Variations on Four-Neutrino Oscillations

We make a model-independent analysis of all available data that indicate neutrino oscillations. Using probability diagrams, we confirm that a mass spectrum with two nearly degenerate pairs of neutrinos separated by a mass gap of $\simeq1$ eV is preferred over a spectrum with one mass eigenstate separated from the others. We derive some new relations among the four-neutrino mixing matrix elements. We design four-neutrino mass matrices with three active neutrinos and one sterile neutrino that naturally incorporate maximal oscillations of atmospheric $\nu_\mu$ and explain the solar neutrino and LSND results. The models allow either a large or small angle MSW or vacuum oscillation description of the solar neutrino deficit. The models predict (i) oscillations of either $\nu_e \to \nu_\tau$ or $\nu_e \to\nu_s$ in long-baseline experiments at $L/E \gg 1$ km/GeV, with amplitude determined by the LSND oscillation amplitude and argument given by the atmospheric $\delta m^2$, and (ii) the equality of the $\nu_e$ disappearance probability, the $\nu_\mu$ disappearance probability, and the LSND $\nu_\mu\to\nu_e$ appearance probability in short-baseline experiments.