Abstract The direct CP asymmetry in quasi-two-body decays of $B \rightarrow (V\rightarrow \pi^{+}\pi^{-})P $ is investigated in the perturbative QCD method, where P represents a pseudoscalar meson and V refers to $\rho$, $\omega$ and $\phi$ mesons, respectively. We present the amplitude of the quasi-two-body decay process and investigate the effects of mixed resonances involving $\rho^{0}-\omega$, $\rho^{0}-\phi$ and $\omega-\phi$, while considering the impact of isospin symmetry breaking. We observe a significant CP asymmetry when the invariant mass of the $\pi^{+}\pi^{-}$ pair within the resonance ranges of $\rho$, $\omega$ and $\phi$ mesons. Consequently, we proceed to quantify the regional CP asymmetry in these resonance regions. A significant difference is observed when comparing 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 due to isospin conservation by the perturbative QCD method, are in agreement with the newly updated data acquired by the LHCb experiment. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.
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