where again the index f stands for the particular family of the up quarks ( U = u , c , t ) and down quarks ( D = d , s , b ), respectively ( A f ( a ) and B f ( b ) are some dimensionless proportionality constants of the O ( 1 ) order). These coupling constants normally appear via the sort of the see-saw mechanism due to the exchange of a special set of heavy (of order the family symmetry scale M F ) vectorlike fermions. The VEVs of the horizontal scalars taken in general as large as M F , are supposed to be hierarchically arranged along the different directions in family flavor space. This hierarchy is then transferred to their mass matrices m i j ( U ) and m i j ( D ) , when the conventional Standard Model Higgs boson H develops its own VEV in the corresponding Yukawa couplings