- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

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
  • Access by Xinjiang University

One-point charge correlator in deep inelastic scattering

Haotian Cao1,2,* and Frank Petriello1,†

  • *Contact author: haotiao.cao@northwestern.edu
  • †Contact author: f-petriello@northwestern.edu
PDF

Phys. Rev. D 114, 036023 – Published 21 August, 2026

DOI: https://doi.org/10.1103/3rv6-8dvl

Abstract

In this work, we propose a novel definition of the one-point charge correlator (QC) adapted to the Breit frame in deep-inelastic scattering (DIS). We demonstrate that this observable is infrared and collinear (IRC) safe, ensuring its perturbative calculability. Utilizing soft-collinear effective theory (SCET), we systematically analyze the QC in both the forward and back-to-back limits. In the forward limit, we introduce the nucleon charge correlator as a novel nonperturbative object that encodes the multidimensional microscopic structure of the nucleon. In the back-to-back limit, the QC establishes a direct correspondence with transverse momentum-dependent distributions (TMDs), enabling its description within the standard TMD factorization formalism. The singular distributions are derived within SCET and are verified by the full quantum chromodynamics calculations up to O(αs2). The corresponding collinear logarithms are resummed to all orders with the accuracy of NLL [O(αsnLn−1)], while the transverse momentum-dependent logarithms are resummed to all orders with the accuracy of N3LL for the unpolarized distribution and N2LL for the Sivers asymmetry.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (87)

