Direct CP violation in ${\bar{B}}_s\to K^{+}{K}^{-}{K}^{+}{K}^{-}$ decay process induced by interferences of the intermediate vector particles

Abstract

We investigate CP violation in the decay process ${\bar{B}}_s\to VV\to K^{+}{K}^{-}{K}^{+}{K}^{-}$ within the framework of perturbative QCD, where V represents vector mesons $\varphi$, $\rho$, and $\omega$. We analyze the mixing mechanism among $\varphi -{\rho }^0-\omega$ and provide amplitudes for these decay processes. Moreover, we explore CP violation in the four-body decay process of ${\bar{B}}_s^0\to K^{+}{K}^{-}{K}^{+}{K}^{-}$ 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.