Skip to main content
SpringerLink
Log in

Effect of the Parameterization of the Distribution Functions on the Longitudinal Structure Function at Small x

  • FIELDS, PARTICLES, AND NUCLEI
  • Published:
JETP Letters Aims and scope Submit manuscript

I use a direct method to extract the longitudinal structure function in the next-to-leading order approximation with respect to the number of active flavor from the parametrization of parton distributions. The contribution of charm and bottom quarks corresponding to the gluon distributions (i.e., \({{G}_{{{{n}_{f}} = 3}}}(x,{{Q}^{2}})\) and \({{G}_{{{{n}_{f}} = 5}}}(x,{{Q}^{2}})\)) is considered. I compare the obtained longitudinal structure function at \({{n}_{f}} = 4\) with the H1 data [Eur. Phys. J. C 74, 2814 (2014) and Eur. Phys. J. C 71, 1579 (2011)] and the result L.P. Kaptari et al. [Phys. Rev. D 99, 096019 (2019)] which is based on the Mellin transforms. These calculations compared with the results from CT18 [Phys. Rev. D 103, 014013 (2021)] parametrization model. The nonlinear effects on the gluon distribution improve the behavior of the longitudinal structure function in comparison with the H1 data and CT18 at low values of \({{Q}^{2}}\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. V. Andreev, A. Baghdasaryan, S. Baghdasaryan, et al. (H1 Collab.), Eur. Phys. J. C 74, 2814 (2014).

    Article  ADS  Google Scholar 

  2. F. D. Aaron, C. Alexa, V. Andreev, et al. (H1 Collab.), Eur. Phys. J. C 71, 1579 (2011).

    Article  ADS  Google Scholar 

  3. H. Abramowicz, I. Abt, L. Adamczyk, et al. (ZEUS Collab.), Phys. Rev. D 90, 072002 (2014).

  4. P. Agostini, H. Aksakal, H. Alan, et al. (LHeC Collab. and FCC-he Study Group), CERN-ACC-Note-2020-0002 (2020); arXiv: 2007.14491 [hep-ex].

