- 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

Longitudinal structure function in the limit x=Q2/s

G. R. Boroun*

  • *Contact author: boroun@razi.ac.ir
PDF

Phys. Rev. D 112, 074022 – Published 17 October, 2025

DOI: https://doi.org/10.1103/b1ml-2fht

Abstract

The longitudinal structure function for nucleons and nuclei is considered at fixed s and Q2 to the minimum value of x given by Q2/s. This is done using the expansion method and color dipole model in the next-to-leading order approximation. The extracted longitudinal structure functions were consistent with HERA hepdata and the determination of FL at x=Q2/s [Taylor, Phys. Rev. D 111, 052001 (2025)] at moderate and large Q2 values. The results, consistent with the dipole picture at low Q2 values, show that the longitudinal structure function is small as expected due to the transverse polarization of the exchanged photon and the strong suppression of the dominant gluon component. Nonlinear corrections to the nuclear longitudinal structure function at low values of x and Q2 are also considered. These results may enhance the deep inelastic scattering neutral current data in future colliders at low x and low Q2. The longitudinal structure functions for deuterium at low four-momentum transfer squared, Q2<1  GeV2 at the leading order and next-to-leading order approximations are determined and compared with the JLab E00-002 data.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (78)

  1. C. G. Callan, Jr. and D. J. Gross, Phys. Rev. Lett. 22, 156 (1969).
  2. P. Agostini et al. (LHeC and FCC-he Study Group Collaboration), J. Phys. G 48, 110501 (2021).
  3. EIC BNL, https://www.bnl.gov/eic/.
  4. V. Andreev et al. (H1 Collaboration), Eur. Phys. J. C 74, 2814 (2014).
  5. H. Abramowicz et al. (ZEUS Collaboration), Phys. Rev. D 90, 072002 (2014).
  6. A. Abada et al. (FCC Collaboration), Eur. Phys. J. C 79, 474 (2019).
  7. M. Klein, From My Vast Repertoire …, (World Scientific, Singapore, 2018); Ann. Phys. (Amsterdam) 528, 138 (2016).
  8. N. ArmestoP. R. Newman, W. Słomiński, and A. M. Staśto, Phys. Rev. D 100, 074022 (2019).
  9. E. Iancu, A. Leonidov, and L. McLerran, arXiv:hep-ph/0202270; E. Iancu and R. Venugopalan, Quark–Gluon Plasma 3 (World Scientific, Singapore, 2004); F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, Annu. Rev. Nucl. Part. Sci. 60, 463 (2010).
  10. A. Morreale and F. Salazar, Universe 7, 312 (2021).
  11. B. Z. Kopeliovich, L. I. Lapidus, and A. B. Zamolodchikov, JETP Lett. 33, 595 (1981) [Pis’ma Zh. Eksp. Teor. Fiz. 33, 612 (1981)].
  12. N. N. Nikolaev and B. Zakharov, Z. Phys. C 49, 607 (1991).
  13. J. Bartels, K. Golec-Biernat, and H. Kowalski, Phys. Rev. D 66, 014001 (2002).
  14. E. Iancu, K. Itakura, and S. Munier, Phys. Lett. B 590, 199 (2004).
  15. J. Bartels and E. Levin, Nucl. Phys. B387, 617 (1992).
  16. E. Iancu, K. Itakura, and L. McLerran, Nucl. Phys. A708, 327 (2002).
  17. P. Caucal and E. Iancu, Phys. Rev. D 111, 074008 (2025).
  18. H. Mantysaari, J. Penttala, F. Salazar, and B. Schenke, Phys. Rev. D 111, 054033 (2025).
  19. J. Jimenez-Lopez, P. R. Newman, and K. Wichmann, Phys. Rev. D 111, 056014 (2025).
  20. Frank E. Taylor, Phys. Rev. D 111, 052001 (2025).
  21. L. N. Hand, Phys. Rev. 129, 1834 (1963).
  22. K. Golec-Biernat and M. Wusthoff, Phys. Rev. D 59, 014017 (1998).
  23. P. Caucal and F. Salazar, arXiv:2502.02634.
  24. D. I. Kazakov, A. V. Kotikov, G. Parente, O. A. Sampayo, J. Sánchez Guillén, Phys. Rev. Lett. 65, 1535 (1990).
  25. L. H. Orr and W. J. Stirling, Phys. Rev. Lett. 66, 1673 (1991).
  26. L. P. Kaptari, A. V. Kotikov, N. Yu. Chernikova, and Pengming Zhang, Phys. Rev. D 99, 096019 (2019).
  27. G. R. Boroun and B. Rezaei, Phys. Lett. B 816, 136274 (2021).
  28. M. Niedziela and M. Praszalowicz, Acta Phys. Pol. B 46, 2019 (2015).
  29. N. Baruah, M. K. Das, and J. K. Sarma, Eur. Phys. J. Plus 129, 229 (2014).
