Bruno El-Bennich

Universite Pierre et Marie Curie, France

The interference of scalar and vector mesons in hadronic 3-body B-decays

The interest in non-leptonic three-body decays of B-mesons is twofold: analysing (charmless) three-body final states naturally follows and complements the ongoing efforts to study CP-violation in two-body B-decays, and the many resonances, observed in the vast pion-pion and pion-kaon mass range of the Dalitz plots for three-body decays provide an ideal ground to study hadronic physics. A large CP violating asymmetry of about 30% in B^{+-} --> \rho^0 K^{+-} , \rho^0 --> \pi\pi, was observed by the BaBar and Belle collaborations. I will describe a study of the contribution of the strong interactions between the two pions in S- and P-waves to the weak B --> \pi\pi K decay amplitudes. The interference between these two waves is analysed in the pi pi effective mass range of the \rho^0 and f_0(980) resonances. I will discuss the structure of the decay amplitudes with an intermediate quasi two-body state in QCD factorisation (and point out some current problems in this approach relatedto the B-->\pi K puzzle) as well as the final-state meson-meson interaction based on a coupled-channel model constrained by unitarity. Eventually, we will show how the interplay of weak and strong phases stemming from the weak decay amplitudes and the meson-meson interaction helps to reproduce the experimental data if some assumptions in the QCD-factorisation approach are made.

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