The hidden sunrise in the energy-energy correlator
Abstract
The energy-energy correlator (EEC) is one of a handful of collider observables that can be computed analytically to high orders. As an energy-weighted cross-section, it exposes features of quantum field theory that scattering amplitudes do not, and it can be compared directly to data. As with scattering amplitudes, the analytic expressions require special functions beyond polylogarithms. In Henn et al., the EEC was computed to next-to-next-to-leading order (NNLO) for 𝒩=4 super Yang-Mills (SYM) theory, and the result is expressed in terms of both harmonic polylogarithms (HPLs) and one two-fold integral, which contains elliptic curves. In this work, we report a complete result including the remaining elliptic sector, which is closely related to the sunrise Feynman integrals. We find the j-invariants of the EEC and the sunrise agree identically under a Möbius map, and thus the elliptic sector in the EEC lives on the Γ1(6) modular curve of the sunrise integral. We then express the answer in terms of iterated Eisenstein integrals, which can be evaluated to high precision quickly. The analytic form also allows a first study of the EEC Landau bootstrap, and the understanding of its function space in 𝒩=4 SYM offers a concrete handle on the elliptic sector of the EEC in QCD. Many of the technical results in this paper were completed with AI under human supervision.
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BibTeX
@misc{schwartz2026hidden,
title = {{The hidden sunrise in the energy-energy correlator}},
author = {Matthew D. Schwartz and Xiaoyuan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10734},
eprint = {2610.10734},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10734},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The hidden sunrise in the energy-energy correlator
AU - Matthew D. Schwartz
AU - Xiaoyuan Zhang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10734
UR - https://arxiv.org/abs/2610.10734
AB - The energy-energy correlator (EEC) is one of a handful of collider observables that can be computed analytically to high orders. As an energy-weighted cross-section, it exposes features of quantum field theory that scattering amplitudes do not, and it can be compared directly to data. As with scattering amplitudes, the analytic expressions require special functions beyond polylogarithms. In Henn et al., the EEC was computed to next-to-next-to-leading order (NNLO) for 𝒩=4 super Yang-Mills (SYM) theory, and the result is expressed in terms of both harmonic polylogarithms (HPLs) and one two-fold integral, which contains elliptic curves. In this work, we report a complete result including the remaining elliptic sector, which is closely related to the sunrise Feynman integrals. We find the j-invariants of the EEC and the sunrise agree identically under a Möbius map, and thus the elliptic sector in the EEC lives on the Γ_1(6) modular curve of the sunrise integral. We then express the answer in terms of iterated Eisenstein integrals, which can be evaluated to high precision quickly. The analytic form also allows a first study of the EEC Landau bootstrap, and the understanding of its function space in 𝒩=4 SYM offers a concrete handle on the elliptic sector of the EEC in QCD. Many of the technical results in this paper were completed with AI under human supervision.
ER -