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Charmonium-like exotic hadron productions in $e^{+} e^{-}$ collisions at the BESIII energy with the PACIAE model

Jian Cao ¹, Wen-Chao Zhang ^1,*, Zhi-Lei She ², An-Ke Lei ³, Jin-Peng Zhang ¹, Hua Zheng ¹, Dai-Mei Zhou ^3,†, Yu-Liang Yan ⁴, Zhong-Qi Wang ⁵ et al.

Ben-Hao Sa^4,3,‡

¹School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China
²Wuhan Textile University, Wuhan 430200, China
³Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
⁴China Institute of Atomic Energy, P. O. Box 275 (10), Beijing 102413, China
⁵Nanjing University of Aeronautics and Astronautics, Nanjing 210000, China

^*Contact author: wenchao.zhang@snnu.edu.cn
^†Contact author: zhoudm@mail.ccnu.edu.cn
^‡Contact author: sabhliuym35@qq.com

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Phys. Rev. D 112, 014033 – Published 21 July, 2025

DOI: https://doi.org/10.1103/1gtz-xkgh

Abstract

Inspired by the BESIII observation of exotic hadron $G (3900)$ in the $e^{+} e^{-} \to D \bar{D}$ process [M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 133, 081901 (2024)], we use the parton and hadron cascade model PACIAE to simulate the productions of charmonium-like exotic hadrons, including $X (3872)$ , $Z_{c} (3900)^{0}$ , and $G (3900)$ in the $e^{+} e^{-}$ annihilations at $\sqrt{s} = 4.95 GeV$ . The charmonium-like candidates are recombined by the dynamically constrained phase-space coalescence model using component mesons $D \bar{D}$ [for $G (3900)$ ] or $D {\bar{D}}^{*} / \bar{D} D^{*}$ [for $X (3872)$ , $Z_{c} (3900)^{0}$ , and $G (3900)$ ] in the PACIAE simulated final hadronic state. We then calculate, for the first time, the charmonium-like candidate’s orbital angular momentum quantum number in its rest frame and perform the spectral classification for each of the above candidates. For $G (3900)$ , as its $J^{P C}$ is $1^{- -}$ , it is identified as the $P$ -wave $D \bar{D}$ or $D {\bar{D}}^{*} / \bar{D} D^{*}$ state. Meanwhile, for $X (3872)$ and $Z_{c} (3900)^{0}$ , as their $J^{P C} s$ are, respectively, $1^{+ +}$ and $1^{+ -}$ , they are identified as the $S$ -wave $D {\bar{D}}^{*} / \bar{D} D^{*}$ candidates. It is observed that the yield of the $P$ -wave $G (3900)$ composed of $D {\bar{D}}^{*} / \bar{D} D^{*}$ is significantly larger than that composed of $D \bar{D}$ . Moreover, in the $D {\bar{D}}^{*} / \bar{D} D^{*}$ channel, the yield of the $P$ -wave $G (3900)$ is around three times as large as the yield of the $S$ -wave $Z_{c} (3900)^{0}$ , and it is around two orders of magnitude as large as the yield of the $S$ -wave $X (3872)$ . Finally, significant discrepancies are observed in the transverse momentum spectra and the rapidity distributions among the $X (3872)$ , $Z_{c} (3900)^{0}$ , and $G (3900)$ states. These discrepancies are proposed as valuable criteria for identifying the different charmonium-like exotic hadrons from each other.

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References (56)

