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Vector meson dominance in photon structure functions at small x from holography

Wei Gao1,*, Siming Liu1,†, Wenbin Lin1,2,‡, and Akira Watanabe3,§

  • *Contact author: weigao@my.swjtu.edu.cn
  • †Contact author: liusm@swjtu.edu.cn
  • ‡Contact author: lwb@usc.edu.cn
  • §Contact author: watanabe.akira@oshima-k.ac.jp
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Phys. Rev. D 112, 094030 – Published 18 November, 2025

DOI: https://doi.org/10.1103/q9ph-y6cg

Abstract

We investigate the photon structure functions via the photon-photon and photon-vector meson scattering within the framework of holographic QCD, focusing on the small Bjorken x region and assuming that the Pomeron exchange dominates. The quasireal photon structure functions are formulated as the convolution of the known U(1) vector field wave function with the Brower-Polchinski-Strassler-Tan (BPST) Pomeron exchange kernel in the five-dimensional AdS space. Assuming the vector meson dominance, the photon structure functions can be calculated in a different way with the BPST kernel and vector meson gravitational form factor, which can be obtained in a bottom-up AdS/QCD model, for the Pomeron-vector meson coupling. It is shown that the obtained F2 structure functions in the both ways agree with the experimental data, which implies the realization of the vector meson dominance within the present model setup. Calculations for the longitudinal structure function and the longitudinal-to-transverse ratio are also presented.

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References (60)

