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Revisiting charmonium hybrid spectroscopy

Ri-Qing Qian ^1,2,3,*, Bing Chen ^4,†, and Xiang Liu ^1,2,5,3,‡

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
⁴School of Electrical and Electronic Engineering, Anhui Science and Technology University, Bengbu 233000, China
⁵MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China

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

Phys. Rev. D 114, 034017 – Published 10 August, 2026

DOI: https://doi.org/10.1103/n7v1-tmvp

Abstract

Hadrons with explicit gluonic degrees of freedom, such as charmonium hybrids, are key to understanding nonperturbative behavior of strong interaction, yet they remain experimentally elusive. Within a constituent gluon model treating the hybrid as a $c \bar{c} g$ three-body system with a transverse electric gluon, we predict the masses of the lightest hybrid multiplet ( $J^{P C} = 1^{- -}, 0^{- +}, 1^{- +}, 2^{- +}$ ) to lie in the range 4.19–4.32 GeV. By analyzing their decay patterns, we provide specific, experimentally testable signatures to guide the search for these exotic states at current and future facilities.

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References (63)

H. Aoyagi et al., Study of the $η π^{-}$ system in the $π^{-} p$ reaction at $6.3 GeV / c$ , Phys. Lett. B 314, 246 (1993).
D. R. Thompson et al. (E852 Collaboration), Evidence for exotic meson production in the reaction $π^{-} p \to η π^{-} p$ at 18 GeV/c, Phys. Rev. Lett. 79, 1630 (1997).
G. S. Adams et al. (E852 Collaboration), Observation of a new $J^{P C} = 1^{- +}$ exotic state in the reaction $π^{-} p \to π^{+} π^{-} π^{-} p$ at 18 GeV/c, Phys. Rev. Lett. 81, 5760 (1998).
A. Abele et al. (Crystal Barrel Collaboration), Exotic $η π$ state in $\bar{p} d$ annihilation at rest into $π^{-} π^{0} η p$ (spectator). Phys. Lett. B 423, 175 (1998).
D. Alde et al. (IHEP-IISN-LANL-LAPP Collaboration), Evidence for a $1^{- +}$ exotic meson, Phys. Lett. B 205, 397 (1988).
Y. A. Khokhlov (VES Collaboration), Study of $X (1600) 1^{- +}$ hybrid, Nucl. Phys. A663, 596 (2000).
V. Dorofeev et al. (VES Collaboration), The $J^{P C} = 1^{- +}$ hunting season at VES, AIP Conf. Proc. 619, 143 (2002).
C. A. Baker et al., Confirmation of $a_{0} (1450)$ and $π_{1} (1600)$ in $\bar{p} p \to ω π^{+} π^{-} π^{0}$ at rest, Phys. Lett. B 563, 140 (2003).
M. Alekseev et al. (COMPASS Collaboration), Observation of a $J^{P C} = 1^{- +}$ exotic resonance in diffractive dissociation of $190 GeV / c$ $π^{-}$ into $π^{-} π^{-} π^{+}$ , Phys. Rev. Lett. 104, 241803 (2010).
G. S. Adams et al. (CLEO Collaboration), Amplitude analyses of the decays $χ_{c 1} \to η π^{+} π^{-}$ and $χ_{c 1} \to η^{'} π^{+} π^{-}$ , Phys. Rev. D 84, 112009 (2011).
A. Rodas et al. (JPAC Collaboration), Determination of the pole position of the lightest hybrid meson candidate, Phys. Rev. Lett. 122, 042002 (2019).
M. Albrecht et al. (Crystal Barrel Collaboration), Coupled channel analysis of $\bar{p} p \to π^{0} π^{0} η$ , $π^{0} η η$ and $K^{+} K^{-} π^{0}$ at $900 MeV / c$ and of $π π$ -scattering data, Eur. Phys. J. C 80, 453 (2020).
J. Kuhn et al. (E852 Collaboration), Exotic meson production in the $f_{1} (1285) π^{-}$ system observed in the reaction $π^{-} p \to η π^{+} π^{-} π^{-} p$ at 18 GeV/c, Phys. Lett. B 595, 109 (2004).
M. Lu et al. (E852 Collaboration), Exotic meson decay to $ω π^{0} π^{-}$ , Phys. Rev. Lett. 94, 032002 (2005).
