Neutrino masses, lepton number violation and unification

Theories with parity as a short-distance symmetry lead rather naturally to a small but non-vanishing nu L/sub 2/ mass. A reference formula for the size of the effect is m/sub nu / approximately=m/sup 2 //M with M a huge Majorana mass of the nu /sub R/ field, associated with the breaking of the group down to SU(3)*SU(2)*U(1) and m a typical quark mass, most likely that of charge 2/3. This is because of the Pati-Salam SU(4) which relates neutrinos with charge 2/3 quarks, and is contained in the prototypes of these theories, SO(10) or E/sub 6/. Ten GeV for m requires M approximately=10/sup 11/ GeV in order to saturate the cosmological bound (m/sub nu / of a few eV). This value is not too far from the currently preferred mass approximately=10/sup 14/ GeV of the superheavy gauge bosons. In view of these concepts, the search for neutrino oscillations appears to be of overwhelming importance. A combined effort in all different kinds of possible experiments (reactors, accelerators, deep mines, and solar neutrino observations) may indeed lead to a positive result since the range of values indicated, m/sub nu / approximately 10/sup -5/-1 eV, overlaps considerably with the expected sensitivities. (12 refs).