Can neutrinos be degenerate in mass?

We reconsider the possibility that the masses of the three light neutrinos of the Standard Model might be almost degenerate and close to the present upper limits from Tritium β decay and cosmology. In such a scenario, the cancellations required by the latest upper limit on neutrinoless double-β decay enforce near-maximal mixing that may be compatible only with the vacuum-oscillation scenario for solar neutrinos. We argue that the mixing angles yielded by degenerate neutrino mass-matrix textures are not in general stable under small perturbations. We evaluate within the MSSM the generation-dependent one-loop renormalization of neutrino mass-matrix textures that yielded degenerate masses and large mixing at the tree level. We find that mνe>mνμ>mντ after renormalization, excluding MSW effects on solar neutrinos. We verify that bimaximal mixing is not stable, and show that the renormalized masses and mixing angles are not compatible with all the experimental constraints, even for tanβ as low as unity. These results hold whether the neutrino masses are generated by a see-saw mechanism with heavy neutrinos weighing ∼1013 GeV or by non-renormalizable interactions at a scale ∼105 GeV. We also comment on the corresponding renormalization effects in the minimal Standard Model, in which mνe