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One-point energy correlator for deep inelastic scattering at small x

Zhong-Bo Kang1,2,3,*, Robert Kao1,2,†, Meijian Li4,5,‡, and Jani Penttala1,2,§

  • *Contact author: zkang@physics.ucla.edu
  • †Contact author: rqk@ucla.edu
  • ‡Corresponding author: meijianli@hust.edu.cn
  • §Contact author: janipenttala@physics.ucla.edu
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Phys. Rev. D 114, 074024 – Published 13 October, 2026

DOI: https://doi.org/10.1103/1fr7-f99m

Abstract

We derive the expressions for the one-point energy correlator (OPEC) in deep inelastic scattering in the high-energy (small-x) limit within the Color Glass Condensate (CGC) framework. The OPEC is computed as a function of the angle between the energy flow and the target proton or nucleus, enabling a systematic exploration of different momentum scales in the scattering process. Owing to the momentum sum rule, the dependence on fragmentation functions cancels, leaving the dipole amplitude as the only nonperturbative input. As a result, the OPEC provides a sensitive and promising probe of gluon saturation dynamics at small x. We present numerical results for representative kinematic configurations relevant to the future Electron-Ion Collider, demonstrating sizable nuclear suppression effects within the CGC framework and highlighting the consistency of this observable with predictions from gluon saturation.

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References (89)

