In this work, we analyze the three-body $B_{(s)}\to {\eta }_c(1S,2S)K\pi$ decays within the framework of the perturbative QCD approach (PQCD) under the quasi-two-body approximation, where the kaon-pion invariant mass spectra are dominated by the $K_0^{*}(1430{)}^0$, $K_0^{*}(1950{)}^0$, $K^{*}(892{)}^0$, $K^{*}(1410{)}^0$, $K^{*}(1680{)}^0$, and $K_2^{*}(1430{)}^0$ resonances. The time-like form factors are adopted to parametrize the corresponding $S$, $P$, $D$-wave kaon-pion distribution amplitudes for the concerned decay modes, which describe the final-state interactions between the kaon and pion in the resonant region. The $K\pi S$-wave component at low $K\pi$ mass is described by the LASS line shape, while the time-like form factors of other resonances are modeled by the relativistic Breit-Wigner function. We find the following main points: (a) the PQCD predictions of the branching ratios for most considered $B\to {\eta }_c(1S)(K^{*0}\to )K^{+}{\pi }^{-}$ decays agree well with the currently available data within errors; (b) for $\mathcal{B}(B^0\to {\eta }_c(K_0^{*}(1430)\to )K^{+}{\pi }^{-})$ and $\mathcal{B}(B^0\to {\eta }_c{K}^{+}{\pi }^{-}(\mathrm{NR}))$ (where NR means nonresonant), our predictions of the branching ratios are a bit smaller than the measured ones; and (c) the PQCD results for the $D$-wave contributions considered in this work can be tested once precise data from the future LHCb and Belle-II experiments become available.

• Received 26 November 2019

DOI:https://doi.org/10.1103/PhysRevD.101.016015

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Published by the American Physical Society