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 $m_t^2/(10^{16}\mathrm{GeV})\sim 3\times 10^{-3}\mathrm{eV}$. This suggests that the solution of the solar-neutrino puzzle should be either the MSW effect in ${\nu }_e$--${\nu }_{\tau }$ oscillations, with $m_{{\nu }_{\tau }}^2\sim 10^{-5}{\mathrm{eV}}^2$, or long-wavelength ${\nu }_e$--${\nu }_{\mu }$ oscillations, with $m_{{\nu }_{\mu }}^2\sim 10^{-10}{\mathrm{eV}}^2$. 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.

Comments: 10 pages, standard LATEX, no figures, Carnegie-Mellon University Report CMU-HEP93-27 and DOE-ER/40682-52