Can Massless and Light Yukawaons be Harmless?

In the so-called yukawaon model, where the effective Yukawa coupling constants Y_f^{eff} (f=e,\nu,u,d) are given by vacuum expectation values (VEVs) of gauge singlet scalars (yukawaons) Y_f with 3\times 3 components, i.e. Y_f^{eff}= y_f < Y_f>/\Lambda, massless (and light) scalars appear because a global flavor symmetry is assumed. In order to demonstrate whether such massless scalars in the yukawaon model are harmless or not, yukawaon masses are explicitly estimated, as an example, in the charged lepton sector.