We present an extension of the singlet majoron gauge model which realizes a novel scheme of geometrical neutrino mass hierarchy proposed recently by Glashow, wherein ${\nu }_{\mathit{e}}$ and ${\nu }_{\mathrm{\mu }}$ are Majorana particles with ${\mathit{m}}_{\nu \mathit{e}}$≊${\mathit{m}}_{\nu \mathrm{\mu }}$≊${10}^{\mathrm{-}3}$ eV while ${\nu }_{\mathrm{\tau }}$ is a Dirac particle with a mass of 17 keV. Our model explains the solar-neutrino deficit via the Mikheyev-Smirnov-Wolfenstein mechanism and accounts for the recently reported anomaly in beta-decay spectra in a natural manner without any undesirable fine tuning of parameters. An interesting consequence of the model is that ${\nu }_{\mathrm{\tau }}$ is short lived with a lifetime of ≊${10}^{\mathrm{-}3–}$${10}^{\mathrm{-}1}$ sec.

• Received 31 January 1991

DOI:https://doi.org/10.1103/PhysRevLett.67.1498