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

We present a search for nonzero θ₁₃ and deviations of sin²θ₂₃ 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 θ₁₃ are found and both neutrino mass hierarchy hypotheses are in agreement with the data. The data are best fit at Δm²=2.1×10^-3 eV², sin²θ₁₃=0.0, and sin²θ₂₃=0.5. In the normal (inverted) hierarchy θ₁₃ and Δm² are constrained at the one-dimensional 90% C.L. to sin²θ₁₃<0.04(0.09) and 1.9(1.7)×10^-3<Δm²<2.6(2.7)×10^-3 eV². The atmospheric mixing angle is within 0.407≤sin²θ₂₃≤0.583 at 90% C.L.