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 -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 __ oscillations are preferred over _₄, 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 __ channel. Without the CHOOZ constraints, the amplitudes of the subdominant _₄ and ₄_ transitions can also be relatively large, indicating that, at present, current SK data do not exclude sizable ₄ 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 ₄ 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.