CP asymmetry from the effect of isospin symmetry breaking during <i>B-</i>meson decay*

Abstract The direct CP asymmetry in quasi-two-body decays of is investigated using the perturbative QCD (PQCD) method, where P represents a pseudoscalar meson, and V refers to ρ , ω, and ϕ mesons. We present the amplitude of the quasi-two-body decay process and investigate the effects of mixed resonances involving , , and while considering the impact of isospin symmetry breaking. We observe significant CP asymmetry when the invariant mass of the pair is within the resonance ranges of ρ , ω, and ϕ mesons. Consequently, we quantify the regional CP asymmetry in these resonance regions. A significant difference is observed when comparing the results obtained with and without the interference of the three vector mesons and isospin conservation. The CP asymmetry results obtained from the three-body decay process, without interference owing to isospin conservation by the PQCD method, are in agreement with the newly updated data acquired by the LHCb experiment.