# Energy-energy correlations at next-to-next-to-leading order

## TL;DR

This paper presents a novel approach to calculating energy-energy correlations in $ ext{N}=4$ super Yang-Mills theory at NNLO, avoiding infrared divergences and revealing connections to elliptic functions.

## Contribution

It introduces a simple formula relating EEC to a triple discontinuity of a four-point correlation function, enabling straightforward numerical evaluation at NNLO.

## Key findings

- Derived a new formula for EEC in $ ext{N}=4$ sYM
- Computed EEC at NNLO using a two-fold integral representation
- Identified elliptic functions in the integral kernels

## Abstract

We develop further an approach to computing energy-energy correlations (EEC) directly from finite correlation functions. In this way, one completely avoids infrared divergences. In maximally supersymmetric Yang-Mills theory ($\mathcal{N}=4$ sYM), we derive a new, extremely simple formula relating the EEC to a triple discontinuity of a four-point correlation function. We use this formula to compute the EEC in $\mathcal{N}=4$ sYM at next-to-next-to-leading order in perturbation theory. Our result is given by a two-fold integral representation that is straightforwardly evaluated numerically. We find that some of the integration kernels are equivalent to those appearing in sunrise Feynman integrals, which evaluate to elliptic functions. Finally, we use the new formula to provide the expansion of the EEC in the back-to-back and collinear limits.