$CP$ violation induced by the double resonance for pure annihilation decay process in Perturbative QCD

Abstract

In Perturbative QCD (PQCD) approach we study the direct $CP$ violation in the pure annihilation decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$ induced by the $ρ$ and $ω$ double resonance effect. Generally, the $CP$ violation is small in the pure annihilation type decay process. However, we find that the $CP$ violation can be enhanced by double $ρ-ω$ interference when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$, the maximum $CP$ violation can reach 28.64{\%}.