- Physical Review Journals
All JournalsPhysics Magazine

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

Exclusive photoproduction of χcγ pairs in the small-x kinematics

M. Siddikov1,2, I. Zemlyakov1,3, and M. Roa1,4

PDF

Phys. Rev. D 113, 034024 – Published 20 February, 2026

DOI: https://doi.org/10.1103/y73d-hzdd

Abstract

In this manuscript we extend our previous analysis of the exclusive photoproduction of the χcγ pairs to the high-energy (small-x) kinematics, evaluate in detail the cross section in the color glass condensate framework, and discuss the potential of this channel as a novel complementary probe of the hadronic interactions. In the leading order in strong coupling αs, the cross section is controlled by the dipole scattering amplitude. Using available phenomenological parametrizations of the latter, we estimated numerically the cross sections for different polarizations of χc mesons and final-state photons in the kinematics of the ultraperipheral collisions at LHC and the future Electron Ion Collider. We found that the expected number of produced and detected events is significant for experimental study. We suggest that the ratio of the cross sections with different spins σγχc1/σγχc2 can be used to test the validity of the heavy quark spin symmetry relations for χc, and in this way resolve a long-standing ambiguity observed in hadroproduction of χc mesons. Finally, we also analyzed the role of this process as a potential background to exclusive χc photoproduction, which has been recently suggested as an alternative channel for studies of odderons.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (104)

