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.

28 Pages, and 3 figures

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• Analysis of CKM-Favored Quasi-Two-Body $B\to D(R\to )K\pi$ Decays in PQCD Approach
• Data-based analysis of Forward-Backward Asymmetry in $B^{\pm }\to K^{\pm }{K}^{\mp }{K}^{\pm }$
• Resonances $\varphi (1020)$ and $\varphi (1680)$ contributions for the three-body decays $B^{+}\to D_s^{+}K\bar{K}$
• The $\rho (770,1450)\to \omega \pi$ contributions for three-body decays $B\to {\bar{D}}^{(\ast )}\omega \pi$
• Resonance contributions from ${\chi }_{c0}$ in the charmless three-body hadronic $B$ meson decays
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays