- 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

Twist-3 generalized parton distributions of sea quarks at zero skewness in the light-cone quark model

Xiaoyan Luan and Zhun Lu*

  • *Contact author: zhunlu@seu.edu.cn
PDF

Phys. Rev. D 112, 034004 – Published 5 August, 2025

DOI: https://doi.org/10.1103/34lm-pr91

Abstract

We present a systematic study of twist-3 generalized parton distributions (GPDs) for u¯ and d¯ sea quarks in the proton at zero skewness (ξ=0) using the light-cone formalism with overlap representation. The proton wave functions are derived from a meson-baryon fluctuation model that incorporates |qq¯B⟩ Fock states, providing a natural framework for investigating sea quark contributions. Within this approach, we compute the complete set of twist-3 GPDs and present the numerical results, including both chiral-odd (H2, E2, E˜2, and H˜2′) and chiral-even (E˜2T, H2T′, E2T′, and H˜2T′) distributions for u¯ and d¯ quarks at zero skewness. By taking the forward limit, we also calculate the corresponding twist-3 parton distribution functions e(x) of u¯ and d¯ quarks. The kinetic orbital angular momenta of sea quarks deduced from the twist-3 GPDs are studied and compared to those from the twist-2 GPDs.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (74)

  1. D. Müller, D. Robaschik, B. Geyer, F. M. Dittes, and J. Hořejši, Fortschr. Phys. 42, 101 (1994)
  2. X. D. Ji, Phys. Rev. D 55, 7114 (1997).
  3. A. V. Radyushkin, Phys. Rev. D 56, 5524 (1997).
  4. M. Diehl, Eur. Phys. J. A 52, 149 (2016).
  5. C. Adloff et al. (H1 Collaboration), Eur. Phys. J. C 13, 371 (2000).
  6. C. Adloff et al. (H1 Collaboration), Phys. Lett. B 517, 47 (2001).
  7. A. Aktas et al. (H1 Collaboration), Eur. Phys. J. C 44, 1 (2005).
  8. J. Breitweg et al. (ZEUS Collaboration), Eur. Phys. J. C 6, 603 (1999).
  9. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 573, 46 (2003).
  10. A. Airapetian et al. (HERMES Collaboration), Phys. Rev. Lett. 87, 182001 (2001).
  11. A. Airapetian et al. (HERMES Collaboration), Phys. Lett. B 704, 15 (2011).
  12. A. Airapetian et al. (HERMES Collaboration), J. High Energy Phys. 07 (2012) 032.
  13. N. d’Hose, E. Burtin, P. A. M. Guichon, and J. Marroncle, Eur. Phys. J. A 19, 47 (2004).
  14. S. Stepanyan et al. (CLAS Collaboration), Phys. Rev. Lett. 87, 182002 (2001).
  15. M. Burkardt, Phys. Rev. D 62, 071503 (2000); 66, 119903(E) (2002).
  16. M. Burkardt, Int. J. Mod. Phys. A 18, 173 (2003).
  17. M. Diehl, Eur. Phys. J. C 25, 223 (2002); 31, 277(E) (2003).
  18. S. Boffi and B. Pasquini, Riv. Nuovo Cimento 30, 387 (2007).
  19. K. Kumerički and D. Mueller, Nucl. Phys. B841, 1 (2010).
  20. M. Burkardt, Phys. Rev. D 66, 114005 (2002).
  21. S. Bhattacharya, C. Cocuzza, and A. Metz, Phys. Lett. B 788, 453 (2019).
  22. S. Bhattacharya, C. Cocuzza, and A. Metz, Phys. Rev. D 102, 054021 (2020).
  23. M. Goharipour, H. Hashamipour, F. Irani, and K. Azizi (MMGPDs Collaboration), Phys. Rev. D 109, 074042 (2024).
  24. H. Hashamipour, M. Goharipour, K. Azizi, and S. V. Goloskokov, Phys. Rev. D 107, 096005 (2023).
  25. I. V. Anikin, B. Pire, and O. V. Teryaev, Phys. Rev. D 62, 071501 (2000).
  26. M. Penttinen, M. V. Polyakov, A. G. Shuvaev, and M. Strikman, Phys. Lett. B 491, 96 (2000).
  27. A. V. Belitsky and D. Mueller, Nucl. Phys. B589, 611 (2000).
  28. N. Kivel and M. V. Polyakov, Nucl. Phys. B600, 334 (2001).