  1. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. Lett. 41, 1585 (1978).
  2. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D 19, 2018 (1979).
  3. I. Moult and H. X. Zhu, arXiv:2506.09119.
  4. H. Chen, I. Moult, X. Zhang, and H. X. Zhu, Phys. Rev. D 102, 054012 (2020).
  5. H. Chen, I. Moult, and H. X. Zhu, Phys. Rev. Lett. 126, 112003 (2021).
  6. P. T. Komiske, I. Moult, J. Thaler, and H. X. Zhu, Phys. Rev. Lett. 130, 051901 (2023).
  7. C. Andres, F. Dominguez, J. Holguin, C. Marquet, and I. Moult, J. High Energy Phys. 09 (2023) 088.
  8. C. Andres, F. Dominguez, J. Holguin, C. Marquet, and I. Moult, Phys. Rev. Lett. 136, 122301 (2026).
  9. Z. Yang, Y. He, I. Moult, and X.-N. Wang, Phys. Rev. Lett. 132, 011901 (2024).
  10. W.-J. Xing, S. Cao, G.-Y. Qin, and X.-N. Wang, Phys. Rev. Lett. 134, 052301 (2025).
  11. L. Apolinário, R. Kunnawalkam Elayavalli, N. O. Madureira, J.-X. Sheng, X.-N. Wang, and Z. Yang, Phys. Rev. D 112, 054018 (2025).
  12. H.-Y. Liu, S.-Y. Chen, W. Dai, and B.-W. Zhang, Chin. Phys. C 50, 074103 (2026).
  13. W. Ke, B. Mecaj, and I. Vitev, J. High Energy Phys. 04, 155 (2026).
  14. A. Budhraja and B. Singh, Phys. Lett. B 872, 140079 (2026).
  15. B. Singh and V. Vaidya, J. High Energy Phys. 06 (2025) 071.
  16. J. Barata, Z.-B. Kang, X. Mayo López, and J. Penttala, Phys. Rev. Lett. 134, 251903 (2025).
  17. J. Barata, M. V. Kuzmin, J. G. Milhano, and A. V. Sadofyev, Phys. Rev. D 112, 016005 (2025).
  18. J. Barata, J. G. Milhano, A. V. Sadofyev, and J. M. Silva, arXiv:2512.17009.
  19. J. Barata, J. G. Milhano, and A. V. Sadofyev, Eur. Phys. J. C 84, 174 (2024).
  20. J. Barata, P. Caucal, A. Soto-Ontoso, and R. Szafron, J. High Energy Phys. 11 (2024) 060.
  21. W. Zhao, V. Koch, and F. Yuan, arXiv:2507.18790.
  22. M. A. Ebert, B. Mistlberger, and G. Vita, J. High Energy Phys. 08 (2021) 022.
  23. Z.-B. Kang, K. Lee, D. Y. Shao, and F. Zhao, J. High Energy Phys. 03 (2024) 153.
  24. Z.-B. Kang, J. Penttala, and C. Zhang, arXiv:2410.21435.
  25. A.-P. Chen, X. Liu, and Y.-Q. Ma, Phys. Rev. Lett. 133, 19 (2024).
  26. J.-p. Zhang, Q. Yang, W.-C. Zhang, and Y.-j. Zhao, Phys. Rev. D 113, 054038 (2026).
  27. J. Barata, J. Brewer, K. Lee, and J. M. Silva, arXiv:2508.19404.
  28. K. Lee and I. Stewart, Phys. Rev. Lett. 136, 081902 (2026).
  29. Y. Guo, F. Yuan, and W. Zhao, Phys. Rev. Lett. 136, 081904 (2026).
  30. C.-H. Chang, H. Chen, X. Liu, D. Simmons-Duffin, F. Yuan, and H. X. Zhu, Phys. Rev. Lett. 136, 081903 (2026).
  31. Z.-B. Kang, A. Metz, D. Pitonyak, and C. Zhang, Phys. Rev. Lett. 136, 081905 (2026).
  32. E. Herrmann, Z.-B. Kang, J. Penttala, and C. Zhang, arXiv:2507.17704.
  33. D. M. Hofman and J. Maldacena, J. High Energy Phys. 05 (2008) 012.
  34. A. V. Belitsky, S. Hohenegger, G. P. Korchemsky, E. Sokatchev, and A. Zhiboedov, Phys. Rev. Lett. 112, 071601 (2014).
  35. A. V. Belitsky, S. Hohenegger, G. P. Korchemsky, E. Sokatchev, and A. Zhiboedov, Nucl. Phys. B884, 305 (2014).
  36. G. P. Korchemsky, J. High Energy Phys. 01 (2020) 008.
  37. L. J. Dixon, I. Moult, and H. X. Zhu, Phys. Rev. D 100, 014009 (2019).
  38. K. Lee, B. Meçaj, and I. Moult, Phys. Rev. D 111, L011502 (2025).
  39. A. Gao, H. T. Li, I. Moult, and H. X. Zhu, Phys. Rev. Lett. 123, 062001 (2019).
  40. A. Ali, F. Barreiro, J. Llorente, and W. Wang, Phys. Rev. D 86, 114017 (2012).
  41. H. T. Li, I. Vitev, and Y. J. Zhu, J. High Energy Phys. 11 (2020) 051.
  42. Z.-B. Kang, J. Penttala, F. Zhao, and Y. Zhou, Phys. Rev. D 109, 094012 (2024).
  43. Z.-B. Kang, S. Lee, J. Penttala, F. Zhao, and Y. Zhou, Phys. Rev. D 112, 014012 (2025).
  44. Z.-B. Kang, R. Kao, M. Li, and J. Penttala, Phys. Rev. D 112, 076006 (2025).
