Symmetry-breaking mass scales and fermion mass relations in SU(8) grand unification

Abstract

Possible symmetry-breaking patterns of SU(8) into SUc(3 ) X SUL(2) X Uy( 1) and their mass scales, consistent with known values of a3 and sin20w, are examined and most are found to be nearly equivalent to direct breaking of SU(8) into SUc(3) X S U L ( 2 ) x U y ( 1). However, there exist patterns in which the intermediate mass scales can be low or completely arbitrary. The method of maximal-subgroup chains is used to determine zerothorder fermion mass relations. These are then renormalized to present energies. It is found that a three-step pattern which eliminates the desert inherent in the SU(5) model in the most interesting way also predicts fermion mass ratios consistent with experiment.