0 Consequences of a Z 2 Symmetry for Neutrino Oscillations

A Z 2L × Z 2R generation symmetry in the neutrino sector predicts the atmospheric neutrino mixing to be maximal, and the MNS matrix element U e3 to be zero, consistent with observations. Solar neutrino mixing may be maximal but is not required by the symmetry. Neutrino masses of the first two generations are predicted to vanish, providing a first approximation to the oscillation data. The consequence of a smaller Z 2 symmetry is also discussed. In that case, deviation from the Z 2L × Z 2R result is of the order of the neutrino mass ratio between the first two generations and the third generation. Right-handed neutrinos must be present to explain the deficit of solar and atmospheric neutrinos through oscillations. These are unique probes at high energy for they have no standard-model quantum numbers to allow a pollution by standard-model interactions. Recent results from Super-Kamiokande suggest that the mixing for solar neutrinos and the atmospheric neutrinos are both maximal, and the (∆m) 2 for solar neutrino oscillation is much smaller than the (∆m) 2 for atmospheric neutrino oscillations [1]. The negative result of CHOOZ [2] also limits the magnitude of the MNS mixing matrix [3] element |U e3 | 2 to be smaller than 0.02 to 0.047, depending on the exact value of the atomospheric neutrino mass difference. Is there a simple way to understand these facts? Many models have been proposed [4]. We suggest that a Z 2L × Z 2R generation symmetry in the sea-saw scenario 1