Mass Splitting of Three Seesaw Neutrinos

Abstract

If a family symmetry exists so that all three neutrinos have equal Majorana masses (via the seesaw mechanism), then the breaking of this symmetry from charged-lepton masses (via two-loop double $W$ exchange) implies $\Delta m$ less than about $10^{-9}{m}_0$. With the common mass $m_0\sim$ eV for hot dark matter, $\Delta m^2\sim 10^{-10}$ eV${}^2$ is natural for vacuum solar neutrino oscillations.

Comments: 8 pages including 1 figure, talk at WIN99