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Simple Scaling Laws for Energy Correlators in Nuclear Matter

Carlota Andres1, Fabio Dominguez2, Jack Holguin3, Cyrille Marquet4, and Ian Moult5

Phys. Rev. Lett. 136, 122301 – Published 24 March, 2026

DOI: https://doi.org/10.1103/sw7p-7jbp

Abstract

Collider experiments involving nuclei provide a direct means of studying exotic states of nuclear matter. Recent measurements of energy correlators in both proton-nucleus (p-A) and nucleus-nucleus (A-A) collisions reveal sizable modifications, attributable to nuclear effects, compared to proton-proton (p-p) collisions. Energy correlators, and their associated light-ray operator product expansion (OPE), allow scaling behaviors of the measured spectrum to be directly mapped to properties of the underlying quantum field theory. Here, we demonstrate for the first time how this mapping occurs in nuclear collisions, and highlight how the light-ray OPE characterizes leading nuclear effects. We show that the leading modification to the energy correlator distribution is characterized by an enhancement of the expectation value of twist-4 light-ray operators, resulting in a scaling for the ratio of the two-point correlator in nuclear matter to that in vacuum of ∼1+aθ2 up to quantum corrections. We verify that this leading twist-4 correction accurately describes recent A-A and p-A data, and is thus sufficient to capture the scaling behavior within the angular range measured for jet radii used in nuclear experiments. Our light-ray OPE based approach lays the groundwork for a rigorous characterization of nuclear modification to energy correlator observables.

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References (138)

