The LSND Experiment and the Zee Model

A recent experiment LSND at Los Alamos has provided\cite{1} an indication of $\overline{\nu}_{\mu} - \overline{\nu}_e$ oscillations with $\Delta m^2$ of order 1ev$^2$ or greater and $\sin^2 2 \theta_{e \mu}$ between $2 \times 10^{-3}$ and $10^{2}$. Such a value of $\Delta m^2$ for $\nu_{\mu} - \nu_e$ oscillations was not expected in the standard see-saw model\cite{2} suggested by SO(10) with a large mass hierarchy because it leads to too large a value of $m(\nu_{\tau})$ to fit cosmological constraints. Furthermore within that model the LSND result is inconsistent with the indications of oscillations from both atmospheric neutrinos\cite{3} and solar neutrinos.\cite{4}