Variations on four-neutrino oscillations

Abstract

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 $\ensuremath{\simeq}1\mathrm{eV}$ 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 ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ 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 ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ or ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s}$ in long-baseline experiments at $L/E\ensuremath{\gg}1\mathrm{k}\mathrm{m}/\mathrm{G}\mathrm{e}\mathrm{V},$ with amplitude determined by the LSND oscillation amplitude and argument given by the atmospheric $\ensuremath{\delta}{m}^{2},$ and (ii) the equality of the ${\ensuremath{\nu}}_{e}$ disappearance probability, the ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ disappearance probability, and the LSND ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}$ appearance probability in short-baseline experiments.