  30. G. R. Boroun, B. Rezaei, and J. K. Sarma, Int. J. Mod. Phys. A 29, 1450189 (2014).
  31. K. Golec-Biernat and A. M. Stasto, Phys. Rev. D 80, 014006 (2009).
  32. A. D. Martin, W. J. Stirling, and R. S. Thorne, Phys. Lett. B 635, 305 (2006).
  33. A. V. Kotikov and G. Parente, Mod. Phys. Lett. A 12, 963 (1997).
  34. M. Gluck, C. Pisano, and E. Reya, Phys. Rev. D 77, 074002 (2008).
  35. S. Moch and A. Vogt, J. High Energy Phys. 04 (2009) 081.
  36. M. Modarres, M. R. Masouminia, H. Hosseinkhani, and N. Olanj, Nucl. Phys. A945, 168 (2016).
  37. M. Mottaghizadeh and A. Mirjalili, Phys. Lett. B 820, 136534 (2021).
  38. S. Zarrin and S. Dadfar, Int. J. Theor. Phys. 60, 3822 (2021).
  39. G. Altarelli and G. Martinelli, Phys. Lett. B 76, 89 (1978).
  40. M. Gluck and E. Reya, Nucl. Phys. B145, 24 (1978).
  41. S. Moch, J. A. M. Vermaseren, and A. Vogt, Phys. Lett. B 606, 123 (2005).
  42. G. R. Boroun, Phys. Rev. C 97, 015206 (2018).
  43. G. R. Boroun and B. Rezaei, Eur. Phys. J. C 72, 2221 (2012).
  44. M. B. Gay Ducati and P. B. Goncalves, Phys. Lett. B 390, 401 (1997).
  45. J. X. Chen, X. P. Wang et al., Chin. Phys. C 48, 063104 (2024).
  46. G. R. Boroun and Y. Cai, Chin. Phys. C 49, 053104 (2025).
  47. G. R. Boroun, Commun. Theor. Phys. 77, 055201 (2025).
  48. Yuri V. Kovchegov and E. Levin, Quantum Choromodynamics at High Energies, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (Cambridge University Press, Cambridge, England, 2012).
  49. Dmitri E. Kharzeev and E. Levin, Phys. Rev. D 104, 031503 (2021).
  50. Yu Seon Jeong, C. S. Kim, Minh Vu Luu, and Mary Hall Reno, J. High Energy Phys. 11 (2014) 025.
  51. A. Donnachie and P. V. Landshoff, Z. Phys. C 61, 139 (1994).
  52. M. M. Block, L. Durand, and P. Ha, Phys. Rev. D 89, 094027 (2014).
  53. R. S. Thorne, Phys. Rev. D 71, 054024 (2005).
  54. R. S. Thorne, arXiv:hep-ph/9805298.
  55. A. D. Martin, W. J. Stirling, and R. S. Thorne, Phys. Lett. B 636, 259 (2006).
  56. G. R. Boroun, JETP Lett. 114, 1 (2021).
  57. S. Catani, M. Ciafaloni, and F. Hautmann, Nucl. Phys. B366, 135 (1991).
  58. J. C. Collins and R. K. Ellis, Nucl. Phys. B360, 3 (1991).
  59. K. Golec-Biernat and S. Sapeta, J. High Energy Phys. 03 (2018) 102.
  60. M. A. Peredo and M. Hentschinski, Phys. Rev. D 109, 014032 (2024).
  61. F. Carvalho, F. O. Duraes, F. S. Navarra, and S. Szpigel, Phys. Rev. C 79, 035211 (2009).
  62. N. Armesto, H. Paukkunen, C. A. Salgado, and K. Tywoniuk, Phys. Lett. B 694, 38 (2010).
  63. N. Armesto, T. Lappi, H. Mäntysaari, H. Paukkunen, and M. Tevio, Phys. Rev. D 105, 114017 (2022).
  64. B. Rezaei, Nucl. Phys. A1053, 122971 (2025).
  65. K. Kovarik et al., Phys. Rev. D 93, 085037 (2016).
  66. H. Khanpour and S. Atashbar Tehrani, Phys. Rev. D 93, 014026 (2016).
  67. N. Armesto, C. A. Salgado, and U. A. Wiedemann, Phys. Rev. Lett. 94, 022002 (2005).
  68. D. A. Fagundes and M. V. T. Machado, Phys. Rev. D 107, 014004 (2023).
  69. N. N. Nikolaev, W. Schafer, B. G. Zakharov, and V. R. Zoller, JETP Lett. 84, 537 (2006).
  70. K. J. Eskola, H. Paukkunen, and C. A. Salgado, J. High Energy Phys. 04 (2009) 065.
  71. D. de Florian and R. Sassot, Phys. Rev. D 69, 074028 (2004).
  72. M. Hirai, S. Kumano, and T. H. Nagai, Phys. Rev. C 76, 065207 (2007).
  73. L. Frankfurt, V. Guzey, and M. Strikman, Phys. Rep. 512, 255 (2012).
  74. M. V. T. Machado, Eur. Phys. J. C 47, 365 (2006).
  75. E. C. Aschenauer, S. Fazio, M.  A.  C. Lamont, H. Paukkunen, and P. Zurita, Phys. Rev. D 96, 114005 (2017).
  76. HERAhepdata, https://www.hepdata.net/record/ins1377206.
  77. E. R. Cazaroto, F. Carvalho, V. P. Goncalves, and F. S. Navarra, Phys. Lett. B 671, 233 (2009).
  78. V. Tvaskis et al., Phys. Rev. C 97, 045204 (2018).

Outline

Information

Phys. Rev. D 112, 074022– Published 17 October, 2025
  • Received 7 July 2025
  • Accepted 1 October 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