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

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