The LSND Experiment and the Zee Model

A recent experiment LSND at Los Alamos has provided\cite{1} an indication of ${\bar{\nu }}_{\mu }-{\bar{\nu }}_e$ oscillations with $\mathrm{\Delta }{m}^2$ of order 1ev${}^2$ or greater and ${\sin }^{2}2{\theta }_{e\mu }$ between $2 \times 10^{-3}$and$10^{2}$\mathrm{.}Suchavalueof$\Delta m^2$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}