- Physical Review Journals
All JournalsPhysics Magazine

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

Charmonium-nucleon femtoscopy as a possible probe of the nucleon gravitational form factor

Ren Ejima1,*, Daisuke Fujii2,3,†, and Mamiya Kawaguchi4,‡

  • *Contact author: ejima@cns.s.u-tokyo.ac.jp
  • †Contact author: daisuke@rcnp.osaka-u.ac.jp
  • ‡Contact author: mamiya@aust.edu.cn
PDF

Phys. Rev. D 114, 054059 – Published 29 September, 2026

DOI: https://doi.org/10.1103/tfbv-chjm

Abstract

We investigate the charmonium-nucleon interaction, focusing on its connection with the internal structure of the nucleon encoded in the gravitational form factors. To describe this interaction, we employ an effective potential based on the QCD multipole expansion within the leading chromoelectric dipole approximation. In this framework, the potential is expressed in terms of the energy and pressure distributions inside the nucleon. We first construct these distributions from the gravitational form factors fitted to lattice-QCD data. The remaining model parameters are then fixed by requiring that the resulting ***J/ψ−N potential reproduce the Hadrons to Atomic nuclei from Lattice QCD (HAL QCD) potential outside the short-distance region, as well as the scattering phase shift estimated from the HAL QCD data. Based on this potential, we evaluate the J/ψ−N correlation function and further investigate the ψ(2S)−N system. We then examine the sensitivity of these correlation functions to the nucleon D-form factor.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (100)

