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Energy dependence of exclusive heavy vector meson photoproduction cross sections and NLO BFKL evolution

Martin Hentschinski and Ricardo Rangel Ramírez

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Phys. Rev. D 113, 014043 – Published 30 January, 2026

DOI: https://doi.org/10.1103/ryqz-qc49

Abstract

We study the energy dependence of the cross section for exclusive photoproduction of vector mesons J/ψ and ϒ, using a solution to the next-to-leading order (NLO) Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Our goal is to use BFKL evolution as a benchmark to provide evidence for the presence of nonlinear QCD dynamics and signs for the onset of gluon saturation at the highest center-of-mass energies. Our approach determines initial conditions for the proton from the Bartels-Golec Biernat-Kowalski (BGK) dipole model and evolves the resulting unintegrated gluon distribution using NLO BFKL evolution. For the nucleus, initial conditions are generated through both the impact parameter dependent saturation model (IP-Sat), using a Wood-Saxon distribution, and a A1/3 scaling of the saturation scale of the original BGK model. We find that NLO BFKL evolution provides a very good description of the nuclear modification factor for J/ψ production if initial conditions are generated through an A1/3 scaled BGK model, while the description fails if initial conditions are created using the IP-Sat model.

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References (87)

  1. L. V. Gribov, E. M. Levin, and M. G. Ryskin, Phys. Rep. 100, 1 (1983).
  2. A. Morreale and F. Salazar, Universe 7, 312 (2021).
  3. M. Hentschinski, C. Royon, M. A. Peredo, C. Baldenegro, A. Bellora, R. Boussarie, F. G. Celiberto, S. Cerci, G. Chachamis, J. G. Contreras et al., Acta Phys. Pol. B 54, 3-A2 (2023).
  4. A. C. Aguilar, A. Bashir, J. J. Cobos-Martínez, A. Courtoy, B. El-Bennich, D. de Florian, T. Frederico, V. P. Gonçalves, M. Hentschinski, and R. J. Hernández-Pinto et al., Braz. J. Phys. 55, 145 (2025).
  5. E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 45, 199 (1977).
  6. E. A. Kuraev, L. N. Lipatov, and V. S. Fadin, Sov. Phys. JETP 44, 443 (1976).
  7. I. I. Balitsky and L. N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978).
  8. E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, Nucl. Phys. A703, 489 (2002).
  9. E. Iancu, A. Leonidov, and L. D. McLerran, Phys. Lett. B 510, 133 (2001).
  10. E. Iancu, A. Leonidov, and L. D. McLerran, Nucl. Phys. A692, 583 (2001).
  11. H. Weigert, Nucl. Phys. A703, 823 (2002).
  12. Y. V. Kovchegov, Phys. Rev. D 60, 034008 (1999).
  13. J. Jalilian-Marian, A. Kovner, and H. Weigert, Phys. Rev. D 59, 014015 (1998).
  14. I. Balitsky, Nucl. Phys. B463, 99 (1996).
  15. I. Bautista, A. Fernandez Tellez, and M. Hentschinski, Phys. Rev. D 94, 054002 (2016).
  16. J. Cepila, J. G. Contreras, and M. Matas, Phys. Rev. D 99, 051502 (2019).
  17. A. Arroyo Garcia, M. Hentschinski, and K. Kutak, Phys. Lett. B 795, 569 (2019).
  18. M. Krelina, V. P. Goncalves, and J. Cepila, Nucl. Phys. A989, 187 (2019).
  19. S. R. Klein and H. Mäntysaari, Nat. Rev. Phys. 1, 662 (2019).