M. Gell-Mann, A schematic model of baryons and mesons, Phys. Lett. B 8, 214 (1964).
R. J. Jaffe, Multi-quark hadrons. 1. The phenomenology of (2 quark 2 anti-quark) mesons, Phys. Rev. D 15, 267 (1977).
S.-K. Choi et al. (Belle Collaboration), Observation of a narrow charmoniumlike state in exclusive $B^{\pm} \to K^{\pm} π^{+} π^{-} J / ψ$ , Phys. Rev. Lett. 91, 262001 (2003).
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).
T. Aushev et al. (Belle Collaboration), Study of the $B \to X (3872) (\to D^{* 0} {\bar{D}}^{0}) K$ decay, Phys. Rev. D 81, 031103 (2010).
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. 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).
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).
M. Ablikim et al. (BESIII Collaboration), Observation of $Z_{c} (3900)^{0}$ in $e^{+} e^{-} \to π^{0} π^{0} J / ψ$ , Phys. Rev. Lett. 115, 112003 (2015).
M. Ablikim et al. (BESIII Collaboration), Coupled-channel analysis of the $χ_{c 1} (3872)$ line shape with BESIII data, Phys. Rev. Lett. 132, 151903 (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).
R. Aaij et al. (LHCb Collaboration), Probing the nature of the $χ_{c 1} (3872)$ state using radiative decays, J. High Energy Phys. 11 (2024) 121.
Y. Chen et al., Glueball spectrum and matrix elements on anisotropic lattices, Phys. Rev. D 73, 014516 (2006).
V. Mathieu, N. Kochelev, and V. Vento, The physics of glueballs, Int. J. Mod. Phys. E 18, 1 (2009).
L.-C. Gui, J.-M. Dong, Y. Chen, and Y.-B. Yang, Study of the pseudoscalar glueball in $J / ψ$ radiative decays, Phys. Rev. D 100, 054511 (2019).
Y.-B. Yang et al., Lattice study on $η_{c 2}$ and $X (3872)$ , Phys. Rev. D 87, 014501 (2013).
M. Padmanath and C. B. Lang, $X (3872)$ and $Y (4140)$ using diquark-antidiquark operators with lattice QCD, Phys. Rev. D 92, 034501 (2015).
H.-X. Chen, W. Chen, and S.-L. Zhu, Two- and three-gluon glueballs of $C = +$ , Phys. Rev. D 104, 094050 (2021).
H. Mutuk, Y. Sarac, H. Gumus, and A. Ozpineci, $X (3872)$ and its heavy quark spin symmetry partners in QCD sum rules, Eur. Phys. J. C 78, 904 (2018).
Z.-G. Wang, Decipher the width of the $X (3872)$ via the QCD sum rules, Phys. Rev. D 109, 014017 (2024).
W.-L. Wu, Y.-K. Chen, L. Meng, and S.-L. Zhu, Benchmark calculations of fully heavy compact and molecular tetraquark states, Phys. Rev. D 109, 054034 (2024).
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 $\sqrt{s} = 3.75$ $4.7 GeV$ , arXiv:2312.17658.
Z.-L. She, A.-K. Lei, Y.-L. Yan, D.-M. Zhou, W.-C. Zhang, H. Zheng, L. Zheng, Y.-L. Xie, G. Chen, and B.-H. Sa, Identifying an $X (3872)$ tetraquark state versus a molecular state by formation time, velocity, and temperature in relativistic nuclear collisions, Phys. Rev. C 110, 014910 (2024).
H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
A. Esposito, A. Pilloni, and A. Polosa, Multiquark resonances, Phys. Rep. 668, 1 (2017).
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018).
S. L. Olsen, T. Skwarnicki, and D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, 015003 (2018).
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).
A.-K. Lei, Y.-L. Yan, D.-M. Zhou, Z.-L. She, L. Zheng, G.-C. Yong, X.-M. Li, G. Chen, X. Cai, and B.-H. Sa, Introduction to the parton and hadron cascade model PACIAE 3.0, Phys. Rev. C 108, 064909 (2023).
A.-K Lei, Z.-L. She, Y.-L. Yan, D.-M. Zhou, L. Zheng, W.-C. Zhang, H. Zheng, L. V. Bravina, E. E. Zabrodin, and B.-H. Sa, A brief introduction to PACIAE 4.0, Comput. Phys. Commun. 310, 109520 (2025).
Y.-L. Yan, G. Chen, X.-M. Li, D.-M. Zhou, M.-J. Wang, S.-Y. Hu, L. Ye, and B.-H. Sa, Predictions for the production of light nuclei in $p p$ collisions at $\sqrt{s} = 7$ and $14 TeV$ , Phys. Rev. C 85, 024907 (2012).
C.-T. Wu, Z.-L. She, X.-Y. Peng, X.-L. Kang, H.-G. Xu, D.-M. Zhou, G. Chen, and B.-H. Sa, Study on the structure of exotic states $χ_{c 1} (3872)$ via beauty-hadron decays in $p p$ collisions at $\sqrt{s} = 8 TeV$ , Phys. Rev. D 107, 114022 (2023).
H.-G. Xu, Z.-L. She, D.-M. Zhou, L. Zheng, X.-L. Kang, G. Cheng, and B.-H. Sa, Investigation of exotic state $X (3872)$ in $p p$ collisions at $\sqrt{s} = 7$ , $13 TeV$ , Eur. Phys. J. C 81, 784 (2021).
