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 $⟨Y_f⟩$ are given by a bilinear form of VEVs of flavons ${\Phi }_f$, $⟨Y_f{⟩}_i^j=k_f⟨{\Phi }_f{⟩}_{ik}⟨{\bar{\Phi }}_f{⟩}^{kj}$, where ${\Phi }_f$ is assigned to $6$ 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.

Comments: 17 pages, 2 figures, Accepted for publication in PRD