Fermion masses and coupling unification inE6: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 vectorlike heavy quarks and leptons. The lightest of those can lie in the low-TeV range, being accessible to future collider experiments. As a result of 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 $\mathcal{C}P$ violation arise from a single antisymmetric matrix. The ${E}_{6}$ breaking proceeds via an intermediate-energy region with ${\mathrm{SU}(3)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{R}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{C}$ 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.