- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Parton Distribution Functions from Large-Momentum Expansion of Current-Current Correlators

Jia-Lu Zhang1, Xiangdong Ji1, Andreas Schäfer2, Rui Zhang3,*, and Christian Zimmermann4,5,†

  • *Contact author: rzhang93@mit.edu
  • †Contact author: chrzim@lbl.gov
PDF

Phys. Rev. Lett. 137, 181901 – Published 30 October, 2026

DOI: https://doi.org/10.1103/vdtk-mps3

Abstract

The universality of the large-momentum effective theory (LaMET) allows computing parton distribution functions starting from any Euclidean correlator with appropriate large-momentum Fourier components. Nevertheless, only the Wilson-line operators have been widely studied in this framework. In this Letter, we provide the first LaMET formulation using current-current correlators up to the next-to-leading order. The advantage of this new method is its simple renormalization property due to the absence of Wilson-line linear divergences. This provides an alternative approach for LaMET calculation with very different systematics, making it crucial for cross-validating future precision calculations. A first numerical example is presented using newly generated correlators for specific LaMET application from existing four-point function data.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (53)

  1. The ATLAS and CMS Collaborations, CERN Yellow Rep. Monogr. 7, 1 (2019).
  2. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
  3. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  4. X. Ji, Phys. Rev. Lett. 110, 262002 (2013).
  5. X. Ji, Sci. China Phys. Mech. Astron. 57, 1407 (2014).
  6. H.-W. Lin et al., Prog. Part. Nucl. Phys. 100, 107 (2018).
  7. K. Cichy and M. Constantinou, Adv. High Energy Phys. 2019, 3036904 (2019).
  8. M. Constantinou, Eur. Phys. J. A 57, 77 (2021).
  9. M. Constantinou et al., arXiv:2202.07193.
  10. H.-W. Lin, Prog. Part. Nucl. Phys. 144, 104177 (2025).
  11. X. Ji, Y.-S. Liu, Y. Liu, J.-H. Zhang, and Y. Zhao, Rev. Mod. Phys. 93, 035005 (2021).
  12. X. Gao, W.-Y. Liu, and Y. Zhao, Phys. Rev. D 109, 094506 (2024).
  13. Y. Zhao, Phys. Rev. Lett. 133, 241904 (2024).
  14. X. Ji, J.-H. Zhang, and Y. Zhao, Phys. Rev. Lett. 120, 112001 (2018).
  15. T. Ishikawa, Y.-Q. Ma, J.-W. Qiu, and S. Yoshida, Phys. Rev. D 96, 094019 (2017).
  16. J. Green, K. Jansen, and F. Steffens, Phys. Rev. Lett. 121, 022004 (2018).
  17. M. Constantinou and H. Panagopoulos, Phys. Rev. D 96, 054506 (2017).
  18. I. W. Stewart and Y. Zhao, Phys. Rev. D 97, 054512 (2018).
  19. C. Alexandrou, K. Cichy, M. Constantinou, K. Hadjiyiannakou, K. Jansen, H. Panagopoulos, and F. Steffens, Nucl. Phys. B923, 394 (2017).
  20. T. Izubuchi, X. Ji, L. Jin, I. W. Stewart, and Y. Zhao, Phys. Rev. D 98, 056004 (2018).
  21. Z.-Y. Li, Y.-Q. Ma, and J.-W. Qiu, Phys. Rev. Lett. 126, 072001 (2021).
  22. L.-B. Chen, W. Wang, and R. Zhu, Phys. Rev. Lett. 126, 072002 (2021).
