A general analysis of γ determinations from B → πK decays

We present a general parameterization of B^± → π^± K, π⁰ K^± and B_d → π⁰ K, π^∓ K^± decays, taking into account both electroweak penguin and rescattering effects. This formalism allows - among other things - a generalized implementation of the strategies that were recently proposed by Neubert and Rosner to probe the CKM angle γ with the help of B^± → π^± K, π⁰ K^± decays. In particular, it allows us to investigate the sensitivity of the extracted value of γ to the basic assumptions of their approach. We find that certain rescattering processes may have an important impact and emphasize that additional hadronic uncertainties may be due to non-factorizable SU (3)-breaking effects. The former can be controlled by using SU (3) flavour symmetry arguments and additional experimental information provided by B^± → K^± K modes. We propose a new strategy to probe the angle γ with the help of the neutral decays B_d → π⁰ K, π^∓ K^±, which is theoretically cleaner than the B^± → π^± K, π⁰ K^± approach. Here rescattering processes can be taken into account by just measuring the CP-violating observables of the decay B_d → π⁰ K_s. Finally, we point out that an experimental analysis of B_s → K⁺ K^- modes would also be very useful to probe the CKM angle γ, as well as electroweak penguins, and we critically compare the virtues and weaknesses of the various approaches discussed in this paper. As a by-product, we point out a strategy to include the electroweak penguins in the determination of the CKM angle α from B → ππ decays.