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

## TL;DR

This paper investigates how double resonance effects in perturbative QCD can significantly enhance direct CP violation in a pure annihilation decay of B_s mesons, reaching up to 28.64%.

## Contribution

It demonstrates that double $
ho-\omega$ resonance interference can substantially increase CP violation in specific B_s decay processes, a novel insight in PQCD studies.

## Key findings

- Maximum CP violation reaches 28.64%.
- Double resonance enhances CP violation near the $
ho$-$\omega$ resonance region.
- Pure annihilation decay processes can exhibit sizable CP violation due to resonance effects.

## Abstract

In Perturbative QCD (PQCD) approach we study the direct $CP$ violation in the pure annihilation decay process of $\bar{B}^0_{s}\rightarrow\pi^+\pi^-\pi^+\pi^-$ induced by the $\rho$ and $\omega$ 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 $\rho-\omega$ interference when the invariant masses of the $\pi^+\pi^-$ pairs are in the vicinity of the $\omega$ resonance. For the decay process of $\bar{B}^0_{s}\rightarrow\pi^+\pi^-\pi^+\pi^-$, the maximum $CP$ violation can reach 28.64{\%}.