A 3-3-1 model with SU(8) unification

Abstract

We construct a 3-3-1 model for three families that can be embedded into a single SU(8) unified model. Assuming appropriate branching rules and symmetry-breaking pattern, we find a complete fermion content within irreducible representations of SU(8), where light standard model fermions, heavy 3-3-1 fermions and super-heavy fermions may be distinguished. In the framework of the doubly lopsided mechanism, we obtain mass matrix structures which exhibit nontrivial flavor hierarchical features. Among the up-type quarks, one (top quark) has tree-level mass and two (charm and up) get masses at one-loop level. Considering only dominant contributions, we may obtain the ratios $|m_c/m_t| \approx 7.4 \times 10^{-3}$ and $|m_u/m_c| \approx 1.9 \times 10^{-3}$ with few assumptions on the free parameters and without any hierarchical requirements on the Yukawa couplings.