Abstract
We make a further study of the CP-violating asymmetry for the decays B d 0→D +D −, π +π −, and K +π −, which have both tree-level and penguin amplitudes. We confirm that the final-state phase shifts can lead to significant direct CP violation for these decays, and find that the absorptive part in the penguin amplitude can also lead to direct CP-violating asymmetry for each decay, which is about 5% in the standard model. The numerical predictions of the CP-violating asymmetries are given against final-state phase shifts, and they are quite different from those by Tanimoto et al. [Phys. Rev. D 42 (1990) 252].
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