Energy-energy correlation in N=4 super Yang-Mills theory at next-to-next-to-leading order

J M Henn,E Sokatchev,A Zhiboedov,K Yan

doi:10.1103/physrevd.100.036010

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.

Highlights

The energy-energy correlation (EEC) [1] measures the energy flow through a pair of detectors separated by an angle χ; see Fig. 1
We develop further an approach to computing energy-energy correlations (EEC) directly from finite correlation functions
We show that for an analog of the electromagnetic current in N 1⁄4 4 super Yang-Mills (sYM), the EEC is computed by a new, extremely simple formula, given by a twofold integral of a particular triple discontinuity of the four-point correlation function; see Eq (7) below

Summary

INTRODUCTION

The energy-energy correlation (EEC) [1] measures the energy flow through a pair of detectors separated by an angle χ; see Fig. 1. These ideas were applied in N 1⁄4 4 super Yang-Mills (sYM) [30,31,32], culminating in the first analytic calculation of and EEC at NLO [33]. The structure of this result, and in particular the types of polylogarithmic functions appearing in it, foreshadowed the structures later found in QCD [24]. We show that for an analog of the electromagnetic current in N 1⁄4 4 sYM, the EEC is computed by a new, extremely simple formula, given by a twofold integral of a particular triple discontinuity of the four-point correlation function; see Eq (7) below. We use the integral formula (7) in order to obtain limits of the energy correlator, namely the small angle and the back-to-back limits

EEC FROM CORRELATION FUNCTIONS

EEC AT LO

EEC AT NLO AND NNLO

BACK-TO-BACK AND COLLINEAR EXPANSION

DISCUSSION AND OUTLOOK