  1. W. Busza, K. Rajagopal, and W. van der Schee, Annu. Rev. Nucl. Part. Sci. 68, 339 (2018).
  2. A. Hayrapetyan et al. (CMS Collaboration), Phys. Rep. 1115, 219 (2025).
  3. S. Acharya et al. (ALICE Collaboration), Eur. Phys. J. C 84, 813 (2024).
  4. S. Cao and X.-N. Wang, Rep. Prog. Phys. 84, 024301 (2021).
  5. L. Apolinário, Y.-J. Lee, and M. Winn, Prog. Part. Nucl. Phys. 127, 103990 (2022).
  6. L. Cunqueiro and A. M. Sickles, Prog. Part. Nucl. Phys. 124, 103940 (2022).
  7. M. Connors, C. Nattrass, R. Reed, and S. Salur, Rev. Mod. Phys. 90, 025005 (2018).
  8. J. W. Harris and B. Müller, Eur. Phys. J. C 84, 247 (2024).
  9. M. Arratia, Y. Song, F. Ringer, and B. V. Jacak, Phys. Rev. C 101, 065204 (2020).
  10. J. Brewer, A. Mazeliauskas, and W. van der Schee, in Opportunities of OO and pO Collisions at the LHC (2021), arXiv:2103.01939
  11. R. Abdul Khalek et al., arXiv:2203.13199.
  12. R. Abir et al., arXiv:2305.14572.
  13. J. C. Collins, D. E. Soper, and G. F. Sterman, Nucl. Phys. B261, 104 (1985).
  14. J. C. Collins, D. E. Soper, and G. F. Sterman, Adv. Ser. Dir. High Energy Phys. 5, 1 (1989).
  15. H. D. Politzer, Nucl. Phys. B172, 349 (1980).
  16. R. K. Ellis, W. Furmanski, and R. Petronzio, Nucl. Phys. B212, 29 (1983).
  17. R. K. Ellis, W. Furmanski, and R. Petronzio, Nucl. Phys. B207, 1 (1982).
  18. R. L. Jaffe, Nucl. Phys. B229, 205 (1983).
  19. R. L. Jaffe and M. Soldate, Phys. Lett. 105B, 467 (1981).
  20. R. L. Jaffe and M. Soldate, Phys. Rev. D 26, 49 (1982).
  21. J.-w. Qiu and G. F. Sterman, Nucl. Phys. B353, 137 (1991).
  22. J.-w. Qiu and G. F. Sterman, Nucl. Phys. B353, 105 (1991).
  23. M. Luo, J.-w. Qiu, and G. F. Sterman, Phys. Rev. D 49, 4493 (1994).
  24. M. Luo, J.-w. Qiu, and G. F. Sterman, Phys. Rev. D 50, 1951 (1994).
  25. M. Luo, J.-w. Qiu, and G. F. Sterman, in Proceedings of the 7th Meeting of the APS Division of Particles Fields (World Scientific, Singapore, 1992), pp. 951–953.
  26. J.-w. Qiu and G. F. Sterman, Nucl. Phys. B378, 52 (1992).
  27. M. Luo, J.-w. Qiu, and G. F. Sterman, Phys. Lett. B 279, 377 (1992).
  28. M. Luo, J.-w. Qiu, and G. F. Sterman, in Particles & Fields 91: Meeting of the Division of Particles & Fields of the APS (World Scientific, River Edge, NJ, 1991), pp. 0633–636.
  29. K. Kastella, G. F. Sterman, and J. Milana, Phys. Rev. D 39, 2586 (1989).
  30. K. Kastella, J. Milana, and G. F. Sterman, Phys. Rev. Lett. 62, 730 (1989).
  31. X.-N. Wang and X.-f. Guo, Nucl. Phys. A696, 788 (2001).
  32. X.-f. Guo and X.-N. Wang, Phys. Rev. Lett. 85, 3591 (2000).
  33. E. Wang and X.-N. Wang, Phys. Rev. Lett. 89, 162301 (2002).
  34. J. Osborne and X.-N. Wang, Nucl. Phys. A 710, 281 (2002).
  35. S. S. Adler et al. (PHENIX Collaboration), Phys. Rev. Lett. 94, 082302 (2005).
  36. C. Aidala et al. (PHENIX Collaboration), Phys. Rev. C 101, 034910 (2020).
  37. S. Acharya et al. (ALICE Collaboration), Phys. Lett. B 827, 136943 (2022).
  38. B. B. Back et al. (PHOBOS Collaboration), Phys. Rev. C 70, 061901 (2004).
  39. I. Arsene et al. (BRAHMS Collaboration), Phys. Rev. Lett. 93, 242303 (2004).
  40. G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 763, 313 (2016).
  41. C. Aidala et al. (PHENIX Collaboration), Phys. Rev. C 96, 064901 (2017).
  42. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 128, 142004 (2022).
  43. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 131, 102301 (2023).
  44. S. Acharya et al. (ALICE Collaboration), J. High Energy Phys. 11 (2018) 013.
  45. M. S. Abdallah et al. (STAR Collaboration), Phys. Rev. Lett. 129, 092501 (2022).
  46. A. Tumasyan et al. (CMS Collaboration), Phys. Rev. Lett. 131, 262301 (2023).
  47. E. Braidot (STAR Collaboration), in Proceedings of the 45th Rencontres de Moriond on QCD and High Energy Interactions (Gioi Publishers, 2010), pp. 355–338, https://moriond.in2p3.fr/Proceedings/2010/Moriond_QCD_2010.pdf.
  48. J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 97, 152302 (2006).
  49. A. Adare et al. (PHENIX Collaboration), Phys. Rev. Lett. 107, 172301 (2011).
  50. A. J. Larkoski, I. Moult, and B. Nachman, Phys. Rep. 841, 1 (2020).
  51. R. Kogler et al., Rev. Mod. Phys. 91, 045003 (2019).
  52. S. Marzani, G. Soyez, and M. Spannowsky, Looking Inside Jets: An Introduction to Jet Substructure and Boosted-Object Phenomenology (Springer, New York, 2019), Vol. 958.
  53. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Lett. 85B, 297 (1979).
  54. C. Basham, L. Brown, S. Ellis, and S. Love, Phys. Rev. D 19, 2018 (1979).
  55. C. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. Lett. 41, 1585 (1978).
  56. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Phys. Rev. D 17, 2298 (1978).
  57. N. Sveshnikov and F. Tkachov, Phys. Lett. B 382, 403 (1996).
  58. F. V. Tkachov, Int. J. Mod. Phys. A 12, 5411 (1997).
  59. G. P. Korchemsky and G. F. Sterman, Nucl. Phys. B555, 335 (1999).
  60. C. W. Bauer, S. P. Fleming, C. Lee, and G. F. Sterman, Phys. Rev. D 78, 034027 (2008).
  61. D. M. Hofman and J. Maldacena, J. High Energy Phys. 05 (2008) 012.
  62. A. Belitsky, S. Hohenegger, G. Korchemsky, E. Sokatchev, and A. Zhiboedov, Nucl. Phys. B884, 305 (2014).
  63. A. Belitsky, S. Hohenegger, G. Korchemsky, E. Sokatchev, and A. Zhiboedov, Nucl. Phys. B884, 206 (2014).
