Final State Interaction Effects on Γ from B → Dk

The implications of a negligible annihilation contribution in B → DK decays are reanalyzed and are shown to lead to no new constraints on the weak phase γ from color-allowed B → DK decays. A test of negligible annihilation is proposed in B → DK (or B → DK), and an application is presented in which γ can be determined from these processes (or corresponding B → DK decays) supplemented with isospin-related neutral B decays. PACS codes: 12.15.Hh, 12.15.Ji, 13.25.Hw, 14.40.Nd Recently one of us proposed a method [1] to constrain the CKM weak phase γ = −Arg(V ∗ ubVud/V ∗ cbVcd) from color-allowed B → DK decays [2], when both flavor and CP-eigenstate neutral D mesons are considered. Decays with flavor states have already been observed by CLEO [3] with branching ratio B(B± → DK±)/B(B± → Dπ) = 0.055 ± 0.014 ± 0.005, or B(B± → DK) ≃ 3 × 10. Our approach was general and involved no dynamical assumptions about hadronic weak matrix elements and about final state interactions. Subsequently Xing [4] claimed that a certain improvement in this method may be achieved by making the dynamical assumption of a negligible annihilation contribution. While this assumption is reasonable, it may be spoiled by rescattering effects [5, 6] and would have to be tested experimentally. One of the purposes of the present letter is to suggest such a test. Our second purpose is to go over the arguments in [4] and to point out a certain flaw in the treatment of final state interactions. By presenting a correct analysis we will show that, in fact, the assumption of a vanishing annihilation contribution does not lead to any further constraint on γ beyond the one obtained in [1]. Finally, we will present a scheme [7] which involves also neutral Permanent Address: Physics Department, Technion – Israel Institute of Technology, 32000 Haifa, Israel.