CKM Matrix Elements

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.

Comments: v5, LaTeX, 6 pages, 2 figures, minor changes