Resonant contribution of the three-body decay process ${\bar{B}}_s\to K^{+}{K}^{-}P$ in perturbation QCD

Abstract

We investigate the CP violation in the decay process ${\bar{B}}_s\to \varphi (\rho ,\omega )P\to K^{+}{K}^{-}P$ by considering the interference effects of $\varphi \to K^{+}{K}^{-}$, $\rho \to K^{+}{K}^{-}$ and $\omega \to K^{+}{K}^{-}$ within the framework of perturbative QCD method (P refers to $\pi$, K, $\eta$ and ${\eta }^{\prime }$ pseudoscalar mesons, respectively). We analyse the mixings of $\varphi -{\rho }^0$, $\varphi -\omega$ and $\omega -{\rho }^0$ and provide the amplitudes of the quasi-two-body decay processes. The CP violation for ${\bar{B}}_s\to K^{+}{K}^{-}P$ decay process is obvious at the ranges of the three vector mesons interferences. Meanwhile, the localised CP violation can be found for comparing with the experiment results from three-body decay process at the LHC in the near future.