Three Point Energy Correlators in the Collinear Limit: Symmetries, Dualities and Analytic Results

TL;DR

This paper analytically computes the three-point energy correlator in the collinear limit for QCD and $ abla$4 super Yang-Mills, revealing symmetries, dualities, and providing the first such analytic results relevant for LHC jet substructure analysis.

Contribution

It introduces a novel analytic calculation of the three-point energy correlator in the collinear limit, uncovering dualities and simplifying the understanding of jet substructure.

Findings

First analytic calculation of a three-prong jet observable.

Discovery of a duality linking correlator integrals to Feynman parameter integrals.

Expression of results as sums of simple Feynman integrals in $ abla$4 theory.

Abstract

Energy Correlators measure the energy deposited in multiple detectors as a function of the angles between the detectors. In this paper, we analytically compute the three particle correlator in the collinear limit in QCD for quark and gluon jets, and also in $\mathcal{N}=4$ super Yang-Mills theory. We find an intriguing duality between the integrals for the energy correlators and infrared finite Feynman parameter integrals, which maps the angles of the correlators to dual momentum variables. In $\mathcal{N}=4$, we use this duality to express our result as a rational sum of simple Feynman integrals (triangles and boxes). In QCD our result is expressed as a sum of the same transcendental functions, but with more complicated rational functions of cross ratio variables as coefficients. Our results represent the first analytic calculation of a three-prong jet substructure observable of phenomenological relevance for the LHC, revealing unexplored simplicity in the energy flow of QCD jets. They also provide valuable data for improving the understanding of the light-ray operator product expansion.