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Resolved photoproduction of the Bc meson in electron-proton collisions

Na Cai* and Xi-Jie Zhan†

Tai-Fu Feng‡

  • *Contact author: yoloitw@outlook.com
  • †Contact author: zhanxj@hbu.edu.cn
  • ‡Contact author: fengtf@hbu.edu.cn
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Phys. Rev. D 114, 014060 – Published 27 July, 2026

DOI: https://doi.org/10.1103/ltbz-4cdg

Abstract

We present a systematic study of prompt Bc meson photoproduction at electron-proton colliders within the framework of nonrelativistic QCD factorization. In addition to the dominant direct channel γ+g→Bc+X, we include resolved contributions initiated by g+g and q+q¯ (q=u, d, s) subprocesses. The production of the 1S, 2S, and 1P color-singlet Bc states is calculated, and the feeddown contributions from the excited states are included in the prompt-Bc yield. Total cross sections and transverse-momentum distributions are presented for several collider configurations, including HERA, LHeC, FCC-ep, and EIC. The numerical results show that the direct γ+g channel provides the leading contribution over the entire kinematic range. The resolved g+g channel gives a non-negligible correction, reaching the level of O(10%) in the low-pT region where most events are produced, and it becomes increasingly important at higher collision energies.

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References (71)

  1. C.-H. Chang and Y.-Q. Chen, Phys. Rev. D 48, 4086 (1993).
  2. C.-H. Chang, Y.-Q. Chen, G.-P. Han, and H.-T. Jiang, Phys. Lett. B 364, 78 (1995).
  3. F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 81, 2432 (1998).
  4. F. Abe et al. (CDF Collaboration), Phys. Rev. D 58, 112004 (1998).
  5. G. Aad et al. (ATLAS Collaboration), Phys. Rev. Lett. 113, 212004 (2014).
  6. A. M. Sirunyan et al. (CMS Collaboration), Phys. Rev. Lett. 122, 132001 (2019).
  7. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 122, 232001 (2019).
  8. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 135, 231902 (2025).
  9. K. Kolodziej, A. Leike, and R. Ruckl, Phys. Lett. B 355, 337 (1995).
  10. E. Braaten, K.-m. Cheung, and T. C. Yuan, Phys. Rev. D 48, R5049 (1993).
  11. A. V. Berezhnoy, A. K. Likhoded, and M. V. Shevlyagin, Phys. At. Nucl. 58, 672 (1995), https://inspirehep.net/literature/376495.
  12. S. S. Gershtein, V. V. Kiselev, A. K. Likhoded, and A. V. Tkabladze, Phys. Usp. 38, 1 (1995).
  13. C.-H. Chang, Y.-Q. Chen, and R. J. Oakes, Phys. Rev. D 54, 4344 (1996).
  14. A. V. Berezhnoy, V. V. Kiselev, and A. K. Likhoded, Z. Phys. A 356, 79 (1996).
  15. S. P. Baranov, Phys. Rev. D 55, 2756 (1997).
  16. S. P. Baranov, Phys. Rev. D 56, 3046 (1997).
  17. K.-m. Cheung, Phys. Lett. B 472, 408 (2000).
  18. C.-H. Chang and X.-G. Wu, Eur. Phys. J. C 38, 267 (2004).
  19. C.-H. Chang, J.-X. Wang, and X.-G. Wu, Phys. Rev. D 70, 114019 (2004).
  20. C.-H. Chang, C.-F. Qiao, J.-X. Wang, and X.-G. Wu, Phys. Rev. D 71, 074012 (2005).
  21. C.-H. Chang, C.-F. Qiao, J.-X. Wang, and X.-G. Wu, Phys. Rev. D 72, 114009 (2005).
  22. C.-H. Chang, C. Driouichi, P. Eerola, and X. G. Wu, Comput. Phys. Commun. 159, 192 (2004).
  23. C.-H. Chang, J.-X. Wang, and X.-G. Wu, Comput. Phys. Commun. 174, 241 (2006).
  24. X.-Y. Wang and X.-G. Wu, Comput. Phys. Commun. 183, 442 (2012).
  25. H.-Y. Bi, R.-Y. Zhang, H.-Y. Han, Y. Jiang, and X.-G. Wu, Phys. Rev. D 95, 034019 (2017).
  26. G. Chen, C.-H. Chang, and X.-G. Wu, Phys. Rev. D 97, 114022 (2018).
  27. A. V. Berezhnoy, I. N. Belov, A. K. Likhoded, and A. V. Luhinsky, Mod. Phys. Lett. A 34, 1950331 (2019).
  28. Z. Yang, X.-G. Wu, G. Chen, Q.-L. Liao, and J.-W. Zhang, Phys. Rev. D 85, 094015 (2012).
  29. G. Chen, X.-G. Wu, Z. Sun, X.-C. Zheng, and J.-M. Shen, Phys. Rev. D 89, 014006 (2014).
