ar X iv : h ep - p h / 06 10 35 5 v 1 2 6 O ct 2 00 6 1 Strong and Weak Interactions in B → π + π − K Decays

It is important to understand charmless three-body B decays to probe the standard model. These decays are sensitive to CP violation and supply information on strong interactions. To interpret in a reliable way weak decay observables it is important to take into account final state interactions between produced meson pairs. In the weak decays B → ππK [ 1, 2] one sees maxima around the ππ effective mass distributions in the ρ(770) and f0(980) resonance regions. For ππ effective mass mππ up to 1.2 GeV, the contribution of the isospin-zero S-wave (ππ)S final state interactions was described in Ref. [ 3] and that of the isospin-one P wave (ππ)P was included in Ref. [ 4]. The amplitudes, based on the QCD factorization approach without the inclusion of hard-spectator and annihilation terms, underestimate the B to ρ(770)K and f0(980)K branching fractions. Therefore, phenomenological amplitudes arising from enhanced cc̄ loop diagrams (charming penguin terms [ 5]) were added. Our presentation at the conference was based on the work described in Ref. [ 4]. Here we show the sensitivity of the model [ 4] to two inputs of the S-wave amplitude: the B to f0(980) transition form factor and the effective decay constant of the f0(980).