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Published February 23, 2026 | Version Published
Journal Article Open

Quantum Scaling in Energy Correlators beyond the Confinement Transition

Creators

  • 1. ROR icon University of Chicago
  • 2. ROR icon Massachusetts Institute of Technology
  • 3. ROR icon Beijing Normal University
  • 4. ROR icon California Institute of Technology
  • 5. ROR icon Lawrence Berkeley National Laboratory
  • 6. ROR icon Peking University

Abstract

We study the QCD scaling behavior of the small-angle energy-energy correlator (EEC), focusing on the transition between its perturbative preconfinement and nonperturbative postconfinement regimes. Applying the light-ray operator product expansion (OPE), we develop a formalism that describes the scaling of the EEC with the input energy 𝑄 in the transition and the postconfinement region, where the latter quantum scaling is determined by the 𝐽=5 DGLAP anomalous dimension. A key result of our Letter is a novel connection between the light-ray OPE and the dihadron fragmentation function (DFF), where we show that the nonperturbative OPE coefficients correspond to moments of the DFF. This finding establishes a new paradigm for studying hadronization. Our theoretical predictions are validated against Monte Carlo simulations for both 𝑒+⁒𝑒− and 𝑝⁒𝑝 collisions, showing excellent agreement. The potential role of the quantum scaling in the precision determination of 𝛼𝑠 is also discussed.

Copyright and License

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.

Acknowledgement

This work was initiated during a C3 ⁒NT program on “New Opportunities in Particle and Nuclear Physics with Energy Correlators” at CCNU, Wuhan, May 7–16, 2025. We thank Wei-Yao Ke and Xin-Nian Wang for the warm hospitality. We also thank Petr Kravchuk for related discussions. H. C. is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Contract No. DE-SC0011090. F. Y. is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. H. X. Z. is supported by the National Natural Science Foundation of China under Contract No. 12425505 and The Fundamental Research Funds for the Central Universities, Peking University. X. L. is supported by the National Natural Science Foundation of China under Contracts No. 12547109, No. 12175016 and the Fundamental Research Funds for the Central Universities, Beijing Normal University. D. S. D. is supported in part by Simons Foundation Grant No. 488657 (Simons Collaboration on the Nonperturbative Bootstrap) and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. C. H. C. is supported by a Kadanoff fellowship at the University of Chicago.

Data Availability

The data that support the findings of this article are not publicly available upon publication because it is not technically feasible and/or the cost of preparing, depositing, and hosting the data would be prohibitive within the terms of this research project. The data are available from the authors upon reasonable request.

Supplemental Material

The Supplemental Material provides additional technical details and supporting discussions that complement the results presented in the main text.

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Additional details

Related works

Is new version of
Discussion Paper: arXiv:2507.15923 (arXiv)

Funding

United States Department of Energy
DE-SC0011090
United States Department of Energy
DE-AC02-05CH11231
National Natural Science Foundation of China
12425505
National Natural Science Foundation of China
12547109
National Natural Science Foundation of China
12175016
Ministry of Finance of the People's Republic of China
Peking University
Beijing Normal University
Simons Foundation
488657
United States Department of Energy
DE-SC0011632
University of Chicago
SCOAP3

Dates

Submitted
2025-07-23
Accepted
2026-01-09

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Caltech groups
Division of Physics, Mathematics and Astronomy (PMA) , Walter Burke Institute for Theoretical Physics , Physics Department
Publication Status
Published