$CP$ 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 ${\bar{B}}_s^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ induced by the $\ddot{I}$ and $\ddot{I}‰$ 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 $\ddot{I}-\ddot{I}‰$ interference when the invariant masses of the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ pairs are in the vicinity of the $\ddot{I}‰$ resonance. For the decay process of ${\bar{B}}_s^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, the maximum $CP$ violation can reach 28.64{\%}.