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 $ ν_τ $ 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 $ν_e$--$ν_τ$ oscillations, with $ m_{ν_τ}^2 \sim 10^{-5}\, {\rm eV}^2 $, or long-wavelength $ν_e$--$ν_μ$ oscillations, with $ m_{ν_μ}^2 \sim 10^{-10}\, {\rm eV}^2 $. These solutions require unexpectedly large mixings of $ ν_e $ with $ ν_τ $ and $ ν_μ $, respectively. I suggest a variation of the Dimopoulos--Hall--Raby model for the fermion mass matrices which can accomodate such large mixings.