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Convergence in charmonium structure: Light-front wave functions from basis light-front quantization and Dyson-Schwinger equations

Xianghui Cao1, Yang Li1,2, Chao Shi3, James P. Vary4, and Qun Wang1,2,5

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Phys. Rev. D 113, 014028 – Published 26 January, 2026

DOI: https://doi.org/10.1103/g6t6-7ykh

Abstract

We present a systematic comparison of charmonium light-front wave functions obtained through two complementary nonperturbative approaches: basis light-front quantization (BLFQ) and Dyson-Schwinger equations (DSEs). Key observables include the charge form factor, gravitational form factors, light-cone distribution amplitudes, decay constants, and two-photon transition form factors. Despite their distinct theoretical foundations and model parameters, the predictions from BLFQ and DSEs exhibit remarkable agreement across all observables. This convergence validates both frameworks for studying charmonium structure and highlights the complementary strengths of Hamiltonian-based (BLFQ) and Lagrangian-based (DSEs) methods in addressing nonperturbative QCD.

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References (87)

  1. N. Brambilla, S. Eidelman, B. K. Heltsley, R. Vogt, G. T. Bodwin, E. Eichten, A. D. Frawley, A. B. Meyer, R. E. Mitchell, V. Papadimitriou et al., Eur. Phys. J. C 71, 1534 (2011).
  2. N. Brambilla, S. Eidelman, P. Foka, S. Gardner, A. S. Kronfeld, M. G. Alford, R. Alkofer, M. Butenschoen, T. D. Cohen, J. Erdmenger et al., Eur. Phys. J. C 74, 2981 (2014).
  3. L. Favart, M. Guidal, T. Horn, and P. Kroll, Eur. Phys. J. A 52, 158 (2016).
  4. Y. V. Kovchegov and E. Levin, Cambridge Monogr. Part. Phys., Nucl. Phys., Cosmol. 33, 1 (2012).
  5. I. P. Ivanov, N. N. Nikolaev, and A. A. Savin, Phys. Part. Nucl. 37, 1 (2006).
  6. A. Rothkopf, Phys. Rep. 858, 1 (2020).
  7. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).
  8. F. Gross, E. Klempt, S. J. Brodsky, A. J. Buras, V. D. Burkert, G. Heinrich, K. Jakobs, C. A. Meyer, K. Orginos, M. Strickland et al., Eur. Phys. J. C 83, 1125 (2023).
  9. J. P. Vary, H. Honkanen, J. Li, P. Maris, S. J. Brodsky, A. Harindranath, G. F. de Teramond, P. Sternberg, E. G. Ng, and C. Yang, Phys. Rev. C 81, 035205 (2010).
  10. P. Wiecki, Y. Li, X. Zhao, P. Maris, and J. P. Vary, Phys. Rev. D 91, 105009 (2015).
  11. Y. Li, P. Maris, X. Zhao, and J. P. Vary, Phys. Lett. B 758, 118 (2016).
  12. S. Tang, Y. Li, P. Maris, and J. P. Vary, Phys. Rev. D 98, 114038 (2018).
  13. S. Tang, Y. Li, P. Maris, and J. P. Vary, Eur. Phys. J. C 80, 522 (2020).
  14. W. Qian, S. Jia, Y. Li, and J. P. Vary, Phys. Rev. C 102, 055207 (2020).
  15. S. Jia and J. P. Vary, Phys. Rev. C 99, 035206 (2019).
  16. J. Lan, K. Fu, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Lett. B 825, 136890 (2022).
  17. C. Mondal, S. Xu, J. Lan, X. Zhao, Y. Li, D. Chakrabarti, and J. P. Vary, Phys. Rev. D 102, 016008 (2020).
  18. S. Xu, C. Mondal, J. Lan, X. Zhao, Y. Li, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 104, 094036 (2021).
  19. S. Xu, Y. Liu, C. Mondal, J. Lan, X. Zhao, Y. Li, and J. P. Vary, Phys. Lett. B 867, 139599 (2025).
