Active-active and active-sterile neutrino oscillation solutions to the atmospheric neutrino anomaly

We perform a fit to the full data set corresponding to 33.3 kt-yr of data of the Super-Kamiokande experiment as well as to all other experiments in order to compare the two most likely solutions to the atmospheric neutrino anomaly in terms of oscillations in the $\nu_\mu \to \nu_\tau$ and $\nu_\mu \to \nu_s$ channels. Using state-of-the-art atmospheric neutrino fluxes we have determined the allowed regions of oscillation parameters for both channels. We find that the $\Delta m^2$ values for the active-sterile oscillations (both for positive and negative $\Delta m^2$) are higher than for the $\nu_\mu \to \nu_\tau$ case, and that the increased Super-Kamiokande sample slightly favours $\nu_\mu \to \nu_\tau$ oscillations over oscillations into a sterile species $\nu_s$, $\nu_\mu \to \nu_s$, and disfavours $\nu_\mu \to \nu_e$. We also give the zenith angle distributions predicted for the best fit points in each of the possible oscillation channels. Finally we compare our determinations of the atmospheric neutrino oscillation parameters with the expected sensitivities of future long-baseline experiments K2K, MINOS, ICARUS, OPERA and NOE.