Three Inequivalent Mass-Degenerate Majorana Neutrinos and a Model of Their Splitting for Neutrino Oscillations

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 model with additional explicit breaking of the threefold degeneracy to account for the atmospheric neutrino data, while the radiative breaking explains the solar neutrino data, using the large-angle Mikheyev-Smirnov-Wolfenstein solution. Our model requires a nonzero effective $\nu_e$ mass for neutrinoless double beta decay close to the present experimental upper limit of 0.2 eV.