C.-H. Chen, Y.-L. Xie, H.-G. Xu, Z. Zhanga, D.-M. Zhou, Z.-L. She, and G. Chen, Exotic states $P_{c} (4312)$ , $P_{c} (4440)$ , and $P_{c} (4457)$ in $p p$ collisions at $\sqrt{s} = 7$ , $1 3 TeV$ , Phys. Rev. D 105, 054013 (2022).
J. Cao, Z.-L. She, J.-P. Zhang, J.-H. Shi, Z.-Y. Qin, W.-C. Zhang, H. Zheng, A.-K. Lei, D.-M. Zhou, Y.-L. Yan, and B.-H. Sa, $X (2370)$ glueball-like particle productions in $e^{+} e^{-}$ collisions at the BESIII energy and in $p p$ collisions at the LHC energy with the PACIAE model, Phys. Rev. D 110, 054046 (2024).
Z.-Y. Lin, J.-Z. Wang, J.-B. Cheng, L. Meng, and S.-L. Zhu, Identification of the $G (3900)$ Structure as the P-wave $D {\bar{D}}^{*} / \bar{D} D^{*}$ resonance, Phys. Rev. Lett. 133, 241903 (2024).
R. Aaij et al. (LHCb Collaboration), Determination of the $X (3872)$ meson quantum numbers, Phys. Rev. Lett. 110, 222001 (2013).
M. Ablikim et al. (BESIII Collaboration), Study of the process $e^{+} e^{-} \to π^{0} π^{0} J / ψ$ and neutral charmoniumlike state $Z_{c} (3900)^{0}$ , Phys. Rev. D 102, 012009 (2020).
B. R. Martin and G. Shaw, Particle Physics, 3rd ed. (John Wiley and Sons Ltd, West Sussex, 2008).
T. Sjöstrand, S. Mrenna, and P. Z. Skands, PYTHIA 6.4 physics and manual, J. High Energy Phys. 05 (2006) 026.
C. Bierlich et al., A comprehensive guide to the physics and usage of PYTHIA 8.3, SciPost Phys. Codebases 2022, 8 (2022).
B. L. Combridge, Associated production of heavy flavour states in pp and $\bar{p} p$ interactions: Some QCD estimates, Nucl. Phys. B151, 429 (1979).
A. Baldini et al., Total Cross Section for Reactions of High Energy Particles (Spring-Veslay, Berlin, 1988).
R. Kubo, Statistical Mechanics (North-Holland Publishing Company, Amsterdam, 1965).
K. Stowe, An Introduction to Thermodynamics and Statistical Mechanics (Cambridge University, Cambridge, England, 2007).
L. Zhu, C. M Ko, and X. Yin, Light (anti-)nuclei production and flow in relativistic heavy-ion collisions, Phys. Rev. C 92, 064911 (2015).
L. Zhu, H. Zheng, C. M. Ko, and Y. Sun, Light nuclei production in Pb+Pb collisions at $\sqrt{s_{N N}} = 2.76 TeV$ , Eur. Phys. J. A 54, 175 (2018).
B. Chen, L. Jiang, X.-H. Liu, Y. Liu, and J. Zhao, $X (3872)$ production in relativistic heavy-ion collisions, Phys. Rev. C 105, 054901 (2022).
B. Grinstein, L. Maiani, and A. D. Polosa, Radiative decays of $X (3872)$ discriminate between the molecular and compact interpretations, Phys. Rev. D 109, 074009 (2024).
Z. Zhang, L. Zheng, G. Chen, H.-G. Xu, D.-M. Zhou, Y.-L. Yan, and B.-H. Sa, The study of $Z_{c}^{\pm} (3900)$ exotic state decaying to $J / ψ π^{\pm}$ in $p p$ collisions at $\sqrt{s} = 1.96$ , 7, and $13 TeV$ , Eur. Phys. J. C 81, 198 (2021).
H.-G. Xu, G. Chen, Y.-L. Yan, D.-M. Zhou, L. Zheng, Y.-L. Xie, Z.-L. She, and B.-H. Sa, Investigation of $Ω_{c}^{0}$ states decaying to $Ξ_{c}^{+} K^{-}$ in $p p$ collisions at $\sqrt{s} = 7$ , $13 TeV$ , Phys. Rev. C 102, 054319 (2020).
A. Suprano et al., Orbital angular momentum based intra- and inter- particle entangled states generated via a quantum dot source, arXiv:2211.05160.
R.-G. Ping, J. G. Messchendorp, and C.-Z. Yuan, Helicity amplitude analysis of $Z_{c} (3900)^{\pm}$ in $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ , Chin. Phys. Lett. 33, 061401 (2016).
R. Aaij et al. (LHCb Collaboration), Quantum numbers of the $X (3872)$ state and orbital angular momentum in its $ρ^{0} J / ψ$ decay, Phys. Rev. D 92, 011102(R) (2015).
X.-F. Wang, X. Liu, and Y.-N. Gao, Hadron production in open-charm meson pair at $e^{+} e^{-}$ collider, arXiv:2502.15117.

Phys. Rev. D 112, 014033– Published 21 July, 2025

Vol. 112, Iss. 1 — 1 July 2025

Received 24 February 2025
Accepted 25 June 2025

DOI: https://doi.org/10.1103/1gtz-xkgh

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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Charmonium-like exotic hadron productions in $e^{+} e^{-}$ collisions at the BESIII energy with the PACIAE model

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Charmonium-like exotic hadron productions in e+e− collisions at the BESIII energy with the PACIAE model

Abstract

Physics Subject Headings (PhySH)

Article Text

References (56)

Charmonium-like exotic hadron productions in $e^{+} e^{-}$ collisions at the BESIII energy with the PACIAE model