SIMPLE NON-ABELIAN FINITE FLAVOR GROUPS AND FERMION MASSES

Abstract

The use of non-Abelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g=31, the most appealing candidates are two subgroups of SU(2): the dicyclic (double dihedral) group G=Q6= (d) D3(g=12) and the double tetrahedral group [Formula: see text]. Both can allow a hierarchy t>b, τ>c>s, μ>u, d, e. The top quark is uniquely allowed to have a G symmetric mass. Sequential breaking of G and radiative corrections give the smaller masses. Anomaly freedom for gauging G⊂ SU (2) is a strong constraint in assignment of fermions to representations of G.