  64. P. Kravchuk and D. Simmons-Duffin, J. High Energy Phys. 11 (2018) 102.
  65. A. Hayrapetyan et al. (CMS Collaboration), Phys. Rev. Lett. 133, 071903 (2024).
  66. A. Tamis (STAR Collaboration), Proc. Sci. HardProbes2023 (2024) 175 [arXiv:2309.05761].
  67. S. Acharya et al. (ALICE Collaboration), arXiv:2409.12687.
  68. P. T. Komiske, I. Moult, J. Thaler, and H. X. Zhu, Phys. Rev. Lett. 130, 051901 (2023).
  69. H.-Y. Liu, X. Liu, J.-C. Pan, F. Yuan, and H. X. Zhu, Phys. Rev. Lett. 130, 181901 (2023).
  70. E. Craft, K. Lee, B. Meçaj, and I. Moult, arXiv:2210.09311.
  71. C. Andres, F. Dominguez, J. Holguin, C. Marquet, and I. Moult, Phys. Rev. D 110, L031503 (2024).
  72. W.-J. Xing, S. Cao, G.-Y. Qin, and X.-N. Wang, Phys. Rev. Lett. 134, 052301 (2025).
  73. C. Andres, F. Dominguez, R. Kunnawalkam Elayavalli, J. Holguin, C. Marquet, and I. Moult, Phys. Rev. Lett. 130, 262301 (2023).
  74. C. Andres, F. Dominguez, J. Holguin, C. Marquet, and I. Moult, J. High Energy Phys. 09 (2023) 088.
  75. Z. Yang, Y. He, I. Moult, and X.-N. Wang, Phys. Rev. Lett. 132, 011901 (2024).
  76. J. a. Barata, P. Caucal, A. Soto-Ontoso, and R. Szafron, J. High Energy Phys. 11 (2024) 060.
  77. C. Andres, F. Dominguez, J. Holguin, C. Marquet, and I. Moult, J. High Energy Phys. 03 (2025) 166.
  78. H. Bossi, A. S. Kudinoor, I. Moult, D. Pablos, A. Rai, and K. Rajagopal, J. High Energy Phys. 12 (2024) 073.
  79. C. Andres and J. Holguin, arXiv:2409.07526.
  80. C. Andres, J. Holguin, R. Kunnawalkam Elayavalli, and J. Viinikainen, Phys. Rev. Lett. 134, 082303 (2025).
  81. B. Singh and V. Vaidya, J. High Energy Phys. 06 (2025) 071.
  82. K. Devereaux, W. Fan, W. Ke, K. Lee, and I. Moult, Phys. Rev. C 112, 035202 (2025).
  83. Y. Fu, B. Müller, and C. Sirimanna, Phys. Rev. Lett. 135, 112302 (2025).
  84. J. a. Barata, Z.-B. Kang, X. Mayo López, and J. Penttala, Phys. Rev. Lett. 134, 251903 (2025).
  85. CMS Collaboration, Energy-energy correlators from PbPb and pp collisions at 5.02 TeV, Technical Report CMS-PAS-HIN-23-004, CERN, Geneva, 2024.
  86. V. Chekhovsky et al. (CMS Collaboration), Phys. Lett. B 866, 139556 (2025).
  87. A. Nambrath, Energy-energy Correlators of Inclusive Jets from Small to Large Collision Systems with the ALICE Experiment (Hard Probes, Nagasaki, Japan, 2024).
  88. J. Chen, First Measurement of the Energy-Energy Correlator in the Back-to-Back Limit using Archived ALEPH e+e− Data at 91.2 GeV (Hard Probes, Nagasaki, Japan, 2024).
  89. L. J. Dixon, I. Moult, and H. X. Zhu, Phys. Rev. D 100, 014009 (2019).
  90. K. Lee, B. Meçaj, and I. Moult, Phys. Rev. D 111, L011502 (2025).
  91. W. Chen, J. Gao, Y. Li, Z. Xu, X. Zhang, and H. X. Zhu, J. High Energy Phys. 05 (2024) 043.
  92. M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, J. High Energy Phys. 01 (2021) 128.
  93. C.-H. Chang, M. Kologlu, P. Kravchuk, D. Simmons-Duffin, and A. Zhiboedov, J. High Energy Phys. 05 (2022) 059.
  94. H. Chen, I. Moult, and H. X. Zhu, Phys. Rev. Lett. 126, 112003 (2021).
  95. H. Chen, I. Moult, J. Sandor, and H. X. Zhu, J. High Energy Phys. 09 (2022) 199.
  96. H. Chen, I. Moult, and H. X. Zhu, J. High Energy Phys. 08 (2022) 233.
  97. H. Chen, J. High Energy Phys. 01 (2024) 035.
  98. C.-H. Chang and D. Simmons-Duffin, J. High Energy Phys. 02 (2023) 126.
  99. A. Homrich, D. Simmons-Duffin, and P. Vieira, J. High Energy Phys. 10 (2024) 125.
  100. S. Ekhammar, N. Gromov, and M. Preti, arXiv:2406.18639.
  101. H. Chen, P. F. Monni, Z. Xu, and H. X. Zhu, Phys. Rev. Lett. 133, 231901 (2024).
  102. D. Chicherin, G. P. Korchemsky, E. Sokatchev, and A. Zhiboedov, J. High Energy Phys. 11 (2023) 134.
  103. Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, Phys. Rev. Lett. 106, 122002 (2011).
  104. J. Casalderrey-Solana and E. Iancu, J. High Energy Phys. 08 (2011) 015.
  105. Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, J. High Energy Phys. 10 (2012) 197.
  106. J. Casalderrey-Solana, Y. Mehtar-Tani, C. A. Salgado, and K. Tywoniuk, Phys. Lett. B 725, 357 (2013).
  107. Y. Mehtar-Tani and K. Tywoniuk, Nucl. Phys. B979, 165 (2018).
  108. P. Caucal, E. Iancu, A. H. Mueller, and G. Soyez, Phys. Rev. Lett. 120, 232001 (2018).
  109. R. L. Jaffe and X.-D. Ji, Nucl. Phys. B375, 527 (1992).
  110. J. Viinikainen, Energy-Energy Correlators from PbPb and pp Collisions at 5.02 TeV with CMS, Energy Correlators at the Collider Frontier (MITP, Mainz, Germany, 2024).
  111. V. M. Braun, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B603, 69 (2001).
  112. V. M. Braun, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B597, 370 (2001).
  113. S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B566, 203 (2000).
  114. V. M. Braun, G. P. Korchemsky, and A. N. Manashov, Phys. Lett. B 476, 455 (2000).
  115. V. M. Braun, S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Nucl. Phys. B553, 355 (1999).
  116. A. V. Belitsky, Nucl. Phys. B574, 407 (2000).
  117. A. V. Belitsky, Phys. Lett. B 453, 59 (1999).
  118. See Supplemental Material at http://link.aps.org/supplemental/10.1103/sw7p-7jbp for the fits performed with the light-ray OPE.
  119. At present, it is not possible to conclusively determine whether the differing quark/gluon fractions in Pb-Pb relative to p-p originate from a selection bias toward quark jets (see Supplemental Material [118]).

