U(3)-flavor nonet scalar as an origin of the flavor mass spectra

According to an idea that the quark and lepton mass spectra originate in a VEV structure of a U(3)-flavor nonet scalar Φ, the mass spectra of the down-quarks and charged leptons are investigated. The U(3) flavor symmetry is spontaneously and completely broken by non-zero and non-degenerated VEVs of Φ, without passing any subgroup of U(3). The ratios (me+mμ+mτ)/(me+mμ+mτ)2 and memμmτ/(me+mμ+mτ)3 are investigated based on a toy model.