Quark Mass Matrices, textures and CKM precision measurements

TL;DR

This paper reconstructs simplified, texture-specific quark mass matrices within the Standard Model, using CKM matrix unitarity and quark mass hierarchies, to explain quark mixing and CP violation with minimal parameters.

Contribution

It introduces a model-independent approach to derive quark mass matrices that align with experimental data, highlighting the sufficiency of a single CP phase in explaining mixing patterns.

Findings

Vanishing (11) element in down quark mass matrix from measured parameters.

Single CP phase $ ext{delta}_{13}$ explains observed mixing.

Analytic solutions for quark mass matrices derived from CKM data.

Abstract

In the light of several recent analyses pointing towards texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and simplified structure of texture specific quark mass matrices in a generalized 'u-diagonal' basis within the Standard Model framework using the Unitarity of CKM matrix and the observed hierarchies in quark mass spectra and mixing angles. It is observed that the measured 1$\sigma$ values of the three physical parameters namely $m_{\rm{u}}$, $m_{\rm{d}}$ and $s_{12}$ naturally lead to the vanishing of (11) element in the down type quark mass matrix and that the single measurable CP violating phase $\delta_{13}$ in the CKM matrix is sufficient enough in $M^{\prime}_{\rm{d}}$ to explain the observed mixing pattern in a suitable basis. The leading order as well as exact analytic phenomenological solutions are addressed for the modest pattern of quark mass matrices derived from CKM matrix and precision measurements of mixing parameters.