Unitarity Boomerang

TL;DR

The paper introduces the unitarity boomerang as a new way to represent the quark flavor mixing matrix, capturing all four parameters simultaneously, unlike the traditional unitarity triangle.

Contribution

It proposes the unitarity boomerang as an alternative visualization that displays all four parameters of the CKM matrix at once.

Findings

Unitarity boomerang visually encodes all four CKM parameters.

Provides a comprehensive picture of quark mixing.

Enhances understanding of CP violation in the Standard Model.

Abstract

For the three family quark flavor mixing, the best parametrization is the original Kobayashi-Maskawa matrix, $V_{KM}$, with four real parameters: three rotation angles $\theta_{1,2,3}$ and one phase $\delta$. A popular way of presentation is by the unitarity triangle which, however, explicitly displays only three, not four, independent parameters. Here we propose an alternative presentation which displays simultaneously all four parameters: the unitarity boomerang.