Scale hierarchies, symmetry breaking, and particle spectra in SU(3)-family extended SUSY trinification

A unification of left-right SU(3)L×SU(3)R, color SU(3)C, and family SU(3)F symmetries in a maximal rank-8 subgroup of E8 is proposed as a landmark for future explorations beyond the Standard Model (SM). We discuss the implications of this scheme in a supersymmetric (SUSY) model based on the trinification gauge [SU(3)]3 and global SU(3)F-family symmetries. Among the key properties of this model are the unification of SM Higgs and lepton sectors, a common Yukawa coupling for chiral fermions, the absence of the μ problem, gauge couplings unification, and proton stability to all orders in perturbation theory. The minimal field content consistent with a SM-like effective theory at low energies is composed of one E6 27-plet per generation as well as three gauge and one family SU(3) octets inspired by the fundamental sector of E8. The details of the corresponding (SUSY and gauge) symmetry-breaking scheme, multiscale gauge couplings' evolution, and resulting effective low-energy scenarios are discussed.