Forward-backward asymmetry induced $CP$ asymmetry of $B^{\pm}\rightarrow π^{\pm}π^{+}π^{-}$

$C P$ violation of the decay $B^{\pm} \to π^{\pm} π^{+} π^{-}$ in the $f_{0} (500) - ρ (770)^{0}$ interfering region is analyzed. The forward-backward asymmetries (FBAs) and the corresponding $C P$ asymmetries FB- $C P$ As are particularly investigated. To isolate the $C P$ V caused by the interference of different partial wave more cleanly, we also introduce the direct- $C P$ V-subtracted FB- $C P$ A. Based on the LHCb data, we extract the FBAs, FB- $C P$ As, direct- $C P$ V-subtracted FB- $C P$ A, as well as the regional $C P$ As with invariant mass of the $π^{+} π^{-}$ pair in the range 0.2 GeV/ $c^{2} < \sqrt{s_{low}} < 1.8$ GeV/ $c^{2}$ . It is found that the (direct- $C P$ V-subtracted) FB- $C P$ As are quite large in the $f_{0} (500) - ρ (770)^{0}$ interfering region, which confirms that the interference of the intermediate resonances $f_{0} (500)$ and $ρ (770)^{0}$ plays an important role for the $C P$ violation of the three-body decay channel $B^{\pm} \to π^{\pm} π^{+} π^{-}$ .

Forward-backward asymmetry induced $C P$ asymmetry of $B^{\pm} \to π^{\pm} π^{+} π^{-}$

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Forward-backward asymmetry induced $C P$ asymmetry of $B^{\pm} \to π^{\pm} π^{+} π^{-}$

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Forward-backward asymmetry induced CPCP asymmetry of B±→π±π+π−B±→π±π+π−

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Forward-backward asymmetry induced CPCP asymmetry of B±→π±π+π−B±→π±π+π−

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Forward-backward asymmetry induced $C P$ asymmetry of $B^{\pm} \to π^{\pm} π^{+} π^{-}$

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Forward-backward asymmetry induced $C P$ asymmetry of $B^{\pm} \to π^{\pm} π^{+} π^{-}$

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