Relations among Elements of the Quark Mass Matrices

TL;DR

This paper investigates empirical relations between quark mixing matrix elements and mass ratios, exploring their implications for the structure of quark mass matrices and the origin of Yukawa couplings.

Contribution

It systematically examines the suggested relations and derives new relations among quark mass matrix elements, providing insights into Yukawa coupling origins.

Findings

Relations between CKM matrix elements and quark mass ratios are supported.

Derived relations among mass matrix elements suggest underlying patterns.

Potential clues to the origin of Yukawa couplings are identified.

Abstract

Current experimental data suggest some relations between the Kobayashi-Maskawa Matrix and the quark mass ratios, namely $|V_{us}| \sim \sqrt{m_d / m_s}$, $|V_{ub} / V_{cb}| \sim \sqrt{m_u / m_c}$ and $|V_{cb}| \sim m_s / m_b$. We consider these relations seriously in this paper. As a result, they offer us some attractive relations among the elements of the mass matrices and bring us a problem. They might give us informations about the origin of Yukawa couplings.