- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Energy-Energy Correlator for Jet Production in pp and pA Collisions

João Barata1,*, Zhong-Bo Kang2,3,4,†, Xoán Mayo López5,‡, and Jani Penttala2,3,§

  • *Contact author: joao.lourenco.henriques.barata@cern.ch
  • †Contact author: zkang@physics.ucla.edu
  • ‡Contact author: xoan.mayo.lopez@usc.es
  • §Contact author: janipenttala@physics.ucla.edu
PDF

Phys. Rev. Lett. 134, 251903 – Published 24 June, 2025

DOI: https://doi.org/10.1103/96xh-bd1w

Abstract

In this Letter, we study the collinear limit of the energy-energy correlator in single-inclusive jet production in proton-proton and proton-nucleus collisions. We introduce a nonperturbative model that allows us to describe the energy-energy correlator in the entire angular region of the current experiments. Our results for proton-proton collisions show excellent agreement with CMS and ALICE data over a wide range of jet transverse momenta. For proton-nucleus collisions, we include modifications from the nuclear medium, and our predictions align well with the trends observed in recent ALICE measurements.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (78)

  1. A. J. Larkoski, I. Moult, and B. Nachman, Jet substructure at the large hadron collider: A review of recent advances in theory and machine learning, Phys. Rep. 841, 1 (2020).
  2. G. P. Salam, Towards jetography, Eur. Phys. J. C 67, 637 (2010).
  3. S. Sapeta, QCD and jets at hadron colliders, Prog. Part. Nucl. Phys. 89, 1 (2016).
  4. F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, The color glass condensate, Annu. Rev. Nucl. Part. Sci. 60, 463 (2010).
  5. A. Morreale and F. Salazar, Mining for gluon saturation at colliders, Universe 7, 312 (2021).
  6. W. Busza, K. Rajagopal, and W. van der Schee, Heavy ion collisions: The big picture, and the big questions, Annu. Rev. Nucl. Part. Sci. 68, 339 (2018).
  7. E. Craft, K. Lee, B. Meçaj, and I. Moult, Beautiful and charming energy correlators, arXiv:2210.09311.
  8. K. Lee, B. Meçaj, and I. Moult, Conformal colliders meet the LHC, Phys. Rev. D 111, L011502 (2025).
  9. L. J. Dixon, I. Moult, and H. X. Zhu, Collinear limit of the energy-energy correlator, Phys. Rev. D 100, 014009 (2019).
  10. I. Moult and H. X. Zhu, Simplicity from recoil: The three-loop soft function and factorization for the energy-energy correlation, J. High Energy Phys. 08 (2018) 160.
  11. Z.-B. Kang, J. Penttala, and C. Zhang, Determination of the strong coupling constant and the Collins-Soper kernel from the energy-energy correlator in e+e− collisions, arXiv:2410.21435.
  12. X. Liu and H. X. Zhu, Nucleon energy correlators, Phys. Rev. Lett. 130, 091901 (2023).
  13. H. Chen, I. Moult, and H. X. Zhu, Quantum interference in jet substructure from spinning gluons, Phys. Rev. Lett. 126, 112003 (2021).
  14. K. Lee and I. Moult, Energy correlators taking charge, arXiv:2308.00746.
  15. CMS Collaboration, Energy-energy correlators from PbPb and pp collisions at 5.02 TeV (2024), https://inspirehep.net/literature/2817909.
  16. A. Hayrapetyan et al. (CMS Collaboration), Measurement of energy correlators inside jets and determination of the strong coupling αS(mZ), Phys. Rev. Lett. 133, 071903 (2024).
  17. S. Acharya et al. (ALICE Collaboration), Exposing the parton-hadron transition within jets with energy-energy correlators in pp collisions at s=5.02  TeV, arXiv:2409.12687.
  18. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Energy correlations in perturbative quantum chromodynamics: A conjecture for all orders, Phys. Lett. 85B, 297 (1979).
  19. C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Energy correlations in electron—positron annihilation: Testing QCD, Phys. Rev. Lett. 41, 1585 (1978).
  20. D. M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, J. High Energy Phys. 05 (2008) 012.
  21. N. A. Sveshnikov and F. V. Tkachov, Jets and quantum field theory, Phys. Lett. B 382, 403 (1996).
  22. P. T. Komiske, I. Moult, J. Thaler, and H. X. Zhu, Analyzing N-point energy correlators inside jets with CMS open data, Phys. Rev. Lett. 130, 051901 (2023).
  23. B. Singh and V. Vaidya, Factorization for energy-energy correlator in heavy ion collision, arXiv:2408.02753.
