Localized direct CP violation for B± → ρ0(ω)π± → π+π-π± in QCD factorization

We study the localized direct CP violation in the hadronic decays B-+/- -> rho(0)(omega)pi(+/-) -> pi(+)pi(-)pi(+/-), including the effect caused by an interesting mechanism involving the charge symmetry violating mixing between rho(0) and omega in the QCD factorization approach. We find that rho-omega mixing makes the localized integrated CP asymmetry move toward the negative direction when the low invariant mass of pi(+)pi(-)[m(pi(+)pi(-))(low)] is near rho(0)(770). The localized integrated direct CP violation obtained in the QCD factorization approach varies from -0.0724 to -0.0389 in the ranges of parameters when 0.750 < m(pi(+)pi(-))(low) < 0.800 GeV. This result, especially the sign, agrees with the experimental data. We also calculate the localized integrated direct CP violating asymmetries in the QCD factorization approach in the regions 0.470 < m(pi(+)pi(-))(low) < 0.770 GeV and 0.770 < m(pi(+)pi(-))(low)< 0.920 GeV. We find that these results agree with the experimental data and are more accurate than the results obtained through the naive factorization approach. It is more clear that.-. mixing contributes to the sign change in these two regions.