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

We make a detailed study of the three-body decays B ( s ) → χ c 1 h h ′ , where h ( ′ ) is either a pion or kaon, by taking into account the S -wave states in the h h ′ 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 ′ 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 B ( B → χ c 1 K 0 * ( 1430 ) ( → K + π - ) ) = ( 5.1 - 0.8 + 0.6 ) × 10 - 5 consistent with the data from Belle within errors. Moreover, we also predict the differential distributions in the h h ′ invariant mass for the decays under consideration, which await the future experimental test. In addition, the corresponding χ c 1 ( 2 P ) channels are also investigated, which are helpful to clarify the nature of the X ( 3872 ) state.