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

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.

Comments: In this version we added comparison with the experimental data of the known values of the Jarlskog invariants. That comparison shows that some tension is present at the level of the unitarity triangle