Recently, the large CP asymmetries in B ± → π ± π + π − decays were found by the LHCb Collaboration to localize in the region m 2 π + π − < 0.4 GeV 2 . We find such large localized CP asymmetries may be due to the interference between a light scalar and ρ 0 (770) intermediate resonances. Consequently, we argue that the distribution of CP asymmetries in the Dalitz plots of three-body B decays could be very helpful for identifying the presence of the scalar resonance.

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We study the localized direct CP violation in the hadronic decays B ± → ρ 0 (ω)π ± → π + π − π ± , including the effect caused by an interesting mechanism involving the charge symmetry violating mixing between ρ 0 and ω. We calculate the localized integrated direct CP violation when the low invariant mass ofFor the five models of form factors investigated, we find that the localized integrated direct CP violation varies from −0.0752 to −0.0290 in the ranges of parameters in our model when 0.750 < m(π + π − ) low < 0.800 GeV. This result, especially the sign, agrees with the experimental data and is independent of the form factor models. The new experimental data shows that the signs of the localized integrated CP asymmetries in the regions 0.470 < m(π + π − ) low < 0.770 and 0.770 < m(π + π − ) low < 0.920 GeV are positive and negative, respectively. We find that ρ-ω mixing makes the localized integrated CP asymmetry move toward the negative direction, and therefore contributes to the sign change in those two regions. This behavior is also independent of the form factor models. We also calculate the localized integrated direct CP violating asymmetries in the regions 0.470 < m(π + π − ) low < 0.770, 0.770 < m(π + π − ) low < 0.920 and the whole region 0.470 < m(π + π − ) low < 0.920 GeV and find that they agree with the experimental data in some models of the form factors.

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