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The large localized CP asymmetries observed by LHCb in three-body charmlessdecays of $B$ mesons brings new challenge for experimentalists and theirtraditional models to fit data. With higher statistics, rescattering andthree-body effects, previously ignored on data analysis, become more visible.The time is ripe to use better theoretical assumptions as an ingredient inorder to improve the analysis. In this paper we address the issue ofrescattering effects in the charmless three-body decays of $B$ mesons. Inparticular, we study the case of the $B^+ \to \pi^-\pi^+\pi^+$ decay and showthat the presence of hadronic loops shifts the P-wave phase near threshold tobelow zero, and modify the position of the $\rho$-meson peak and it width, inthe Dalitz plot.

Final state interaction on $B^+ \to \pi^-\pi^+\pi^+$