A new simple form of quark mixing matrix

TL;DR

This paper introduces a new simple parametrization of the quark mixing matrix based on the triminimal expansion, which is more convenient for analysis and measurement of CP violation, and useful for exploring new physics.

Contribution

A novel quark mixing matrix parametrization derived from the triminimal expansion, offering advantages over the Wolfenstein form for numerical analysis and CP violation studies.

Findings

The new parametrization aligns with the hierarchical structure of the CKM matrix.

It simplifies numerical analysis and measurement of CP-violating phases.

It is useful in conjunction with the unitarity boomerang for new physics searches.

Abstract

Although different parametrizations of quark mixing matrix are mathematically equivalent, the consequences of experimental analysis may be distinct. Based on the triminimal expansion of Kobayashi-Maskawa matrix around the unit matrix, we propose a new simple parametrization. Compared with the Wolfenstein parametrization, we find that the new form is not only consistent with the original one in the hierarchical structure, but also more convenient for numerical analysis and measurement of the CP-violating phase. By discussing the relation between our new form and the unitarity boomerang, we point out that along with the unitarity boomerang, this new parametrization is useful in hunting for new physics.