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Dipole-pion cross section in the saturation regime

G. R. Boroun*

B. Z. Kopeliovich†

  • *Contact author: boroun@razi.ac.ir
  • †Contact author: boris.kopeliovich@usm.cl
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Phys. Rev. D 112, 014027 – Published 15 July, 2025

DOI: https://doi.org/10.1103/y567-4tb6

Abstract

The scale-dependent dipole-pion cross section is analyzed as a function of the dipole size r and the impact parameter b. This analysis relies on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in μ∼1/r+μ0 at the next-to-leading order (NLO) approximation, with a specific initial condition at μ0. The dipole-pion cross section at small Bjorken variable β is being considered over a wide range of transverse separations r. Using the Laplace transformation technique, we describe the determination of the dipole-pion cross section based on the gluon distribution at the initial scale μ0 within a kinematic region characterized by low values of the Bjorken variable β. We found that geometric scaling for the dipole-pion cross section holds approximately within a wide kinematic region of rQs. The cross section saturates at large dipole sizes.

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References (40)

  1. A. B. Zamolodchikov, B. Z. Kopeliovich, and L. I. Lapidus, Pis’ma Zh. Eksp. Teor. Fiz. 33, 612 (1981) [Sov. Phys. JETP Lett. 33, 595 (1981)].
  2. B. Z. Kopeliovich, I. K. Potashnikova, B. Povh, and I. Schmidt, Phys. Rev. D 76, 094020 (2007).
  3. B. Z. Kopeliovich, A. Schäfer, and A. V. Tarasov, Phys. Rev. C 59, 1609 (1999).
  4. B. Z. Kopeliovich, A. Schäfer, and A. V. Tarasov, Phys. Rev. D 62, 054022 (2000).
  5. N. N. Nikolaev and B. G. Zakharov, Phys. Lett. B 332, 184 (1994).
  6. A. Kumar and T. Toll, Phys. Rev. D 105, 114045 (2022).
  7. A. Kumar, Phys. Rev. D 107, 034005 (2023).
  8. B. Z. Kopeliovich, I. K. Potashnikova, B. Povh, and I. Schmidt, Phys. Rev. D 85, 114025 (2012).
  9. F. Carvalho, V. P. Gonçalves, D. Spiering, and F. S. Navarra, Phys. Lett. B 752, 76 (2016).
  10. A. W. Thomas, W. Melnitchouk, and F. M. Steffens, Phys. Rev. Lett. 85, 2892 (2000).
  11. V. P. Goncalves, F. S. Navarra, and D. Spiering, Phys. Rev. D 93, 054025 (2016).
  12. F. Carvalho, V. P. Gonccalves, F. S. Navarra, and D. Spiering, Phys. Rev. D 103, 034021 (2021).
  13. J. T. Amaral and V. M. Becker, Phys. Rev. D 97, 094026 (2018).
  14. B. Z. Kopeliovich, I. K. Potashnikova, and I. Schmidt, Phys. Rev. C 81, 035204 (2010).
  15. A. H. Mueller, Nucl. Phys. B415, 373 (1994) B437, 107 (1995).
  16. K. Golec-Biernat and M. Wüsthoff, Phys. Rev. D 59, 014017 (1998).
  17. H. Kowalski and D. Teaney, Phys. Rev. D 68, 114005 (2003).
  18. H. Kowalski, L. Motyka, and G. Watt, Phys. Rev. D 74, 074016 (2006).
  19. F. Ferreiro, E. Inacu, K. Itakura, and McLerran, Nucl. Phys. A710, 373 (2002).
  20. A. Kovner and U. A. Wiedemann, Phys. Lett. B 551, 311 (2003).
  21. F. Carvalho, F. O. Duraes, F. S. Navarra, and V. P. Goncalves, Acta Phys. Pol. B 39, 2511 (2008).
  22. A. Morreale and F. Salazar, Universe 7, 312 (2021).
  23. E. Iancu and R. Venugopalan, Quark-Gluon Plasma 3 (2004), pp. 249–363, 10.1142/9789812795533_0005.
  24. J. Jalilian-Marian and Y. V. Kovchrgov, Prog. Part. Nucl. Phys. 56, 104 (2006).
  25. J. T. Amaral, D. A. Fagundes, and M. V. T. Machado, Phys. Rev. D 103, 016013 (2021).
  26. A. M. Stasto, K. J. Golec-Biernat, and J. Kwiecinski, Phys. Rev. Lett. 86, 596 (2001).
  27. Yu. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977).
  28. G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977).
  29. V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972).
  30. H. Mäntysaari and P. Zurita, Phys. Rev. D 98, 036002 (2018).
  31. S. Uehara et al., Phys. Rev. D 86, 092007 (2012); M. Masuda et al., 93, 032003 (2016).
  32. N. Nikolaev, J. Speth, and V. Zoller, Phys. Lett. B 473, 157 (2000).
  33. M. Block, L. Durand, and D. W. McKay, Phys. Rev. D 79, 014031 (2009).
  34. M. Block, L. Durand, P. Ha, and D. W. McKay, Phys. Rev. D 83, 054009 (2011).
  35. M. M. Block, L. Durand, P. Ha, and D. W. McKay, Phys. Rev. D 84, 094010 (2011).
  36. M. M. Block, L. Durand, P. Ha, and D. W. McKay, Phys. Rev. D 88, 014006 (2013).
  37. G. R. Boroun and P. Ha, Phys. Rev. D 109, 094037 (2024).
  38. P. C. Barry, C.-R. Ji, N. Sato, and W. Melnitchouk, Phys. Rev. Lett. 127, 232001 (2021).
  39. N. Y. Cao, P. C. Barry, N. Sato, and W. Melnitchouk, Phys. Rev. D 103, 114014 (2021).
  40. K. Golec-Biernat and S. Sapeta, J. High Energy Phys. 03 (2018) 102.

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Phys. Rev. D 112, 014027– Published 15 July, 2025
  • Received 18 April 2025
  • Accepted 27 June 2025
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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.

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