A general analysis of

Abstract

We present a general parametrization of $B^\pm\to\pi^\pm K$ , $\pi^0K^\pm$ and $B_d\to\pi^0 K$ , $\pi^\mp K^\pm$ 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 $\gamma$ with the help of $B^\pm\to\pi^\pm K$ , $\pi^0K^\pm$ decays. In particular, it allows us to investigate the sensitivity of the extracted value of $\gamma$ 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 $B^\pm\to K^\pm K$ modes. We propose a new strategy to probe the angle $\gamma$ with the help of the neutral decays $B_d\to\pi^0 K$ , $\pi^\mp K^\pm$ , which is theoretically cleaner than the $B^\pm\to\pi^\pm K$ , $\pi^0K^\pm$ approach. Here rescattering processes can be taken into account by just measuring the CP-violating observables of the decay $B_d\to\pi^0K_{\rm S}$ . Finally, we point out that an experimental analysis of $B_s\to K^+K^-$ modes would also be very useful to probe the CKM angle $\gamma$ , 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 $\alpha$ from $B\to\pi\pi$ decays.