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 $\simeq 1\mathrm{eV}$ 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 $L/E\gg 1\mathrm{k}\mathrm{m}/\mathrm{G}\mathrm{e}\mathrm{V},$ 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.