$S$, $P$ and $D$-wave resonance contributions to $B_{(s)}\to {\eta }_c(1S,2S)K\pi$ decays in the perturbative QCD approach

Abstract

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 $K_0^{\ast }(1430{)}^0,K_0^{\ast }(1950{)}^0,K^{\ast }(892{)}^0,K^{\ast }(1410{)}^0,K^{\ast }(1680{)}^0$ and $K_2^{\ast }(1430{)}^0$ 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 $B\to {\eta }_c(1S)(K^{\ast 0}\to )K^{+}{\pi }^{-}$ decays agree well with the currently available data within errors; (b) for $\mathcal{B}(B^0\to {\eta }_c(K_0^{\ast }(1430)\to )K^{+}{\pi }^{-})$ and $\mathcal{B}(B^0\to {\eta }_c{K}^{+}{\pi }^{-}(\mathrm{NR}))$ (here 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 the precise data from the future LHCb and Belle-II experiments are available.

Comments: 18 pages, 3 figures