breaking explains the solar neutrino data, but only with the large-angle Mikheyev-Smirnov-Wolfenstein (MSW) solution. The exclusion of the small-angle MSW solution is independent of the value of the common mass m of the three neutrinos. For m∼0.5 eV, the effective ν_e mass for neutrinoless double beta decay is then predicted to be close to the present experimental upper limit of 0.2 eV.