Accelerator, reactor, solar, and atmospheric neutrino oscillations: Beyond three generations

We perform a phenomenological analysis of neutrino oscillations introducing an additional sterile neutrino. In such a scenario, more than one spectrum is possible that can accommodate three hierarchically different mass-squared differences as required by the present experiments. We considered two different spectra. Choosing the $\Delta m^{2}s$ in the ranges suitable for the LSND, atmospheric, and solar neutrino oscillations, limits on the mixing angles are derived, consistent with the most restrictive accelerator and reactor data as well as the atmospheric and solar neutrino results. We show that the present data disfavor one of these mass spectra leaving us with a very stringent choice of mass and mixing angle. The potential of the future heavy water solar neutrino experiment SNO to distinguish between the four-neutrino mixing and two-neutrino mixing cases is explored.