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.
Categories: hep-ph