  1. L. D. McLerran and R. Venugopalan, Computing quark and gluon distribution functions for very large nuclei, Phys. Rev. D 49, 2233 (1994).
  2. L. D. McLerran and R. Venugopalan, Gluon distribution functions for very large nuclei at small transverse momentum, Phys. Rev. D 49, 3352 (1994).
  3. L. D. McLerran and R. Venugopalan, Green’s function in the color field of a large nucleus, Phys. Rev. D 50, 2225 (1994).
  4. F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, The color glass condensate, Annu. Rev. Nucl. Part. Sci. 60, 463 (2010).
  5. E. Iancu and A. H. Mueller, From color glass to color dipoles in high-energy onium onium scattering, Nucl. Phys. A730, 460 (2004).
  6. C. A. Aidala et al., Probing nucleons and nuclei in high energy collisions, arXiv:2002.12333.
  7. Y. Q. Ma and R. Venugopalan, Comprehensive description of J/ψ production in proton-proton collisions at collider energies, Phys. Rev. Lett. 113, 192301 (2014).
  8. V. Cheung, Z. B. Kang, F. Salazar, and R. Vogt, Direct quarkonium production in DIS from a joint CGC and NRQCD framework, Phys. Rev. D 110, 094039 (2024).
  9. H. Mäntysaari, K. Roy, F. Salazar, and B. Schenke, Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider, Phys. Rev. D 103, 094026 (2021).
  10. Z. B. Kang, E. Li, and F. Salazar, Direct quarkonium-plus-gluon production in DIS in the color glass condensate, J. High Energy Phys. 03 (2024) 027.
  11. K. Tuchin, Heavy quark production by a quasiclassical color field in proton nucleus collisions, Phys. Lett. B 593, 66 (2004).
  12. J. P. Blaizot, F. Gelis, and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. 2. Quark production, Nucl. Phys. A743, 57 (2004).
  13. B. Abelev et al. (ALICE Collaboration), Transverse momentum distribution and nuclear modification factor of charged particles in p-Pb collisions at sNN=5.02  TeV, Phys. Rev. Lett. 110, 082302 (2013).
  14. G. Aad et al. (ATLAS Collaboration), Transverse momentum, rapidity, and centrality dependence of inclusive charged-particle production in sNN=5.02  TeV p+Pb collisions measured by the ATLAS experiment, Phys. Lett. B 763, 313 (2016).
  15. A. H. Rezaeian, M. Siddikov, M. Van de Klundert, and R. Venugopalan, Analysis of combined HERA data in the impact-parameter dependent saturation model, Phys. Rev. D 87, 034002 (2013).
  16. A. H. Rezaeian and I. Schmidt, Impact-parameter dependent color glass condensate dipole model and new combined HERA data, Phys. Rev. D 88, 074016 (2013).
  17. G. Watt and H. Kowalski, Impact parameter dependent color glass condensate dipole model, Phys. Rev. D 78, 014016 (2008).
  18. G. G. Da Silveira and (ATLAS, LHCb and CMS Collaborations), QCD probes at LHC, arXiv:1805.00772.
  19. J. L. Albacete, Testing the CGC in proton-lead collisions at the LHC, Nucl. Phys. A910-911, 155 (2013).
  20. R. Aaij et al. (LHCb Colllaboration), Study of exclusive photoproduction of charmonium in ultra-peripheral lead-lead collisions, J. High Energy Phys. 06 (2023) 146.
  21. H. Mäntysaari, F. Salazar, and B. Schenke, Energy dependent nuclear suppression from gluon saturation in exclusive vector meson production, Phys. Rev. D 109, L071504 (2024).
  22. Y. V. Kovchegov, Small x F2. structure function of a nucleus including multiple pomeron exchanges, Phys. Rev. D 60, 034008 (1999).
  23. Y. V. Kovchegov and H. Weigert, Triumvirate of running couplings in small-x evolution, Nucl. Phys. A784, 188 (2007).
  24. I. Balitsky and G. A. Chirilli, Next-to-leading order evolution of color dipoles, Phys. Rev. D 77, 014019 (2008).
  25. I. Balitsky, Operator expansion for high-energy scattering, Nucl. Phys. B463, 99 (1996).
  26. I. Balitsky, Effective field theory for the small x evolution, Phys. Lett. B 518, 235 (2001).
  27. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, The BFKL equation from the Wilson renormalization group, Nucl. Phys. B504, 415 (1997).
  28. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, Wilson renormalization group for low x physics: Towards the high density regime, Phys. Rev. D 59, 014014 (1998).
  29. E. Iancu, A. Leonidov, and L. D. McLerran, The renormalization group equation for the color glass condensate, Phys. Lett. B 510, 133 (2001).
