Analytic Computation of Three-point Energy Correlator in QCD

TL;DR

This paper presents the first analytic formula for the three-point energy correlator in QCD at leading order, enabling detailed phenomenological analysis of three-jet events in electron-positron collisions.

Contribution

It provides the first analytic computation of the three-point energy correlator in QCD with full angular dependence at leading order, using direct integration and parameterizations.

Findings

Analytic formula for three-point energy correlator derived

Provides expansions in various kinematic regions

Facilitates studies on factorization and resummation

Abstract

The energy correlator measures the energy deposited in multiple detectors as a function of the angles among them. In this paper, an analytic formula is given for the three-point energy correlator with full angle dependence at leading order in electron-positron annihilation. This is the first analytic computation of trijet event shape observables in QCD, which provides valuable data for phenomenological studies. The result is computed with direct integration, where appropriate parameterizations of both phase space and kinematic space are adopted to simplify the calculation. With full shape dependence, our result provides the expansions in various kinematic regions such as equilateral, triple collinear and squeezed limits, which benefit studies on both factorization and large logarithm resummation.