- 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
  • Letter
  • Open Access

Origin of the nucleon gravitational form factor BN(t): Exposition in light-front holographic QCD

Xianghui Cao1, Bheemsehan Gurjar1,2, Chandan Mondal3,4, Chen Chen5,6, and Yang Li1,7,*

  • *Contact author: leeyoung1987@ustc.edu.cn
PDF

Phys. Rev. D 113, L071503 – Published 22 April, 2026

DOI: https://doi.org/10.1103/c9ph-w9bw

Abstract

Recent lattice QCD simulations and phenomenological models indicate that the nucleon’s gravitational form factor BN(t) remains remarkably small at finite momentum transfer t. While BN(0)=0 is a known consequence of the equivalence principle, the physical origin of its suppression at finite t has not been fully elucidated. In this work, we demonstrate that the smallness of BN(t) arises from a fundamental cancellation within the nucleon’s wave functions. Using light-front holographic QCD, we show that BN(t) is governed by an antisymmetric factor in the longitudinal dynamics that leads to an exact vanishing in the symmetric limit and significant suppression for realistic nucleon structures. Our results suggest that the smallness of BN(t) is a signature of the nucleon’s dominant S-wave character, providing a formal justification for its frequent omission in practical applications like near-threshold J/ψ production.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. I. Y. Kobzarev and L. B. Okun’, Zh. Eksp. Teor. Fiz. 43, 1904 (1962), http://jetp.ras.ru/cgi-bin/dn/e_016_05_1343.pdf.
  2. H. Pagels, Phys. Rev. 144, 1250 (1966).
  3. X. D. Ji, Phys. Rev. Lett. 78, 610 (1997).
  4. O. V. Teryaev, arXiv:hep-ph/9904376.
  5. M. V. Polyakov and P. Schweitzer, Int. J. Mod. Phys. A 33, 1830025 (2018).
  6. V. D. Burkert, L. Elouadrhiri, F. X. Girod, C. Lorcé, P. Schweitzer, and P. E. Shanahan, Rev. Mod. Phys. 95, 041002 (2023).
  7. S. J. Brodsky, D. S. Hwang, B. Q. Ma, and I. Schmidt, Nucl. Phys. B593, 311 (2001).
  8. M. Deka, T. Doi, Y. B. Yang, B. Chakraborty, S. J. Dong, T. Draper, M. Glatzmaier, M. Gong, H. W. Lin, K. F. Liu et al., Phys. Rev. D 91, 014505 (2015).
  9. D. C. Hackett, D. A. Pefkou, and P. E. Shanahan, Phys. Rev. Lett. 132, 251904 (2024).
  10. C. Cebulla, K. Goeke, J. Ossmann, and P. Schweitzer, Nucl. Phys. A794, 87 (2007).
  11. K. Goeke, J. Grabis, J. Ossmann, M. V. Polyakov, P. Schweitzer, A. Silva, and D. Urbano, Phys. Rev. D 75, 094021 (2007).
  12. K. Goeke, J. Grabis, J. Ossmann, P. Schweitzer, A. Silva, and D. Urbano, Phys. Rev. C 75, 055207 (2007).
  13. M. J. Neubelt, A. Sampino, J. Hudson, K. Tezgin, and P. Schweitzer, Phys. Rev. D 101, 034013 (2020).
  14. K. Azizi and U. Özdem, Eur. Phys. J. C 80, 104 (2020).
  15. I. V. Anikin, Phys. Rev. D 99, 094026 (2019).
  16. D. Chakrabarti, C. Mondal, A. Mukherjee, S. Nair, and X. Zhao, Phys. Rev. D 102, 113011 (2020).
  17. M. Fujita, Y. Hatta, S. Sugimoto, and T. Ueda, Prog. Theor. Exp. Phys. 2022, 093B06 (2022).
  18. S. Nair, C. Mondal, S. Xu, X. Zhao, A. Mukherjee, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 110, 056027 (2024).