  24. J. Barata, P. Caucal, A. Soto-Ontoso, and R. Szafron, Advancing the understanding of energy-energy correlators in heavy-ion collisions, J. High Energy Phys. 11 (2024) 060.
  25. Z. Yang, Y. He, I. Moult, and X.-N. Wang, Probing the short-distance structure of the quark-gluon plasma with energy correlators, Phys. Rev. Lett. 132, 011901 (2024).
  26. W.-J. Xing, S. Cao, G.-Y. Qin, and X.-N. Wang, Flavor hierarchy of jet energy correlators inside the quark-gluon plasma, Phys. Rev. Lett. 134, 052301 (2025).
  27. J. Barata, J. G. Milhano, and A. V. Sadofyev, Picturing QCD jets in anisotropic matter: From jet shapes to energy correlators, Eur. Phys. J. C 84, 174 (2024).
  28. K. Devereaux, W. Fan, W. Ke, K. Lee, and I. Moult, Imaging cold nuclear matter with energy correlators, arXiv:2303.08143.
  29. H. T. Li, I. Vitev, and Y. J. Zhu, Transverse-energy-energy correlations in deep inelastic scattering, J. High Energy Phys. 11 (2020) 051.
  30. H. T. Li, Y. Makris, and I. Vitev, Energy-energy correlators in deep inelastic scattering, Phys. Rev. D 103, 094005 (2021).
  31. H.-Y. Liu, X. Liu, J.-C. Pan, F. Yuan, and H. X. Zhu, Nucleon energy correlators for the color glass condensate, Phys. Rev. Lett. 130, 181901 (2023).
  32. H. Cao, X. Liu, and H. X. Zhu, Toward precision measurements of nucleon energy correlators in lepton-nucleon collisions, Phys. Rev. D 107, 114008 (2023).
  33. X. L. Li, X. Liu, F. Yuan, and H. X. Zhu, Illuminating nucleon-gluon interference via calorimetric asymmetry, Phys. Rev. D 108, L091502 (2023).
  34. H. Bossi, A. S. Kudinoor, I. Moult, D. Pablos, A. Rai, and K. Rajagopal, Imaging the wakes of jets with energy-energy-energy correlators, J. High Energy Phys. 12 (2024) 073.
  35. Y. Fu, B. Müller, and C. Sirimanna, Modification of the jet energy-energy correlator in cold nuclear matter, arXiv:2411.04866.
  36. C. Andres, F. Dominguez, R. Kunnawalkam Elayavalli, J. Holguin, C. Marquet, and I. Moult, Resolving the scales of the quark-gluon plasma with energy correlators, Phys. Rev. Lett. 130, 262301 (2023).
  37. M. Jaarsma, Y. Li, I. Moult, W. J. Waalewijn, and H. X. Zhu, Energy correlators on tracks: Resummation and non-perturbative effects, J. High Energy Phys. 12 (2023) 087.
  38. J. C. Collins and D. E. Soper, Back-to-back jets in QCD: Comparison with experiment, Phys. Rev. Lett. 48, 655 (1982).
  39. D. de Florian and M. Grazzini, The back-to-back region in e+e− energy-energy correlation, Nucl. Phys. B704, 387 (2005).
  40. Z. Tulipánt, A. Kardos, and G. Somogyi, Energy–energy correlation in electron–positron annihilation at NNLL+NNLO accuracy, Eur. Phys. J. C 77, 749 (2017).
  41. A. Kardos, S. Kluth, G. Somogyi, Z. Tulipánt, and A. Verbytskyi, Precise determination of αS(MZ) from a global fit of energy–energy correlation to NNLO+NNLL predictions, Eur. Phys. J. C 78, 498 (2018).
  42. X. Liu, W. Vogelsang, F. Yuan, and H. X. Zhu, Universality in the near-side energy-energy correlator, Phys. Rev. Lett. 134, 151901 (2025).
  43. H.-y. Liu, K. Xie, Z. Kang, and X. Liu, Single inclusive jet production in pA collisions at NLO in the small-x regime, J. High Energy Phys. 07 (2022) 041.
  44. J. L. Albacete and C. Marquet, Single inclusive hadron production at RHIC and the LHC from the color glass condensate, Phys. Lett. B 687, 174 (2010).
  45. E. Levin and A. H. Rezaeian, Gluon saturation and inclusive hadron production at LHC, Phys. Rev. D 82, 014022 (2010).
  46. A. M. Staśto, B.-W. Xiao, F. Yuan, and D. Zaslavsky, Matching collinear and small x factorization calculations for inclusive hadron production in pA collisions, Phys. Rev. D 90, 014047 (2014).
  47. J. P. Blaizot, F. Gelis, and R. Venugopalan, High-energy pA collisions in the color glass condensate approach. 1. Gluon production and the Cronin effect, Nucl. Phys. A743, 13 (2004).
  48. 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).
  49. M. Bury, H. Van Haevermaet, A. Van Hameren, P. Van Mechelen, K. Kutak, and M. Serino, Single inclusive jet production and the nuclear modification ratio at very forward rapidity in proton-lead collisions with sNN=5.02  TeV, Phys. Lett. B 780, 185 (2018).
  50. A. Dumitru, A. Hayashigaki, and J. Jalilian-Marian, The color glass condensate and hadron production in the forward region, Nucl. Phys. A765, 464 (2006).
