Study of $K\pi$ final states from four-body deacy of $\bar{B}_{s}$ meason under perturbation QCD

In the perturbative QCD framework, we use the quasi-two-body method to study the CP violations and branching ratios in the $\bar B_{s} \rightarrow [\phi(\rho^{0},\omega)\rightarrow K^{+}K^{-}][K^{*0}\rightarrow K^{+}\pi^{-}]$ and $\bar B_{s} \rightarrow [\rho^{0}(\omega,\phi)\rightarrow (\pi^{+}\pi^{-})][K^{*0}\rightarrow K^{+}\pi^{-}]$ decay processes. Owing to the interference effects of $\rho^{0}$, $\omega$, and $\phi$, new strong phases associated with vector mesons will be generated, resulting in relatively large CP violation within the interference region. Moreover, we provide numerical comparisons of CP violation from resonance effects and non-resonance contributions. In order to provide better theoretical predictions for future experiments, we integrate CP violation over invariant mass to obtain the regional CP violation value. Furthermore, we have calculated the polarization fractions and branching ratios for different intermediate states in the four-body decay process, which may be influenced by vector interference effects. Additionally, we discuss the possibility of observing the predicted CP violation at the LHC.