A three generation oscillation analysis of the Super-Kamiokande atmospheric neutrino data beyond one mass scale dominance approximation

Abstract

In this paper we do a three-generation oscillation analysis of the latest (1144 days) Super-Kamiokande (SK) atmospheric neutrino data going beyond the One Mass Scale Dominance (OMSD) approximation. We fix Δ₁₂ = Δ₁₃ (Δ_LSND) in the range eV² as allowed by the results from LSND and other accelerator and reactor experiments on neutrino oscillation and keep Δ₂₃ (Δ_ATM) and the three mixing angles as free parameters. We incorporate the matter effects, indicate some new allowed regions with small Δ₂₃ (<10⁻⁴eV²) and sin ²2θ₂₃ close to 0 and discuss the differences with the two-generation and OMSD pictures. In our scenario, the oscillation probabilities for the accelerator and reactor neutrinos involve only two of the mixing angles θ₁₂ and θ₁₃ and one mass scale. But the atmospheric neutrino oscillation is in general governed by both mass scales and all the three mixing angles. The higher mass scale gives rise to Δm² independent average oscillations for atmospheric neutrinos and does not enter the χ² analysis as an independent parameter. The Δ₂₃ and the three mixing angles on the other hand appear as independent parameters in the χ² analysis and the best-fit values of these are determined from an analysis of (a) the SK data, (b) the SK and CHOOZ data. The allowed values of the mixing angles θ₁₂ and θ₁₃ from the above analysis are compared with the constraints from all accelerator and reactor experiments including the latest results from LSND and KARMEN2. Implications for future long baseline experiments are discussed.