Hierarchical Quark Mixing and Bimaximal Lepton Mixing on the Same Footing

TL;DR

This paper presents a unified approach to deriving both the hierarchical quark mixing matrix and the bimaximal lepton mixing matrix from a common mass matrix ansatz, explaining observed mixing angles and predicting CP violation measures.

Contribution

It introduces a single mass matrix framework based on broken permutation symmetry that accounts for quark and lepton mixing patterns and predicts CP violation parameters in both sectors.

Findings

Reproduces the measured $eta$ angle in the unitarity triangle.

Matches observed values of the CKM matrix elements.

Predicts a sizable CP violation in the lepton sector.

Abstract

We show that not only the hierarchical quark CKM mixing matrix but also the "bimaximal" lepton flavor mixing matrix can be derived from the same mass matrix ansatz based on the broken permutation symmetry, by assuming the hierarchy of neutrino masses to be $m_1\simeq m_2 <<m_3$. We also reproduce the recently measured angle of unitary triangle, $\sin 2\beta$, as well as all the observed experimental values of $V_{{\tiny CKM}}$ of the quark CKM matrix. And we predict Jarlskog rephasing invariant quantity, $J_{{\tiny CP}} \simeq 0.18 \times 10^{-4}$, and the upper bound of the same quantity in the lepton sector, $J^l_{{\tiny CP}} \leq 0.012$, which may be indeed large enough to generate the lepton number violation of the universe.