Fermion Masses and Coupling Unification in E6. Life in the Desert

Abstract

We present an $E_6$ Grand Unified model with a realistic pattern of fermion masses. All standard model fermions are unified in three fundamental 27-plets (i.e. supersymmetry is not invoked), which involve in addition right handed neutrinos and three families of vector like heavy quarks and leptons. The lightest of those can lie in the low TeV range, being accessible to future collider experiments. Due to the high symmetry, the masses and mixings of all fermions are closely related. The new heavy fermions play a crucial role for the quark and lepton mass matrices and the bilarge neutrino oscillations. In all channels generation mixing and ${\cal CP}$ violation arise from a single antisymmetric matrix. The $E_6$ breaking proceeds via an intermediate energy region with $SU(3)_L\tm SU(3)_R\tm SU(3)_C$ gauge symmetry and a discrete left-right symmetry. This breaking pattern leads in a straightforward way to the unification of the three gauge coupling constants at high scales, providing for a long proton lifetime. The model also provides for the unification of the top, bottom and tau Yukawa couplings and for new interesting relations in flavor and generation space.