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Charmonium-glueball spectroscopy with improved hadron creation operators

Juan Andrés Urrea-Niño*

Francesco Knechtli and Tomasz Korzec

Michael Peardon

  • *Contact author: urreanij@tcd.ie
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Phys. Rev. D 114, 014509 – Published 16 July, 2026

DOI: https://doi.org/10.1103/rs22-dx23

Abstract

Construction of creation operators which can properly sample the underlying energy eigenstates remains a fundamental first step in lattice QCD spectroscopy calculations, particularly when the spectrum includes states with different compositions such as mesons, glueballs, multiparticle states, etc. We tackle this issue in the study of the scalar glueball and charmonium mixing, where we use improved operators for both types of states to resolve the low-lying spectrum and identify the dominant composition of each state in a mass regime where the glueball is stable. We include derivative-based meson operators combined with distillation profiles, as well as glueball operators built from the chromomagnetic field and its derivatives which retain angular momentum information from their continuum counterparts. We comment on the advantages of these operators, particularly on the construction and implementation of the glueball ones, thanks to which we identify the lightest isoscalar state as glueball-dominated 0++.

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References (95)

  1. H. Fritzsch and M. Gell-Mann, Current algebra: Quarks and what else?, eConf C 720906V2, 135 (1972).
  2. H. Fritzsch and P. Minkowski, Psi resonances, gluons and the Zweig rule, Nuovo Cimento A 30, 393 (1975).
  3. R. L. Jaffe, K. Johnson, and Z. Ryzak, Qualitative features of the glueball spectrum, Ann. Phys. (N.Y.) 168, 344 (1986).
  4. V. Crede and C. Meyer, The experimental status of glueballs, Prog. Part. Nucl. Phys. 63, 74 (2009).
  5. W. Ochs, The status of glueballs, J. Phys. G 40, 043001 (2013).
  6. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  7. C. J. Morningstar and M. Peardon, Glueball spectrum from an anisotropic lattice study, Phys. Rev. D 60, 034509 (1999).
  8. H.-Y. Cheng, C.-K. Chua, and K.-F. Liu, Scalar glueball, scalar quarkonia, and their mixing, Phys. Rev. D 74, 094005 (2006).
  9. H.-Y. Cheng, C.-K. Chua, and K.-F. Liu, Revisiting scalar glueballs, Phys. Rev. D 92, 094006 (2015).
  10. S. Janowski, F. Giacosa, and D. H. Rischke, Is f0(1710) a glueball?, Phys. Rev. D 90, 114005 (2014).
  11. J.-M. Frère and J. Heeck, Scalar glueballs: Constraints from the decays into η or η′, Phys. Rev. D 92, 114035 (2015).
  12. M. Ablikim et al. (BESIII Collaboration), Determination of spin-parity quantum numbers of X(2370) as 0−+ from J/ψ→γKS0KS0η′, Phys. Rev. Lett. 132, 181901 (2024).
  13. C. Morningstar, Update on glueballs, Proc. Sci., LATTICE2024 (2024) 004.
  14. D. Vadacchino, A review on glueball hunting, in 39th International Symposium on Lattice Field Theory (2023), arXiv:2305.04869.
  15. G. Parisi, The strategy for computing the hadronic mass spectrum, Phys. Rep. 103, 203 (1984).
  16. G. P. Lepage, The analysis of algorithms for lattice field theory, in Theoretical Advanced Study Institute in Elementary Particle Physics (Cornell University, Ithaca, 1989).
  17. H. B. Meyer, Locality and statistical error reduction on correlation functions, J. High Energy Phys. 01 (2003) 048.
  18. H. B. Meyer, The Yang-Mills spectrum from a 2-level algorithm, J. High Energy Phys. 01 (2004) 030.
