A 2-3 Symmetry in Neutrino Oscillations

Maximum mixing in atmospheric neutrino oscillation, as well as vanishing of the MNS matrix element Ue3, are consequences of a 2-3 symmetry, under which the neutrino mass matrix is invariant under the interchange of second and third generation neutrinos. These predictions of the 2-3 symmetry are consistent with the results of Super-Kamiokande, K2K, and CHOOZ experiments. If the symmetry is exact at a high-energy scale set by right-handed neutrinos, a deviation from these predictions generated by renormalizationgroup corrections will occur at experimental energies. With an MSSM dynamics, the result can be made to agree with a global fit of the neutrino data, if normal hierarchy is assumed on the neutrino mass spectrum and if the mass of the electron-neutrino is at least about 0.025 eV. The presence of this mass lower bound is a novel and interesting feature of the symmetry that can be falsified by future experiments. Of the three viable solar neutrino solutions, only LMA gives a sizable MNS matrix element Ue3 that can hopefully be detected in future reactor experiments. Inverted neutrino mass hierarchy is not permitted by this symmetry. In the basis where the mass matrix of the charged leptons is diagonal, the left-handed flavor-based (symmetric) neutrino mass matrix m′ is related to its diagonal form m = diag[m1, m2, m3] by 1 umu = m, (1) where u is the unitary MNS mixing matrix [1], conventionally parametrized as