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 $P=\mathrm{daig}(e^{i{\varphi }_1},e^{i{\varphi }_2},e^{i{\varphi }_3})$ 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 ${\delta }_{CP}^{\ell }$ 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.e. ${\delta }_{CP}^{\ell }\sim -{\delta }_{CP}^q$.

Comments: 24 pages, 2 figures