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 u pper limits from Tritium beta decay and cosmology. In such a scenario, the cancellations required by the latest upper limit on neutrinoless double-bet a decay enforce near-maximal mixing that may be compatible only with the va cuum-oscillation scenario for solar neutrinos. We argue that the mixing ang les yielded by degenerate neutrino mass-matrix textures are not in general stable under small perturbations. We evaluate within the MSSM the generatio n-dependent one-loop renormalization of neutrino mass-matrix textures that yielded degenerate masses and large mixing at the tree level. We find that m(vc) > m(v mu) > m(v tau) after renormalization, excluding MSW effects on solar neutrinos. We verify that bimaximal mixing is not stable, and show th at the renormalized masses and mixing angles are not compatible with all th e experimental constraints, even for tan beta as low as unity. These result s hold whether the neutrino masses are generated by a see-saw mechanism wit h heavy neutrinos weighing similar to 10(13) GeV or by non-renormalizable i nteractions at a scale similar to 10(5) GeV. We also comment on the corresp onding renormalization effects in the minimal Standard Model, in which m(vc ) < m(v mu) < m(v tau). Although a solar MSW effect is now possible, the pe rturbed neutrino masses and mixings are still not compatible with atmospher ic-and solar-neutrino data. (C) 1999 Published by Elsevier Science B.V. All rights reserved.