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A model for the $B^\pm \to \pi^-\pi^+\pi^\pm$ decay amplitude is proposed tostudy the large CP violation observed at the high mass region of the Dalitzplane. A short distance $ b \to u $ amplitude with the weak phase $\gamma$ isconsidered together with the contribution of a hadronic charm loop and a s-wave$D\bar{D}\to \pi\pi$ rescattering. In the model, the $\chi_c^0$ appears as anarrow resonant state of the $D\bar D$ system below threshold. It is introducedin an unitary two channel S-matrix model of the coupled $D\bar D$ and $\pi\pi$channels, where the $\chi_c^0$ complex pole in $D\bar D$ channel shows itssignature in the off-diagonal matrix element and in the associated $D\bar{D}\to\pi\pi$ transition amplitude. The strong phase of the resulting decay amplitudehas a sharp sign change at the $D\bar D$ threshold, changing the sign of the CPasymmetry, as it is observed in the data. We conclude that the hadronic charmloop and rescattering mechanism are relevant to the broadening of the CPasymmetry around the $\chi_c^0$ resonance in the $\pi\pi$ channel. This novelmechanism provides a possible interpretation of the CP asymmetry defierexperimental result presented by the LHCb collaboration for the $B^\pm \to\pi^-\pi^+\pi^\pm$ decay in the high mass region.

CP asymmetry from hadronic charm rescattering in $B^\pm \to \pi^-\pi^+\pi^\pm$ decays at the high mass region