Universal bilinear form of quark and lepton mass matrices

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. In the present model, all of the VEV matrices $\langle Y_f \rangle$ are given by a bilinear form of VEVs of flavons $\Phi_f$, $\langle Y_f \rangle_i^{\ j} = k_f \langle \Phi_f\rangle_{ik} \langle \bar{\Phi}_f\rangle^{kj}$, where $\Phi_f$ is assigned to ${\bf 6}$ of U(3) family symmetry. As input parameters with family-number dependent values, we use only charged lepton mass values. Under this formulation, we can give reasonable values of quark and lepton masses and their mixings. A $CP$ violating phase $\delta_{CP}^\ell=26^\circ$ in the lepton sector is predicted. The effective Majorana neutrino mass is also predicted.