  19. M. Lüscher and P. Weisz, Locality and exponential error reduction in numerical lattice gauge theory, J. High Energy Phys. 09 (2001) 010.
  20. M. Cè, L. Giusti, and S. Schaefer, A local factorization of the fermion determinant in lattice QCD, Phys. Rev. D 95, 034503 (2017).
  21. M. Cè, L. Giusti, and S. Schaefer, Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD, Phys. Rev. D 93, 094507 (2016).
  22. M. Cè, L. Giusti, and S. Schaefer, Local multiboson factorization of the quark determinant, EPJ Web Conf. 175, 11005 (2018).
  23. M. Cè, Locality and multi-level sampling with fermions, Eur. Phys. J. Plus 134, 299 (2019).
  24. P. Majumdar, Y. Koma, and M. Koma, Glueball masses in 4-D U(1) lattice gauge theory using the multilevel algorithm, Nucl. Phys. B677, 273 (2004).
  25. P. Majumdar, N. Mathur, and S. Mondal, Noise reduction algorithm for glueball correlators, Phys. Lett. B 736, 415 (2014).
  26. M. Lüscher, A new approach to the problem of dynamical quarks in numerical simulations of lattice QCD, Nucl. Phys. B418, 637 (1994).
  27. L. Giusti, M. Cè, and S. Schaefer, Multi-boson block factorization of fermions, EPJ Web Conf. 175, 01003 (2018).
  28. L. Barca, F. Knechtli, M. J. Peardon, S. Schaefer, and J. A. Urrea Niño, Performance of two-level sampling for the glueball spectrum in pure gauge theory, Proc. Sci., LATTICE2023 (2023) 030.
  29. L. Barca, J. Finkenrath, F. Knechtli, M. J. Peardon, S. Schaefer, and J. A. Urrea Niño, Update on two-level sampling for glueball observables in quenched QCD, Proc. Sci., LATTICE2024 (2025) 062.
  30. L. Barca, S. Schaefer, and J. Finkenrath, Investigating a two-level algorithm for fermionic observables, Phys. Rev. D 113, 034505 (2026).
  31. M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B339, 222 (1990).
  32. B. Blossier, M. D. Morte, G. von Hippel, T. Mendes, and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, J. High Energy Phys. 04 (2009) 094.
  33. J. A. Urrea-Niño, F. Knechtli, J. Finkenrath, T. Korzec, M. J. Peardon, and R. Höllwieser, Flavor mixing in charmonium and light mesons with optimal distillation profiles, Proc. Sci., LATTICE2024 (2025) 080.
  34. J. J. Dudek, R. G. Edwards, N. Mathur, and D. G. Richards, Charmonium excited state spectrum in lattice QCD, Phys. Rev. D 77, 034501 (2008).
  35. J. J. Dudek, R. G. Edwards, M. J. Peardon, D. G. Richards, and C. E. Thomas (for the Hadron Spectrum Collaboration), Toward the excited meson spectrum of dynamical QCD, Phys. Rev. D 82, 034508 (2010).
  36. Y. Chen, D. Liu, Y. Liu, and J. Wu, Independent operators at different dimension, arXiv:hep-lat/0512033.
  37. K. Jansen and R. Sommer, O(a) improvement of lattice QCD with two flavors of Wilson quarks, Nucl. Phys. B530, 185 (1998).
  38. K. Jansen and R. Sommer, Erratum to: “O(a) improvement of lattice QCD with two flavors of Wilson quarks”: [Nucl. Phys. B 530 (1998) 185–203], Nucl. Phys. B643, 517 (2002).
  39. P. Fritzsch, F. Knechtli, B. Leder, M. Marinkovic, S. Schaefer, R. Sommer, and F. Virotta, The strange quark mass and lambda parameter of two flavor QCD, Nucl. Phys. B865, 397 (2012).
  40. S. Cali, F. Knechtli, and T. Korzec, How much do charm sea quarks affect the charmonium spectrum?, Eur. Phys. J. C 79, 607 (2019).
  41. M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, J. High Energy Phys. 08 (2010) 071.
  42. M. Lüscher, Erratum: Properties and uses of the Wilson flow in lattice QCD, J. High Energy Phys. 03 (2014) 092.
  43. F. Knechtli, T. Korzec, M. Peardon, and J. A. Urrea-Niño, Optimizing creation operators for charmonium spectroscopy on the lattice, Phys. Rev. D 106, 034501 (2022).
