Letter
Open Access

Unified coupled-channel description for the five near-threshold structures $ψ (3770)$ , $G (3900)$ , $R (3760)$ , $R (3780)$ and $R (3810)$ from $e^{+} e^{-}$ annihilation

Ri-Qing Qian ^1,2,3,* and Xiang Liu ^1,2,4,3,†

¹School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
²Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
³Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
⁴MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China

^*Contact author: qianrq@lzu.edu.cn
^†Contact author: xiangliu@lzu.edu.cn

Phys. Rev. D 112, L091502 – Published 21 November, 2025

DOI: https://doi.org/10.1103/c5vs-2l1k

Abstract

The recent observation of multiple near-threshold structures in $e^{+} e^{-}$ annihilation—including $ψ (3770)$ , $G (3900)$ , $R (3760)$ , $R (3780)$ , and $R (3810)$ —reveals limitations in existing models of charmonium and exotic hadrons. In this paper, we propose a unified coupled-channel description that simultaneously incorporates all five near-threshold structures using parameters constrained by hadron spectroscopy. Our model accurately reproduces the line shapes in both $D \bar{D}$ and nonopen-charm hadron (nOCH) channels, resolves the asymmetric profile of $ψ (3770)$ , and produces the $G (3900)$ bump. We identify the $R (3780)$ as the dominant manifestation of $ψ (3770)$ , attribute $R (3760)$ to $D \bar{D} \to nOCH$ rescattering and suggest that $R (3810)$ arises from coupling between the $ψ (1 D)$ state and the $h_{c} π π$ channel. The significant non- $D \bar{D}$ decay of $ψ (3770)$ is explained by its near-threshold position. This analysis provides a coherent, unquenched framework centered on a charmonium $ψ (1 D)$ core for near-threshold phenomena and offers a predictive approach extendable to bottomonium systems and future data from Belle II.

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References (46)

