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 performed a fit to atmospheric and solar Super-Kamiokande data. We have investigated a large parameter range, where the mixing angles were restricted to $0\le {\theta }_i\le \pi /2$, $i=1,2,3$, and the mass squared differences were taken to be in the intervals $10^{-11}{\mathrm{eV}}^2\le \Delta m^2\le 10^{-2}{\mathrm{eV}}^2$ and $10^{-4}{\mathrm{eV}}^2\le \Delta M^2\le 10{\mathrm{eV}}^2$. 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.

Comments: 13 pages, 5 figures; Eq. (22) and Ref. [1] corrected