Flavor dependence of annihilation parameters in QCD factorization

For B_d,s→π^∓K^± and K^(*)K^(*) decays, the flavor symmetry-breaking effects may be particularly small since the final-state interactions should be the same between the corresponding B_d and B_s decays due to the charge conjugation symmetry of the final states. This is consistent with the newly measured direct CP asymmetry of B_s→π⁺K^-. These decays are thus supposed to be important in testing the Standard Model and in probing new physics effects. However, the observation of pure annihilation decay B_s→π⁺π^- appears to imply a large annihilation scenario with ρ_A∼3, in contrast to the case of ρ_A∼1 in B_u,d decays in the framework of QCD factorization. This seems to indicate unexpectedly large flavor symmetry-breaking effects between the annihilation amplitudes of B_s and B_u,d decays. This apparent contradiction could be resolved by noticing that there is a priori no reason to justify the common practice of assuming the universality of annihilation parameters for different Dirac structures of effective operators. We then argue that, for B_d,s→π^∓K^± decays, the flavor symmetry-breaking effects of annihilation amplitudes have all been included in the initial-state decay constants and are thus small. But the flavor symmetry-breaking effects in B_d,s→K^(*)K^(*) decays are likely to be much larger, as part of the annihilation topologies of B_s→KK decay could be related to B_s→π⁺π^- decay. Therefore when new physics effects are searched for in these decay channels, care must be taken to consider the potentially large flavor symmetry-breaking effects in more detail.