The forward-backward asymmetry induced $CP$ asymmetry in ${\overline{B}}^{0}\rightarrow K^{-}π^{+}π^{0}$ in phase space around the resonances ${\overline{K}}^{*}(892)^{0}$ and ${\overline{K}}^{*}_{0}(700)$

The interference between amplitudes corresponding to different intermediate resonances plays an important role in generating large CP asymmetries in phase space in multi-body decays of bottom and charmed mesons. In this paper, we study the CP violation in the decay channel ${\overline{B}}^{0} \to K^{-} π^{+} π^{0}$ in phase space region where the intermediate resonances ${\overline{K}}^{*} (892)^{0}$ and ${\overline{K}}_{0}^{*} (700)$ dominate. The Forward-Backward Asymmetry (FBA) and the CP asymmetry induced by FBA (FB-CPA), which are closely related to the interference effects between the two aforementioned resonances, are especially investigated. The non-trivial correlation between FBA and FB-CPA is analyzed. The analysis indicates that the FB-CPAs around the resonance ${\overline{K}}^{*} (892)^{0}$ can be as large as about 35%, which can be potentially accessible by Belle and Belle-II collaborations in the near future.

The forward-backward asymmetry induced $C P$ asymmetry in ${\overline{B}}^{0} \to K^{-} π^{+} π^{0}$ in phase space around the resonances ${\overline{K}}^{} (892)^{0}$ and ${\overline{K}}_{0}^{} (700)$

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The forward-backward asymmetry induced $C P$ asymmetry in ${\overline{B}}^{0} \to K^{-} π^{+} π^{0}$ in phase space around the resonances ${\overline{K}}^{} (892)^{0}$ and ${\overline{K}}_{0}^{} (700)$

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The forward-backward asymmetry induced CPCP asymmetry in B‾0→K−π+π0B0→K−π+π0 in phase space around the resonances K‾∗(892)0K∗(892)0 and K‾0∗(700)K0∗​(700)

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The forward-backward asymmetry induced CPCP asymmetry in B‾0→K−π+π0B0→K−π+π0 in phase space around the resonances K‾∗(892)0K∗(892)0 and K‾0∗(700)K0∗​(700)

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The forward-backward asymmetry induced $C P$ asymmetry in ${\overline{B}}^{0} \to K^{-} π^{+} π^{0}$ in phase space around the resonances ${\overline{K}}^{} (892)^{0}$ and ${\overline{K}}_{0}^{} (700)$

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The forward-backward asymmetry induced $C P$ asymmetry in ${\overline{B}}^{0} \to K^{-} π^{+} π^{0}$ in phase space around the resonances ${\overline{K}}^{} (892)^{0}$ and ${\overline{K}}_{0}^{} (700)$

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