Constraint on the CKM angleαfrom the experimental measurements ofCPviolation inBd0→π+π−decay

In this paper, we study and try to find the constraint on the Cabibbo-Kobayashi-Maskawa (CKM) angle $\alpha$ from the experimental measurements of $\mathrm{CP}$ violation in $B_d^0\to {\pi }^{+}{\pi }^{-}$ decay, as reported very recently by the BaBar and Belle Collaborations. After considering the uncertainties of the data and the ratio r of the penguin to the tree amplitudes, we found that a strong constraint on both the CKM angle $\alpha$ and the strong phase $\delta$ can be obtained from the measured $\mathrm{CP}$ asymmetries $S_{\pi \pi }$ and $A_{\pi \pi }:$ (a) The ranges of $87°<~\alpha <~131°$ and $36°<~\delta <~144°$ are allowed by $1\sigma$ of the averaged data for $r=0.31;$ (b) for the Belle result alone, the limits on $\alpha$ and $\delta$ are $104°<~\alpha <~139°$ and $42°<~\delta <~138°$ for $0.32<~r<~0.41;$ and (c) an angle $\alpha$ larger than $90°$ is preferred.