Quark Flavor Mixings from Hierarchical Mass Matrices

TL;DR

This paper extends hierarchical quark mass matrices based on the Fritzsch ansatz to better explain the CKM matrix features, including mixing angles and CP violation, with analytical expressions and phenomenological analysis.

Contribution

It introduces an extended hierarchical mass matrix model with non-zero off-diagonal elements to accurately reproduce CKM matrix features and CP violation phenomenology.

Findings

CKM matrix features are well explained by the extended model

Analytical expressions for CKM elements are derived

Model agrees with observed quark mixing angles and CP phase at 1σ level

Abstract

In this paper, we extend the Fritzsch ansatz of quark mass matrices while retaining their hierarchical structures and show that the main features of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $V$, including $|V^{}_{us}| \simeq |V^{}_{cd}|$, $|V^{}_{cb}| \simeq |V^{}_{ts}|$ and $|V^{}_{ub}|/|V^{}_{cb}| < |V^{}_{td}|/|V^{}_{ts}|$, can be well understood. This agreement is observed especially when the mass matrices have non-vanishing $(1,3)$ and $(3,1)$ off-diagonal elements. The phenomenological consequences of these for the allowed texture content and gross structural features of `hierarchical' quark mass matrices are addressed from a model independent prospective under the assumption of factorizable phases in these. The approximate and analytical expressions of the CKM matrix elements are derived, and a detailed analysis reveals that such structures are in good agreement with the observed quark flavor mixing angles and the CP-violating phase at the $1\sigma$ level and call upon a further investigation of the realization of these structures from a top-down prospective.