  30. E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, Nonlinear gluon evolution in the color glass condensate: II, Nucl. Phys. A703, 489 (2002).
  31. E. Iancu, A. Leonidov, and L. D. McLerran, Nonlinear gluon evolution in the color glass condensate: I, Nucl. Phys. A692, 583 (2001).
  32. E. Iancu and D. N. Triantafyllopoulos, Higher-point correlations from the JIMWLK evolution, J. High Energy Phys. 11 (2011) 105.
  33. G. Beuf, T. Lappi, and R. Paatelainen, Massive quarks in NLO dipole factorization for DIS: Transverse photon, Phys. Rev. D 106, 034013 (2022).
  34. G. Beuf, T. Lappi, and R. Paatelainen, Massive quarks in NLO dipole factorization for DIS: Longitudinal photon, Phys. Rev. D 104, 056032 (2021).
  35. B. Ducloué, H. Hänninen, T. Lappi, and Y. Zhu, Deep inelastic scattering in the dipole picture at next-to-leading order, Phys. Rev. D 96, 094017 (2017).
  36. H. Mäntysaari and J. Penttala, Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture, J. High Energy Phys. 08 (2022) 247.
  37. H. Mäntysaari and J. Penttala, Exclusive production of light vector mesons at next-to-leading order in the dipole picture, Phys. Rev. D 105, 114038 (2022).
  38. E. Iancu and Y. Mulian, Dihadron production in DIS at NLO: The real corrections, J. High Energy Phys. 07 (2023) 121.
  39. K. Roy and R. Venugopalan, Extracting many-body correlators of saturated gluons with precision from inclusive photon+dijet final states in deeply inelastic scattering, Phys. Rev. D 101, 071505 (2020).
  40. K. Roy and R. Venugopalan, NLO impact factor for inclusive photon+dijet production in e+A DIS at small x, Phys. Rev. D 101, 034028 (2020).
  41. J. W. Qiu and Z. Yu, Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering, Phys. Rev. D 109, 074023 (2024).
  42. J. W. Qiu and Z. Yu, Extraction of the parton momentum-fraction dependence of generalized parton distributions from exclusive photoproduction, Phys. Rev. Lett. 131, 161902 (2023).
  43. K. Deja, V. Martinez-Fernandez, B. Pire, P. Sznajder, and J. Wagner, Phenomenology of double deeply virtual Compton scattering in the era of new experiments, Phys. Rev. D 107, 094035 (2023).
  44. M. Siddikov and I. Schmidt, Exclusive production of quarkonia pairs in collinear factorization framework, Phys. Rev. D 107, 034037 (2023).
  45. M. Siddikov and I. Schmidt, Exclusive photoproduction of D-meson pairs with large invariant mass, Phys. Rev. D 108, 096031 (2023).
  46. J.-W. Qiu and Z. Yu, Exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions for extracting generalized parton distributions, J. High Energy Phys. 08 (2022) 103.
  47. J.-W. Qiu and Z. Yu, Single diffractive hard exclusive processes for the study of generalized parton distributions, Phys. Rev. D 107, 014007 (2023).
  48. M. Mangano, CERN Yellow Reports: Monographs, arXiv:1710.06353.
  49. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC Yellow Report, Nucl. Phys. A1026, 122447 (2022).
  50. V. Burkert, L. Elouadrhiri, A. Afanasev, J. Arrington, M. Contalbrigo, W. Cosyn, A. Deshpande, D. Glazier, X. Ji and S. Liuti et al., Precision studies of QCD in the low energy domain of the EIC, Prog. Part. Nucl. Phys. 131, 104032 (2023).
  51. G. T. Bodwin, E. Braaten, and G. P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51, 1125 (1995); 55, 5853(E) (1997).
  52. F. Maltoni, M. L. Mangano, and A. Petrelli, Quarkonium photoproduction at next-to-leading order, Nucl. Phys. B519, 361 (1998).
  53. Y. Feng, J. P. Lansberg, and J. X. Wang, Energy dependence of direct-quarkonium production in pp collisions from fixed-target to LHC energies: Complete one-loop analysis, Eur. Phys. J. C 75, 313 (2015).
  54. N. Brambilla, S. Eidelman, B. Heltsley, R. Vogt, G. Bodwin et al., Heavy quarkonium: Progress, puzzles, and opportunities, Eur. Phys. J. C 71, 1534 (2011).
  55. M. Siddikov, I. Zemlyakov, M. Roa, and S. Valdebenito, Photoproduction of pairs in the CGC framework, Phys. Rev. D 111, 056024 (2025).
  56. Y. Q. Ma, K. Wang, and K. T. Chao, QCD radiative corrections to χcJ production at hadron colliders, Phys. Rev. D 83, 111503 (2011).
