能量-能量关联器中的隐藏日出
The hidden sunrise in the energy-energy correlator
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中文总结 AI 辅助
本研究在人类监督下借助AI，完成了$\boldsymbol{\textit{N}=4}$ SYM理论中EEC的NNLO完整解析计算，明确其椭圆部分与日出积分的关联，为QCD中EEC的椭圆部分研究提供了关键支撑。
中文摘要 AI 辅助
能量-能量关联器（EEC）是少数可被高精度解析计算的对撞机观测量之一。作为一种能量加权截面，它能揭示散射振幅无法呈现的量子场论特征，且可直接与实验数据对比。与散射振幅类似，其解析表达式需要多重对数函数之外的特殊函数。Henn等人已针对$\boldsymbol{\textit{N}=4}$超杨-米尔斯（SYM）理论，将EEC计算至次-次-领头阶（NNLO），结果由调和多重对数函数（HPLs）和一个含椭圆曲线的二重积分表示。本研究报告了包含剩余椭圆部分的完整结果，该部分与日出费曼积分密切相关。我们发现，在莫比乌斯映射下，EEC与日出积分的$\boldsymbol{j}$不变量完全一致，因此EEC中的椭圆部分位于日出积分的$\boldsymbol{\textit{Γ}_1(6)}$模曲线上。随后，我们将结果表示为迭代艾森斯坦积分，该积分可快速计算至高精度。此解析形式还支持对EEC朗道自举的首次研究，且对$\boldsymbol{\textit{N}=4}$ SYM中函数空间的理解，为量子色动力学（QCD）中EEC的椭圆部分提供了具体处理手段。本文多项技术成果是在人类监督下借助AI完成的。
英文摘要
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 $\mathcal{N}=4$ 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 $\mathcal{N}=4$ 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.
发表机构
- Harvard University（哈佛大学）
- Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。
