SUSY SU(6) GIFT for doublet-triplet splitting and fermion masses

Abstract

The supersymmetric $SU(6)$ model equipped by the flavour-blind discrete gauge symmetry $Z_3$ is considered. It provides simultaneous solution to the doublet-triplet splitting problem, $μ$-problem and leads to natural understanding of fermion flavour. The Higgs doublets arise as Goldstone modes of the spontaneously broken {\em accidental} global symmetry $SU(6)\times U(6)$ of the Higgs superpotential. Their couplings to fermions have peculiarities leading to the 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 direct $O(1)$ Yukawa coupling with the Higgs doublet is top quark. Other fermion masses arise from the higher order operators, with natural mass hierarchy described in terms of small ratios $\eps_Σ=V_Σ/V_H$ and $\eps_H=V_H/M$, where $V_H$ and $V_Σ$ correspondingly are the $SU(6)$ and $ SU(5)$ symmetry breaking scales, and $M$ is a large (Planck or string) scale. The model automatically implies $b-τ$ Yukawa unification. Specific mass formulas are also obtained, relating the down quark and charged lepton masses. Neutrinos get small ($\sim 10^{-5}\,$eV) masses which can be relevant for solving the solar neutrino problem via long wavelength vacuum oscillation.