  20. Z. Kuang, K. Serafin, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 105, 094028 (2022).
  21. Y. Li, P. Maris, and J. P. Vary, Phys. Rev. D 96, 016022 (2017).
  22. S. Nair, C. Mondal, S. Xu, X. Zhao, A. Mukherjee, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 110, 056027 (2024).
  23. S. Xu, X. Cao, T. Hu, Y. Li, X. Zhao, and J. P. Vary, Phys. Rev. D 109, 114024 (2024).
  24. T. Hu, X. Cao, S. Xu, Y. Li, X. Zhao, and J. P. Vary, Phys. Rev. D 111, 074031 (2025).
  25. M. Li, Y. Li, P. Maris, and J. P. Vary, Phys. Rev. D 98, 034024 (2018).
  26. S. Tang, S. Jia, P. Maris, and J. P. Vary, Phys. Rev. D 104, 016002 (2021).
  27. Y. Li, M. Li, and J. P. Vary, Phys. Rev. D 105, L071901 (2022).
  28. Z. Wang, M. Li, Y. Li, and J. P. Vary, Phys. Rev. D 109, 3 (2024).
  29. J. Lan, C. Mondal, S. Jia, X. Zhao, and J. P. Vary, Phys. Rev. Lett. 122, 172001 (2019).
  30. L. Adhikari, Y. Li, M. Li, and J. P. Vary, Phys. Rev. C 99, 035208 (2019).
  31. L. Adhikari, C. Mondal, S. Nair, S. Xu, S. Jia, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 104, 114019 (2021).
  32. Y. Liu, S. Xu, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 105, 094018 (2022).
  33. Z. Zhang, Z. Hu, S. Xu, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 109, 034031 (2024).
  34. B. Lin, S. Nair, S. Xu, Z. Hu, C. Mondal, X. Zhao, and J. P. Vary(BLFQ Collaboration), Phys. Lett. B 847, 138305 (2023).
  35. S. Kaur, S. Xu, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 109, 014015 (2024).
  36. B. Lin, S. Nair, C. Mondal, S. Xu, Z. Hu, P. Zhang, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Lett. B 860, 139153 (2025).
  37. Y. Liu, C. Mondal, Z. Hu, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Lett. B 855, 138809 (2024).
  38. J. Lan, C. Mondal, X. Zhao, T. Frederico, and J. P. Vary, Phys. Rev. D 111, L111903 (2025).
  39. S. Xu, C. Mondal, X. Zhao, Y. Li, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 108, 094002 (2023).
  40. S. Xu, C. Mondal, X. Zhao, Y. Li, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 108, 094002 (2023).
  41. Z. Hu, S. Xu, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Lett. B 833, 137360 (2022).
  42. Z. Zhu, Z. Hu, J. Lan, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Lett. B 839, 137808 (2023).
  43. Z. Zhu, S. Xu, J. Wu, H. Yu, Z. Hu, J. Lan, C. Mondal, X. Zhao, and J. P. Vary(BLFQ Collaboration), Phys. Lett. B 855, 138829 (2024).
  44. F. J. Dyson, Phys. Rev. 75, 1736 (1949).
  45. J. S. Schwinger, Proc. Natl. Acad. Sci. U.S.A. 37, 452 (1951).
  46. J. S. Schwinger, Proc. Natl. Acad. Sci. U.S.A. 37, 455 (1951).
  47. P. Maris and C. D. Roberts, Int. J. Mod. Phys. E 12, 297 (2003).
  48. S. x. Qin, L. Chang, Y. x. Liu, C. D. Roberts, and D. J. Wilson, Phys. Rev. C 84, 042202 (2011).
  49. C. D. Roberts, Prog. Part. Nucl. Phys. 61, 50 (2008).
  50. I. C. Cloet and C. D. Roberts, Prog. Part. Nucl. Phys. 77, 1 (2014).
  51. G. Eichmann, H. Sanchis-Alepuz, R. Williams, R. Alkofer, and C. S. Fischer, Prog. Part. Nucl. Phys. 91, 1 (2016).
  52. C. Shi and I. C. Cloët, Phys. Rev. Lett. 122, 082301 (2019).
