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CKM Matrix Elements

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 $δ$. 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 $\sinβ$ imply $γ=(68\pm 3)^{\circ}$ at which $\sinβ$ and $\sinα$ are near its maximum, consistent with the global fit.