Origin of Hierarchical Structures of Quark and Lepton Mass Matrices

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 $P=\mathrm{d}\mathrm{a}\mathrm{i}\mathrm{g}(e^{i{\varphi }_1},e^{i{\varphi }_2},e^{i{\varphi }_3})$ with the phase parameters $({\varphi }_1,{\varphi }_2,{\varphi }_3)$ 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 ${\delta }_{CP}^q$ and ${\delta }_{CP}^{\mathrm{\ell }}$ in the standard expression of $V_{CKM}$ and $U_{PMNS}$ are predicted as $\delta_{CP}^q \simeq 72^\circ$and$\delta_{CP}^\ell \simeq -76^\circ$,respectively,i\mathrm{.}e\mathrm{.}$\delta_{CP}^\ell \sim - \delta_{CP}^q$.