Super-Kamiokande neutrino oscillations and the supersymmetric model

The standard model predicts a ratio of 2 for the number of atmospheric muon to electron neutrinos, while super-Kamiokande and others measure a much smaller value (1.30±0.02 for super-Kamiokande). Super-Kamiokande is also able to measure roughly the direction and the energy of the neutrinos. The zenith-angle dependence for the muon neutrinos suggests that the muon neutrinos oscillate into a third neutrino species, either into the r neutrino or a sterile neutrino. This finding is inves- tigated within the supersymmetric model. The neutrinos mix with the neutralinos, this meaning the wino, the bino and the two higgsinos. The 7 x 7 mass matrix is calculated on the tree level. One finds that the mass matrix has three linearly dependent rows, which means that two masses are zero. They are identified with the two lightest neutrino masses. The fit of the super-Kamiokande data to oscillations between three neutrinos yields, together with the result of supersymmetry, that the third neutrino mass lies between 2x10^-2 and 10^-1 eV. The two lightest neutrino masses are in supersymmetry on the tree level zero. The averaged electron neutrino mass which is the essential parameter in the neutrinoless double-beta decay is given by {m_ve) ~ m_v3 P_ze < 0.8 x10^-2 eV (95% confidence limit). It is derived from the super-Kamiokande data in this supersymmetric model to be two orders smaller than the best value (1 eV) from the neutrinoless double-beta decay.