This class of the family symmetry models was first studied by Froggatt and Nielsen in 1979 and extended later on in. In this mechanism, one introduces a new complex scalar field called flavon ϕ ϕ whose vacuum expectation value (VEV) ⟨ ⟨ ϕ ϕ ⟩ ⟩ presumably breaks a global family symmetry U ( 1 ) F imposed. Under this symmetry different quark-lepton families carry different charges I i ( i = 1 , 2 , 3 ) . Aсcordingly, the connection between families is provided by inclusion into play (via the relevant see-saw mechanism) some intermediate heavy fermion(s) being properly charged under the family symmetry U ( 1 ) F . So, the effective Yukawa coupling constants Y i j ( i , j = 1 , 2 , 3 ) for quark-lepton families are arranged in a way that they may only appear through the primary couplings of these families with the messenger fermion(s) and the flavon field ϕ ϕ . The hierarchy of these couplings is determined by some small parameter ϵ ϵ , which is given by ratio of the flavon VEV ⟨ ⟨ ϕ ϕ ⟩ ⟩ to the mass M F of the intermediate heavy fermion, ϵ ϵ = ⟨ ⟨ ϕ ϕ ⟩ ⟩ / M F (or ϵ ϵ = ⟨ ⟨ ϕ ϕ ⟩ ⟩ / Λ Λ F , if the messenger fermions have been integrated out at some high-energy cut-off scale Λ Λ F ). Since different quark-lepton families carry different charges the various coupling constants Y i j are suppressed by different powers of ϵ ϵ being primarily controlled by the postulated fermion charge assignment.