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 $ν_μ$ 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 $ν_e \to ν_τ$ or $ν_e \toν_s$ 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 $δm^2$, and (ii) the equality of the $ν_e$ disappearance probability, the $ν_μ$ disappearance probability, and the LSND $ν_μ\toν_e$ appearance probability in short-baseline experiments.