  5. J. Bartels, K. Golec-Biernat, and L. Motyka, Phys. Rev. D 81, 054017 (2010).

  6. V. Tvaskis, A. Tvaskis, I. Niculescu, et al., Phys. Rev. C 97, 045204 (2018).

  7. V. Chekelian, arXiv: 0810.5112 [hep-ex] (2008).

  8. G. Altarelli and G. Martinelli, Phys. Lett. B 76, 89 (1978).

    Article  ADS  Google Scholar 

  9. R. S. Thorne, arXiv: hep-ph/9805298 (1998).

  10. A. D. Martin, W. J. Stirling, and R. S. Thorne, Phys. Lett. B 636, 259 (2006).

    Article  ADS  Google Scholar 

  11. M. M. Block, L. Durand, and D. W. McKay, Phys. Rev. D 77, 094003 (2008).

  12. M. M. Block and L. Durand, arXiv: 0902.0372 [hep-ph] (2009).

  13. L. P. Kaptari, A. V. Kotikov, N. Yu. Chernikova, and P. Zhang, JETP Lett. 109, 281 (2019).

    Article  ADS  Google Scholar 

  14. A. V. Kotikov, JETP Lett. 111, 67 (2020).

    Article  ADS  Google Scholar 

  15. L. P. Kaptari, A. V. Kotikov, N. Yu. Chernikova, and P. Zhang, Phys. Rev. D 99, 096019 (2019).

  16. B. Rezaei and G. R. Boroun, Eur. Phys. J. A 56, 262 (2020).

    Article  ADS  Google Scholar 

  17. G. R. Boroun, Phys. Rev. C 97, 015206 (2018).

  18. G. R. Boroun, Eur. Phys. J. Plus 129, 19 (2014).

    Article  ADS  Google Scholar 

  19. G. R. Boroun and B. Rezaei, Eur. Phys. J. C 72, 2221 (2012).

    Article  ADS  Google Scholar 

  20. N. Baruah, M. K. Das, and J. K. Sarma, Eur. Phys. J. Plus 129, 229 (2014).

    Article  Google Scholar 

  21. G. R. Boroun and B. Rezaei, Eur. Phys. Lett. 133, 61002 (2021).

    Article  ADS  Google Scholar 

  22. G. R. Boroun, Chin. Phys. C 45, 063105 (2021).

  23. G. R. Boroun and B. Rezaei, Phys. Lett. B 816, 136274 (2021).

  24. G. R. Boroun, Eur. Phys. J. Plus 135, 68 (2020).

    Article  Google Scholar 

  25. G. R. Boroun and B. Rezaei, Nucl. Phys. A 1006, 122062 (2021).

  26. B. Rezaei and G. R. Boroun, Commun. Theor. Phys. 59, 462 (2013).

    Article  ADS  Google Scholar 

  27. G. R. Boroun and B. Rezaei, Eur. Phys. J. C 72, 2221 (2012).

    Article  ADS  Google Scholar 

  28. B. Rezaei and G. R. Boroun, Nucl. Phys. A 857, 42 (2011).

    Article  ADS  Google Scholar 

  29. G. R. Boroun, Int. J. Mod. Phys. E 18, 131 (2009).

    Article  ADS  Google Scholar 

  30. S. Moch, J. A. M. Vermaseren, and A. Vogt, Phys. Lett. B 606, 123 (2005).

    Article  ADS  Google Scholar 

  31. S. Alekhin, J. Blümlein, and S.-O. Moch, arXiv: 1808.08404 [hep-ph] (2018).

  32. A. M. Cooper-Sarkar, R. C. E. Devenish, and A. de Roeck, Int. J. Mod. Phys. A 13, 3385 (1998).

    Article  ADS  Google Scholar 

  33. R. Thorne, Phys. Rev. D 73, 054019 (2006).

  34. R. Thorne, Phys. Rev. D 86, 074017 (2012).

  35. S. Alekhin, J. Blümlein, S. Klein, and S. Moch, arXiv: 0908.3128 [hep-ph] (2009).

  36. G. Beuf, C. Royon, and D. Salek, arXiv: 0810.5082 [hep-ph] (2008).

  37. J. Blümlein, A. de Freitas, C. Schneider, and K. Schönwald, Phys. Lett. B 782, 362 (2018).

    Article  ADS  Google Scholar 

  38. S. Alekhin, J. Blümlein, and S. Moch, arXiv: 2006.07032 [hep-ph] (2020).

  39. M. Glück, C. Pisano, and E. Reya, Phys. Rev. D 77, 074002 (2008).

  40. S. Riemersma, J. Smith, and W. L. van Neerven, Phys. Lett. B 347, 143 (1995).

    Article  ADS  Google Scholar 

  41. A. V. Kisselev, Phys. Rev. D 60, 074001 (1999).

  42. E. Laenen, S. Riemersma, J. Smith, and W. L. van Neerven, Nucl. Phys. B 392, 162 (1993).

    Article  ADS  Google Scholar 

  43. A. Y. Illarionov, B. A. Kniehl, and A. V. Kotikov, Phys. Lett. B 663, 66 (2008).

    Article  ADS  Google Scholar 

  44. S. Catani and F. Hautmann, Nucl. Phys. B 427, 475 (1994).

    Article  ADS  Google Scholar 

  45. W.-K. Tung, S. Kretzer, and C. Schmidt, J. Phys. G 28, 983 (2002).

    Article  ADS  Google Scholar 

  46. G. R. Boroun, B. Rezaei, and J. K. Sarma, Int. J. Mod. Phys. A 29, 1450189 (2014).

  47. G. R. Boroun and B. Rezaei, Nucl. Phys. A 929, 119 (2014).

    Article  ADS  Google Scholar 

  48. G. R. Boroun, Nucl. Phys. B 884, 684 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  49. G. R. Boroun, PoS (HQL 2012), 069 (2012).