  1. M. V. Polyakov and P. Schweitzer, Int. J. Mod. Phys. A 33, 1830025 (2018).
  2. V. D. Burkert, L. Elouadrhiri, F. X. Girod, C. Lorcé, P. Schweitzer, and P. E. Shanahan, Rev. Mod. Phys. 95, 041002 (2023).
  3. X.-D. Ji, W. Melnitchouk, and X. Song, Phys. Rev. D 56, 5511 (1997).
  4. M. V. Polyakov and C. Weiss, Phys. Rev. D 60, 114017 (1999).
  5. A. V. Belitsky and X. Ji, Phys. Lett. B 538, 289 (2002).
  6. P. Schweitzer, S. Boffi, and M. Radici, Phys. Rev. D 66, 114004 (2002).
  7. M. V. Polyakov, Phys. Lett. B 555, 57 (2003).
  8. M. Wakamatsu, Phys. Lett. B 648, 181 (2007).
  9. K. Goeke, J. Grabis, J. Ossmann, M. V. Polyakov, P. Schweitzer, A. Silva, and D. Urbano, Phys. Rev. D 75, 094021 (2007).
  10. C. Cebulla, K. Goeke, J. Ossmann, and P. Schweitzer, Nucl. Phys. A794, 87 (2007).
  11. P. Hagler et al. (LHPC Collaboration), Phys. Rev. D 77, 094502 (2008).
  12. M. V. Polyakov and H.-D. Son, J. High Energy Phys. 09 (2018) 156.
  13. P. E. Shanahan and W. Detmold, Phys. Rev. Lett. 122, 072003 (2019).
  14. I. V. Anikin, Phys. Rev. D 99, 094026 (2019).
  15. P. Avelino, Phys. Lett. B 795, 627 (2019).
  16. R. Yanagihara and M. Kitazawa, Prog. Theor. Exp. Phys. 2019, 093B02 (2019).
  17. C. Lorcé, H. Moutarde, and A. P. Trawiński, Eur. Phys. J. C 79, 89 (2019).
  18. K. A. Mamo and I. Zahed, Phys. Rev. D 101, 086003 (2020).
  19. M. J. Neubelt, A. Sampino, J. Hudson, K. Tezgin, and P. Schweitzer, Phys. Rev. D 101, 034013 (2020).
  20. M. Varma and P. Schweitzer, Phys. Rev. D 102, 014047 (2020).
  21. D. Chakrabarti, C. Mondal, A. Mukherjee, S. Nair, and X. Zhao, Phys. Rev. D 102, 113011 (2020).
  22. K. Azizi and U. Özdem, Eur. Phys. J. C 80, 104 (2020).
  23. A. Freese and G. A. Miller, Phys. Rev. D 103, 094023 (2021).
  24. J. Y. Panteleeva and M. V. Polyakov, Phys. Rev. D 104, 014008 (2021).
  25. A. Freese and G. A. Miller, Phys. Rev. D 104, 014024 (2021).
  26. J.-Y. Kim and H.-C. Kim, Phys. Rev. D 104, 074019 (2021).
  27. S. Owa, A. Thomas, and X. Wang, Phys. Lett. B 829, 137136 (2022).
  28. D. A. Pefkou, D. C. Hackett, and P. E. Shanahan, Phys. Rev. D 105, 054509 (2022).
  29. J. More, A. Mukherjee, S. Nair, and S. Saha, Phys. Rev. D 105, 056017 (2022).
  30. M. Fujita, Y. Hatta, S. Sugimoto, and T. Ueda, Prog. Theor. Exp. Phys. 2022, 093B06 (2022).
  31. P. Choudhary, B. Gurjar, D. Chakrabarti, and A. Mukherjee, Phys. Rev. D 106, 076004 (2022).
  32. H.-Y. Won, J.-Y. Kim, and H.-C. Kim, Phys. Rev. D 106, 114009 (2022).
  33. J.-Y. Kim, B.-D. Sun, D. Fu, and H.-C. Kim, Phys. Rev. D 107, 054007 (2023).
  34. H.-Y. Won, H.-C. Kim, and J.-Y. Kim, Phys. Rev. D 108, 094018 (2023).
  35. D. Fujii, A. Iwanaka, and M. Tanaka, Phys. Rev. D 110, L091501 (2024).
  36. D. C. Hackett, D. A. Pefkou, and P. E. Shanahan, Phys. Rev. Lett. 132, 251904 (2024).
  37. Y. Hatta, Phys. Rev. D 109, L051502 (2024).
  38. W.-Y. Liu, E. Shuryak, and I. Zahed, Phys. Rev. D 110, 054005 (2024).
  39. H.-Y. Won, H.-C. Kim, and J.-Y. Kim, J. High Energy Phys. 05 (2024) 173.
  40. M. Tanaka, D. Fujii, and M. Kawaguchi, Phys. Rev. D 112, 054048 (2025).
  41. D. Fujii, M. Kawaguchi, and M. Tanaka, Phys. Lett. B 866, 139559 (2025).
  42. D. Fujii, A. Iwanaka, and M. Tanaka, Phys. Rev. D 112, 094051 (2025).
  43. M. Goharipour, H. Hashamipour, H. Fatehi, F. Irani, K. Azizi, and S. V. Goloskokov (MMGPDs Collaboration), Phys. Rev. D 112, 014016 (2025).
  44. W. Broniowski and E. R. Arriola, Phys. Rev. D 112, 054028 (2025).
  45. S. Sugimoto and T. Tsukamoto, Prog. Theor. Exp. Phys. 2025, 083B01 (2025).
  46. S. Nair, C. Mondal, S. Xu, X. Zhao, and J. P. Vary, Phys. Rev. D 112, 114001 (2025).
  47. X.-H. Cao, F.-K. Guo, Q.-Z. Li, B.-W. Wu, and D.-L. Yao, Eur. Phys. J. Spec. Top. 235, 2121 (2025).
  48. Z. Dehghan, F. Almaksusi, and K. Azizi, J. High Energy Phys. 06 (2025) 025.
  49. Z.-Q. Yao, Y.-Z. Xu, D. Binosi, Z.-F. Cui, M. Ding, K. Raya, C. D. Roberts, J. Rodríguez-Quintero, and S. M. Schmidt, Eur. Phys. J. A 61, 92 (2025).
  50. X.-H. Cao, F.-K. Guo, Q.-Z. Li, and D.-L. Yao, Nat. Commun. 16, 6979 (2025).