  20. B. Z. Kopeliovich, M. Krelina, J. Nemchik, and I. K. Potashnikova, Phys. Rev. D 107, 054005 (2023).
  21. D. Bendova, J. Cepila, J. G. Contreras, and M. Matas, Phys. Lett. B 817, 136306 (2021).
  22. M. Hentschinski and E. Padrón Molina, Phys. Rev. D 103, 074008 (2021).
  23. L. Jenkovszky, V. Libov, and M. V. T. Machado, Phys. Lett. B 824, 136836 (2022).
  24. C. A. Flett, Exclusive observables to NLO and Low x PDF phenomenology at the LHC, Ph.D. thesis, University of Liverpool, https://livrepository.liverpool.ac.uk/3123138/.
  25. H. Mäntysaari and J. Penttala, Phys. Lett. B 823, 136723 (2021).
  26. H. Mäntysaari and J. Penttala, J. High Energy Phys. 08 (2022) 247.
  27. V. P. Goncalves, B. D. Moreira, and L. Santana, Phys. Rev. C 107, 055205 (2023).
  28. X. Y. Wang, F. Zeng, and Q. Wang, Phys. Rev. D 105, 096033 (2022).
  29. H. Mäntysaari, F. Salazar, and B. Schenke, Phys. Rev. D 109, L071504 (2024).
  30. J. Cepila, J. G. Contreras, M. Matas, and A. Ridzikova, Phys. Lett. B 852, 138613 (2024).
  31. H. Mäntysaari, J. Penttala, F. Salazar, and B. Schenke, Phys. Rev. D 111, 5 (2025).
  32. J. Cepila, J. G. Contreras, M. Matas, and M. Vaculciak, Phys. Rev. D 111, 096015 (2025).
  33. J. Penttala and C. Royon, Phys. Lett. B 864, 139394 (2025).
  34. J. Nemchik and J. Óbertová, Phys. Rev. D 112, 094005 (2025).
  35. V. P. Goncalves, B. D. Moreira, and L. Santana, Eur. Phys. J. C 84, 893 (2024).
  36. J. Cepila, J. G. Contreras, and M. Vaculciak, Phys. Rev. D 111, 056002 (2025).
  37. S. Klein, D. Tapia Takaki, J. Adam, C. Aidala, A. Angerami, B. Audurier, C. Bertulani, C. Bierlich, B. Blok, J. D. Brandenburg et al., arXiv:2009.03838.
  38. A. Bylinkin, J. Nystrand, and D. Tapia Takaki, J. Phys. G 50, 055105 (2023).
  39. ALICE Collaboration, Report No. ALICE-PUBLIC-2023-001, European Organization for Nuclear Research CERN, https://cds.cern.ch/record/2858858/files/pubnote.pdf?version=1.
  40. P. E. A. da Costa, A. V. Giannini, V. P. Goncalves, and B. D. Moreira, Phys. Rev. D 112, 034012 (2025).
  41. S. Amoroso, A. Apyan, N. Armesto, R. D. Ball, V. Bertone, C. Bissolotti, J. Bluemlein, R. Boughezal, G. Bozzi, D. Britzger et al., Acta Phys. Pol. B 53, 12-A1 (2022).
  42. L. Frankfurt, V. Guzey, A. Stasto, and M. Strikman, Rep. Prog. Phys. 85, 126301 (2022).
  43. F. Arleo, P. Caucal, A. Deshpande, J. M. Durham, G. M. Innocenti, J. Jalilian-Marian, A. Kusina, M. X. Liu, Y. Mehtar-Tani, C. J. Naïm et al., arXiv:2506.17454.
  44. S. Acharya et al. (ALICE Collaboration), J. High Energy Phys. 10 (2023) 119.
  45. A. Tumasyan et al. (CMS Collaboration), Phys. Rev. Lett. 131, 262301 (2023).
  46. M. Hentschinski, A. Sabio Vera, and C. Salas, Phys. Rev. Lett. 110, 041601 (2013).
  47. M. Hentschinski, A. Sabio Vera, and C. Salas, Phys. Rev. D 87, 076005 (2013).
  48. K. Golec-Biernat and S. Sapeta, J. High Energy Phys. 03 (2018) 102.
  49. J. Bartels, K. J. Golec-Biernat, and H. Kowalski, Phys. Rev. D 66, 014001 (2002).
  50. H. Kowalski and D. Teaney, Phys. Rev. D 68, 114005 (2003).
  51. G. Chachamis, M. Deák, M. Hentschinski, G. Rodrigo, and A. Sabio Vera, J. High Energy Phys. 09 (2015) 123.