  29. A. V. Radyushkin and C. Weiss, Phys. Rev. D 63, 114012 (2001).
  30. N. Kivel, M. V. Polyakov, and M. Vanderhaeghen, Phys. Rev. D 63, 114014 (2001).
  31. X. D. Ji, Phys. Rev. Lett. 78, 610 (1997).
  32. X. Ji, X. Xiong, and F. Yuan, Phys. Rev. Lett. 109, 152005 (2012).
  33. X. Ji, X. Xiong, and F. Yuan, Phys. Rev. D 88, 014041 (2013).
  34. Y. Hatta, Phys. Lett. B 708, 186 (2012).
  35. Y. Hatta and S. Yoshida, J. High Energy Phys. 10 (2012) 080.
  36. M. Burkardt, Phys. Rev. D 88, 114502 (2013).
  37. F. P. Aslan, M. Burkardt, and M. Schlegel, Phys. Rev. D 100, 096021 (2019).
  38. C. Lorcé, Phys. Lett. B 735, 344 (2014).
  39. A. Bhoonah and C. Lorcé, Phys. Lett. B 774, 435 (2017).
  40. Y. Guo, X. Ji, B. Kriesten, and K. Shiells, J. High Energy Phys. 06 (2022) 096.
  41. S. Meissner, A. Metz, M. Schlegel, and K. Goeke, J. High Energy Phys. 08 (2008) 038.
  42. S. Meissner, A. Metz, and M. Schlegel, J. High Energy Phys. 08 (2009) 056.
  43. C. Lorcé and B. Pasquini, J. High Energy Phys. 09 (2013) 138.
  44. A. Rajan, M. Engelhardt, and S. Liuti, Phys. Rev. D 98, 074022 (2018).
  45. A. Mukherjee and M. Vanderhaeghen, Phys. Lett. B 542, 245 (2002).
  46. A. Mukherjee and M. Vanderhaeghen, Phys. Rev. D 67, 085020 (2003).
  47. F. Aslan and M. Burkardt, Phys. Rev. D 101, 016010 (2020).
  48. S. Bhattacharya, K. Cichy, M. Constantinou, J. Dodson, A. Metz, A. Scapellato, and F. Steffens, Phys. Rev. D 108, 054501 (2023).
  49. C. Tan and Z. Lu, Phys. Rev. D 110, 074027 (2024).
  50. S. Jain, S. Sharma, and H. Dahiya, arXiv:2408.07332.
  51. Z. Zhang, Z. Hu, S. Xu, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Rev. D 109, 034031 (2024).
  52. S. J. Brodsky and B. Q. Ma, Phys. Lett. B 381, 317 (1996).
  53. B. Pasquini and S. Boffi, Phys. Rev. D 73, 094001 (2006).
  54. X. Luan and Z. Lu, Phys. Lett. B 833, 137299 (2022).
  55. F. Aslan, M. Burkardt, C. Lorcé, A. Metz, and B. Pasquini, Phys. Rev. D 98, 014038 (2018).
  56. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).
  57. S. J. Brodsky, D. S. Hwang, B. Q. Ma, and I. Schmidt, Nucl. Phys. B593, 311 (2001).
  58. B. W. Xiao and B. Q. Ma, Phys. Rev. D 68, 034020 (2003).
  59. A. Bacchetta, F. Conti, and M. Radici, Phys. Rev. D 78, 074010 (2008).
  60. Z. Lu and I. Schmidt, Phys. Rev. D 75, 073008 (2007).
  61. D. Müller and D. S. Hwang, arXiv:1407.1655.
  62. S. J. Brodsky, M. Diehl, and D. S. Hwang, Nucl. Phys. B596, 99 (2001).
  63. M. Burkardt and D. S. Hwang, Phys. Rev. D 69, 074032 (2004).
  64. X. Luan and Z. Lu, Eur. Phys. J. C 83, 504 (2023).
  65. Z. L. Ma and Z. Lu, Phys. Rev. D 98, 054024 (2018).
  66. S. Kaur and H. Dahiya, AIP Conf. Proc. 2249, 030043 (2020).
  67. X. Luan and Z. Lu, Phys. Rev. D 109, 094016 (2024).
  68. S. Kumano and Q. T. Song, J. High Energy Phys. 09 (2021) 141.
  69. S. Sharma and H. Dahiya, arXiv:2310.03463.
  70. M. Gluck, E. Reya, and A. Vogt, Z. Phys. C 53, 651 (1992).
  71. A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, Eur. Phys. J. C 63, 189 (2009).
  72. D. V. Kiptily and M. V. Polyakov, Eur. Phys. J. C 37, 105 (2004).
  73. C. Lorcé and K. F. Liu, Few-Body Syst. 57, 379 (2016).
  74. P. Choudhary, D. Chakrabarti, and C. Mondal, Eur. Phys. J. C 84, 626 (2024).

Outline

Information

Phys. Rev. D 112, 034004– Published 5 August, 2025
  • Received 25 April 2025
  • Accepted 8 July 2025
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