Long-distance effects and final state interactions in B→ππK and B→KK¯K decays

B decays into ππK and KK¯K, where the ππ and K¯K pairs interact in isospin zero S-wave, are studied in the ππ effective mass range from threshold to 1.2 GeV. The interplay of strong and weak decay amplitudes is analyzed using an unitary ππ and KK¯ coupled channel model. Final state interactions are described in terms of four scalar form factors constrained by unitarity and chiral perturbation theory. Branching ratios for the B→f0(980)K decay, calculated in the factorization approximation with some QCD corrections, are too low as compared to recent data. In order to improve agreement with experiment, we introduce long-distance contributions called charming penguins. Effective mass distributions, branching ratios and asymmetries are compared with the existing data from BaBar and Belle Collaborations. A particularly large negative asymmetry in charged B decays is predicted for one set of the charming penguin amplitudes.