Neutrino masses in grand unified theories

Various models proposed in the context of a SO(10) grand unified theory to keep the neutrino masses 'naturally' small are discussed. Their connection with the breaking scheme of B-L as a local symmetry is emphasized. Finite and naturally small one-loop radiative corrections to zeroth order neutrino masses arise. The very existence of these corrections leads, however, to a two-loop divergence connected with the existence of explicit Higgs particles in the theory. The renormalization of such a divergence leads in turn to a Higgs potential for which the vanishing neutrino mass is not naturally guaranteed. Possible ways out are indicated. (orig.)