Yukawaon Model with Anomaly Free Set of Quarks and Leptons in a U(3) Family Symmetry

Abstract: In the so-called "yukawaon" model, the (effective) Yukawa coupling constants $Y_f^{eff}$ are given by vacuum expectation values (VEVs) of scalars $Y_f$ (yukawaons) with $3\times 3$ components. So far, yukawaons $Y_f$ have been assigned to ${\bf 6}$ or ${\bf 6}^*$ of U(3) family symmetry, so that quarks and leptons were not anomaly free in U(3). In this paper, yukawaons are assigned to ${\bf 8}+{\bf 1}$ of U(3), so that quarks and leptons are anomaly free. Since VEV relations among yukawaons are also considerably changed, parameter fitting of the model is renewed. After fixing our free parameters by observed mass ratios, we have only two and one remaining free parameters for quark and lepton mixings, respectively. We obtain successful predictions for the quark and lepton mixing parameters including magnitudes of $CP$ violation. The effective Majorana neutrino mass is also predicted.