Direct CP violation in $\bar B_{s} \rightarrow K^{+}K^{-} K^{+}K^{-}$ decay process induced by interferences of the intermediate vector particles

We investigate CP violation in the decay process $\bar B_{s} \rightarrow V V \rightarrow K^{+}K^{-}K^{+}K^{-}$ within the framework of perturbative QCD, where V represents vector mesons $\phi$, $\rho$, and $\omega$. We analyze the mixing mechanism among $\phi-\rho^{0}-\omega$ and provide amplitudes for these decay processes. Moreover, we explore CP violation in the four-body decay process of $\bar{B}_{s}^{0} \rightarrow K^{+} K^{-} K^{+} K^{-}$ involving intermediate vector mesons and their mixing. Notably, significant CP violation is observed for specific two-vector meson intermediate states. Additionally, a substantial amount of CP violation arises from vector mixing when the invariant mass of $K^{+}K^{-}$ falls within a certain range. This study holds potential implications for future detection by the LHC experiment.