$S$-wave contributions to the $B_{(s)}\rightarrow \chi_{c1} (\pi\pi,K\pi,KK)$ decays

TL;DR

This paper studies S-wave contributions in specific B meson decays involving chi_c1 and two light mesons, calculating branching ratios and distributions using perturbative QCD, with predictions testable at LHCb and Belle II.

Contribution

It introduces a detailed perturbative QCD analysis of S-wave effects in B decays to chi_c1 and two light mesons, including new predictions for branching ratios and invariant mass distributions.

Findings

Large S-wave branching ratios of order 10^{-4} for some decays.

Calculated branching ratio for B→ chi_c1 K*_0(1430) matches Belle data.

Predicted invariant mass distributions for future experimental verification.

Abstract

We make a detailed study of the three-body decays $B_{(s)}\rightarrow \chi_{c1} hh'$, where $h^{(')}$ is either a pion or kaon, by taking into account the $S$-wave states in the $hh'$ invariant mass distribution within the perturbative QCD approach. The two meson distribution amplitudes (DAs) are introduced to capture the strong interaction related to the production of the $hh'$ 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 $\mathcal{B}(B\rightarrow \chi_{c1}K^*_{0}(1430)(\rightarrow K^+\pi^-))=(5.1^{+0.6}_{-0.8})\times 10^{-5}$ consistent with the data from Belle within errors. Moreover, we also predict the differential distributions in the $hh'$ invariant mass for the decays under consideration, which await the future experimental test. In addition, the corresponding $\chi_{c1}(2P)$ channels are also investigated, which are helpful to clarify the nature of the $X(3872)$ state.