  120. R. Abdul Khalek, R. Gauld, T. Giani, E. R. Nocera, T. R. Rabemananjara, and J. Rojo, Eur. Phys. J. C 82, 507 (2022).
  121. K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, Eur. Phys. J. C 82, 413 (2022).
  122. Z.-B. Kang, I. Vitev, and H. Xing, Phys. Rev. D 88, 054010 (2013).
  123. E. Iancu and R. Venugopalan, The color glass condensate and high-energy scattering in QCD, in Quark-Gluon Plasma 4, edited by R. C. Hwa and X.-N. Wang (World Scientific, 2003), pp. 249–3363, 10.1142/9789812795533_0005.
  124. L. D. McLerran and R. Venugopalan, Phys. Rev. D 49, 2233 (1994).
  125. L. D. McLerran and R. Venugopalan, Phys. Rev. D 49, 3352 (1994).
  126. L. D. McLerran and R. Venugopalan, Phys. Rev. D 50, 2225 (1994).
  127. Z.-B. Kang, F. Ringer, and I. Vitev, J. High Energy Phys. 11 (2016) 155.
  128. Z.-B. Kang, F. Ringer, and I. Vitev, J. High Energy Phys. 10 (2016) 125.
  129. M. van Beekveld, M. Dasgupta, B. K. El-Menoufi, J. Helliwell, A. Karlberg, and P. F. Monni, J. High Energy Phys. 07 (2024) 239.
  130. M. van Beekveld, M. Dasgupta, B. K. El-Menoufi, J. Helliwell, P. F. Monni, and G. P. Salam, J. High Energy Phys. 03 (2025) 209.
  131. H.-y. Liu, K. Xie, Z. Kang, and X. Liu, J. High Energy Phys. 07 (2022) 041.
  132. K. Lee, I. Moult, and X. Zhang, J. High Energy Phys. 05 (2025) 129.
  133. K. Lee, I. Moult, and X. Zhang, arXiv:2410.01902.
  134. E. Firat, A. Monin, R. Rattazzi, and M. T. Walters, J. High Energy Phys. 03 (2024) 067.
  135. O. Aharony, S. Minwalla, and T. Wiseman, Classical Quantum Gravity 23, 2171 (2006).
  136. H. Chen, I. Moult, X. Zhang, and H. X. Zhu, Phys. Rev. D 102, 054012 (2020).
  137. K. Lee and I. Moult, arXiv:2308.01332.
  138. K. Lee and I. Moult, arXiv:2308.00746.

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