Constraint on the CKM angle alpha from the experimental measurements of CP violation in B_d⁰ --> pi^+ pi^- 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 --> 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 strong constraint on both the CKM angle alpha and the strong phase delta can be obtained from the measured CP asymmetries S_{pi pi} and A_{pi pi}: (a) the ranges of 87 degrees <= alpha <= 131 degrees and 36 degrees <= delta <= 144 degrees are allowed by 1 sigma of the averaged data for r = 0.31; (b) for Belle's result alone, the limits on alpha and delta are 104 degrees <= alpha <= 139 degrees and 42 degrees <= delta <= 138 degrees for 0.32 <= r <= 0.41; and (c) the angle alpha larger than 90 degrees is preferred.