  19. 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).
  20. S. Nair, C. Mondal, S. Xu, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 112, 114001 (2025).
  21. B. Renner, Phys. Lett. 33B, 599 (1970).
  22. H. F. Jones and A. Salam, Phys. Lett. 34B, 149 (1971).
  23. X. H. Cao, F. K. Guo, Q. Z. Li, and D. L. Yao, Nat. Commun. 16, 6979 (2025).
  24. W. Broniowski and E. Ruiz Arriola, Phys. Rev. D 112, 054028 (2025).
  25. X. H. Cao, F. K. Guo, Q. Z. Li, B. W. Wu, and D. L. Yao, Eur. Phys. J. Special Topics (2025).
  26. Y. Hatta and D. L. Yang, Phys. Rev. D 98, 074003 (2018).
  27. K. A. Mamo and I. Zahed, Phys. Rev. D 101, 086003 (2020).
  28. Y. Hatta, A. Rajan, and D. L. Yang, Phys. Rev. D 100, 014032 (2019).
  29. Y. Guo, X. Ji, and Y. Liu, Phys. Rev. D 103, 096010 (2021).
  30. K. A. Mamo and I. Zahed, Phys. Rev. D 103, 094010 (2021).
  31. B. Duran, Z. E. Meziani, S. Joosten, M. K. Jones, S. Prasad, C. Peng, W. Armstrong, H. Atac, E. Chudakov, H. Bhatt et al., Nature (London) 615, 813 (2023).
  32. Y. Guo, X. Ji, M. G. Santiago, J. Yang, and H. C. Zhang, Phys. Rev. D 112, 054036 (2025).
  33. Y. Guo, F. Yuan, and W. Zhao, Phys. Rev. Lett. 135, 111902 (2025).
  34. Z. E. Meziani, Proc. Sci. QCHSC24 (2025) 076 [arXiv:2505.05671].
  35. Y. Guo, F. P. Aslan, X. Ji, and M. G. Santiago, Phys. Rev. Lett. 135, 261903 (2025).
  36. O. V. Teryaev, arXiv:hep-ph/9803403.
  37. J. Ossmann, M. V. Polyakov, P. Schweitzer, D. Urbano, and K. Goeke, Phys. Rev. D 71, 034011 (2005).
  38. X. D. Ji, W. Melnitchouk, and X. Song, Phys. Rev. D 56, 5511 (1997).
  39. R. Brout and F. Englert, Phys. Rev. 141, 1231 (1966).
  40. J. Polchinski and M. J. Strassler, Phys. Rev. Lett. 88, 031601 (2002).
  41. Z. Abidin and C. E. Carlson, Phys. Rev. D 79, 115003 (2009).
  42. D. Fujii, A. Iwanaka, and M. Tanaka, Phys. Rev. D 110, L091501 (2024).
  43. S. Mamedov, M. Allahverdiyeva, and N. Akbarova, Eur. Phys. J. C 85, 361 (2025).
  44. J. Deng and D. Hou, Phys. Rev. D 112, 036011 (2025).
  45. Z. Liu and A. Watanabe, Phys. Rev. D 112, 114032 (2025).
  46. A. d. d. Nascimento, H. Boschi-Filho, and J. Noronha, arXiv:2505.13649.
  47. D. Fujii, A. Iwanaka, and M. Tanaka, Phys. Rev. D 112, 094051 (2025).
  48. A. Nascimento and H. Boschi-Filho, arXiv:2511.20715.
  49. Z. Liu, H. Nakajima, H. Abuki, and A. Watanabe, J. High Energy Phys. 03 (2026) 051.
  50. A. Hippeläinen, N. Jokela, and M. Järvinen, arXiv:2601.14939.
  51. G. F. de Teramond, H. G. Dosch, and S. J. Brodsky, Phys. Rev. D 91, 045040 (2015).
  52. H. G. Dosch, G. F. de Teramond, and S. J. Brodsky, Phys. Rev. D 91, 085016 (2015).
  53. S. J. Brodsky, G. F. de Teramond, H. G. Dosch, and J. Erlich, Phys. Rep. 584, 1 (2015).
  54. N. Kumar, C. Mondal, and N. Sharma, Eur. Phys. J. A 53, 237 (2017).
  55. Y. Li and J. P. Vary, Phys. Lett. B 825, 136860 (2022).
  56. G. F. de Teramond and S. J. Brodsky, Phys. Rev. D 104, 116009 (2021).

Outline

Information

Phys. Rev. D 113, L071503– Published 22 April, 2026
  • Received 6 February 2026
  • Accepted 31 March 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