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

Meng-Kun Jia,Jia-Ming Li,Zhou Rui,Chao-Qi Zhang

doi:10.1103/physrevd.104.073001

Meng-Kun Jia, Jia-Ming Li + Show 2 more

Open Access

https://doi.org/10.1103/physrevd.104.073001

Copy DOI

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.

Highlights

B meson decays to final states containing a charmonium meson have played a crucial role in the observation of CP violation in the weak interactions of quarks and provided powerful probes of the strong interaction in a heavy meson system
Some multibody decay modes, such as B0 → χc1Kþπ− [7], Bs → χcJKþK− [8], and B → χc1ππK [9], were observed, for which one can search for charmonium or charmoniumlike exotic states in the pion-charmonium invariant mass distribution
The S-wave contributions are parametrized into the timelike form factors involved in the two meson distribution amplitudes (DAs), which have been well established in the corresponding J=ψ decays

Summary

INTRODUCTION

B meson decays to final states containing a charmonium meson have played a crucial role in the observation of CP violation in the weak interactions of quarks and provided powerful probes of the strong interaction in a heavy meson system. [52] analyzed the two-body B → χc1ð1P; 2PÞ decays in QCD factorization by treating charmonia as nonrelativistic bound states. They found that the B → χc1ð2PÞK decay rate can be comparable to that of the χc1ð1PÞ mode and argued that Xð3872Þ may be dominated by the χc1ð2PÞ charmonium but mixed with a D0D Ã0=DÃ0D 0 molecule state. [53], the branching ratio of the B → Xð3872ÞK was calculated in the perturbative QCD (PQCD) approach, by assuming Xð3872Þ to be a regular χc1ð2PÞ charmonium state. For recent works applying triangle singularities to interpreting several charmoniumlike structures in the Xccπþ invariant mass distributions of B 0 → XccK−πþ with Xcc 1⁄4 J=ψ; ψð2SÞ; χc, we refer the reader to Refs.

KINEMATICS AND THE S-WAVE TWO MESON DISTRIBUTION AMPLITUDES

RESULTS AND DISCUSSIONS

CONCLUSION