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 1eV 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 νₑ→ν_τ or νₑ→νₛ in long-baseline experiments at L/E1km/GeV, with amplitude determined by the LSND oscillation amplitude and argument given by the atmospheric δm², and (ii) the equality of the νₑ disappearance probability, the ν_μ disappearance probability, and the LSND ν_μ→νₑ appearance probability in short-baseline experiments.