M. Ablikim et al. (BESIII Collaboration), Partial wave analysis of $J / ψ \to γ η η^{'}$ , Phys. Rev. D 106, 072012 (2022); 107, 079901(E) (2023).
M. Ablikim et al. (BESIII Collaboration), Observation of an isoscalar resonance with exotic $J^{P C} = 1^{- +}$ quantum numbers in $J / ψ \to γ η η^{'}$ , Phys. Rev. Lett. 129, 192002 (2022); 130, 159901(E) (2023).
F.-Y. Zhang, Q. Huang, and L.-M. Wang, Spectral analysis and decay mechanisms of $1^{- +}$ hybrid states in light meson sector, Phys. Rev. D 113, 014002 (2026).
Z.-X. Ma, Q. Huang, R. Chen, L.-M. Wang, Y. Tan, X.-H. Hu, J. He, and H.-X. Huang, Proper constituent gluon mass as the final piece to construct hybrid mesons, Phys. Rev. D 112, L111503 (2025).
T. Barnes, F. E. Close, and E. S. Swanson, Hybrid and conventional mesons in the flux tube model: Numerical studies and their phenomenological implications, Phys. Rev. D 52, 5242 (1995).
S.-L. Zhu, Masses and decay widths of heavy hybrid mesons, Phys. Rev. D 60, 014008 (1999).
Y. S. Kalashnikova and A. V. Nefediev, Spectra and decays of hybrid charmonia, Phys. Rev. D 77, 054025 (2008).
W. Chen, R. T. Kleiv, T. G. Steele, B. Bulthuis, D. Harnett, J. Ho, T. Richards, and S.-L. Zhu, Mass spectrum of heavy quarkonium hybrids, J. High Energy Phys. 09 (2013) 019.
Y. S. Kalashnikova and A. V. Nefediev, QCD string in excited heavy-light mesons and heavy-quark hybrids, Phys. Rev. D 94, 114007 (2016).
R. Oncala and J. Soto, Heavy quarkonium hybrids: Spectrum, decay and mixing, Phys. Rev. D 96, 014004 (2017).
C. Farina, H. Garcia Tecocoatzi, A. Giachino, E. Santopinto, and E. S. Swanson, Heavy hybrid decays in a constituent gluon model, Phys. Rev. D 102, 014023 (2020).
P. R. Page, Why hybrid meson coupling to two $S$ -wave mesons is suppressed, Phys. Lett. B 402, 183 (1997).
N. Isgur and J. E. Paton, A flux tube model for hadrons in QCD, Phys. Rev. D 31, 2910 (1985).
F. E. Close and P. R. Page, The Production and decay of hybrid mesons by flux tube breaking, Nucl. Phys. B443, 233 (1995).
Y. S. Kalashnikova and D. S. Kuzmenko, Hybrid adiabatic potentials in the QCD string model, Phys. At. Nucl. 66, 955 (2003).
D. Horn and J. Mandula, A model of mesons with constituent gluons, Phys. Rev. D 17, 898 (1978).
E. S. Swanson and A. P. Szczepaniak, Heavy hybrids with constituent gluons, Phys. Rev. D 59, 014035 (1999).
B. Chen and X. Liu, Investigating hybrid mesons with $0^{+ -}$ and $2^{+ -}$ exotic quantum numbers, Eur. Phys. J. C 85, 788 (2025).
T. Barnes, F. E. Close, and F. de Viron, $Q \bar{Q} G$ hermaphrodite mesons in the MIT bag model, Nucl. Phys. B224, 241 (1983).
M. S. Chanowitz and S. R. Sharpe, Hybrids: Mixed states of quarks and gluons, Nucl. Phys. B222, 211 (1983); B228, 588(E) (1983).
L. Liu, G. Moir, M. Peardon, S. M. Ryan, C. E. Thomas, P. Vilaseca, J. J. Dudek, R. G. Edwards, B. Joo, and D. G. Richards (Hadron Spectrum Collaboration), Excited and exotic charmonium spectroscopy from lattice QCD, J. High Energy Phys. 07 (2012) 126.
G. K. C. Cheung, C. O’Hara, G. Moir, M. Peardon, S. M. Ryan, C. E. Thomas, and D. Tims (Hadron Spectrum Collaboration), Excited and exotic charmonium, $D_{s}$ and $D$ meson spectra for two light quark masses from lattice QCD, J. High Energy Phys. 12 (2016) 089.
K. J. Juge, J. Kuti, and C. Morningstar, Fine structure of the QCD string spectrum, Phys. Rev. Lett. 90, 161601 (2003).
