Model for Particle Masses, Flavor Mixing, and CP Violation Based on   Spontaneously Broken Discrete Chiral Symmetry as the Origin of Families
  We construct extensions of the standard model based on the hypothesis that the Higgs bosons also exhibit a family structure, and that the flavor weak eigenstates in the three families are distinguished by a discrete $Z_6$ chiral symmetry that is spontaneously broken by the Higgs sector. We study in detail at the tree level models with three Higgs doublets, and with six Higgs doublets comprising two weakly coupled sets of three. In a leading approximation of $S_3$ cyclic permutation symmetry the three Higgs model gives a ``democratic'' mass matrix of rank one, while the six Higgs model gives either a rank one mass matrix, or in the case when it spontaneously violates CP, a rank two mass matrix corresponding to nonzero second family masses. In both models, the CKM matrix is exactly unity in leading approximation. Allowing small explicit violations of cyclic permutation symmetry generates small first family masses in the six Higgs model, and first and second family masses in the three Higgs model, and gives a non-trivial CKM matrix in which the mixings of the first and second family quarks are naturally larger than mixings involving the third family. Complete numerical fits are given for both models, flavor changing neutral current constraints are discussed in detail, and the issues of unification of couplings and neutrino masses are addressed. On a technical level, our analysis uses the theory of circulant and retrocirculant matrices, the relevant parts of which are reviewed. 
Stephen L. Adler