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

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0 \leq \theta_i \leq \pi/2$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$i=1,2,3$\end{document}, and the mass squared differences were taken to be in the intervals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{-11} {\mathrm{eV}}^2 \leq \Delta m^ 2 \leq 10^{-2} {\mathrm{eV}}^2$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{-4} {\mathrm {eV}}^2 \leq \Delta M^2 \leq 10 {\mathrm{eV}}^2$\end{document}, i.e., the hierarchy between the mass squared differences is not completely determined. This yielded a best solution characterized by the parameter values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\theta_1 \simeq 45^\circ$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\theta_2 \simeq 10^\circ$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\theta_3 \simeq 45^\circ$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta m^2 \simeq 4.4 \times 10^{-10} {\mathrm {eV}}^2$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta M^2 \simeq 1.01 \times 10^{-3} {\mathrm{eV}}^2$\end{document}, 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.