Resonant Contributions to Three-body $B\to KKK$ Decays in Perturbative QCD Approach

Abstract

In this work, we study the ($S$, $P$ and $D$)-wave $K^{+}{K}^{-}$ contributions to $B\to KKK$ decays in the perturbative QCD approach at leading order. Within the two-meson wave functions describing the nonperturbative dynamics in the kaon-pair for different waves, we calculate the branching fractions and the direct $CP$ asymmetries of these decay modes in the corresponding resonance regions. Most of our numerical results are well consistent with the current measurements. We note that the narrow-width approximation is invalid in the quasi-two-body decays $B\to K{f}_0(980)\to KKK$. For other decays, under the narrow-width approximation we can extract the branching fractions of the corresponding two-body decays involving the intermediate resonant states, and the related branching fractions agree with the current experimental data well. Furthermore, we also predict the corresponding quasi-two-body decays $B\to K{\pi }^{+}{\pi }^{-}$, which are expected to be measured in the ongoing LHCb and Belle-II experiments.

arXiv comment28 Pages, and 3 figures

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