Phenomenological formula for CKM matrix and its physical interpretation

TL;DR

This paper introduces a phenomenological formula linking quark masses and the CKM matrix, aligning well with experimental data and suggesting the maximization of the weak interaction amplitude.

Contribution

It proposes a novel phenomenological relation between quark masses and the CKM matrix, providing physical insight into weak interactions.

Findings

The formula agrees with experimental CKM data.

It indicates the invariant amplitude of charged current interactions is maximized.

Provides a new perspective on quark mass and mixing relationships.

Abstract

We propose a phenomenological formula relating the Cabibbo--Kobayashi--Masukawa matrix $V_{CKM}$ and quark masses in the form $(\sqrt{m_d} \, \sqrt{m_s} \, \sqrt{m_b}) \propto (\sqrt{m_u} \, \sqrt{m_c} \, \sqrt{m_t})V_{CKM}$. The results of the proposed formula are in agreement with experimental data. Under the constraint of the formula, we show that the invariant amplitude of the charged current weak interactions is maximized.