Direct CP violation for ${\bar{B}}_s^0\to K^0{\pi }^{+}{\pi }^{-}$ 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 $\bar{B}{s}^{0} \to K^{0}\rho^{0}(\omega)\to K^{0}\pi^{+}\pi^{-}$includingtheeffectof$\rho-\omega$mixing\mathrm{.}WefindthattheCPviolatingasymmetryislargevia$\rho-\omega$mixingmechanismwhentheinvariantmassofthe$\pi^{+}\pi^{-}$pairisinthevicinityofthe$\omega$resonance\mathrm{.}Forthedecayof$\bar{B}{s}^{0} \to K^{0}\rho^{0}(\omega)\to K^{0}\pi^{+}\pi^{-}$, the maximum CP violating asymmetries can reach about 46%. We also discuss the possibility to observe the predicted CP violating asymmetries at the LHC.