Analysis of a three flavor neutrino oscillation fit to recent Super-Kamiokande data

Abstract.

We have analyzed the most recent available Super-Kamiokande data in a three flavor neutrino oscillation model. We have here neglected possible matter effects and we performed a fit to atmospheric and solar Super-Kamiokande data. We have investigated a large parameter range where the mixing angles were restricted to $0 \leq \theta_i \leq \pi/2$, $i=1,2,3$, and the mass squared differences were taken to be in the intervals $10^{-11} {\mathrm{eV}}^2 \leq \Delta m^ 2 \leq 10^{-2} {\mathrm{eV}}^2$ and $10^{-4} {\mathrm {eV}}^2 \leq \Delta M^2 \leq 10 {\mathrm{eV}}^2$, i.e., the hierarchy between the mass squared differences is not completely determined. This yielded a best solution characterized by the parameter values $\theta_1 \simeq 45^\circ$, $\theta_2 \simeq 10^\circ$, $\theta_3 \simeq 45^\circ$, $\Delta m^2 \simeq 4.4 \times 10^{-10} {\mathrm {eV}}^2$, and $\Delta M^2 \simeq 1.01 \times 10^{-3} {\mathrm{eV}}^2$, which shows that the analyzed experimental data speak in favor of a bimaximal mixing scenario with one of the mass squared differences in the “just-so” domain and the other one in the range capable of providing a solution to the atmospheric neutrino problem.