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 (848 days) Super-Kamiokande (SK) atmospheric neutrino data going beyond the one mass scale dominance (OMSD) approximation. We fix ${\Delta }_{12}={\Delta }_{13}$ (${\Delta }_{LSND}$) in the range 0.5 - 2 eV${}^2$ as allowed by the results from LSND and other accelerator and reactor experiments on neutrino oscillation and keep ${\Delta }_{23}$ (${\Delta }_{ATM}$) and the three mixing angles as free parameters. In such a scenario, the oscillation probabilities for the accelerator and reactor neutrinos involve only two of the mixing angles ${\theta }_{12}$ and ${\theta }_{13}$ 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 $\Delta m^2$ independent average oscillations for atmospheric neutrinos and does not enter the ${\chi }^2$ analysis as an independent parameter. The ${\Delta }_{23}$ and the three mixing angles on the other hand appear as independent parameters in the ${\chi }^2$ 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 ${\theta }_{12}$ and ${\theta }_{13}$ from the above analysis are compared with the constraints from LSND and other accelerator and reactor experiments. Implications for future long baseline experiments are discussed.

Comments: 40 pages with figures included