Right-handed-neutrino Majorana mass at the SUSY GUT scale and the solution of the solar-neutrino problem

Abstract

In the SUSY GUT scenario, it is natural to assume the right-handed-neutrino Majorana-mass scale to be $10^{16}$ GeV. This will in principle lead, by the seesaw mechanism, to a $ \nu_{\tau} $ mass of order $ m_t^2 / (10^{16}\, {\rm GeV}) \sim 3 \times 10^{-3}\, {\rm eV} $. This suggests that the solution of the solar-neutrino puzzle should be either the MSW effect in $\nu_e$--$\nu_{\tau}$ oscillations, with $ m_{\nu_{\tau}}^2 \sim 10^{-5}\, {\rm eV}^2 $, or long-wavelength $\nu_e$--$\nu_{\mu}$ oscillations, with $ m_{\nu_{\mu}}^2 \sim 10^{-10}\, {\rm eV}^2 $. These solutions require unexpectedly large mixings of $ \nu_e $ with $ \nu_{\tau} $ and $ \nu_{\mu} $, respectively. I suggest a variation of the Dimopoulos--Hall--Raby model for the fermion mass matrices which can accomodate such large mixings.