Contributions of the subprocesses $\rho(770,1450,1700)\to K \bar{K}$ and $\omega(782,1420,1650)\to K \bar{K}$ for the three-body decays $B\to \eta^{(\prime)} K\bar{K}$

TL;DR

This paper extends previous work by analyzing resonance contributions from $ ho$ and $\\omega$ states in $B\to \eta^{(\prime)} K\bar{K}$ decays using perturbative QCD, highlighting the significance of virtual contributions.

Contribution

It introduces a detailed analysis of subprocesses involving multiple resonances in three-body $B$ decays, incorporating their effects into distribution amplitudes with form factors.

Findings

Virtual contributions from $ ho(770)$ and $\\omega(782)$ are comparable to higher resonances.

Resonance effects significantly impact the decay amplitudes and CP asymmetries.

Predictions are consistent with expectations for future experimental tests.

Abstract

As an extension of our prior work, we analyze the resonance contributions for the kaon pair originating from the intermediate $\rho(770)$, $\omega(782)$ and their excited states in the three-body decays $B\to \eta^{(\prime)} K\bar{K}$ within the perturbative QCD approach. The information of subprocesses $\rho(770,1450,1700)\to K\bar K$ and $\omega(782,1420,1650)\to K\bar K$ are included in the distribution amplitudes for $K\bar K$ system by using the kaon vector time-like form factors. We calculate the $CP$ averaged branching fractions and the direct $CP$ asymmetries for the relevant quasi-two-body $B$ meson decays. The branching fractions of the virtual contributions for $K\bar K$ from the Breit-Wigner formula tails of $\rho(770)$ and $\omega(782)$ for these decays are found comparable to the corresponding contributions from the resonances $\rho(1450,1700)$ and $\omega(1420,1650)$. Consequently, they constitute a significant component that should be accounted for in the considered three-body decays. All the predictions in this work are expected to be tested by the LHCb and Belle-II experiments in the future.