Energy Correlators from Star Integrals via Mellin Space

TL;DR

This paper develops a Mellin space approach to express N-point energy correlators in super-Yang-Mills theory as operators acting on star integrals, enabling systematic analysis of their structure.

Contribution

It introduces a Mellin space representation for energy correlators, relating them to star integrals and providing explicit forms for three- and four-point cases.

Findings

Three-point correlator related to massive box integral.

Four-point correlator expressed as sum of box and hexagon integrals.

Systematic method to connect higher-point correlators to known star integrals.

Abstract

We explore the Mellin space representation for the collinear limit of $N$-point energy correlators in ${\cal N}=4$ super-Yang-Mills theory. We show that these correlators can be written as integro-differential operators acting on star integrals: one-loop $n$-gons in $n$ dimensions. For the three-point energy correlator, we obtain the Mellin representation, use it to relate the correlator to the massive box integral, and show how to solve this relation to match with the expected result. For the four-point energy correlator, we obtain the Mellin representation and use it to write the correlator to a sum of various box and hexagon integrals in special kinematics. Our results provide a systematic method to relate higher-point energy correlators in the collinear limit to star integrals, which are known exactly.