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 to sub-GeV and multi-GeV \mu-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 \nu_\mu<--->\nu_\tau oscillations are preferred over \nu_\mu<--->\nu_e, 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 \nu_\mu<--->\nu_\tau channel. Without the CHOOZ constraints, the amplitudes of the subdominant \nu_\mu<--->nu_e and \nu_e<--->\nu_\tau transitions can also be relatively large, indicating that, at present, current SK data do not exclude sizable \nu_e 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 nonnegligible role both in atmospheric and other neutrino oscillation searches. In particular, we find that the \nu_e appearance probability expected in long baseline experiments can reach the testable level of ~15%.