  23. X. Ji, Y. Liu, A. Schäfer, W. Wang, Y.-B. Yang, J.-H. Zhang, and Y. Zhao, Nucl. Phys. B964, 115311 (2021).
  24. X. Gao, K. Lee, S. Mukherjee, C. Shugert, and Y. Zhao, Phys. Rev. D 103, 094504 (2021).
  25. Y.-K. Huo et al. (Lattice Parton (LPC) Collaboration), Nucl. Phys. B969, 115443 (2021).
  26. Y. Su, J. Holligan, X. Ji, F. Yao, J.-H. Zhang, and R. Zhang, Nucl. Phys. B991, 116201 (2023).
  27. R. Zhang, J. Holligan, X. Ji, and Y. Su, Phys. Lett. B 844, 138081 (2023).
  28. X. Ji, Y. Liu, and Y. Su, J. High Energy Phys. 08 (2023) 037.
  29. Y. Liu and Y. Su, J. High Energy Phys. 02 (2024) 204.
  30. X. Ji, Y. Liu, Y. Su, and R. Zhang, J. High Energy Phys. 03 (2025) 045.
  31. J.-W. Chen et al., Phys. Rev. D 113, 014509 (2026).
  32. X. Ji, Y. Liu, and Y. Su, arXiv:2601.12189.
  33. J.-W. Chen, X. Ji, and J.-H. Zhang, Nucl. Phys. B915, 1 (2017).
  34. K.-F. Liu, Phys. Rev. D 62, 074501 (2000).
  35. V. Braun and D. Müller, Eur. Phys. J. C 55, 349 (2008).
  36. A. J. Chambers, R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, A. Schiller, K. Somfleth, R. D. Young, and J. M. Zanotti, Phys. Rev. Lett. 118, 242001 (2017).
  37. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. Lett. 120, 022003 (2018).
  38. M. Diehl, D. Ostermeier, and A. Schäfer, J. High Energy Phys. 03 (2012) 089; 03 (2016) 1.
  39. G. S. Bali, V. M. Braun, B. Gläßle, M. Göckeler, M. Gruber, F. Hutzler, P. Korcyl, A. Schäfer, P. Wein, and J.-H. Zhang, Phys. Rev. D 98, 094507 (2018).
  40. J. Liang, T. Draper, K.-F. Liu, A. Rothkopf, and Y.-B. Yang (XQCD Collaboration), Phys. Rev. D 101, 114503 (2020).
  41. R. S. Sufian, C. Egerer, J. Karpie, R. G. Edwards, B. Joó, Y.-Q. Ma, K. Orginos, J.-W. Qiu, and D. G. Richards, Phys. Rev. D 102, 054508 (2020).
  42. G. S. Bali, M. Diehl, B. Gläßle, A. Schäfer, and C. Zimmermann, J. High Energy Phys. 09 (2021) 106.
  43. C. Zimmermann and A. Schäfer, Phys. Rev. D 110, 074503 (2024).
  44. X. Ji, Nucl. Phys. B1007, 116670 (2024).
  45. X. Ji, Research 8, 0695 (2025).
  46. Y.-Q. Ma and J.-W. Qiu, Phys. Rev. D 98, 074021 (2018).
  47. A. V. Grebe, D. C. Hackett, M. L. Wagman, R. Zhang, and Y. Zhao, arXiv:2606.16877.
  48. M. Bruno et al., J. High Energy Phys. 02 (2015) 043.
  49. G. S. Bali, B. Lang, B. U. Musch, and A. Schäfer, Phys. Rev. D 93, 094515 (2016).
  50. G. S. Bali, S. Collins, and A. Schafer, Comput. Phys. Commun. 181, 1570 (2010).
  51. T.-J. Hou et al., Phys. Rev. D 103, 014013 (2021).
  52. R. Zhang, A. V. Grebe, D. C. Hackett, M. L. Wagman, and Y. Zhao, Phys. Rev. D 112, L051502 (2025).
  53. G. S. Bali, P. C. Bruns, L. Castagnini, M. Diehl, J. R. Gaunt, B. Gläßle, A. Schäfer, A. Sternbeck, and C. Zimmermann, J. High Energy Phys. 12 (2018) 061.

Outline

Information

Phys. Rev. Lett. 137, 181901– Published 30 October, 2026
  • Received 4 May 2026
  • Revised 17 July 2026
  • Accepted 8 October 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