Spontaneous family symmetry breaking and fermion mixing

We propose a theory to describe fermion mixing. The theory respects the maximal abelian family symmetries which are spontaneously broken down at a large scale. We find that quark mixing can be well described in this theory. Some concrete models are constructed. The crucial point for model building is to introduce some new particles which are SU(2) gauge singlets and carry −13 electric charge. The approximate family symmetries in our low-energy effective theory are naturally achieved. Some interesting phenomena in the effective theory, especially with two Higgs-doublets, are discussed.