Present knowledge of the Cabibbo-Kobayashi-Maskawa matrix

TL;DR

This paper reviews the current knowledge of the CKM matrix, analyzes experimental data to improve precision, tests the Standard Model's CP violation interpretation, and employs Bayesian methods for independent estimation.

Contribution

It provides a comprehensive review, refined measurements, a unitarity test, and Bayesian estimates of the CKM matrix elements, enhancing understanding of CP violation.

Findings

Improved accuracy of CKM matrix elements

Confirmed unitarity constraints within experimental uncertainties

Estimated CP violation parameters with higher precision

Abstract

A complete review of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and of the experimental methods for their determination is presented. A critical analysis of the relevant experimental results, and in particular of the most recent ones, allows to improve the accuracies of all the matrix elements. A chi-square minimization with the three-family unitarity constraint on the CKM matrix is performed to test the current interpretation of the CP violating phenomena inside the Standard Model. A complete and unambiguous solution satisfying all the imposed constraints is found. As a by-product of the fit, the precision on the values of the matrix elements is further increased and it is possible to obtain estimates for the important CP violation observables $sin 2\beta$, $sin 2\alpha$ and $\gamma$. Finally, an independent estimation of the CKM elements based on a Bayesian approach is performed. This complementary method constitutes a check of the results obtained, providing also the probability functions of the CKM elements and of the related quantities.