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

Abstract

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