J. Merlin and J. E. Paton, Spin interactions in the flux tube model and hybrid meson masses, Phys. Rev. D 35, 1668 (1987).
E. Braaten, C. Langmack, and D. H. Smith, Born-Oppenheimer approximation for the $X Y Z$ mesons, Phys. Rev. D 90, 014044 (2014).
M. Berwein, N. Brambilla, J. Tarrús Castellà, and A. Vairo, Quarkonium hybrids with nonrelativistic effective field theories, Phys. Rev. D 92, 114019 (2015).
N. Brambilla, W. K. Lai, J. Segovia, J. Tarrús Castellà, and A. Vairo, Spin structure of heavy-quark hybrids, Phys. Rev. D 99, 014017 (2019); 101, 099902(E) (2020).
N. Brambilla, W. K. Lai, J. Segovia, and J. Tarrús Castellà, QCD spin effects in the heavy hybrid potentials and spectra, Phys. Rev. D 101, 054040 (2020).
J. Soto and S. T. Valls, Hyperfine splittings of heavy quarkonium hybrids, Phys. Rev. D 108, 014025 (2023).
A. Le Yaouanc, L. Oliver, O. Pene, J. C. Raynal, and S. Ono, $q \bar{q} g$ hybrid mesons in $ψ \to γ +$ hadrons, Z. Phys. C 28, 309 (1985).
A. P. Szczepaniak and P. Krupinski, Energy spectrum of the low-lying gluon excitations in the Coulomb gauge, Phys. Rev. D 73, 116002 (2006).
P. Guo, A. P. Szczepaniak, G. Galata, A. Vassallo, and E. Santopinto, Heavy quarkonium hybrids from Coulomb gauge QCD, Phys. Rev. D 78, 056003 (2008).
J. Govaerts, L. J. Reinders, H. R. Rubinstein, and J. Weyers, Hybrid quarkonia from QCD sum rules, Nucl. Phys. B258, 215 (1985).
J. Govaerts, L. J. Reinders, and J. Weyers, Radial excitations and exotic mesons via QCD sum rules, Nucl. Phys. B262, 575 (1985).
J. Govaerts, L. J. Reinders, P. Francken, X. Gonze, and J. Weyers, Coupled QCD sum rules for hybrid mesons, Nucl. Phys. B284, 674 (1987).
C.-F. Qiao, L. Tang, G. Hao, and X.-Q. Li, Determining $1^{- -}$ heavy hybrid masses via QCD sum rules, J. Phys. G 39, 015005 (2012).
D. Harnett, R. T. Kleiv, T. G. Steele, and H.-y. Jin, Axial vector $J^{P C} = 1^{+ +}$ charmonium and bottomonium hybrid mass predictions with QCD sum-rules, J. Phys. G 39, 125003 (2012).
Z.-G. Wang, Mass spectrum of the hidden-charm hybrid states via QCD sum rules, Phys. Rev. D 111, 114009 (2025).
S. S. Agaev, K. Azizi, and H. Sundu, Tensor hybrid charmonia, Phys. Rev. D 112, 014003 (2025).
F. E. Close and S. Godfrey, Charmonium hybrid production in exclusive B meson decays, Phys. Lett. B 574, 210 (2003).
P. R. Page, E. S. Swanson, and A. P. Szczepaniak, Hybrid meson decay phenomenology, Phys. Rev. D 59, 034016 (1999).
S.-L. Zhu, The possible interpretations of $Y (4260)$ , Phys. Lett. B 625, 212 (2005).
F. E. Close and P. R. Page, Gluonic charmonium resonances at BABAR and BELLE?, Phys. Lett. B 628, 215 (2005).
S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
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).
X. Wang, X. Liu, and Y. Gao, Colloquium: Hadron production in open-charm meson pairs at $e^{+} e^{-}$ colliders, Rev. Mod. Phys. 98, 021001 (2026).
A. Abele et al. (Crystal Barrel Collaboration), Evidence for a $π η$ P wave in $\bar{p} p$ annihilations at rest into $π^{0} π^{0} η$ , Phys. Lett. B 446, 349 (1999).
D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, USA, 1995).

Phys. Rev. D 114, 034017– Published 10 August, 2026

Vol. 114, Iss. 3 — 1 August 2026

Received 18 February 2026
Accepted 22 July 2026

DOI: https://doi.org/10.1103/n7v1-tmvp

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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Revisiting charmonium hybrid spectroscopy

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