  51. H.-Y. Liu, Y.-Q. Ma, and K.-T. Chao, Improvement for color glass condensate factorization: Single hadron production in pA collisions at next-to-leading order, Phys. Rev. D 100, 071503 (2019).
  52. Y. Guo, X. Liu, and F. Yuan, Long range energy-energy correlator at the LHC, arXiv:2408.14693.
  53. J. C. Collins, D. E. Soper, and G. F. Sterman, Factorization of hard processes in QCD, Adv. Ser. Dir. High Energy Phys. 5, 1 (1989).
  54. G. T. Bodwin, Factorization of the Drell-Yan cross-section in perturbation theory, Phys. Rev. D 31, 2616 (1985); 34, 3932(E) (1986).
  55. J. C. Collins, D. E. Soper, and G. F. Sterman, Soft gluons and factorization, Nucl. Phys. B308, 833 (1988).
  56. J. Collins, Foundations of Perturbative QCD, Vol. 32 of Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (Cambridge University Press, Cambridge, England, 2023).
  57. J. F. Owens, Large momentum transfer production of direct photons, jets, and particles, Rev. Mod. Phys. 59, 465 (1987).
  58. Z.-B. Kang, F. Ringer, and I. Vitev, The semi-inclusive jet function in SCET and small radius resummation for inclusive jet production, J. High Energy Phys. 10 (2016) 125.
  59. Z.-B. Kang, K. Lee, X. Liu, and F. Ringer, Soft drop groomed jet angularities at the LHC, Phys. Lett. B 793, 41 (2019).
  60. K. Lee, I. Moult, and X. Zhang, Revisiting single inclusive jet production: Timelike factorization and reciprocity, J. High Energy Phys. 05 (2025) 129.
  61. See Supplemental Material at http://link.aps.org/supplemental/10.1103/96xh-bd1w for the evolution of the jet function in position space and for the medium modification factors.
  62. J. C. Collins, D. E. Soper, and G. F. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B250, 199 (1985).
  63. J. Collins and T. Rogers, Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel, Phys. Rev. D 91, 074020 (2015).
  64. Z.-B. Kang, X. Liu, F. Ringer, and H. Xing, The transverse momentum distribution of hadrons within jets, J. High Energy Phys. 11 (2017) 068.
  65. T.-J. Hou et al., Progress in the CTEQ-TEA NNLO global QCD analysis, arXiv:1908.11394.
  66. B. Jacak (private communication).
  67. J. H. Isaksen and K. Tywoniuk, Wilson line correlators beyond the large-Nc, J. High Energy Phys. 11 (2020) 125.
  68. J. H. Isaksen and K. Tywoniuk, Precise description of medium-induced emissions, J. High Energy Phys. 09 (2023) 049.
  69. L. Apolinário, N. Armesto, J. G. Milhano, and C. A. Salgado, Medium-induced gluon radiation and colour decoherence beyond the soft approximation, J. High Energy Phys. 02 (2015) 119.
  70. A. Kovner and U. A. Wiedemann, Eikonal evolution and gluon radiation, Phys. Rev. D 64, 114002 (2001).
  71. T. Altinoluk, N. Armesto, G. Beuf, M. Martínez, and C. A. Salgado, Next-to-eikonal corrections in the CGC: Gluon production and spin asymmetries in pA collisions, J. High Energy Phys. 07 (2014) 068.
  72. J. Barata, C. A. Salgado, and J. M. Silva, Gluon to qq¯ antenna in anisotropic QCD matter: Spin-polarized and azimuthal jet observables, J. High Energy Phys. 12 (2024) 023.
  73. M. Attems, J. Brewer, G. M. Innocenti, A. Mazeliauskas, S. Park, W. van der Schee, and U. A. Wiedemann, The medium-modified g→cc¯ splitting function in the BDMPS-Z formalism, J. High Energy Phys. 01 (2023) 080.
  74. Y.-Y. Zhang and X.-N. Wang, Parton rescattering and gluon saturation in dijet production at EIC, Phys. Rev. D 105, 034015 (2022).
  75. P. Ru, Z.-B. Kang, E. Wang, H. Xing, and B.-W. Zhang, Global extraction of the jet transport coefficient in cold nuclear matter, Phys. Rev. D 103, L031901 (2021).
  76. K. J. Eskola, P. Paakkinen, H. Paukkunen, and C. A. Salgado, EPPS21: A global QCD analysis of nuclear PDFs, Eur. Phys. J. C 82, 413 (2022).
  77. A. Nambrath, Energy-energy correlators of inclusive jets from small to large collision systems with the ALICE experiment, Presented at Hard Probes 2024, Nagasaki, Japan, 2024, https://indico.cern.ch/event/1339555/contributions/6040810/attachments/2932582/5150292/HP24_ALICE_EECs.pdf.
  78. J. Barata, M. V. Kuzmin, J. G. Milhano, and A. V. Sadofyev, Jet EEC aWAKEning: Hydrodynamic response on the celestial sphere, https://inspirehep.net/literature/2856224.

Outline

Information

Phys. Rev. Lett. 134, 251903– Published 24 June, 2025
  • Received 26 November 2024
  • Revised 22 April 2025
  • Accepted 2 June 2025
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