Test of the 4-th quark generation from the Cabibbo-Kobayashi-Maskawa matrix

TL;DR

This paper investigates the implications of a potential fourth quark generation on the CKM matrix, suggesting that certain measurements could reveal its existence and highlighting tensions with the three-generation model.

Contribution

It introduces a method to test for a fourth quark generation using Jarlskog invariants and analyzes how this affects the CKM matrix and CP violation measures.

Findings

Unitarity quadrangle area is not a reliable CP violation measure.

Possible tension with three-generation CKM unitarity from current data.

Scalar product measurements could indicate the existence of a fourth quark generation.

Abstract

The structure of the mixing matrix, in the electroweak quark sector with four generations of quarks is investigated. We conclude that the area of the unitarity quadrangle is not a good choice as a possible measure of the CP~violation. In search of new physics we analyze how the existence of the 4-th quark family may influence on the values of the Cabibbo-Kobayashi-Maskawa matrix and we show that one can test for the existence of the 4-th generation using the Jarlskog invariants of the known quarks only. The analysis based on the measured unitary triangle exhibits some tension with the assumption of three quark generations. The measurement of the unitarity triangle obtained from the scalar product of the second row/column of the CKM matrix by the complex conjugate of third row/column can provide information about the existence of the fourth generation of quarks.