S -wave contributions to the B(s)→χc1(ππ,Kπ,KK) decays

We make a detailed study of the three-body decays ${B}_{(s)}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}h{h}^{\ensuremath{'}}$, where ${h}^{{(}^{\ensuremath{'}})}$ is either a pion or kaon, by taking into account the $S$-wave states in the $h{h}^{\ensuremath{'}}$ invariant mass distribution within the perturbative QCD approach. The two meson distribution amplitudes are introduced to capture the strong interaction related to the production of the $h{h}^{\ensuremath{'}}$ system. We calculate the branching ratios for the $S$-wave components and observe large values of order ${10}^{\ensuremath{-}4}$ for some Cabibbo-favored decays, which are accessible to the LHCb and Belle II experiments. The obtained branching ratio $\mathcal{B}(B\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}{K}_{0}^{*}(1430)(\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}))=({5.1}_{\ensuremath{-}0.8}^{+0.6})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ consistent with the data from Belle within errors. Moreover, we also predict the differential distributions in the $h{h}^{\ensuremath{'}}$ invariant mass for the decays under consideration, which await the future experimental test. In addition, the corresponding ${\ensuremath{\chi}}_{c1}(2P)$ channels are also investigated, which are helpful to clarify the nature of the $X(3872)$ state.