CP asymmetry from the effect of the isospin symmetry breaking during B-meson decay

TL;DR

This paper investigates how isospin symmetry breaking affects direct CP asymmetry in B-meson decays involving vector mesons, revealing significant asymmetries in resonance regions and aligning with recent LHCb data.

Contribution

It introduces a perturbative QCD approach to quantify CP asymmetry considering isospin breaking and resonance interference effects in B-meson decays.

Findings

Significant CP asymmetry observed in resonance regions.

Interference effects markedly influence CP asymmetry results.

Results agree with recent LHCb experimental data.

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 is 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 interferences 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.