  30. G. Chen, X.-G. Wu, Z. Sun, S.-Q. Wang, and J.-M. Shen, Phys. Rev. D 88, 074021 (2013).
  31. Z. Sun, X.-G. Wu, G. Chen, J. Jiang, and Z. Yang, Phys. Rev. D 87, 114008 (2013).
  32. G. Chen, X.-G. Wu, H.-B. Fu, H.-Y. Han, and Z. Sun, Phys. Rev. D 90, 034004 (2014).
  33. Z. Sun, X.-G. Wu, G. Chen, Y. Ma, H.-H. Ma, and H.-Y. Bi, Phys. Rev. D 89, 074035 (2014).
  34. Z. Sun, X.-G. Wu, and H.-F. Zhang, Phys. Rev. D 92, 074021 (2015).
  35. Y.-B. Wei, R.-H. Li, D. Luo, C.-D. Lü, and Y.-L. Shen, Chin. Phys. C 42, 083107 (2018).
  36. Z.-G. He and B. A. Kniehl, CERN Yellow Rep. 3, 89 (2020).
  37. Z. Yang, X.-G. Wu, and X.-Y. Wang, Comput. Phys. Commun. 184, 2848 (2013).
  38. Z. Yang, X.-C. Zheng, and X.-G. Wu, Comput. Phys. Commun. 281, 108503 (2022).
  39. X.-P. Wang, Y.-J. Li, G.-Z. Xu, and K.-Y. Liu, Chin. Phys. C 50, 043107 (2026).
  40. C.-H. Chang and Y.-Q. Chen, Phys. Rev. D 46, 3845 (1992); 50, 6013(E) (1994).
  41. C.-H. Chang, J.-X. Wang, and X.-G. Wu, Phys. Rev. D 77, 014022 (2008).
  42. L.-C. Deng, X.-G. Wu, Z. Yang, Z.-Y. Fang, and Q.-L. Liao, Eur. Phys. J. C 70, 113 (2010).
  43. Z. Yang, X.-G. Wu, L.-C. Deng, J.-W. Zhang, and G. Chen, Eur. Phys. J. C 71, 1563 (2011).
  44. J. Jiang, L.-B. Chen, and C.-F. Qiao, Phys. Rev. D 91, 034033 (2015).
  45. J. Jiang and C.-F. Qiao, Phys. Rev. D 93, 054031 (2016).
  46. X.-C. Zheng, C.-H. Chang, X.-G. Wu, J. Zeng, and X.-D. Huang, Phys. Rev. D 101, 034029 (2020).
  47. D. Yang and W. Zhang, Chin. Phys. C 43, 083101 (2019).
  48. Z.-Q. Chen, H. Yang, and C.-F. Qiao, Phys. Rev. D 102, 016011 (2020).
  49. X.-C. Zheng, X.-G. Wu, X.-J. Zhan, G.-Y. Wang, and H.-T. Li, Phys. Rev. D 107, 074005 (2023).
  50. H.-Y. Bi, R.-Y. Zhang, X.-G. Wu, W.-G. Ma, X.-Z. Li, and S. Owusu, Phys. Rev. D 95, 074020 (2017).
  51. K. He, H.-Y. Bi, R.-Y. Zhang, X.-Z. Li, and W.-G. Ma, J. Phys. G 45, 055005 (2018).
  52. Z. Sun and X.-G. Wu, J. High Energy Phys. 07 (2020) 034.
  53. H. Yang, Z.-Q. Chen, and C.-F. Qiao, Phys. Rev. D 105, 094014 (2022).
  54. X.-J. Zhan, X.-G. Wu, and X.-C. Zheng, Phys. Rev. D 106, 094036 (2022).
  55. S. Frixione, M. L. Mangano, P. Nason, and G. Ridolfi, Phys. Lett. B 319, 339 (1993).
  56. M. Gluck, E. Reya, and I. Schienbein, Phys. Rev. D 60, 054019 (1999); 62, 019902(E) (2000).
  57. J.-X. Wang, Nucl. Instrum. Methods Phys. Res., Sect. A 534, 241 (2004).
  58. G. T. Bodwin and A. Petrelli, Phys. Rev. D 66, 094011 (2002); 87, 039902(E) (2013).
  59. D. Binosi and L. Theussl, Comput. Phys. Commun. 161, 76 (2004).
  60. S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, and C. P. Yuan, Phys. Rev. D 93, 033006 (2016).
  61. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
  62. E. J. Eichten and C. Quigg, Phys. Rev. D 49, 5845 (1994).
  63. E. J. Eichten and C. Quigg, Phys. Rev. D 52, 1726 (1995).
  64. U. Karshon (H1, ZEUS Collaborations), Acta Phys. Pol. B Proc. Suppl. 7, 511 (2014).
  65. J. L. Abelleira Fernandez et al. (LHeC Study Group Collaboration), J. Phys. G 39, 075001 (2012).
  66. Y. C. Acar, A. N. Akay, S. Beser, A. C. Canbay, H. Karadeniz, U. Kaya, B. B. Oner, and S. Sultansoy, Nucl. Instrum. Methods Phys. Res., Sect. A 871, 47 (2017).
  67. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
  68. H. Abramowicz et al. (H1 and ZEUS Collaborations), Eur. Phys. J. C 75, 580 (2015).
  69. P. Agostini et al., J. Phys. G 48, 110501 (2021).
  70. O. Brüning, J. Jowett, M. Klein, D. Pellegrini, D. Schulte, and F. Zimmermann, Technical Report CERN-ACC-2017-0019, CERN, 2017.
  71. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).

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Phys. Rev. D 114, 014060– Published 27 July, 2026
  • Received 15 April 2026
  • Accepted 10 July 2026
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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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