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arXiv · 2506.02061

Differential Equations for Energy Correlators in Any Angle

Rourou Ma·Jianyu Gong·Jingwen Lin·Kai Yan·Gang Yang·Yang Zhang
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Abstract

Energy Correlators (EC) are the simplest IR finite observables, which connect theories and experiments. In this paper, we provide a systematic algorithm to calculate the canonical differential equations for energy correlators at generic angle in $\mathcal{N}=4$ super Yang-Mills theory. The integrand is obtained from the 5-point form factor square for scalar half-BPS operators. Applying the algorithm, we obtain the canonical basis for three-point EC and the full set of master integrals for four-point EC. We analyze the function space for four-point case. For multiple polylogrithmic (MPLs) integrals, we calculate their symbols, and for integrals beyond MPLs, we make further investigation by Picard-Fuchs operators. We find two elliptic curves and one genus 2 hyperelliptic curve. The results are achieved by means of integration by part (IBP) reduction and differential equations powered by computational algebraic geometry methods. We provide a package that implements the algorithm. The data is a valuable reference for exploring the structure of physical observables in perturbation theories.

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Rourou Ma, Jianyu Gong, Jingwen Lin, Kai Yan, Gang Yang, Yang Zhang. 2025-06-01. Differential Equations for Energy Correlators in Any Angle. https://arxiv.org/abs/2506.02061

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