Threefold maximal lepton mixing and the solar and atmospheric neutrino deficits

Abstract

Threefold maximal mixing would imply a cyclic permutation symmetry among the generations. The data from solar and atmospheric neutrino experiments are consistent with such mixing, and require a hierarchical spectrum of mass-squared differences for the neutrinos. A fit for the two independent mass-squared differences (excluding only the HOMESTAKE solar neutrino result) yields: Δm 2 = (0.72±0.18) × 10 −2 eV 2 and Δm′ 2 < 0.9 × 10 −11 eV 2 at 90% confidence. In the case that the neutrino mass spectrum is qualitatively similar to that of the charged leptons and quarks, these results can be re-expressed in terms of the neutrino masses as follows: m 3 ⋍ 85 ± 10 meV, and m 1, m 2 < 3 μeV at 90% confidence. Implications for future experiments are discussed.