Neutrino Oscillations with Four Generations

There have been several experiments 10,11,12,13 which suggest neutrino oscillations. To explain the solar, atmospheric and LSND data within the framework of neutrino oscillations, it is necessary to have at least four kinds of neutrinos. It has been shown in the two flavor framework that the solar neutrino deficit can be explained by neutrino oscillation with the sets of parameters (∆m⊙, sin 2 2θ⊙) ≃ (O(10−5eV),O(10−2)) (SMA (small mixing angle) MSW solution), (O(10−5eV),O(1)) (LMA (large mixing angle) MSW solution), (O(10−7eV),O(1)) (LOW solution) or (O(10−10eV),O(1)) (VO (vacuum oscillation) solution). At the Neutrino 2000 Conference the Superkamiokande group has updated their data of the solar neutrinos and they reported that the LMA MSW solution gives the best fit to the data . At the same time they also showed that the scenario of pure sterile neutrino oscillations νe ↔ νs is excluded at 95%CL. It has been known that the atmospheric neutrino anomaly can be accounted for by dominant νμ ↔ ντ oscillations with almost maximal mixing (∆matm, sin 2 2θatm) ≃ (10−2.5eV, 1.0). Again the Superkamiokande group has announced 10 that the possibility of pure sterile neutrino oscillations νμ ↔ νs is excluded at 99%CL. On the other hand, combining the final result of LSND and the negative results by E776 14 (νμ → νe), Karmen2 15 (νμ → νe) and Bugey 16 (ν̄e → ν̄e), the oscillation parameter satisfies 0.1 eV < ∼∆m2 < ∼ 8 eV and 8 × 10−4 < ∼ sin 2 2θ < ∼ 0.04 at 99%CL. In this talk I will review the present status of four neutrino scenarios in the light of the recent Superkamiokande data of the solar and atmospheric neutrinos.