Atmospheric neutrino oscillation analysis with subleading effects in Super-Kamiokande I, II, and III

We present a search for nonzero ${\ensuremath{\theta}}_{13}$ and deviations of ${sin}^{2}{\ensuremath{\theta}}_{23}$ from 0.5 in the oscillations of atmospheric neutrino data from Super-Kamiokande I, II, and III. No distortions of the neutrino flux consistent with nonzero ${\ensuremath{\theta}}_{13}$ are found and both neutrino mass hierarchy hypotheses are in agreement with the data. The data are best fit at $\ensuremath{\Delta}{m}^{2}=2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{eV}}^{2}$, ${sin}^{2}{\ensuremath{\theta}}_{13}=0.0$, and ${sin}^{2}{\ensuremath{\theta}}_{23}=0.5$. In the normal (inverted) hierarchy ${\ensuremath{\theta}}_{13}$ and $\ensuremath{\Delta}{m}^{2}$ are constrained at the one-dimensional 90% C.L. to ${sin}^{2}{\ensuremath{\theta}}_{13}<0.04(0.09)$ and $1.9(1.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}<\ensuremath{\Delta}{m}^{2}<2.6(2.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{eV}}^{2}$. The atmospheric mixing angle is within $0.407\ensuremath{\le}{sin}^{2}{\ensuremath{\theta}}_{23}\ensuremath{\le}0.583$ at 90% C.L.