  50. G. R. Boroun and B. Rezaei, Eur. Phys. Lett. 100, 41001 (2012).

    Article  ADS  Google Scholar 

  51. G. R. Boroun and B. Rezaei, Nucl. Phys. B 857, 143 (2012).

    Article  ADS  Google Scholar 

  52. G. R. Boroun and B. Rezaei, J. Exp. Theor. Phys. 115, 427 (2012).

    Article  ADS  Google Scholar 

  53. A. N. Khorramian, S. Atashbar Tehrani, and A. Mirjalili, Nucl. Phys. B Proc. Suppl. 186, 379 (2009).

    Article  ADS  Google Scholar 

  54. S. Khatibi and H. Khanpour, Nucl. Phys. B 967, 115432 (2021).

  55. J. Blumlein, A. de Freitas, W. L. van Neerven, and S. Klein, Nucl. Phys. B 755, 272 (2006).

    Article  ADS  Google Scholar 

  56. H. Khanpour, Nucl. Phys. B 958, 115141 (2020).

  57. H. Khanpour, Phys. Rev. D 99, 054007 (2019).

  58. G. R. Boroun, Phys. Lett. B 744, 142 (2015).

    Article  ADS  Google Scholar 

  59. G. R. Boroun, Phys. Lett. B 741, 197 (2015).

    Article  ADS  Google Scholar 

  60. A. V. Kotikov, A. V. Lipatov, and P. Zhang, arXiv: 2104.13462 [hep-ph] (2021).

  61. F. D. Aaron, H. Abramowicz, I. Abt, et al. (H1 and ZEUS Collab.), J. High Energy Phys. 1001, 109 (2010).

    Article  ADS  Google Scholar 

  62. H. Abramowicz, I. Abt, L. Adamczyk, et al. (H1 and ZEUS Collab.), Eur. Phys. J. C 78, 473 (2018).

    Article  ADS  Google Scholar 

  63. T.-J. Hou, J. Gao, T. J. Hobbs, K. Xie, S. Dulat, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, I. Sitiwaldi, D. Stump, and C.-P. Yuan, Phys. Rev. D 103, 014013 (2021).

  64. A. V. Giannini and F. O. Dureaes, Phys. Rev. D 88, 114004 (2013).

  65. G. R. Boroun and B. Rezaei, arXiv: 2105.01121 [hep-ph] (2021).

  66. R. Wang and X. Chen, Chin. Phys. C 41, 053103 (2017).

  67. G. R. Boroun and S. Zarrin, Eur. Phys. J. Plus 128, 119 (2013).

    Article  Google Scholar 

  68. B. Rezaei and G. R. Boroun, Phys. Lett. B 692, 247 (2010).

    Article  ADS  Google Scholar 

  69. G. R. Boroun, Eur. Phys. J. A 43, 335 (2010).

    Article  ADS  Google Scholar 

  70. G. R. Boroun, Eur. Phys. J. A 42, 251 (2009).

    Article  ADS  Google Scholar 

  71. Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977).

    ADS  Google Scholar 

  72. V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972).

    Google Scholar 

  73. G. Altarelli and G. Parisi, Nucl. Phys. B 126, 298 (1977).

    Article  ADS  Google Scholar 

  74. L. V. Gribov, E. M. Levin, and M. G. Ryskin, Phys. Rep. 100, 1 (1983).

    Article  ADS  Google Scholar 

  75. A. H. Mueller and J. Qiu, Nucl. Phys. B 268, 427 (1986).

    Article  ADS  Google Scholar 

  76. K. Prytz, Eur. Phys. J. C 22, 317 (2001).

    Article  ADS  Google Scholar 

  77. K. J. Eskola, H. Honkanen, V. J. Kolhinen, J. Qiu, and C. A. Salgado, Nucl. Phys. B 660, 211 (2003).

    Article  ADS  Google Scholar 

  78. M. A. Kimber, J. Kwiecinski, and A. D. Martin, Phys. Lett. B 508, 58 (2001).

    Article  ADS  Google Scholar 

  79. A. D. Martin, W. J. Stirling, and R. G. Roberts, Phys. Rev. D 47, 867 (1993).

    Article  ADS  Google Scholar 

  80. J. Kwiecinski, A. D. Martin, and P. J. Sutton, Phys. Rev. D 44, 2640 (1991).

    Article  ADS  Google Scholar 

  81. A. J. Askew, J. Kwiecinski, A. D. Martin, and P. J. Sutton, Phys. Rev. D 47, 3775 (1993).

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

I am especially grateful to A.V. Kotikov for carefully reading the manuscript and for critical notes. I am also grateful to H. Khanpour for help with preparation of the QCD parametrization model.

Funding

This work was supported by the Razi University.

Author information

Authors and Affiliations

  1. Physics Department, Razi University, 67149, Kermanshah, Iran

    G. R. Boroun

Authors
  1. G. R. Boroun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. R. Boroun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Boroun, G.R. Effect of the Parameterization of the Distribution Functions on the Longitudinal Structure Function at Small x. Jetp Lett. 114, 1–7 (2021). https://doi.org/10.1134/S0021364021130014

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364021130014

Search

Navigation