Constraints on the CKM angle $��$ from the measured CP asymmetries and branching ratios of $B \to ��^+ ��^-, ��^+ ��^0$ and $K^0��^+$ decays

In this paper, we draw constraints on the Cabibbo-Kobayashi-Maskawa (CKM) angle $��$ and the strong phase $��$ from the experimental measurements of $\ssb$, the CP-violating asymmetries and branching ratios of $B \to ��^+ ��^-, ��^+ ��^0$ and $K^0 ��^+$ decays. In the SM, the measured $\ssb$ leads to an upper limit on $��$: $��\leq 180^\circ-��$. Taking the weighted-average of the newest BaBar and Belle measurements of $\spp$ and $\app$ in $B^0 \to ��^+��^-$ decay as the experimental input, we find the allowed range of angle $��$, $76^\circ \leq ��\leq 135^\circ$ for $r=|P/T| =0.3 \pm 0.1 $. From the measured CP-averaged branching ratios of $B \to ��^+ ��^-, ��^+ ��^0$ and $K^0 ��^+$ decays, we found an inequality, $\cos�� \cos�� \geq 0.45$. The region of $70^\circ \leq ��\leq 110^\circ$ is thus excluded by applying this inequality. The combined constraints on $��$ and $��$ are $117^\circ \leq ��\leq 135^\circ$ and $-160^\circ \leq ��\leq -132^\circ$ if we take $\spp=0.49 \pm 0.27$ and $\app=0.51 \pm 0.19$ as the experimental input. The new lower limit on the angle $��$ is dominated by the measured branching ratios considered in this paper, and is much stronger than those obtained before.
31 pages, Revtex, 10 PS/EPs figures, some corrections have been made, several new references added. Repot-no: BIHEP-TH-2003-7