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. ${\delta }_{CP}^{\ell }\sim -{\delta }_{CP}^q$.

24 pages, 2 figures

References in corpus (6)

• Big-Bang Nucleosynthesis
• Updated Values of Running Quark and Lepton Masses
• O(3) Flavor Symmetry and an Empirical Neutrino Mass Matrix
• Yukawaon Model in the Quark Sector and Nearly Tribimaximal Neutrino Mixing
• Universal Bilinear Form of Quark and Lepton Mass Matrices
• Leptonic $CP$ violating Phase in the Yukawaon Model

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• A modified version of the Koide formula from flavor nonets in a scalar potential model and in a Yukawaon model
• On uplimit of accurate measurement of tau mass