Elastic and inelastic SU(3)-breaking final-state interactions in B decays to pseudoscalar mesons

Abstract

We discuss all contributions from Zweig-rule-satisfying SU(3)-breaking final state interactions (FSIs)in the B -> PP decays (neglecting charmed intermediate states), where PP=pi pi, pi K, KK, pi eta (eta'), and K eta (eta'). First, effects of SU(3) breaking in rescattering through Pomeron exchange are studied. Then, after making a plausible assumption concerning the pattern of SU(3) breaking in non-Pomeron FSIs, we give general formulas for how the latter modify short-distance (SD) amplitudes. In the SU(3) limit, these formulas depend on three effective parameters characterizing the strength of all non-Pomeron rescattering effects. We point out that the experimental bounds on the B -> K^+K^- branching ratio may limit the value of only one of these FSI parameters. Thus, the smallness of the B -> K^+K^- decay rate does not imply negligible rescattering effects in other decays. Assuming a vanishing value of this parameter, we perform various fits to the available B -> PP branching ratios. The fits determine the quark-diagram SD amplitudes, the two remaining FSI parameters and the weak angle gamma. While the set of all B -> PP branching ratios is well described with gamma around its expected SM value, the fits permit other values of gamma as well. For a couple of such good fits, we predict asymmetries for the B -> K pi, pi^+ eta (eta'), K^+ eta (eta') decays as well as the values of the CP-violating parameters S_{pi pi} and C_{pi pi} for the time-dependent rate of B^0(t) -> pi^+ pi^-. Apart from a problem with the recent B^+ -> pi^+ eta asymmetry measurement, comparison with the data seems to favour the values of gamma in accordance with SM expectations.