Radiative fermion masses in grand unified theories

Abstract

We study the radiative quark and lepton masses appearing in grand unified theories (GUT's) based on SU( N), SO(10), SO(4 N + 10) and E 6 groups. Even in simple one-family models like SO(10) and E 6, radiative graphs give rise to substantial contributions to the fermion masses. For example, in those models, in order not to get an excessively big u-quark radiative mass we must have M νe R ⪅ 10 12−10 13 GeV. We also suggest that all the observed fermion masses may have a radiative origin. In such a case the observed hierarchy of fermion masses (10 −3−10 2 GeV) may be a reflection of a “cascade decay” of the GUT occurring in the energy range 10 14−10 19 GeV. SU( N) GUT's provide us with specific examples of this scenario. We discuss models based on SU(9), SU(10) and SU(11). However, SU( N) models may lead to big Kobayashi-Maskawa angles. Models based on SO(4 N + 10) groups may also lead to hierarchical change − 2 3 quark masses. An interesting SO(18) example is discussed. As a general feature of most of the models, the charge + 2 3 quarks tend to get bigger radiative masses than their charge − 1 3 partners. It is finally argued that the fermion spectrum may give us invaluable information about the 10 14−10 19 GeV energy range.