SO₁₀ as a Viable Unification Group

Abstract

The simplest unification of electroweak and strong interactions is realized by the SU₅ model of Georgi and Glashow¹ which incorporates the electric charge. There are, however, several indications that the SU₅ model is only a step in the right direction and not the definitive model, even though it gives a roughly successful account of the value for sin²θ_W and of certain mass ratios². For one, there just are too many known elementary fermions, and in SU₅ left- and right-handed components of the same mass fermion must appear in different representations: each family of “comparable” mass is described by a reducible combination $\bar 5 + 10$ of left-handed Weyl spinors. The lightest such family contains ${e^ - },{\upsilon _{eL}},\vec u\,{\text{and}}\,\vec d$, the additional families for the $\bar \mu \,{\text{and }}\bar \tau$ are just clones of the first family^[F1].