New origin of a bilinear mass matrix form

A charged lepton mass formula is explained when the masses are proportional to the squared vacuum expectation values (VEVs) of scalar fields. We introduce a U(3) flavor symmetry and its nonet scalar field Φ, whose VEV structure plays an essential role for generating the fermion mass spectrum. We can naturally obtain a bilinear form of the Yukawa coupling Yij∝∑k〈Φik〉〈Φkj〉 without non-renormalizable interactions, when the flavor symmetry is broken only through Yukawa coupling and tadpole terms. We also speculate a possible VEV structure of 〈Φ〉.