CKM Matrix Elements

TL;DR

This paper proposes expressing CKM matrix parameters directly in terms of known matrix elements and CP phase, providing a more convenient parametrization consistent with current measurements.

Contribution

It introduces a new parametrization of the CKM matrix using known elements and CP phase, simplifying analysis and aligning with experimental data.

Findings

Derived a relation for the CKM phase gamma from known matrix elements.

Found that measured values of |V_{td}/V_{ts}| and sin beta imply gamma ≈ 68°.

Demonstrated the new parametrization's consistency with global fit results.

Abstract

The current analysis of the Cabibbo-Kobayashi-Maskawa(CKM) quark mixing matrix uses the standard parametrisation by 3 mixing angles and the CP-violating KM phase. However it would be more convenient to express these mixing angle parameters in terms of the known CKM matrix elements like $V_{ud}$, $ V_{us}$, $ V_{ub}$, $V_{cb}$ and the CP-violating phase $\delta$. The other CKM matrix elements are then expressed in terms of these known matrix elements instead of the standard mixing angles. In this paper, using $V_{ud}$, $ V_{us}$, $ V_{ub}$ and $V_{cb}$ from the current global fit, we show that the measured values for $|V_{td}/V_{ts}|$ and $\sin\beta$ imply $\gamma=(68\pm 3)^{\circ}$ at which $\sin\beta$ and $\sin\alpha$ are near its maximum, consistent with the global fit.