  51. M. Kawaguchi, M. Harada, and Y.-L. Ma, Phys. Lett. B 876, 140400 (2026).
  52. R. Stegeman and R. Zwicky, J. High Energy Phys. 03 (2026) 184.
  53. R. Stegeman and R. Zwicky, J. High Energy Phys. 05 (2026) 159.
  54. K. Fukushima and T. Uji, Phys. Rev. D 113, 016025 (2026); 113, 099902(E) (2026).
  55. K. Fukushima and T. Uji, Phys. Rev. D 113, 114049 (2026).
  56. V. D. Burkert, L. Elouadrhiri, and F. X. Girod, Nature (London) 557, 396 (2018).
  57. V. D. Burkert, L. Elouadrhiri, and F. X. Girod, arXiv:2104.02031.
  58. B. Duran et al., Nature (London) 615, 813 (2023).
  59. P. Chatagnon et al. (CLAS Collaboration), Phys. Rev. C 113, 065203 (2026).
  60. H. Moutarde and T. C. group at Saclay, AIP Conf. Proc. 1374, 133 (2011).
  61. K. Kumerički, S. Liuti, and H. Moutarde, Eur. Phys. J. A 52, 157 (2016).
  62. R. Dupré, M. Guidal, S. Niccolai, and M. Vanderhaeghen, Eur. Phys. J. A 53, 171 (2017).
  63. H. Moutarde, P. Sznajder, and J. Wagner, Eur. Phys. J. C 78, 890 (2018).
  64. G. Christiaens et al. (CLAS Collaboration), Phys. Rev. Lett. 130, 211902 (2023).
  65. K. Mikhaylov (ALICE Collaboration), J. Phys. Conf. Ser. 1690, 012099 (2020).
  66. W. Rzęsa (ALICE Collaboration), Proc. SPIE Int. Soc. Opt. Eng. 11581, 1158114 (2020).
  67. A. Collaboration, Phys. Rev. Lett. 127, 172301 (2021).
  68. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 822, 136708 (2021).
  69. D. L. Mihaylov (ALICE Collaboration), Nucl. Phys. A1005, 121760 (2021).
  70. T. Humanic (ALICE Collaboration), Rev. Mex. Fis. Suppl. 3, 0308039 (2022).
  71. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 833, 137335 (2022).
  72. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 845, 138145 (2023).
  73. S. Acharya et al. (ALICE Collaboration), Eur. Phys. J. A 59, 298 (2023).
  74. S. Acharya et al. (ALICE Collaboration), Phys. Rev. C 107, 054904 (2023).
  75. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 844, 137223 (2023).
  76. W. Rzesa (ALICE Collaboration), Nuovo Cimento Soc. Ital. Fis. 47C, 195 (2024).
  77. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 856, 138915 (2024).
  78. A. Collaboration, arXiv:2508.09867.
  79. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 871, 139921 (2025).
  80. S. Acharya et al. (ALICE Collaboration), Eur. Phys. J. A 61, 194 (2025).
  81. A. Collaboration, arXiv:2605.02321.
  82. S. Acharya et al. (ALICE Collaboration), J. High Energy Phys. 04 (2026) 113.
  83. I. J. Abualrob et al. (ALICE Collaboration), Phys. Lett. B 874, 140252 (2026).
  84. I. J. Abualrob et al. (ALICE Collaboration), Phys. Lett. B 874, 140227 (2026).
  85. G. Krein and T. C. Peixoto, Few-Body Syst. 61, 49 (2020).
  86. Y. Lyu, T. Doi, T. Hatsuda, and T. Sugiura, Phys. Lett. B 860, 139178 (2025).
  87. X.-B. Tong, J.-P. Ma, and F. Yuan, J. High Energy Phys. 10 (2022) 046.
  88. M. E. Peskin, Nucl. Phys. B156, 365 (1979).
  89. G. Bhanot and M. E. Peskin, Nucl. Phys. B156, 391 (1979).
  90. M. I. Eides, V. Y. Petrov, and M. V. Polyakov, Phys. Rev. D 93, 054039 (2016).
  91. J. Ferretti, Phys. Lett. B 782, 702 (2018).
  92. J. Tarrús Castellà and G. a. Krein, Phys. Rev. D 98, 014029 (2018).
  93. M. V. Polyakov and P. Schweitzer, Phys. Rev. D 98, 034030 (2018).
  94. F. K. Guo, P. N. Shen, H. C. Chiang, and R. G. Ping, Nucl. Phys. A761, 269 (2005).
  95. F.-K. Guo, P.-N. Shen, and H.-C. Chiang, Phys. Rev. D 74, 014011 (2006).
  96. J. Yan, X.-H. Cao, M.-L. Du, and F.-K. Guo, Phys. Lett. B 880, 140765 (2026).
  97. Z.-W. Liu, D.-L. Ge, J.-X. Lu, M.-Z. Liu, and L.-S. Geng, Phys. Rev. D 112, 054019 (2025).
  98. I. A. Perevalova, M. V. Polyakov, and P. Schweitzer, Phys. Rev. D 94, 054024 (2016).
  99. M.-L. Du, V. Baru, F.-K. Guo, C. Hanhart, U.-G. Meißner, A. Nefediev, and I. Strakovsky, Eur. Phys. J. C 80, 1053 (2020).
  100. B. Wu, X.-K. Dong, M.-L. Du, F.-K. Guo, and B.-S. Zou, Fund. Res. 5, 2530 (2025).

Outline

Information

Phys. Rev. D 114, 054059– Published 29 September, 2026
  • Received 2 July 2026
  • Accepted 9 September 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