Super-Kamiokande atmospheric neutrino data, zenith distributions, and three-flavor oscillations

We present a detailed analysis of the zenith angle distributions of atmospheric neutrino events observed in the Super-Kamiokande (SK) underground experiment, assuming two-flavor and three-flavor oscillations (with one dominant mass scale) among active neutrinos. In particular, we calculate the five angular distributions associated with sub-GeV and multi-GeV {μ}-like and e-like events and to upward through-going muons, for a total of 30 accurately computed observables (zenith bins). First we study how such observables vary with the oscillation parameters, and then we perform a fit to the experimental data as measured in SK for an exposure of 33 kTy (535 days). In the two-flavor mixing case, we confirm the results of the SK Collaboration analysis, namely, that ν_μ↔ν_τ oscillations are preferred over ν_μ↔νₑ, and that the no oscillation case is excluded with high confidence. In the three-flavor mixing case, we perform our analysis with and without the additional constraints imposed by the CHOOZ reactor experiment. In both cases, the analysis favors a dominance of the ν_μ↔ν_τ channel. Without the CHOOZ constraints, the amplitudes of the subdominant ν_μ↔νₑ and νₑ↔ν_τ transitions can also be relatively large, indicating that, at present, current SK data do not exclude sizable νₑ mixing by themselves. After combining the CHOOZ and SK data, the amplitudes of the subdominant transitions are constrained to be smaller, but they can still play a non-negligible role both in atmospheric and other neutrino oscillation searches. In particular, we find that the νₑ appearance probability expected in long baseline experiments can reach the testable level of {~}15%. We also discuss Earth matter effects, theoretical uncertainties, and various aspects of the statistical analysis.