On one parametrization of Kobayashi-Maskawa matrix

TL;DR

This paper critically examines the Wolfenstein parametrization of the Kobayashi-Maskawa matrix, revealing a fundamental flaw that questions the reliability of many phenomenological analyses based on it.

Contribution

It identifies a key flaw in the Wolfenstein parametrization, showing it depends on three parameters instead of four, which affects its validity in phenomenological studies.

Findings

Wolfenstein parametrization depends on three parameters, not four.

Current phenomenological analyses using this parametrization may be unreliable.

The flaw persists even when the parametrization is made exact.

Abstract

An analysis of Wolfenstein parametrization for the Kobayashi-Maskawa matrix shows that it has a serious flaw: it depends on {\em three} independent parameters instead of {\em four} as it should be. Because this approximation is currently used in phenomenological analyzes from the quark sector, the reliability of almost all phenomenological results is called in question. Such an example is the latest PDG fit from \cite{CA}, p. 150. The parametrization cannot be fixed since even when it is brought to an exact form it has the same flaw and its use lead to many inconsistencies.