  57. A. K. Likhoded, A. V. Luchinsky, and S. V. Poslavsky, Production of χc- and χb-mesons in high energy hadronic collisions, Phys. Rev. D 90, 074021 (2014).
  58. H. F. Zhang, L. Yu, S. X. Zhang, and L. Jia, Global analysis of the experimental data on χc meson hadroproduction, Phys. Rev. D 93, 054033 (2016).
  59. S. P. Baranov and A. V. Lipatov, Are there any challenges in the charmonia production and polarization at the LHC?, Phys. Rev. D 100, 114021 (2019).
  60. S. P. Baranov, A. V. Lipatov, A. A. Prokhorov, and X. Chen, Towards higher-order calculations of quarkonia production with kT-factorization: P-wave charmonia, Eur. Phys. J. C 84, 348 (2024).
  61. A. Schäfer, L. Mankiewicz, and O. Nachtmann, Diffractive eta(c), eta-prime, J/psi and psi-prime production in electronproton collisions at HERA energies, in Proceedings of Physics at HERA, edited by W. Buchmüllerand G. Ingelman (DESY, Hamburg, Germany, 1992).
  62. J. Bartels, High-energy behaviour in a non-abelian gauge theory (II). First corrections to Tn→m beyond the leading In s approximation, Nucl. Phys. B175, 365 (1980); T. Jaroszewicz, Infra-Red divergences and Regge behaviour in QCD, Acta Phys. Pol. B 11, 965 (1980), https://www.actaphys.uj.edu.pl/R/11/12/965; J. Kwiecinski and M. Praszalowicz, Three gluon integral equation and odd C singlet Regge singularities in QCD, Phys. Lett. 94B, 413 (1980).
  63. J. Bartels, M. A. Braun, D. Colferai, and G. P. Vacca, Diffractive eta(c) photoproduction and electroproduction with the perturbative QCD odderon, Eur. Phys. J. C 20, 323 (2001).
  64. J. Czyzewski, J. Kwiecinski, L. Motyka, and M. Sadzikowski, Exclusive ηc photo- and electroproduction at HERA as a possible probe of the odderon singularity in QCD, Phys. Lett. B 398, 400 (1997); Phys. Lett. B411, 402 (1997).
  65. R. Engel, D. Y. Ivanov, R. Kirschner, and L. Szymanowski, Diffractive meson production from virtual photons with odd charge-parity exchange, Eur. Phys. J. C 4, 93 (1998).
  66. A. Dumitru and T. Stebel, Multiquark matrix elements in the proton and three gluon exchange for exclusive ηc production in photon-proton diffractive scattering, Phys. Rev. D 99, 094038 (2019).
  67. S. Benic, D. Horvatic, A. Kaushik, and E. A. Vivoda, Exclusive ηc production from small-x evolved Odderon at a electron-ion collider, Phys. Rev. D 108, 074005 (2023).
  68. Y. Jia, Z. Mo, J. Pan, and J. Y. Zhang, Photoproduction of C-even quarkonia at the EIC and EicC, Phys. Rev. D 108, 016015 (2023).
  69. S. Benić, A. Dumitru, A. Kaushik, L. Motyka, and T. Stebel, Photon-odderon interference in exclusive Xc charmonium production at the Electron-Ion Collider, Phys. Rev. D 110, 014025 (2024).
  70. P. Agostini et al. (LHeC and FCC-he Study Group), The large hadron-electron collider at the HL-LHC, J. Phys. G 48, 110501 (2021).
  71. A. Abada et al. (FCC Collaboration), FCC physics opportunities, Eur. Phys. J. C 79, 474 (2019).
  72. M. Siddikov and I. Zemlyakov, Exclusive photoproduction of χcγ pairs, Phys. Rev. D 112, 014021 (2025).
  73. M. Diehl, Generalized parton distributions, Phys. Rep. 388, 41 (2003).
  74. M. Siddikov, Exclusive photoproduction of χcγ pairs with large invariant mass, Phys. Rev. D 110, 056043 (2024).
  75. S. J. Brodsky, H. C. Pauli, and S. S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rep. 301, 299 (1998).
  76. G. Duplančić, K. Passek-Passek-Kumerički, B. Pire, L. Szymanowski, and S. Wallon, Probing axial quark generalized parton distributions through exclusive photoproduction of a γπ± pair with a large invariant mass, J. High Energy Phys. 11 (2018) 179.
  77. G. Duplančić, S. Nabeebaccus, K. Passek-Kumerički, B. Pire, L. Szymanowski, and S. Wallon, Accessing chiral-even quark generalised parton distributions in the exclusive photoproduction of a γπ± pair with large invariant mass in both fixed-target and collider experiments, J. High Energy Phys. 03 (2023) 241.
  78. G. P. Lepage and S. J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22, 2157 (1980).
  79. S. Navas et al. (Particle Data Group), Review of Particle Physics, Phys. Rev. D 110, 030001 (2024).
  80. C. F. von Weizsacker, Radiation emitted in collisions of very fast electrons, Z. Phys. 88, 612 (1934).
