The three-point energy correlator in the coplanar limit
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13130_2025_Article_26889.pdf
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Author(s)
Gao, Anjie
Yang, Tong-Zhi
Zhang, Xiaoyuan
Date Issued
August 4, 2025
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Gao, A., Yang, TZ. & Zhang, X. The three-point energy correlator in the coplanar limit. J. High Energ. Phys. 2025, 30 (2025).
Version
Final published version
Abstract
Energy correlators are a type of observables that measure how energy is distributed across multiple detectors as a function of the angles between pairs of detectors. In this paper, we study the three-point energy correlator (EEEC) at lepton colliders in the three-particle near-to-plane (coplanar) limit. The leading-power contribution in this limit is governed by the three-jet (trijet) configuration. We introduce a new approach by projecting the EEEC onto the volume of the parallelepiped formed by the unit vectors aligned with three detected final-state particles. Analogous to the back-to-back limit of the two-point energy correlator probing the dijet configuration, the small-volume limit of the EEEC probes the trijet configuration. We derive a transverse momentum dependent (TMD) based factorization theorem that captures the soft and collinear logarithms in the coplanar limit, which enables us to achieve the next-to-next-to-next-to-leading logarithm (N3LL) resummation. To our knowledge, this is the first N3LL result for a trijet event shape. Additionally, we demonstrate that a similar factorization theorem can be applied to the fully differential EEEC in the three-particle coplanar limit, which provides a clean environment for studying different coplanar trijet shapes.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP08(2025)030
