Study of localized CP violation in B− → π−π+π− and the branching ratio of B− → σ(600)π− in the QCD factorization approach

Abstract

In this work, within the QCD factorization approach, we study the localized integrated CP violation in the B−→π−π+π− decay and the branching fraction of the B−→σπ− decay. Both the resonance and nonresonance contributions are included when we study the localized CP asymmetry in the B−→π−π+π− decay. The resonance contributions from the scalar σ(600) and vector ρ0(770) mesons are included. For the σ(600) meson, we apply both the Breit-Wigner and Bugg models to deal with its propagator, and obtain B(B−→σ(600)π−)<1.67×10−6 and B(B−→σ(600)π−)<1.946×10−5 in these two models, respectively. We find that there is no allowed divergence parameters ρS and ϕS to satisfy the experimental data ACP(π−π+π−)=0.584±0.082±0.027±0.007 in the region mπ+π−high2>15GeV2 and mπ+π−low2<0.4GeV2 and the upper limit of B(B−→σ(600)π−) in the Breit-Wigner model, however, there exists the region ρS∈[1.70,3.34] and ϕS∈[0.50,4.50] satisfying the data for ACP(π−π+π−) and the upper limit of B(B−→σ(600)π−) in the Bugg model. This reveals that the Bugg model is more plausible than the Breit-Wigner model to describe the propagator of the σ(600) meson even though the finite width effects are considered in both models. The large values of ρS indicate that the contributions from weak annihilation and hard spectator scattering processes are both large, especially, the weak annihilation contribution should not be neglected for B decays to final states including a scalar meson.