  45. I. Ganguli and P. Kotko, Phys. Rev. D 112, 114020 (2025).
  46. S. Bhattacharya, Z.-B. Kang, D. Padilla, and J. Penttala, arXiv:2504.10475.
  47. X. Liu and H. X. Zhu, Phys. Rev. Lett. 130, 091901 (2023).
  48. H.-Y. Liu, X. Liu, J.-C. Pan, F. Yuan, and H. X. Zhu, Phys. Rev. Lett. 130, 181901 (2023).
  49. K.-B. Chen, J.-P. Ma, and X.-B. Tong, J. High Energy Phys. 08 (2024) 227.
  50. H. Mäntysaari, Y. Tawabutr, and X.-B. Tong, Phys. Rev. D 112, 114027 (2025).
  51. Y. Huang, X.-B. Tong, and H.-L. Wang, Phys. Rev. Lett. 136, 131902 (2026).
  52. H. Cao, X. Liu, and H. X. Zhu, Phys. Rev. D 107, 114008 (2023).
  53. H. Cao, H. T. Li, and Z. Mi, Phys. Rev. D 109, 096004 (2024).
  54. X. L. Li, X. Liu, F. Yuan, and H. X. Zhu, Phys. Rev. D 108, L091502 (2023).
  55. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D 17, 2298 (1978).
  56. H. T. Li, Y. Makris, and I. Vitev, Phys. Rev. D 103, 094005 (2021).
  57. Z. Mi and Z. Wang, J. High Energy Phys. 11 (2025) 090.
  58. M.-S. Gao, Z.-B. Kang, W. Li, and D. Y. Shao, Phys. Rev. Lett. 136, 151902 (2026).
  59. Y.-K. Song, S.-Y. Wei, L. Yang, and J. Zhou, Phys. Rev. Lett. 136, 131901 (2026).
  60. J. Gao, H. T. Li, and Y. J. Zhu, Phys. Rev. D 113, 034028 (2026).
  61. Y. J. Zhu, Phys. Rev. D 113, 014025 (2026).
  62. Q.-H. Cao, Z. Yu, C. P. Yuan, S. Zhang, and H. X. Zhu, J. High Energy Phys. 02 (2026) 244.
  63. Y. Fu, Z.-B. Kang, J. Penttala, and Y. Zhou, J. High Energy Phys. 06 (2026) 247.
  64. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016).
  65. E. C. Aschenauer, S. Fazio, J. H. Lee, H. Mantysaari, B. S. Page, B. Schenke, T. Ullrich, R. Venugopalan, and P. Zurita, Rep. Prog. Phys. 82, 024301 (2019).
  66. D. P. Anderle et al., Front. Phys. (Beijing) 16, 64701 (2021).
  67. F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, Annu. Rev. Nucl. Part. Sci. 60, 463 (2010).
  68. H. Weigert, Prog. Part. Nucl. Phys. 55, 461 (2005).
  69. E. Iancu, A. Leonidov, and L. D. McLerran, Nucl. Phys. A692, 583 (2001).
  70. E. Iancu, A. Leonidov, and L. D. McLerran, Phys. Lett. B 510, 133 (2001).
  71. E. Iancu and L. D. McLerran, Phys. Lett. B 510, 145 (2001).
  72. E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, Nucl. Phys. A703, 489 (2002).
  73. J. Jalilian-Marian, A. Kovner, L. D. McLerran, and H. Weigert, Phys. Rev. D 55, 5414 (1997).
  74. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, Phys. Rev. D 59, 014014 (1998).
  75. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, Nucl. Phys. B504, 415 (1997).
  76. I. Balitsky, Nucl. Phys. B463, 99 (1996).
  77. Y. V. Kovchegov, Phys. Rev. D 60, 034008 (1999).
  78. R.-b. Meng, F. I. Olness, and D. E. Soper, Nucl. Phys. B371, 79 (1992).
  79. P. M. Nadolsky, D. R. Stump, and C. P. Yuan, Phys. Rev. D 61, 014003 (2000); 64, 059903(E) (2001).
  80. C. Marquet, B.-W. Xiao, and F. Yuan, Phys. Lett. B 682, 207 (2009).
  81. I. Balitsky, Phys. Rev. D 75, 014001 (2007).
  82. C. Casuga, M. Karhunen, and H. Mäntysaari, Phys. Rev. D 109, 054018 (2024).
  83. K. Dusling, F. Gelis, T. Lappi, and R. Venugopalan, Nucl. Phys. A836, 159 (2010).
  84. X.-B. Tong, B.-W. Xiao, and Y.-Y. Zhang, Phys. Rev. Lett. 130, 151902 (2023).
  85. K. J. Golec-Biernat and M. Wusthoff, Phys. Rev. D 59, 014017 (1998).
  86. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  87. L. Frankfurt, V. Guzey, and M. Strikman, Phys. Rep. 512, 255 (2012).
  88. Z.-B. Kang, I. Vitev, and H. Xing, Phys. Rev. D 85, 054024 (2012).
  89. D. V. Perepelitsa, Phys. Rev. C 111, 054901 (2025).

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Phys. Rev. D 114, 074024– Published 13 October, 2026
  • Received 10 March 2026
  • Accepted 15 September 2026
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