Forward-backward asymmetry induced CP asymmetry of B± → π±π+π-

CP violation of the decay B-+/- -> pi(+/-)pi(+)pi(-) in the f(0)(500) - rho(770)(0) interfering region is analyzed. The forward-backward asymmetries (FBAs) and the corresponding CP asymmetries FB-CPAs are particularly investigated. To isolate the CPV caused by the interference of different partial wave more cleanly, we also introduce the direct-CPV-subtracted FB-CPA. Based on the LHCb data, we extract the FBAs, FB-CPAs, direct-CPV-subtracted FB-CPA, as well as the regional CPAs with invariant mass of the pair in the range 0.2 GeV/c(2) < root s(low) < 1.8 GeV/c(2). It is found that the (direct-CPV-subtracted) FB-CPAs are quite large in the f(0) (500) - rho(770)(0) interfering region, which confirms that the interference of the intermediate resonances f(0) (500) and rho(770)(0) plays an important role for the CP violation of the three-body decay channel B-+/- -> pi(+/-)pi(+)pi(-).