Permutation symmetries and the fermion mass matrix

Abstract

We consider SU(2)\ifmmode\times\else\texttimes\fi{}U(1) gauge models with an additional global symmetry of ${\mathrm{S}}_{n}$ type. In particular, we study ${\mathrm{S}}_{4}$ symmetry for a six-quark---six-lepton standard model. We find that the Kobayashi-Maskawa matrix is completely determined and the mass of the $t$ quark is predicted. Some of the results persist in ${\mathrm{S}}_{n}$ applied to $n$ families. Restrictions on neutrino masses and mixings are given. Implications of $\mathrm{CP}$ and flavor nonconservation that arise in the neutral-Higgs-boson sector are discussed.