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 similar or equal to 1 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 (1) oscillations of either nu(e) --> nu(tau) or nu(e) --> nu(s) in long-baseline experiments at L/E much greater than 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) --> nu(e) appearance probability in short-baseline experiments. [S0556-2821(98)06921-5]