Zweig-rule-satisfying inelastic rescattering in B decays to pseudoscalar mesons

Abstract

We discuss all contributions from Zweig-rule-satisfying SU(3)-symmetric inelastic FSI-induced corrections in B decays to $\pi \pi$, $\pi K$, $K\bar{K}$, $\pi \eta (\eta ')$, and $K \eta (\eta ')$ . It is shown how all of these FSI corrections lead to a simple redefinition of the amplitudes, permitting the use of a simple diagram-based description, in which, however, weak phases may enter in a modified way. The inclusion of FSI corrections admitted by the present data allows an arbitrary relative phase between the penguin and tree short-distance amplitudes. The FSI-induced error of the method, in which the value of the weak phase $\gamma $ is to be determined by combining future results from $B^+,B^0_d,B^0_s$ decays to $K\pi$, is estimated to be of the order of $5^o$ for $\gamma \approx 50^o-60^o$.