Effect of resonance for $CP$ asymmetry of the decay process ${\bar{B}}_s\to P{\pi }^{+}{\pi }^{-}$ in perturbative QCD

Abstract

In the framework of Perturbative QCD (PQCD) approach we study the direct $CP$ asymmetry for the decay channel ${\bar{B}}_s\to P{\pi }^{+}{\pi }^{-}$ around the resonance range via the $\rho -\omega$ mixing mechanism (where P refer to pseudoscalar meson). We find that the $CP$ asymmetry can be enhanced by $\rho -\omega$ mixing when the masses of the ${\pi }^{+}{\pi }^{-}$ pairs are at the area of $\rho -\omega$ resonance, and the maximum $CP$ asymmetry can reach 59{\%} for the relevant decay channels.