Simple Non-Abelian Finite Flavor Groups and Fermion Masses

Abstract

The use of nonabelian 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 = $Q_6={}^{(d)}{D}_3$ ( g = 12 ) and the double tetrahedral group ${}^{(d)}T=Q_4\tilde{\times }{Z}_3$ ( g = 24 ). Both can allow a hierarchy $t>b,\tau >c>s,\mu >u,d,e$. 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 $G\subset SU(2)$ is a strong constraint in assignment of fermions to representations of G.

Comments: 23 pages, IFP-702-UNC and VAND-TH-94-8