  81. E. J. Williams, Correlation of certain collision problems with radiation theory, Kong. Dan. Vid. Sel. Mat. Fys. Med. 13N4, 1 (1935), https://inspirehep.net/literature/1377275.
  82. V. M. Budnev, I. F. Ginzburg, G. V. Meledin, and V. G. Serbo, The Two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation, Phys. Rep. 15, 181 (1975).
  83. J. P. Ma and Z. G. Si, NRQCD factorization for twist-2 light-cone wave-functions of Charmonia, Phys. Lett. B 647, 419 (2007).
  84. X. P. Wang and D. Yang, The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions, J. High Energy Phys. 06 (2014) 121.
  85. W. Wang, J. Xu, D. Yang, and S. Zhao, Relativistic corrections to light-cone distribution amplitudes of S-wave Bc mesons and heavy quarkonia, J. High Energy Phys. 12 (2017) 012.
  86. I. Babiarz, R. Pasechnik, W. Schaefer, and A. Szczurek, Hadroproduction of scalar P-wave quarkonia in the light-front kT-factorization approach, J. High Energy Phys. 06 (2020) 101.
  87. A. Ayala, M. Hentschinski, J. Jalilian-Marian, and M. E. Tejeda-Yeomans, Spinor helicity methods in high-energy factorization: Efficient momentum-space calculations in the Color Glass Condensate formalism, Nucl. Phys. B920, 232 (2017).
  88. P. Caucal, F. Salazar, and R. Venugopalan, Dijet impact factor in DIS at next-to-leading order in the color glass Condensate, J. High Energy Phys. 11 (2021) 222.
  89. P. Caucal, F. Salazar, B. Schenke, and R. Venugopalan, Back-to-back inclusive dijets in DIS at small x: Sudakov suppression and gluon saturation at NLO, J. High Energy Phys. 11 (2022) 169.
  90. J. B. Bronzan, G. L. Kane, and U. P. Sukhatme, Obtaining real parts of scattering amplitudes directly from cross section data using derivative analyticity relations, Phys. Lett. 49B, 272 (1974).
  91. E. Gotsman, E. M. Levin, and U. Maor, A quantitative investigation of the Pomeron, Z. Phys. C 57, 677 (1993).
  92. A. G. Shuvaev, K. J. Golec-Biernat, A. D. Martin, and M. G. Ryskin, Off-diagonal distributions fixed by diagonal partons at small x and ξ, Phys. Rev. D 60, 014015 (1999).
  93. T. Altinoluk, G. Beuf, A. Czajka, and A. Tymowska, DIS dijet production at next-to-eikonal accuracy in the CGC, Phys. Rev. D 107, 074016 (2023).
  94. Y. V. Kovchegov and M. Li, Weizscker-Williams gluon helicity distribution and inclusive dijet production in longitudinally polarized electron-proton collisions, J. High Energy Phys. 08 (2025) 206.
  95. J. D. Bjorken, J. B. Kogut, and D. E. Soper, Quantum electrodynamics at infinite momentum: Scattering from an external field, Phys. Rev. D 3, 1382 (1971).
  96. H. G. Dosch, T. Gousset, G. Kulzinger, and H. J. Pirner, Vector meson leptoproduction and nonperturbative gluon fluctuations in QCD, Phys. Rev. D 55, 2602 (1997).
  97. F. Gelis and R. Venugopalan, Large mass qq¯ production from the color glass condensate, Phys. Rev. D 69, 014019 (2004).
  98. H. Fujii, F. Gelis, and R. Venugopalan, Quark pair production in high energy pA collisions: General features, Nucl. Phys. A780, 146 (2006).
  99. R. Aaij et al. (LHCb Collaboration), Central exclusive production of J/ψ and ψ(2S) mesons in pp collisions at s=13  TeV, J. High Energy Phys. 10 (2018) 167.
  100. G. Antchev et al. (TOTEM Collaboration), Elastic differential cross section dσ/dt at s=2.76  TeV and implications on the existence of a colourless 3-gluon bound state, Eur. Phys. J. C 80, 91 (2020).
  101. V. M. Abazov et al. (D0 Collaboration), Measurement of the differential cross section dσ/dt in elastic pp¯ scattering at s=1.96  TeV, Phys. Rev. D 86, 012009 (2012).
  102. N. Armesto and A. H. Rezaeian, Exclusive vector meson production at high energies and gluon saturation, Phys. Rev. D 90, 054003 (2014).
  103. C. Adloff et al. (H1 Collaboration), Diffractive photoproduction of ψ(2S) mesons at HERA, Phys. Lett. B 541, 251 (2002).
  104. See Supplemental Material at http://link.aps.org/supplemental/10.1103/y73d-hzdd for tabulated data and the file README.txt in that section for more details.

Outline

Information

Phys. Rev. D 113, 034024– Published 20 February, 2026
  • Received 25 October 2025
  • Accepted 14 January 2026
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