Solar and atmospheric four-neutrino oscillations

We present an analysis of the neutrino oscillation solutions of the solar and atmospheric neutrino problems in the framework of four-neutrino mixing where a sterile neutrino is added to the three standard ones and the mass spectra present two separated doublets. Such scenarios allow for simultaneous transitions of solar ${\nu }_e,$ as well as atmospheric ${\nu }_{\mu },$ into active and sterile neutrinos controlled by the additional mixing angles ${\vartheta }_{23}$ and ${\vartheta }_{24},$ and they contain as limiting cases the pure solar ${\nu }_e$-active and ${\nu }_e$-sterile neutrino oscillations, and the pure atmospheric ${\nu }_{\mu }\to {\nu }_s$ and ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillations, respectively. We evaluate the allowed active-sterile admixture in both solar and atmospheric oscillations from the combined analysis. Our results show that, although the Super-Kamiokande data disfavor both the pure ${\nu }_{\mu }\to {\nu }_s$ atmospheric channel and the pure ${\nu }_e\to {\nu }_s$ solar channel, the result from the combined analysis still favors close-to-pure active and sterile oscillations and disfavors oscillations into a near-maximal active-sterile admixture.