  44. B. Berg and A. Billoire, Glueball spectroscopy in 4d SU(3) lattice gauge theory (i), Nucl. Phys. B221, 109 (1983).
  45. T. Shrimal, S. Collins, P. Jana, M. Padmanath, and S. Prelovsek, Lattice study of ccu¯s¯ tetraquark channels in D(*)Ds(*) scattering, Phys. Rev. D 112, 054513 (2025).
  46. L. Barca, G. Bali, and S. Collins, Toward N to Nπ matrix elements from lattice QCD, Phys. Rev. D 107, L051505 (2023).
  47. S. Prelovsek, E. Ortiz-Pacheco, S. Collins, L. Leskovec, M. Padmanath, and I. Vujmilovic, Doubly heavy tetraquarks from lattice QCD: Incorporating diquark-antidiquark operators and the left-hand cut, Phys. Rev. D 112, 014507 (2025).
  48. H. Yan, C. Liu, L. Liu, and Y. Meng, Construction of general N-body lattice operators with arbitrary momenta, J. High Energy Phys. 10 (2025) 210.
  49. X. Liao and T. Manke, Excited charmonium spectrum from anisotropic lattices, arXiv:hep-lat/0210030.
  50. C. Gattringer, L. Y. Glozman, C. B. Lang, D. Mohler, and S. Prelovsek, Derivative sources in lattice spectroscopy of excited light-quark mesons, Phys. Rev. D 78, 034501 (2008).
  51. P. R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, 2nd ed. (NRC Press, Ottawa, ON, Canada, 1998).
  52. S. L. Altmann and P. Herzig, Point Group Theory Tables (Clarendon Press, Oxford, England, 1994).
  53. 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.
  54. G. Bailas, B. Blossier, and V. Morénas, Some hadronic parameters of charmonia in Nf=2 lattice QCD, Eur. Phys. J. C 78, 1018 (2018).
  55. M. Peardon, J. Bulava, J. Foley, C. Morningstar, J. Dudek, R. G. Edwards, B. Joó, 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).
  56. J. Balog, M. Niedermaier, F. Niedermayer, A. Patrascioiu, E. Seiler, and P. Weisz, Comparison of the o(3) bootstrap σ model with lattice regularization at low energies, Phys. Rev. D 60, 094508 (1999).
  57. F. Niedermayer, P. Rüfenacht, and U. Wenger, Fixed point gauge actions with fat links: scaling and glueballs, Nucl. Phys. B597, 413 (2001).
  58. W. Sun, L.-C. Gui, Y. Chen, M. Gong, C. Liu, Y.-B. Liu, Z. Liu, J.-P. Ma, and J.-B. Zhang, Glueball spectrum from Nf=2 lattice QCD study on anisotropic lattices, Chin. Phys. C 42, 093103 (2018).
  59. K. Sakai and S. Sasaki, Glueball spectroscopy in lattice QCD using gradient flow, Phys. Rev. D 107, 034510 (2023).
  60. L. Barca, S. Schaefer, F. Knechtli, J. A. Urrea-Niño, S. Martins, and M. Peardon, Exponential error reduction for glueball calculations using a two-level algorithm in pure gauge theory, Phys. Rev. D 110, 054515 (2024).
  61. D. Q. Liu, J. M. Wu, and Y. Chen, The combination of Wilson loops into JPC operators in lattice pure gauge theory, arXiv:hep-lat/0011087.
  62. D. Q. Liu, J. M. Wu, and Y. Chen, A new approach to construct the operator on lattice for the calculation of glueball masses, arXiv:hep-lat/0103018.
  63. D. Q. Liu and J. M. Wu, The first calculation for the mass of the ground 4++ glueball state on lattice, Mod. Phys. Lett. A 17, 1419 (2002).
  64. R. Abbott, D. C. Hackett, D. A. Pefkou, F. Romero-López, and P. E. Shanahan, Lattice evidence that scalar glueballs are small, Phys. Rev. Lett. 136, 041901 (2026).
  65. C. Gattringer and C. B. Lang, Quantum Chromodynamics on the Lattice, 2010th ed., Lecture Notes in Physics (Springer, Berlin, Germany, 2009).
  66. W. Lee, Perturbative improvement of staggered fermions using fat links, Phys. Rev. D 66, 114504 (2002).
  67. N. Husung, opbasis—a Python package to derive minimal operator bases, Eur. Phys. J. C 86, 427 (2026).

