Controlling rescattering effects in constraints on the CKM angle γ arising from B→πK decays

It has recently been pointed out that the observables of the decay B+ --> K+(K) over bar(0) and its charge conjugate allow us to take into account rescattering effects in constraints on the CKM angle gamma arising from B+/- --> pi(+/-)K and B-d --> pi(+/-)K(+/-) modes, and that they play an important role to obtain insights into final-state interactions. In this paper, the formalism needed to accomplish this task is discussed in detail. Furthermore, using a transparent model to describe the rescattering processes, as well as electroweak penguins, we calculate the quantities parametrizing the B+ --> pi(+)K(0) and B-d(0) --> pi(-)K(+) decay amplitudes for specific examples, and illustrate the constraints on gamma arising from the corresponding observables. Although this model is very crude, it shows nicely the power of B+/- --> K+/-K both to include the rescattering effects in the bounds on gamma and to obtain insights into final-state interactions. Moreover this model exhibits the interesting feature that the combined branching ratio BR(B+/- --> K+/-K) may be considerably enhanced through rescattering processes. as was recently pointed out within a general framework. (C) 1998 Elsevier Science B.V. All rights reserved.