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

Abstract

Possible symmetry-breaking patterns of SU(8) into $\mathrm{S}{\mathrm{U}}_{C}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{Y}(1)$ and their mass scales, consistent with known values of ${\ensuremath{\alpha}}_{3}$ and ${{sin}^{2}\ensuremath{\theta}}_{W}$, are examined and most are found to be nearly equivalent to direct breaking of SU(8) into $\mathrm{S}{\mathrm{U}}_{C}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{Y}(1)$. 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 zeroth-order 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.