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 $\simeq 1$ 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 (i) oscillations of either ${\nu }_e\to {\nu }_{\tau }$ or ${\nu }_e\to {\nu }_s$ 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 $\delta m^2$, 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.

Latex2.09, 40 pages, uses epsf.sty to include 8 postscript figures

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