Direct $CP$ violation for ${\bar{B}}_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ in Perturbative QCD

Abstract

In perturbative QCD approach, we study the direct $CP$ violation in the decay of ${\bar{B}}_s^0\to \rho (\omega )\varphi \to {\pi }^{+}{\pi }^{-}\varphi$ via isospin symmetry breaking. An interesting mechanism involving the charge symmetry violating between $\rho$ and $\omega$ is applied to enlarge the $CP$ violating asymmetry. We find that the $CP$ violation can be enhanced by the $\rho -\omega$ mixing mechanism when the invariant masses of the ${\pi }^{+}{\pi }^{-}$ pairs are in the vicinity of the $\omega$ resonance. For the decay process of ${\bar{B}}_s^0\to \rho (\omega )\varphi \to {\pi }^{+}{\pi }^{-}\varphi$, the maximum $CP$ violation can reach $5.98\%$. The possibility of detecting the $CP$ violation is also presented.