Direct CP violation for $\bar{B}_{s}^{0}\to K^{0}π^{+}π^{-}$ decay in QCD factorization

In the framework of QCD factorization, based on the first order of isospin violation, we study direct CP violation in the decay of $\bar{B}_{s}^{0} \to K^{0}ρ^{0}(ω)\to K^{0}π^{+}π^{-}$ including the effect of $ρ-ω$ mixing. We find that the CP violating asymmetry is large via $ρ-ω$ mixing mechanism when the invariant mass of the $π^{+}π^{-}$ pair is in the vicinity of the $ω$ resonance. For the decay of $\bar{B}_{s}^{0} \to K^{0}ρ^{0}(ω)\to K^{0}π^{+}π^{-}$, the maximum CP violating asymmetries can reach about 46%. We also discuss the possibility to observe the predicted CP violating asymmetries at the LHC.

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