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

TL;DR

This paper analyzes $B_{(s)}$ decays to $ ext{eta}_c$ and $K ext{-} extpi$ final states using perturbative QCD, focusing on resonance contributions and final-state interactions, with predictions aligning with current data and future tests anticipated.

Contribution

It introduces a detailed PQCD analysis of three-body $B$ decays including $S$, $P$, and $D$-wave resonance effects with specific form factor parametrizations.

Findings

Most branching ratio predictions agree with experimental data.

Predictions for some $B^0$ decay modes are slightly smaller than measurements.

Future experiments can test the $D$-wave contribution predictions.

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 $K_0^*(1430)^0,K_0^*(1950)^0,K^*(892)^0,K^*(1410)^0,K^*(1680)^0$ 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 ${\cal B}(B^0 \to \eta_c (K_0^*(1430)\to )K^+\pi^-)$ and ${\cal B}(B^0 \to \eta_c K^+\pi^-({\rm NR}))$ (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.