  1. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  2. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D 19, 2018 (1979).
  3. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. Lett. 41, 1585 (1978).
  4. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D 17, 2298 (1978).
  5. F. R. Ore, Jr. and G. F. Sterman, Nucl. Phys. B165, 93 (1980).
  6. N. A. Sveshnikov and F. V. Tkachov, Phys. Lett. B 382, 403 (1996).
  7. G. P. Korchemsky, G. Oderda, and G. F. Sterman, AIP Conf. Proc. 407, 988 (1997).
  8. G. P. Korchemsky and G. F. Sterman, Nucl. Phys. B555, 335 (1999).
  9. A. V. Belitsky, G. P. Korchemsky, and G. F. Sterman, Phys. Lett. B 515, 297 (2001).
  10. C. Lee and G. F. Sterman, Phys. Rev. D 75, 014022 (2007).
  11. D. M. Hofman and J. Maldacena, J. High Energy Phys. 05 (2008) 012.
  12. I. Moult and H. X. Zhu, arXiv:2506.09119.
  13. M.-S. Gao, Z.-B. Kang, W. Li, and D. Y. Shao, Phys. Rev. Lett. 136, 151902 (2026).
  14. Y.-K. Song, S.-Y. Wei, L. Yang, and J. Zhou, Phys. Rev. Lett. 136, 131901 (2026).
  15. Z.-B. Kang, A. Metz, D. Pitonyak, and C. Zhang, arXiv:2604.28131.
  16. I. Moult and H. X. Zhu, J. High Energy Phys. 08 (2018) 160.
  17. Z.-B. Kang, K. Lee, D. Y. Shao, and F. Zhao, J. High Energy Phys. 03 (2024) 153.
  18. Z.-B. Kang, J. Penttala, and C. Zhang, arXiv:2410.21435.
  19. S. Bhattacharya, Z.-B. Kang, D. Padilla, and J. Penttala, arXiv:2504.10475.
  20. J. Gao, H. T. Li, and Y. J. Zhu, Phys. Rev. D 113, 034028 (2026).
  21. Y. Fu, Z.-B. Kang, J. Penttala, and Y. Zhou, arXiv:2512.16847.
  22. X. Liu and H. X. Zhu, Phys. Rev. Lett. 130, 091901 (2023).
  23. H. Cao, X. Liu, and H. X. Zhu, Phys. Rev. D 107, 114008 (2023).
  24. X. Liu and H. X. Zhu, arXiv:2403.08874.
  25. K.-B. Chen, J.-P. Ma, and X.-B. Tong, J. High Energy Phys. 08 (2024) 227.
  26. Y. J. Zhu, Phys. Rev. D 113, 014025 (2026).
  27. A. V. Belitsky, S. Hohenegger, G. P. Korchemsky, E. Sokatchev, and A. Zhiboedov, Nucl. Phys. B884, 305 (2014).
  28. A. V. Belitsky, S. Hohenegger, G. P. Korchemsky, E. Sokatchev, and A. Zhiboedov, Nucl. Phys. B884, 206 (2014).
  29. D. Chicherin, J. M. Henn, E. Sokatchev, and K. Yan, J. High Energy Phys. 02 (2021) 053.
  30. P. F. Monni, G. Vita, Z. Xu, and H. X. Zhu, arXiv:2508.00977.
  31. M. Riembau and M. Son, Phys. Rev. D 111, 014004 (2025).
  32. H. Cao, X. Liu, and F. Petriello, arXiv:2605.15280.
  33. H.-Y. Liu, X. Liu, J.-C. Pan, F. Yuan, and H. X. Zhu, Phys. Rev. Lett. 130, 181901 (2023).
  34. G. Cuomo, E. Firat, F. Nardi, and L. Ricci, arXiv:2503.21867.
  35. C. W. Bauer, S. Fleming, and M. E. Luke, Phys. Rev. D 63, 014006 (2000).
  36. C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, Phys. Rev. D 63, 114020 (2001).
  37. C. W. Bauer and I. W. Stewart, Phys. Lett. B 516, 134 (2001).
  38. C. W. Bauer, D. Pirjol, and I. W. Stewart, Phys. Rev. D 65, 054022 (2002).
  39. C. W. Bauer, S. Fleming, D. Pirjol, I. Z. Rothstein, and I. W. Stewart, Phys. Rev. D 66, 014017 (2002).
  40. M. Beneke, A. Chapovsky, M. Diehl, and T. Feldmann, Nucl. Phys. B643, 431 (2002).
  41. T. Sjöstrand et al., Comput. Phys. Commun. 191, 159 (2015).
  42. C. Bierlich et al., SciPost Phys. Codebases 2022, 8 (2022).
  43. S. Catani and M. Grazzini, Phys. Lett. B 446, 143 (1999).
  44. G. P. Salam and J. Rojo, Comput. Phys. Commun. 180, 120 (2009).
  45. V. Bertone, S. Carrazza, and J. Rojo, Comput. Phys. Commun. 185, 1647 (2014).