  53. C. Shi, K. Bednar, I. C. Cloët, and A. Freese, Phys. Rev. D 101, 074014 (2020).
  54. C. Shi, Y. P. Xie, M. Li, X. Chen, and H. S. Zong, Phys. Rev. D 104, L091902 (2021).
  55. C. Shi, M. Li, X. Chen, and W. Jia, Phys. Rev. D 104, 094016 (2021).
  56. C. Shi, J. Li, M. Li, X. Chen, and W. Jia, Phys. Rev. D 106, 014026 (2022).
  57. C. Shi, J. Li, P. L. Yin, and W. Jia, Phys. Rev. D 107, 074009 (2023).
  58. W. Kou, C. Shi, X. Chen, and W. Jia, Phys. Rev. D 108, 036021 (2023).
  59. C. Shi, P. Liu, Y. L. Du, and W. Jia, Phys. Rev. D 110, 094010 (2024).
  60. S. Leitão, Y. Li, P. Maris, M. T. Peña, A. Stadler, J. P. Vary, and E. P. Biernat, Eur. Phys. J. C 77, 696 (2017).
  61. S. J. Brodsky, H. C. Pauli, and S. S. Pinsky, Phys. Rep. 301, 299 (1998).
  62. X. d. Ji, J. P. Ma, and F. Yuan, Eur. Phys. J. C 33, 75 (2004).
  63. O. Leitner, J. F. Mathiot, and N. A. Tsirova, Eur. Phys. J. A 47, 17 (2011).
  64. W. Jaus, Phys. Rev. D 60, 054026 (1999).
  65. H. Y. Cheng, C. K. Chua, and C. W. Hwang, Phys. Rev. D 69, 074025 (2004).
  66. W. Wang, Y. L. Shen, and C. D. Lu, Phys. Rev. D 79, 054012 (2009).
  67. R. C. Verma, J. Phys. G 39, 025005 (2012).
  68. H. M. Choi and C. R. Ji, Phys. Rev. D 70, 053015 (2004).
  69. S. Y. Wang, Y. Y. Yang, Z. J. Sun, H. Yang, P. Li, and Z. Q. Zhang, Chin. Phys. C 48, 123102 (2024).
  70. A. J. Arifi, L. Happ, S. Ohno, and M. Oka, Phys. Rev. D 110, 014020 (2024).
  71. Y. Li, P. Maris, and J. P. Vary, Phys. Lett. B 836, 137598 (2023).
  72. Yang Li (2019), Heavy quarkonium light front wave functions from basis light-front quantization with a running coupling, Mendeley Data, V2, 10.17632/cjs4ykv8cv.2.
  73. C. Shi (2025), Light-front wave functions of the etaC meson from Dyson-Schwinger equations [Data set], Zenodo, 10.5281/zenodo.18041666.
  74. G. A. Miller, Annu. Rev. Nucl. Part. Sci. 60, 1 (2010).
  75. G. A. Miller, Phys. Rev. C 99, 035202 (2019).
  76. R. L. Jaffe, Phys. Rev. D 103, 016017 (2021).
  77. S. D. Drell and T. M. Yan, Phys. Rev. Lett. 24, 181 (1970).
  78. G. B. West, Phys. Rev. Lett. 24, 1206 (1970).
  79. S. J. Brodsky and D. S. Hwang, Nucl. Phys. B543, 239 (1999).
  80. J. J. Dudek, R. G. Edwards, and D. G. Richards, Phys. Rev. D 73, 074507 (2006).
  81. S. J. Brodsky, D. S. Hwang, B. Q. Ma, and I. Schmidt, Nucl. Phys. B593, 311 (2001).
  82. X. Cao, Y. Li, and J. P. Vary, Phys. Rev. D 108, 056026 (2023).
  83. X. Cao, S. Xu, Y. Li, G. Chen, X. Zhao, V. A. Karmanov, and J. P. Vary, J. High Energy Phys. 07 (2024) 095.
  84. X. Cao, Y. Li, and J. P. Vary, Phys. Rev. D 110, 076025 (2024).
  85. M. A. Sultan, Z. Xing, K. Raya, A. Bashir, and L. Chang, Phys. Rev. D 110, 054034 (2024).
  86. C. T. H. Davies, C. McNeile, E. Follana, G. P. Lepage, H. Na, and J. Shigemitsu, Phys. Rev. D 82, 114504 (2010).
  87. I. Babiarz, V. P. Goncalves, R. Pasechnik, W. Schäfer, and A. Szczurek, Phys. Rev. D 100, 054018 (2019).

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Phys. Rev. D 113, 014028– Published 26 January, 2026
  • Received 8 October 2025
  • Accepted 2 January 2026
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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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