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.
Categories: hep-ph hep-ex