Fermion mass hierarchy, Kobayashi-Maskawa matrix, and weak and strongCPsolution with a non-Abelian family symmetry

We present a prototype model in which the observed family structure is entirely due to the family symmetry and its breaking patterns present at the axion scale. The model is based upon an SU(3) global family group and an Abelian group, in which U(1${)}_{\mathrm{PQ}}$ is a subgroup. The model successfully explains the observed fermion mass hierarchy, the Kobayashi-Maskawa (KM) matrix, and the weak and strong-CP problem on the same footing. The observed fermion mass hierarchy is naturally obtained from the smallest dimensionless parameter of order of the Cabibbo angle (theta≃(1/5)) while the weak-CP phase of π/2 is generated by spontaneous symmetry breaking at the axion scale. The entire KM angles are correctly produced in terms of the observed quark mass ratios from the Fritzsch ‘‘texture’’ of quark mass matrices. Three generations of superheavy Dirac fermions are predicted to exist at the axion scale. These fermions are in one-to-one correspondence with the three generations of ordinary quarks and leptons, and can be regarded as their ‘‘mirror image’’. The best way of testing the scenario presented in the model would be to detect some of the familons predicted by the model.