A Symmetry Breaking Pattern in the SU(7) Grand Unified Model

Abstract

A pattern of symmetry breaking is investigated systematically in the SU(7) GUM, in which the fundamental representation 7 of SU(7) consists of 5 of SU(5) and its two singlets with the opposite charges ±q(q = 1/2). By analyzing the Higgs potentials as well as the masses of scalar and gauge bosons at each stage of symmetry breaking, we find, among other things, the following two results;

1. a breaking path with q = 1/2, SU(7) → SU(4)_C × SU(3)_W × U(1) at M → SU(3)_C × SU(2)_W × U(1) at M₁ → SU(3)_C × U(1)^em at M_W, is indeed realized, and

2. the positivity of (mass)²'s of physical scalars under the masslessness condition for the scalars which cause the symmetry breaking at the successive stages is surely guaranteed, in a finite range of the coupling constants of the Higgs potentials participating in the whole stages.