Differential Equations for Energy Correlators in Any Angle

2025/06/01 by Rourou Ma, Ma, Rourou, Jianyu Gong +9 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Numerical methods for differential equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2506.02061

openalex publication_date 2025/06/01 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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 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.

Citations

• Performing integration-by-parts reductions using NeatIBP 1.1 + Kira
• From squared amplitudes to energy correlators
• Recursive Landau Analysis
• NNLL Resummation for Projected Three-Point Energy Correlator
• NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals
• pfd-parallel, a Singular/GPI-Space package for massively parallel multivariate partial fractioning
• Conformal collider physics: energy and charge correlations
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Degenerate Systems and Mass Singularities

Cited by

• Memory Correlators and Ward Identities in the 'in-in' Formalism
• Toward the Analytic Bootstrap of Energy Correlators

Related

• Energy-Energy Correlators at Strong Coupling
• The Collinear Limit of the Four-Point Energy Correlator in N = 4 Super Yang-Mills Theory
• From squared amplitudes to energy correlators
• Toward the Analytic Bootstrap of Energy Correlators
• Leading singularities and chambers of Correlahedron