  68. We thank Nikolai Husung for his help with this.

  69. F. Joswig, S. Kuberski, J. T. Kuhlmann, and J. Neuendorf, pyerrors: A Python framework for error analysis of Monte Carlo data, Comput. Phys. Commun. 288, 108750 (2023).
  70. U. Wolff, Monte Carlo errors with less errors, Comput. Phys. Commun. 156, 143 (2004).
  71. U. Wolff, Erratum to “Monte Carlo errors with less errors” [Comput. Phys. Comm. 156 (2004) 143–153], Comput. Phys. Commun. 176, 383 (2007).
  72. S. Schaefer, R. Sommer, and F. Virotta, Critical slowing down and error analysis in lattice QCD simulations, Nucl. Phys. B845, 93 (2011).
  73. A. Ramos, Automatic differentiation for error analysis of Monte Carlo data, Comput. Phys. Commun. 238, 19 (2019).
  74. L. Struckmeier, R. Höllwieser, F. Knechtli, T. Korzec, M. J. Peardon, and J. A. Urrea Niño, Static-light meson spectroscopy with optimal distillation profiles, Proc. Sci., LATTICE2024 (2025) 104.

  75. We extract the plateau value as a weighted average using the inverse error squared as weights.

  76. M. Albanese et al., Glueball masses and string tension in lattice QCD, Phys. Lett. B 192, 163 (1987).
  77. M. Lüscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys. 97, 59 (1985).
  78. M. Lüscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys. 98, 433 (1985).
  79. M. Gunther, F. Knechtli, and M. Peardon, Lattice Quantum Chromodynamics: Practical Essentials, 1st ed., SpringerBriefs in Physics (Springer, Dordrecht, Netherlands, 2016).
  80. J. A. Urrea-Niño, R. Höllwieser, F. Knechtli, T. Korzec, J. Finkenrath, and M. Peardon, S-wave flavor-singlet meson mixing in QCD with light and charm quarks, Phys. Rev. D 112, 074502 (2025).
  81. G. K. C. Cheung, C. E. Thomas, D. J. Wilson, G. Moir, M. Peardon, and S. M. Ryan (Hadron Spectrum Collaboration), DK I=0, DK¯ I=0, 1 scattering and the Ds0*(2317) from lattice QCD, J. High Energy Phys. 02 (2020) 100.
  82. M. T. Hansen, R. A. Briceño, R. G. Edwards, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), Energy-dependent π+π+π+ scattering amplitude from QCD, Phys. Rev. Lett. 126, 012001 (2021).
  83. L. Gayer, N. Lang, S. M. Ryan, D. Tims, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), Isospin-1/2 Dπ scattering and the lightest D0* resonance from lattice QCD, J. High Energy Phys. 07 (2021) 123.
  84. D. J. Wilson, C. E. Thomas, J. J. Dudek, and R. G. Edwards (for the Hadron Spectrum Collaboration), Scalar and tensor charmonium resonances in coupled-channel scattering from lattice QCD, Phys. Rev. Lett. 132, 241901 (2024).
  85. D. J. Wilson, C. E. Thomas, J. J. Dudek, and R. G. Edwards (for the Hadron Spectrum Collaboration), Charmonium χc0 and χc2 resonances in coupled-channel scattering from lattice QCD, Phys. Rev. D 109, 114503 (2024).
  86. J. D. E. Yeo, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), DK/Dπ scattering and an exotic virtual bound state at the SU(3) flavour symmetric point from lattice QCD, J. High Energy Phys. 07 (2024) 012.
  87. T. Whyte, D. J. Wilson, and C. E. Thomas (for the Hadron Spectrum Collaboration), Near-threshold states in coupled DD*−D*D* scattering from lattice QCD, Phys. Rev. D 111, 034511 (2025).
  88. N. P. Lachini, C. E. Thomas, and D. J. Wilson (for the Hadron Spectrum Collaboration), Coupled-channel scattering of DD, DD*, and D*D* in isospin-1 from lattice QCD, Phys. Rev. D 112, 114511 (2025).
  89. G. Li, C. Shi, Y. Chen, and W. Sun, Tensor resonance in J/ψJ/ψ scattering from lattice QCD, arXiv:2505.24213.
  90. G. Li, C. Shi, Y. Chen, and W. Sun, ηcηc and J/ψ  J/ψ scatterings from lattice QCD, arXiv:2505.23220.
  91. L. Meng, E. Ortiz-Pacheco, V. Baru, E. Epelbaum, M. Padmanath, and S. Prelovsek, Doubly charm tetraquark channel with isospin 1 from lattice QCD, Phys. Rev. D 111, 034509 (2025).
  92. M. Sadl, S. Collins, Z.-H. Guo, M. Padmanath, S. Prelovsek, and L.-W. Yan, Charmoniumlike channels 1+ with isospin 1 from lattice and effective field theory, Phys. Rev. D 111, 054513 (2025).
  93. www.gauss-centre.eu.
  94. www.lrz.de.
  95. www.fz-juelich.de.

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Phys. Rev. D 114, 014509– Published 16 July, 2026
  • Received 26 March 2026
  • Accepted 21 May 2026
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