Three flavor neutrino oscillation analysis of atmospheric neutrinos in Super-Kamiokande

We report on the results of a three-flavor oscillation analysis using Super-Kamiokande I atmospheric neutrino data, with the assumption of one mass scale dominance ($\ensuremath{\Delta}{m}_{12}^{2}=0$). No significant flux change due to matter effect, which occurs when neutrinos propagate inside the Earth for ${\ensuremath{\theta}}_{13}\ensuremath{\ne}0$, has been seen either in a multi-GeV ${\ensuremath{\nu}}_{e}$-rich sample or in a ${\ensuremath{\nu}}_{\ensuremath{\mu}}$-rich sample. Both normal and inverted mass hierarchy hypotheses are tested and both are consistent with observation. Using Super-Kamiokande data only, 2-dimensional 90% confidence allowed regions are obtained: mixing angles are constrained to ${sin}^{2}{\ensuremath{\theta}}_{13}<0.14$ and $0.37<{sin}^{2}{\ensuremath{\theta}}_{23}<0.65$ for the normal mass hierarchy. Weaker constraints, ${sin}^{2}{\ensuremath{\theta}}_{13}<0.27$ and $0.37<{sin}^{2}{\ensuremath{\theta}}_{23}<0.69$, are obtained for the inverted mass hierarchy case.