Hiding the Existence of a Family Symmetry in the Standard Model

Abstract

If a family symmetry exists for the quarks and leptons, the Higgs sector is expected to be enlarged to be able to support the transformation properties of this symmetry. There are however three possible generic ways (at tree level) of hiding this symmetry in the context of the Standard Model with just one Higgs doublet. All three mechanisms have their natural realizations in the unification symmetry E_6 and one in SO(10). An interesting example based on SO(10) X A_4 for the neutrino mass matrix is discussed.Comment: 11 pages, including 3 figure