$S$-wave contributions to the $B_{(s)}\to {\chi }_{c1}(\pi \pi ,K\pi ,KK)$ decays

Abstract

We make a detailed study of the three-body decays $B_{(s)}\to {\chi }_{c1}h{h}^{\prime }$, where $h^{{(}^{\prime })}$ is either a pion or kaon, by taking into account the $S$-wave states in the $h{h}^{\prime }$ invariant mass distribution within the perturbative QCD approach. The two meson distribution amplitudes (DAs) are introduced to capture the strong interaction related to the production of the $h{h}^{\prime }$ system. We calculate the branching ratios for the $S$-wave components and observe large values of order $10^{-4}$ for some Cabibbo-favored decays, which are accessible to the LHCb and Belle II experiments. The obtained branching ratio $\mathcal{B}(B\to {\chi }_{c1}{K}_0^{\ast }(1430)(\to K^{+}{\pi }^{-}))=(5.1_{-0.8}^{+0.6})\times 10^{-5}$ consistent with the data from Belle within errors. Moreover, we also predict the differential distributions in the $h{h}^{\prime }$ invariant mass for the decays under consideration, which await the future experimental test. In addition, the corresponding ${\chi }_{c1}(2P)$ channels are also investigated, which are helpful to clarify the nature of the $X(3872)$ state.

17 pages, 5 figures

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