Constraint on the CKM angle $α$ from the experimental measurements of CP violation in $B_d^0 \to π^+ π^-$ decay

In this paper, we study and try to find the constraint on the CKM angle $\alpha$ from the experimental measurements of CP violation in $B_d^0 \to \pi^+ \pi^-$ decay, as reported very recently by BaBar and Belle Collaborations. After considering uncertainties of the data and the ratio $r$ of penguin over tree amplitude, we found that: (a) strong constraint on both the CKM angle $\alpha$ and the strong phase $\delta$ can be obtained from the measured $\spp$, $A_{\pi\pi}$: only the ranges of $86^\circ \leq \alpha \leq 148^\circ$ and $31^\circ \leq \delta \leq 143^\circ$ are still allowed by $1\sigma$ of the averaged data; (b) For Belle's result alone, the limit on $\alpha$ is $95^\circ \leq \alpha \leq 152^\circ$. The angle $\alpha$ larger than $90^\circ$ is strongly preferred.