In perturbative QCD approach, we study the direct CP violation in the decay ofB 0 s → ρ(ω)φ → π + π − φ via isospin symmetry breaking. An interesting mechanism involving the charge symmetry violating between ρ and ω is applied to enlarge the CP violating asymmetry. We find that the CP violation can be enhanced by the ρ − ω mixing mechanism when the invariant masses of the π + π − pairs are in the vicinity of the ω resonance. For the decay process ofB 0 s → ρ(ω)φ → π + π − φ, the maximum CP violation can reach 5.98%. The possibility of detecting the CP violation is also presented.PACS numbers: 11.30. Er, 13.20.He, 12.15.Hh
I. INTRODUCTIONCP violation has obtained extensive attention even since its first discovery in the Neutral kaon systems [1]. Within the standard model (SM), CP violation originates from a non-zero weak phase angle from the complex Cabibbo-Kobayashi-Maskawa (CKM) matrix, which describes the mixing of weak interaction and mass eigenstates of the quarks [2,3]. Although the source of CP violation has not been well understood up to now, physicists are striving to increase their knowledge of the mechanism for the CP violation. Many theoretical studies [4-6] (within and beyond the SM) and experimental investigations have been conducted since 1964. According to theoretical predictions, large CP violation may be expected in B meson decay process due to the large mass of b quark. In recent years, the LHCb Collaboration observed the large CP violation in the three-body decay channels of B ± → π ± π + π − and B ± → K ± π + π − [7-9]. Hence, the non-leptonic B meson three-body decays channels have been focused more attention in searching for CP violation.Direct CP violation in B meson decays process occurs through the interference of at least two amplitudes with different weak phase φ and strong phase δ. The weak phase difference φ is determined by the CKM matrix elements, while the strong phase can be produced by the hadronic matrix elements and interference between the intermediate states. However, one can know that the strong phase δ is not still well determined from the theoretical approach. The non-leptonic weak decay amplitudes of B meson involve the hadronic matrix elements of M 1 M 2 | O i |B , which can be calculated from the different factorization methods. However, the different methods may present different strong phases so as to affect the value of the CP violation. Currently, there are three popular theoretical approaches to study the dynamics of the two-body hadronic decays, which are the naive factorization approach [10-13], the QCD