Neutrino masses in the minimal O(10) theory

Neutrino masses are discussed in the context of the O(10) grand unified theory. In the 'minimal' form of this theory, with minimal Higgs and fermions content, the right-handed neutrinos acquire masses at the two loop level. The left-handed neutrino masses are correspondingly larger by a factor roughly (α/π)-2 than they would be if the right-handed neutrino could acquire mass at the tree level. In the simplest form of this theory, the neutrino mass matrix is proportional to the up quark mass matrix, and the neutrino mixing angles equal the usual Cabibbo angles. The neutrino masses will be roughly in the range 100+-2 eV depending on the strength of O(10) symmetry breaking, and on certain unknown ratios of masses and couplings of superheavy particles. (orig.)