  46. V. Bertone, Proc. Sci. DIS2017 (2018) 201. [arXiv:1708.00911].
  47. D. W. Sivers, Phys. Rev. D 41, 83 (1990).
  48. J. C. Collins, Phys. Lett. B 536, 43 (2002).
  49. X.-d. Ji, J.-p. Ma, and F. Yuan, Phys. Rev. D 71, 034005 (2005).
  50. A. Idilbi, X. Ji, and F. Yuan, Nucl. Phys. B753, 42 (2006).
  51. T. Becher, M. Neubert, and B. D. Pecjak, J. High Energy Phys. 01 (2007) 076.
  52. Y. Li and H. X. Zhu, Phys. Rev. Lett. 118, 022004 (2017).
  53. T. Gehrmann, T. Lubbert, and L. L. Yang, Phys. Rev. Lett. 109, 242003 (2012).
  54. T. Gehrmann, T. Lübbert, and L. L. Yang, J. High Energy Phys. (2014).
  55. T. Lübbert, J. Oredsson, and M. Stahlhofen, J. High Energy Phys. (2016).
  56. M. G. Echevarria, I. Scimemi, and A. Vladimirov, J. High Energy Phys. (2016).
  57. M.-X. Luo, T.-Z. Yang, H. X. Zhu, and Y. J. Zhu, J. High Energy Phys. 01 (2020) 040.
  58. M.-X. Luo et al., J. High Energy Phys. 10 (2019) 083.
  59. M.-x. Luo, T.-Z. Yang, H. X. Zhu, and Y. J. Zhu, J. High Energy Phys. 06 (2021) 115.
  60. M.-x. Luo, T.-Z. Yang, H. X. Zhu, and Y. J. Zhu, Phys. Rev. Lett. 124, 092001 (2020).
  61. M. xing Luo, T.-Z. Yang, H. X. Zhu, and Y. J. Zhu, J. High Energy Phys. (2021).
  62. J. M. Henn, G. P. Korchemsky, and B. Mistlberger, J. High Energy Phys. 04 (2020) 018.
  63. I. Moult, H. X. Zhu, and Y. J. Zhu, arXiv:2205.02249.
  64. J. C. Collins, D. E. Soper, and G. F. Sterman, Nucl. Phys. B250, 199 (1985).
  65. Z.-B. Kang and A. Prokudin, Phys. Rev. D 85, 074008 (2012).
  66. A. Bacchetta et al., J. High Energy Phys. 02 (2007) 093.
  67. M. Anselmino et al., Eur. Phys. J. A 39, 89 (2009).
  68. M. G. Echevarria, Z.-B. Kang, and J. Terry, J. High Energy Phys. 01 (2021) 126.
  69. X. Ji, J.-W. Qiu, W. Vogelsang, and F. Yuan, Phys. Rev. Lett. 97, 082002 (2006).
  70. X. Ji, J.-w. Qiu, W. Vogelsang, and F. Yuan, Phys. Rev. D 73, 094017 (2006).
  71. Y. Koike, W. Vogelsang, and F. Yuan, Phys. Lett. B 659, 878 (2008).
  72. Z.-B. Kang, B.-W. Xiao, and F. Yuan, Phys. Rev. Lett. 107, 152002 (2011).
  73. P. Sun and F. Yuan, Phys. Rev. D 88, 114012 (2013).
  74. L.-Y. Dai, Z.-B. Kang, A. Prokudin, and I. Vitev, Phys. Rev. D 92, 114024 (2015).
  75. I. Scimemi, A. Tarasov, and A. Vladimirov, J. High Energy Phys. 05 (2019) 125.
  76. M. G. Echevarria, A. Idilbi, Z.-B. Kang, and I. Vitev, Phys. Rev. D 89, 074013 (2014).
  77. Z.-B. Kang and J.-W. Qiu, Phys. Lett. B 713, 273 (2012).
  78. H. T. Li, Y. Makris, and I. Vitev, Phys. Rev. D 103, 094005 (2021).
  79. P. Sun, J. Isaacson, C. P. Yuan, and F. Yuan, Int. J. Mod. Phys. A 33, 1841006 (2018).
  80. A. Bacchetta, F. Delcarro, C. Pisano, M. Radici, and A. Signori, J. High Energy Phys. 06 (2017) 081; 06 (2019) 51.
  81. I. Scimemi and A. Vladimirov, J. High Energy Phys. 06 (2020) 137.
  82. J. Gao, C. Liu, X. Shen, H. Xing, and Y. Zhao, Phys. Rev. D 110, 114019 (2024).
  83. R. D. Ball et al. (NNPDF Collaboration), Eur. Phys. J. C 82, 428 (2022).
  84. G. Abelof, R. Boughezal, X. Liu, and F. Petriello, Phys. Lett. B 763, 52 (2016).
  85. H. Abramowicz et al. (H1, ZEUS Collaborations), Eur. Phys. J. C 75, 580 (2015).
  86. H. Mäntysaari, Y. Tawabutr, and X.-B. Tong, Phys. Rev. D 112, 114027 (2025).
  87. Y. Huang, X.-B. Tong, and H.-L. Wang, Phys. Rev. Lett. 136, 131902 (2026).

Outline

Information

Phys. Rev. D 114, 036023– Published 21 August, 2026
  • Received 6 July 2026
  • Accepted 30 July 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