Three-point energy correlator in $\mathcal{N}=4$ super Yang-Mills Theory

TL;DR

This paper presents the first analytic calculation of the three-point energy correlator in $ =4$ super Yang-Mills theory, revealing new mathematical structures and providing comprehensive data across all kinematic regions.

Contribution

It provides the first analytic formula for the three-point energy correlator in $ =4$ sYM, introducing new single-valued polylogarithms and exploring all kinematic limits.

Findings

New class of single-valued polylogarithms with 16-letter alphabet

Analytic formula valid in all kinematic regions including collinear and squeezed limits

Reveals symmetry properties of the event shape

Abstract

An analytic formula is given for the three-point energy correlator (EEEC) at leading order (LO) in maximally supersymmetric Yang-Mills theory ($\mathcal{N}=4$ sYM). This is the first analytic calculation of a three-parameter event shape observable, which provides valuable data for various studies ranging from conformal field theories to jet substructure. The associated class of functions define a new type of single-valued polylogarithms characterized by 16 alphabet letters, which manifest a $D_6 \times Z_2$ dihedral symmetry of the event shape. With the unexplored simplicity in the perturbative structure of EEEC, all kinematic regions including collinear, squeezed and coplanar limits are now available.