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

We present a search for nonzero ${\theta }_{13}$ and deviations of ${sin}^2{\theta }_{23}$ 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 ${\theta }_{13}$ are found and both neutrino mass hierarchy hypotheses are in agreement with the data. The data are best fit at $\Delta m^2=2.1\times {10}^{-3}{\mathrm{eV}}^2$, ${sin}^2{\theta }_{13}=0.0$, and ${sin}^2{\theta }_{23}=0.5$. In the normal (inverted) hierarchy ${\theta }_{13}$ and $\Delta m^2$ are constrained at the one-dimensional 90% C.L. to ${sin}^2{\theta }_{13}<0.04(0.09)$ and $1.9(1.7)\times {10}^{-3}<\Delta m^2<2.6(2.7)\times {10}^{-3}{\mathrm{eV}}^2$. The atmospheric mixing angle is within $0.407\le {sin}^2{\theta }_{23}\le 0.583$ at 90% C.L.