Origin of Hierarchical Structures of Quark and Lepton Mass Matrices

TL;DR

This paper presents a Yukawaon model that unifies quark and lepton mass and mixing parameters using minimal family-dependent parameters, successfully predicting CP violation phases.

Contribution

It introduces a phase matrix with family-independent parameters, enabling a unified description of masses, mixing, and CP violation without hierarchical family-dependent parameters.

Findings

Predicts quark CP phase $ o 72^\u00b0$

Predicts lepton CP phase 76b0

Achieves unified mass and mixing description

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 $P={\rm daig}(e^{i \phi_1}, e^{i \phi_2}, e^{i \phi_3})$ with the phase parameters $(\phi_1, \phi_2, \phi_3)$ 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. $\delta_{CP}^\ell \sim - \delta_{CP}^q$.