Three flavor neutrino oscillation analysis of atmospheric neutrinos in Super-Kamiokande

The nature of the neutrino mass hierarchy and the possibility of a nonzero $\theta_{13}$ are open problems in neutrino physics that can be probed by extending the standard two-flavor neutrino oscillation scenario to include all active flavors. In a three-flavor oscillation scheme there is known resonant enhancement (suppression) of the $\nu_{\mu} \rightarrow \nu_{e}$ transition probability in matter for several GeV neutrinos at long baselines for a normal (inverted) hierarchy when $\theta_{13} > 0 $. This effect is not present for the corresponding anti-neutrino transition. The Super-Kamiokande I atmospheric data has been analyzed using a three-flavor model testing both the normal and inverted mass hierarchies and has found no significant change in flux in its enriched multi-GeV $\nu_{\mu} $ or $\nu_{e}$ samples. Accordingly, confidence intervals for the atmospheric oscillation parameters have been obtained, the best fits being consistent with previous atmospheric results and zero $\theta_{13} $ for both hierarchies.