Abstract :
The supersymmetric SU(6) model equipped with the flavour-blind discrete gauge symmetry Z3 is considered. It provides a simultaneous solution to the doublet-triplet splitting problem, the μ-problem and leads to a natural undertanding of fermion flavour. The Higgs doublets arise as Goldstone modes of the spontaneously broken accidental global SU(6) × U(6) symmetry of the Higgs superpotential. Their couplings to fermions have peculiarities leading to a consistent picture of the quark and lepton masses and mixing, without invoking the horizontal symmetry or zero texture concepts. In particular, the only particle that has a direct O(1) Yukawa coupling with the Higgs doublet is the top quark. Other fermion masses arise from higher order operators, with a natural mass hierarchy described in terms of the small ratios εΣ = VΣVh and εH = VHM, where Vh and VΣ are the corresponding SU(6) and SU(5) symmetry breaking scales, and M is a large (Planck or string) scale. The model automatically implies almost precise b - τ Yukawa unification. Specific mass formulas are also obtained, relating the down quark and charged lepton masses. Neutrinos get small (∼ 10−5 eV) masses which can be relevant for solving the solar neutrino problem via long wavelength vacuum oscillations.