H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Pentaquark and tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019).
N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, The $X Y Z$ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, An updated review of the new hadron states, Rep. Prog. Phys. 86, 026201 (2023).
X. Wang, X. Liu, and Y. Gao, Hadron production in open-charm meson pair at $e^{+} e^{-}$ collider, arXiv:2502.15117.
S. K. Choi et al. (Belle Collaboration), Observation of a narrow charmoniumlike state in exclusive $B^{\pm} \to K^{\pm} π^{+} π^{-} J / ψ$ decays, Phys. Rev. Lett. 91, 262001 (2003).
H. C. Urey, F. G. Brickwedde, and G. M. Murphy, A hydrogen isotope of mass 2, Phys. Rev. 39, 164 (1932).
C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, Charmonium: The model, Phys. Rev. D 17, 3090 (1978); 21, 313(E) (1980).
S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32, 189 (1985).
J.-Z. Wang, D.-Y. Chen, X. Liu, and T. Matsuki, Constructing $J / ψ$ family with updated data of charmoniumlike $Y$ states, Phys. Rev. D 99, 114003 (2019).
M. Ablikim et al. (BES Collaboration), Direct measurements of the non- $D \bar{D}$ cross section $σ_{ψ (3770) \to non - D \bar{D}}$ at $E_{c m} = 3.773 GeV$ and the branching fraction for $ψ (3770) \to non - D \bar{D}$ , Phys. Rev. D 76, 122002 (2007).
M. Ablikim et al. (BES Collaboration), Direct measurements of the cross sections for $e^{+} e^{-} \to hadrons$ (non- $D \bar{D}$ ) in the range from 3.65 GeV to 3.87 GeV and the branching fraction for $ψ (3770) \to non - D \bar{D}$ , Phys. Lett. B 659, 74 (2008).
M. Ablikim et al. (BES Collaboration), Anomalous line shape of the cross section for $e^{+} e^{-} \to$ hadrons in the center-of-mass energy region between 3.650 and 3.872 GeV, Phys. Rev. Lett. 101, 102004 (2008).
M. Ablikim et al. (BESIII Collaboration), Precise measurement of born cross sections for $e^{+} e^{-} \to D \bar{D}$ at $\sqrt{s} = 3.80 - 4.95 GeV$ , Phys. Rev. Lett. 133, 081901 (2024).
B. Aubert et al. (BABAR Collaboration, Study of the exclusive initial-state radiation production of the $D \bar{D}$ system, Phys. Rev. D 76, 111105 (2007).
B. Aubert et al. (BABAR Collaboration, Study of the exclusive initial-state-radiation production of the $D \bar{D}$ system, arXiv:0710.1371.
G. Pakhlova et al. (Belle Collaboration), Measurement of the near-threshold $e^{+} e^{-} \to D \bar{D}$ cross section using initial-state radiation, Phys. Rev. D 77, 011103 (2008).
Z.-Y. Lin, J.-Z. Wang, J.-B. Cheng, L. Meng, and S.-L. Zhu, Identification of the $G (3900)$ as the P-wave $D {\bar{D}}^{*} / \bar{D} D^{*}$ resonance, Phys. Rev. Lett. 133, 241903 (2024).
X. Cao and H. Lenske, The nature and line shapes of charmonium in the $e^{+} e^{-} \to D \bar{D}$ reactions, arXiv:1410.1375.
M.-L. Du, U.-G. Meißner, and Q. Wang, $P$ -wave coupled channel effects in electron-positron annihilation, Phys. Rev. D 94, 096006 (2016).
T. V. Uglov, Y. S. Kalashnikova, A. V. Nefediev, G. V. Pakhlova, and P. N. Pakhlov, Exclusive open-charm near-threshold cross sections in a coupled-channel approach, JETP Lett. 105, 1 (2017).
N. Hüsken, R. F. Lebed, R. E. Mitchell, E. S. Swanson, Y.-Q. Wang, and C.-Z. Yuan, Poles and poltergeists in $e^{+} e^{-} \to D \bar{D}$ data, Phys. Rev. D 109, 114010 (2024).
Q. Ye, Z. Zhang, M.-L. Du, U.-G. Meißner, P.-Y. Niu, and Q. Wang, Resonance parameters of the vector charmoniumlike state $G (3900)$ , Phys. Rev. D 112, 016015 (2025).
S. X. Nakamura, X. H. Li, H. P. Peng, Z. T. Sun, and X. R. Zhou, Global coupled-channel analysis of $e^{+} e^{-} \to c \bar{c}$ processes in $\sqrt{s} = 3.75 - 4.7 GeV$ , Phys. Rev. D 112, 054027 (2025).
M. Ablikim et al. (BESIII Collaboration), $R (3780)$ resonance interpreted as the $1^{3} D_{1}$ -wave dominant state of charmonium from precise measurements of the cross section of $e^{+} e^{-} \to$ hadrons, Phys. Rev. Lett. 133, 241902 (2024).
M. Ablikim et al. (BESIII Collaboration), First observation of a three-resonance structure in $e^{+} e^{-} \to$ nonopen charm hadrons, Phys. Rev. Lett. 132, 191902 (2024).
L. Micu, Decay rates of meson resonances in a quark model, Nucl. Phys. B10, 521 (1969).
A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal, Naive quark pair creation model of strong interaction vertices, Phys. Rev. D 8, 2223 (1973).
D. Morel and S. Capstick, Baryon meson loop effects on the spectrum of nonstrange baryons, arXiv:nucl-th/0204014.
P. G. Ortega, J. Segovia, D. R. Entem, and F. Fernandez, Molecular components in P-wave charmed-strange mesons, Phys. Rev. D 94, 074037 (2016).
Z. Yang, G.-J. Wang, J.-J. Wu, M. Oka, and S.-L. Zhu, Novel coupled channel framework connecting the quark model and lattice QCD for the near-threshold Ds states, Phys. Rev. Lett. 128, 112001 (2022).
Q. Deng, R.-H. Ni, Q. Li, and X.-H. Zhong, Charmonia in an unquenched quark model, Phys. Rev. D 110, 056034 (2024).
J.-Z. Wang, Z.-Y. Lin, Y.-K. Chen, L. Meng, and S.-L. Zhu, Uncovering the mystery of $X (3872)$ with the coupled-channel dynamics, Phys. Rev. D 111, L111502 (2025).
See Supplemental Material at http://link.aps.org/supplemental/10.1103/c5vs-2l1k for further details on the QPC amplitudes and description of nOCH cross section.
S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
M. Ablikim et al. (BESIII Collaboration), Direct measurement of the branching fractions $B (ψ (3686) \to J / ψ X)$ , and $B (ψ (3770) \to J / ψ X)$ observation of the state $R (3760)$ in $e^{+} e^{-} \to J / ψ X$ , Phys. Rev. Lett. 127, 082002 (2021).
M. Ablikim et al. (BESIII Collaboration), Observation of a charged charmoniumlike structure in $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ at $\sqrt{s} = 4.26 GeV$ , Phys. Rev. Lett. 110, 252001 (2013).
Z. Q. Liu et al. (Belle Collaboration), Study of $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ and observation of a charged charmoniumlike state at Belle, Phys. Rev. Lett. 110, 252002 (2013); 111, 019901(E) (2013).
M. Ablikim et al. (BESIII Collaboration), Observation of a charged charmoniumlike structure $Z_{c} (4020)$ and search for the $Z_{c} (3900)$ in $e^{+} e^{-} \to π^{+} π^{-} h_{c}$ , Phys. Rev. Lett. 111, 242001 (2013).
D.-Y. Chen and X. Liu, Predicted charged charmonium-like structures in the hidden-charm dipion decay of higher charmonia, Phys. Rev. D 84, 034032 (2011).
D.-Y. Chen, X. Liu, and T. Matsuki, Predictions of charged charmoniumlike structures with hidden-charm and open-strange channels, Phys. Rev. Lett. 110, 232001 (2013).
D.-Y. Chen, X. Liu, and T. Matsuki, Reproducing the $Z_{c} (3900)$ structure through the initial-single-pion-emission mechanism, Phys. Rev. D 88, 036008 (2013).
E. S. Swanson, $Z_{b}$ and $Z_{c}$ exotic states as coupled channel cusps, Phys. Rev. D 91, 034009 (2015).
Y.-P. Kuang, QCD multipole expansion and hadronic transitions in heavy quarkonium systems, Front. Phys. China 1, 19 (2006).

Phys. Rev. D 112, L091502– Published 21 November, 2025

Vol. 112, Iss. 9 — 1 November 2025

Received 23 September 2025
Accepted 4 November 2025

DOI: https://doi.org/10.1103/c5vs-2l1k

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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Unified coupled-channel description for the five near-threshold structures $ψ (3770)$ , $G (3900)$ , $R (3760)$ , $R (3780)$ and $R (3810)$ from $e^{+} e^{-}$ annihilation

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Unified coupled-channel description for the five near-threshold structures ψ(3770), G(3900), R(3760), R(3780) and R(3810) from e+e− annihilation

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (46)

Unified coupled-channel description for the five near-threshold structures $ψ (3770)$ , $G (3900)$ , $R (3760)$ , $R (3780)$ and $R (3810)$ from $e^{+} e^{-}$ annihilation