Contribution of the non-linear term in the Balitsky–Kovchegov equation to the nuclear structure functions


In this paper, we present nuclear structure functions calculated from the impact-parameter dependent solution of the Balitsky–Kovchegov equation with our recently proposed set of nuclear initial conditions. We calculate the results with and without the non-linear term in the BK equation in order to study the impact of saturation effects on the measurable structure functions and nuclear modification factor. The difference of these results rises with decreasing Bjorken x and increasing scale. These predictions are of interest to the physics program at the future ep and eA colliders.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: For data associated with our previous studies, please visit]


  1. 1.

    A. Accardi et al., Eur. Phys. J. A 52, 268 (2016). arXiv: 1212.1701

    Article  ADS  Google Scholar 

  2. 2.

    J. Abelleira Fernandez et al. (LHeC Study Group), J. Phys. G39, 075001 (2012), arXiv: 1206.2913

  3. 3.

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

    Article  ADS  Google Scholar 

  4. 4.

    A.H. Mueller, J.w. Qiu, Nucl. Phys. B268, 427 (1986)

  5. 5.

    B. Ducloué, E. Iancu, A. Mueller, G. Soyez, D. Triantafyllopoulos, JHEP 04, 081 (2019). arXiv: 1902.06637

    Article  ADS  Google Scholar 

  6. 6.

    I. Balitsky, Nucl. Phys. B 463, 99 (1996). arXiv: hep-ph/9509348

    Article  ADS  Google Scholar 

  7. 7.

    Y.V. Kovchegov, Phys. Rev. D 60, 034008 (1999). arXiv: hep-ph/9901281

    Article  ADS  Google Scholar 

  8. 8.

    J.L. Albacete, N. Armesto, J.G. Milhano, P. Quiroga-Arias, C.A. Salgado, Eur. Phys. J. C 71, 1705 (2011). arXiv: 1012.4408

    Article  ADS  Google Scholar 

  9. 9.

    E. Avsar, E. Iancu, Phys. Lett. B 673, 24 (2009). arXiv: 0901.2873

    Article  ADS  Google Scholar 

  10. 10.

    A. van Hameren, P. Kotko, K. Kutak, C. Marquet, E. Petreska, S. Sapeta, JHEP 12, 034 (2016). [Erratum: JHEP 02, 158 (2019)], arXiv: 1607.03121

  11. 11.

    D. Bendova, J. Cepila, J.G. Contreras, M. Matas, Phys. Rev. D 100, 054015 (2019). arXiv: 1907.12123

    MathSciNet  Article  ADS  Google Scholar 

  12. 12.

    C. Contreras, E. Levin, R. Meneses, Eur. Phys. J. C 79, 842 (2019). arXiv: 1906.09603

    Article  ADS  Google Scholar 

  13. 13.

    J. Cepila, J.G. Contreras, M. Matas, Phys. Rev. D 99, 051502 (2019). arXiv: 1812.02548

    Article  ADS  Google Scholar 

  14. 14.

    E. Iancu, J.D. Madrigal, A.H. Mueller, G. Soyez, D.N. Triantafyllopoulos, Phys. Lett. B 750, 643 (2015). arXiv: 1507.03651

    Article  ADS  Google Scholar 

  15. 15.

    K.J. Golec-Biernat, M. Wusthoff, Phys. Rev. D 59, 014017 (1998). arXiv: hep-ph/9807513

    Article  ADS  Google Scholar 

  16. 16.

    J. Cepila, J. Contreras, M. Matas (2020), arXiv: 2002.11056

  17. 17.

    H. De Vries, C. De Jager, C. De Vries, Atom. Data Nucl. Data Tabl. 36, 495 (1987)

    Article  ADS  Google Scholar 

  18. 18.

    N. Armesto, Eur. Phys. J. C 26, 35 (2002). arXiv: hep-ph/0206017

    Article  ADS  Google Scholar 

  19. 19.

    H. Kowalski, D. Teaney, Phys. Rev. D 68, 114005 (2003). arXiv: hep-ph/0304189

    Article  ADS  Google Scholar 

  20. 20.

    A.H. Mueller, Nucl. Phys. B 415, 373 (1994)

    Article  ADS  Google Scholar 

  21. 21.

    A.H. Mueller, Nucl. Phys. B 335, 115 (1990)

    Article  ADS  Google Scholar 

  22. 22.

    N.N. Nikolaev, B. Zakharov, Z. Phys. C 49, 607 (1991)

    Article  Google Scholar 

  23. 23.

    M.R. Adams et al., E665. Z. Phys. C 67, 403 (1995). arXiv: hep-ex/9505006

    Article  ADS  Google Scholar 

Download references


This work has been supported from Grant LTC17038 of the INTER-EXCELLENCE program at the Ministry of Education, Youth and Sports of the Czech Republic and the COST Action CA15213 THOR.

Author information



Corresponding author

Correspondence to Marek Matas.

Additional information

Communicated by Laura Tolos.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cepila, J., Matas, M. Contribution of the non-linear term in the Balitsky–Kovchegov equation to the nuclear structure functions. Eur. Phys. J. A 56, 232 (2020).

Download citation