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

Abstract

Abstract In a perturbative QCD approach we study the direct CP violation in the pure annihilation decay process of $$\bar{B}^0_{s}\rightarrow \pi ^+\pi ^-\pi ^+\pi ^-$$ B ¯ s 0 → π + π - π + π - induced by the $$\rho $$ ρ and $$\omega $$ 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 $$\rho $$ ρ – $$\omega $$ ω interference when the invariant masses of the $$\pi ^+\pi ^-$$ π + π - pairs are in the vicinity of the $$\omega $$ ω resonance. For the decay process of $$\bar{B}^0_{s}\rightarrow \pi ^+\pi ^-\pi ^+\pi ^-$$ B ¯ s 0 → π + π - π + π - , the CP violation can reach $$A_{CP}(\bar{B}^0_{s}\rightarrow \pi ^+\pi ^-\pi ^+\pi ^-)=27.20^{+0.05+0.28+7.13}_{-0.15-0.31-6.11}\%$$ A C P ( B ¯ s 0 → π + π - π + π - ) = 27 . 20 - 0.15 - 0.31 - 6.11 + 0.05 + 0.28 + 7.13 % .