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

In the SUSY GUT scenario, it is natural to assume the right-handed-neutrino Majorana-mass scale to be 10 GeV. This will in principle lead, by the seesaw mechanism, to a mass of order m 2 t =(10GeV ) 3 10 3 eV . This suggests that the solution of the solar-neutrino puzzle should be either the MSW e ect in e{ oscillations, with m 2 10 5 eV 2, or long-wavelength e{ oscillations, with m 10 10 eV 2. These solutions require unexpectedly large mixings of e with and , respectively. I suggest a variation of the Dimopoulos{Hall{Raby model for the fermion mass matrices which can accomodate such large mixings. Supersymmetric Grand Uni ed Theories (SUSY GUT's) have recently experienced an upsurge in popularity, because they do not require the existence of an intermediateenergy breaking of the grand-uni cation group in order to obtain uni cation of the gauge couplings. In a SUSY GUT, the grand-uni cation gauge group is broken directly to the standard-model gauge group atMG 10GeV , while supersymmetry is broken at a phenomenologically interesting scale MSUSY 10GeV [1]. The seesaw mechanism [2] for the suppression of the left-handed-neutrino masses can be incorporated in a SUSY GUT like SO(10). That mechanism suggests that the mass of the should be of order m2t=MI , where mt is the top-quark mass and MI is the scale of the breaking of the subgroup SU(4) [3] of SO(10). This is because the right-handed-neutrino Majorana mass breaks SU(4), and should therefore be of order MI ; while SU(4) relates the neutrino Dirac mass matrix to the up-type-quark mass matrix, and therefore the Dirac mass should be of order mt. The latter argument also suggests that the masses of the neutrinos should have a strong hierarchy. On leave of absence from Universidade T ecnica de Lisboa, Lisbon, Portugal