Probing the soft rescattering parameters in B decays involving a scalar meson with QCD factorization

In this work, the soft rescattering parameters in the B±→π±π+π− and B±→K±π+π− decays with the light scalar meson f0(500) as the intermediate resonance are studied within the quantum chromodynamics (QCD) factorization. Considering the interference effect between ρ(770)0 and f0(500), we utilize the experimentally more direct event yields for fitting and get the soft rescattering parameters |ρkSP|=3.29±1.01 and |ρkPS|=2.33±0.73 in B→PS and B→SP decays (P and S denote pseudoscalar and scalar mesons, respectively), respectively. We also study the branching ratios and CP asymmetries in the decay modes involving other scalar mesons, including f0(980), a0(980), a0(1450) and K0*(1430), to test the rationality of the values of |ρkSP| and |ρkPS|. Meanwhile, the wealth of experimental data facilitate the examination of the forward-backward asymmetry induced CP asymmetries (FB-CPAs), and the localized CP asymmetries (LACPs). We investigate these asymmetries resulting from the interference between ρ(770)0 and f0(500) for B±→π±π+π− and B±→K±π+π− decays when the invariant mass of π+π− locates in the low-energy region 0.445 GeV<mππ<0.795 GeV. Our theoretical results of FB-CPAs and LACPs align with the experimental findings. We propose that the interference between ρ(770)0 and f0(500) can be extended to other beauty and charmed mesons decays. Published by the American Physical Society 2025