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Constrain the $χ_{c J} \to D^{()} {\bar{D}}^{()}$ effective couplings via the $X (3872) \to π^{0} χ_{c J}$ decays

Zhao-Sai Jia^1,2, Gang Li ^1,*, and Zhen-Hua Zhang ^3,†

¹College of Physics and Engineering, Qufu Normal University, Qufu 273165, China
²CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
³Center for High Energy Physics, Peking University, Beijing 100871, China

^*Contact author: gli@qfnu.edu.cn
^†Contact author: zhhzhang@pku.edu.cn

Phys. Rev. D 112, 074035 – Published 27 October, 2025

DOI: https://doi.org/10.1103/51z1-qls5

Abstract

Hidden-charm decays provide irreplaceable platforms for probing the structures of charmoniumlike states, such as $X (3872)$ , $Y (4260)$ , and $Z_{c} (3900)$ , and their heavy-quark-symmetry partners. In the hadronic molecular scenario, these hidden-charm decays are dominated by intermediate meson loops (IMLs), and the couplings of $χ_{c J} \to D^{(*)} {\bar{D}}^{(*)}$ are essential building blocks of the amplitudes for the pionic and radiative transitions of the charmoniumlike states to the $χ_{c J}$ and $h_{c}$ states, e.g., $X (3872) \to π^{0} χ_{c J}, π π χ_{c J}, γ χ_{c J}$ , and $Y (4260) \to π^{0} h_{c}, η h_{c}$ . These couplings cannot be extracted from the partial decay widths of the $χ_{c J}$ directly and only have estimated values from the vector meson dominance (VMD) model. Utilizing the recent precise determination of the pole position and the isospin breaking properties of the $X (3872)$ , we give an estimation on the upper bounds of the absolute values of the $χ_{c J} \to D^{(*)} {\bar{D}}^{(*)}$ couplings. Our results show that the VMD model may overestimate the $χ_{c J} \to D^{(*)} {\bar{D}}^{(*)}$ couplings considering the $X (3872)$ as a $D {\bar{D}}^{*}$ hadronic molecule with a binding energy about tens of keV. These upper limits can be used and tested in other hidden-charm transitions of the charmoniumlike states to the $χ_{c J}$ and $h_{c}$ .

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Phys. Rev. D 112, 074035– Published 27 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 24 July 2025
Accepted 7 October 2025

DOI: https://doi.org/10.1103/51z1-qls5

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Constrain the $χ_{c J} \to D^{()} {\bar{D}}^{()}$ effective couplings via the $X (3872) \to π^{0} χ_{c J}$ decays

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Constrain the χcJ→D(*)D¯(*) effective couplings via the X(3872)→π0χcJ decays

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Constrain the $χ_{c J} \to D^{()} {\bar{D}}^{()}$ effective couplings via the $X (3872) \to π^{0} χ_{c J}$ decays