Origin of Hierarchical Structures of Quark and Lepton Mass Matrices

Abstract

It is shown that the so-called "Yukawaon" model can give a unified description of masses, mixing and $CP$ violation parameters of quarks and leptons without using any hierarchical (family number-dependent) parameters besides the charged lepton masses. Here, we have introduced a phase matrix $P={\rm daig}(e^{i ϕ_1}, e^{i ϕ_2}, e^{i ϕ_3})$ with the phase parameters $(ϕ_1, ϕ_2, ϕ_3)$ which are described in terms of family number-independent parameters, together with using only the charged lepton mass parameters as the family number-dependent parameters. In this paper, the $CP$ violating phase parameters $δ_{CP}^q$ and $δ_{CP}^\ell$ in the standard expression of $V_{CKM}$ and $U_{PMNS}$ are predicted as $δ_{CP}^q \simeq 72^\circ$ and $δ_{CP}^\ell \simeq -76^\circ$, respectively, i.e. $δ_{CP}^\ell \sim - δ_{CP}^q$.