Hunting for New Physics with Unitarity Boomerangs

TL;DR

This paper explores unitarity boomerangs as a complete tool for determining the CKM matrix, revealing potential for new physics beyond what unitarity triangles can offer.

Contribution

It introduces the concept of unitarity boomerangs formed from two unitarity triangles, showing they can fully determine the quark mixing matrix and are more informative for new physics searches.

Findings

There are 18 possible unitarity boomerangs.

One boomerang is ideal for practical use due to larger angles.

Invariant quantity related to the Jarlskog parameter is identified.

Abstract

Although the unitarity triangles ($UTs$) carry information about the Kobayashi-Maskawa (KM) quark mixing matrix, it explicitly contains just three parameters which is one short to completely fix the KM matrix. It has been shown recently, by us, that the unitarity boomerangs ($UB$) formed using two $UTs$, with a common inner angle, can completely determine the KM matrix and, therefore, better represents, quark mixing. Here, we study detailed properties of the $UBs$, of which there are a total 18 possible. Among them, there is only one which does not involve very small angles and is the ideal one for practical uses. Although the $UBs$ have different areas, there is an invariant quantity, for all $UBs$, which is equal to a quarter of the Jarlskog parameter $J$ squared. Hunting new physics, with a unitarity boomerang, can reveal more information, than just using a unitarity triangle.