  52. F. G. Celiberto, D. Gordo Gómez, and A. Sabio Vera, Phys. Lett. B 786, 201 (2018).
  53. J. Cepila, J. Nemchik, M. Krelina, and R. Pasechnik, Eur. Phys. J. C 79, 495 (2019).
  54. M. A. Peredo and M. Hentschinski, Phys. Rev. D 109, 014032 (2024).
  55. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 817, 136280 (2021).
  56. S. J. Brodsky, T. Huang, and G. P. Lepage, Report No. SLAC-PUB-2540, National Accelerator Laboratory SLAC, https://www.slac.stanford.edu/pubs/slacpubs/2500/slac-pub-2540.pdf.
  57. B. E. Cox, J. R. Forshaw, and R. Sandapen, J. High Energy Phys. 06 (2009) 034.
  58. J. Nemchik, N. N. Nikolaev, and B. G. Zakharov, Phys. Lett. B 341, 228 (1994).
  59. H. Kowalski, L. Motyka, and G. Watt, Phys. Rev. D 74, 074016 (2006).
  60. N. Armesto and A. H. Rezaeian, Phys. Rev. D 90, 054003 (2014).
  61. V. P. Gonçalves, B. D. Moreira, and F. S. Navarra, Phys. Lett. B 742, 172 (2015).
  62. L. Frankfurt, A. Radyushkin, and M. Strikman, Phys. Rev. D 55, 98 (1997).
  63. H. Mäntysaari and P. Zurita, Phys. Rev. D 98, 036002 (2018).
  64. H. De Vries, C. W. De Jager, and C. De Vries, At. Data Nucl. Data Tables 36, 495 (1987).
  65. J. Cepila and M. Matas, Eur. Phys. J. A 56, 232 (2020).
  66. F. Deganutti, C. Royon, and S. Schlichting, J. High Energy Phys. 01 (2024) 159.
  67. V. Guzey, E. Kryshen, M. Strikman, and M. Zhalov, Phys. Lett. B 726, 290 (2013).
  68. S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 24, 345 (2002).
  69. S. Chekanov et al. (ZEUS Collaboration), Nucl. Phys. B695, 3 (2004).
  70. A. Aktas et al. (H1 Collaboration), Eur. Phys. J. C 46, 585 (2006).
  71. C. Alexa et al. (H1 Collaboration), Eur. Phys. J. C 73, 2466 (2013).
  72. A. Aktas et al. (H1 Collaboration), Eur. Phys. J. C 46, 585 (2006).
  73. S. Acharya et al. (ALICE Collaboration), Eur. Phys. J. C 79, 402 (2019).
  74. S. Acharya et al. (ALICE Collaboration), Phys. Rev. D 108, 112004 (2023).
  75. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 10 (2018) 167.
  76. R. Aaij et al. (LHCb Collaboration), SciPost Phys. 18, 071 (2025).
  77. C. Adloff et al. (H1 Collaboration), Phys. Lett. B 483, 23 (2000).
  78. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 680, 4 (2009).
  79. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 09 (2015) 084.
  80. A. M. Sirunyan et al. (CMS Collaboration), Eur. Phys. J. C 79, 277 (2019); 82, 343(E) (2022).
  81. A. Łuszczak, M. Łuszczak, and W. Schäfer, Phys. Lett. B 835, 137582 (2022).
  82. A. Sabio Vera, Nucl. Phys. B746, 1 (2006).
  83. A. Sabio Vera and F. Schwennsen, Nucl. Phys. B776, 170 (2007).
  84. S. J. Brodsky, G. P. Lepage, and P. B. Mackenzie, Phys. Rev. D 28, 228 (1983).
  85. S. J. Brodsky, V. S. Fadin, V. T. Kim, L. N. Lipatov, and G. B. Pivovarov, JETP Lett. 76, 249 (2002).
  86. F. G. Celiberto and M. Fucilla, Eur. Phys. J. C 82, 929 (2022).
  87. G. Chachamis and A. Sabio Vera, J. High Energy Phys. 07 (2022) 109.

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Phys. Rev. D 113, 014043– Published 30 January, 2026
  • Received 20 August 2025
  • Accepted 17 December 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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