  1. T. F. Walsh, Phys. Lett. 36B, 121 (1971).
  2. S. J. Brodsky, T. Kinoshita, and H. Terazawa, Phys. Rev. Lett. 27, 280 (1971).
  3. G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 18, 15 (2000).
  4. G. Abbiendi et al. (OPAL Collaboration), Phys. Lett. B 533, 207 (2002).
  5. E. Witten, Nucl. Phys. 120B, 189 (1977).
  6. C. H. Llewellyn Smith, Phys. Lett. 79B, 83 (1978).
  7. W. A. Bardeen and A. J. Buras, Phys. Rev. D 20, 166 (1979); 21, 2041(E) (1980).
  8. D. W. Duke and J. F. Owens, Phys. Rev. D 22, 2280 (1980).
  9. I. Antoniadis and G. Grunberg, Nucl. Phys. B213, 445 (1983).
  10. M. Gluck and E. Reya, Phys. Rev. D 28, 2749 (1983).
  11. M. Fontannaz and E. Pilon, Phys. Rev. D 45, 382 (1992).
  12. M. Gluck, E. Reya, and A. Vogt, Phys. Rev. D 45, 3986 (1992).
  13. S. Moch, J. A. M. Vermaseren, and A. Vogt, Nucl. Phys. B621, 413 (2002).
  14. J. J. Sakurai, Ann. Phys. (N.Y.) 11, 1 (1960).
  15. A. Taliotis, Nucl. Phys. A830, 299C (2009).
  16. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998).
  17. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
  18. M. Kruczenski, D. Mateos, R. C. Myers, and D. J. Winters, J. High Energy Phys. 07 (2003) 049.
  19. M. Kruczenski, D. Mateos, R. C. Myers, and D. J. Winters, J. High Energy Phys. 05 (2004) 041.
  20. D. T. Son and M. A. Stephanov, Phys. Rev. D 69, 065020 (2004).
  21. T. Sakai and S. Sugimoto, Prog. Theor. Phys. 113, 843 (2005).
  22. T. Sakai and S. Sugimoto, Prog. Theor. Phys. 114, 1083 (2005).
  23. J. Erlich, E. Katz, D. T. Son, and M. A. Stephanov, Phys. Rev. Lett. 95, 261602 (2005).
  24. L. Da Rold and A. Pomarol, Nucl. Phys. B721, 79 (2005).
  25. J. Erdmenger, N. Evans, I. Kirsch, and E. Threlfall, Eur. Phys. J. A 35, 81 (2008).
  26. A. Karch, E. Katz, D. T. Son, and M. A. Stephanov, Phys. Rev. D 74, 015005 (2006).
  27. T. Gherghetta, J. I. Kapusta, and T. M. Kelley, Phys. Rev. D 79, 076003 (2009).
  28. S. J. Brodsky and G. F. de Teramond, Phys. Rev. Lett. 96, 201601 (2006).
  29. H. R. Grigoryan and A. V. Radyushkin, Phys. Rev. D 76, 095007 (2007).
  30. Z. Abidin and C. E. Carlson, Phys. Rev. D 79, 115003 (2009).
  31. J. Polchinski and M. J. Strassler, Phys. Rev. Lett. 88, 031601 (2002).
  32. R. C. Brower, J. Polchinski, M. J. Strassler, and C.-I. Tan, J. High Energy Phys. 12 (2007) 005.
  33. A. Donnachie and P. V. Landshoff, Phys. Lett. B 296, 227 (1992).
  34. J. Polchinski and M. J. Strassler, J. High Energy Phys. 05 (2003) 012.
  35. H. Boschi-Filho, N. R. F. Braga, and H. L. Carrion, Phys. Rev. D 73, 047901 (2006).
  36. Y. Hatta, E. Iancu, and A. H. Mueller, J. High Energy Phys. 01 (2008) 026.
  37. C. A. Ballon Bayona, H. Boschi-Filho, and N. R. F. Braga, J. High Energy Phys. 10 (2008) 088.
  38. B. Pire, C. Roiesnel, L. Szymanowski, and S. Wallon, Phys. Lett. B 670, 84 (2008).
  39. A. Stoffers and I. Zahed, Phys. Rev. D 87, 075023 (2013).
  40. L. Cornalba, M. S. Costa, and J. Penedones, J. High Energy Phys. 09 (2007) 037.
  41. L. Cornalba and M. S. Costa, Phys. Rev. D 78, 096010 (2008).
  42. R. C. Brower, M. J. Strassler, and C.-I. Tan, J. High Energy Phys. 03 (2009) 050.
  43. R. C. Brower, M. J. Strassler, and C.-I. Tan, J. High Energy Phys. 03 (2009) 092.
  44. L. Cornalba, M. S. Costa, and J. Penedones, J. High Energy Phys. 03 (2010) 133.
  45. L. Cornalba, M. S. Costa, and J. Penedones, Phys. Rev. Lett. 105, 072003 (2010).
  46. R. C. Brower, M. Djuric, I. Sarcevic, and C.-I. Tan, J. High Energy Phys. 11 (2010) 051.
  47. A. Watanabe and K. Suzuki, Phys. Rev. D 86, 035011 (2012).
  48. L. Agozzino, P. Castorina, and P. Colangelo, Phys. Rev. Lett. 112, 041601 (2014).
  49. A. Watanabe and K. Suzuki, Phys. Rev. D 89, 115015 (2014).
  50. A. Watanabe and H. Li, Phys. Lett. B 751, 321 (2015).
  51. A. Watanabe and M. Huang, Phys. Lett. B 788, 256 (2019).
  52. A. Watanabe, T. Sawada, and M. Huang, Phys. Lett. B 805, 135470 (2020).
  53. M. Gluck, E. Reya, and I. Schienbein, Phys. Rev. D 60, 054019 (1999); 62, 019902(E) (2000).
  54. F. D. Aaron et al. (H1 Collaboration), Eur. Phys. J. C 71, 1579 (2011).
  55. Z. Abidin and C. E. Carlson, Phys. Rev. D 77, 095007 (2008).
  56. F. James and M. Roos, Comput. Phys. Commun. 10, 343 (1975).
  57. R. Nisius, Phys. Rep. 332, 165 (2000).
  58. M. Krawczyk, A. Zembrzuski, and M. Staszel, Phys. Rep. 345, 265 (2001).
  59. B. Barish and J. E. Brau, Int. J. Mod. Phys. A 28, 1330039 (2013).
  60. W. Abdallah et al. (CEPC Study Group), Radiat. Detect. Technol. Methods 8, 1 (2024); 9, 184(E) (2025).

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Phys. Rev. D 112, 094030– Published 18 November, 2025
  • Received 12 August 2025
  • Accepted 24 October 2025
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