José E. Camargo-Molina, António P. Morais, Astrid Ordell, Roman Pasechnik, Jonas Wessén
Scale hierarchies, symmetry breaking and SM-like fermions 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). While the product of the first three SU(3)'s is known as the gauge trinification originating from E6, an addition of the SU(3)F family symmetry represents yet another possible but unexplored layer of high-scale unification due to an E6×SU(3)F⊂E8 embedding. We discuss the implications of such an embedding in a supersymmetric (SUSY) model based on the trinification gauge [SU(3)]3 and global SU(3)F family symmetries with a constrained set of SUSY conserving and soft SUSY breaking operators. Among the key properties of this model are the unification of SM Higgs and lepton sectors predicting a common Yukawa coupling for chiral fermions, the absence of the μ-problem, gauge couplings unification and baryon number conservation at the Grand Unification scale, as well as light SM fermions. The minimal field content that may lead to a consistent 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 belonging to the fundamental sector of E8. The details of the corresponding (SUSY and gauge) symmetry breaking scheme and the resulting effective low-energy scenarios are discussed.

LU TP 17-37