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Main Authors: Ma, Rourou, Gong, Jianyu, Lin, Jingwen, Yan, Kai, Yang, Gang, Zhang, Yang
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2506.02061
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author Ma, Rourou
Gong, Jianyu
Lin, Jingwen
Yan, Kai
Yang, Gang
Zhang, Yang
author_facet Ma, Rourou
Gong, Jianyu
Lin, Jingwen
Yan, Kai
Yang, Gang
Zhang, Yang
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_02061
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Differential Equations for Energy Correlators in Any Angle
Ma, Rourou
Gong, Jianyu
Lin, Jingwen
Yan, Kai
Yang, Gang
Zhang, Yang
High Energy Physics - Phenomenology
High Energy Physics - Theory
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.
title Differential Equations for Energy Correlators in Any Angle
topic High Energy Physics - Phenomenology
High Energy Physics - Theory
url https://arxiv.org/abs/2506.02061