Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory

TL;DR

This work analyzes two-jet event shapes in e+e− annihilation, showing that their near-two-jet distributions factorize into perturbative resummations convolved with nonperturbative shape functions defined by momentum-flow correlations with lightlike Wilson lines. It proves that leading 1/Q corrections to mean event shapes are universal due to boost invariance of the soft sector and demonstrates how angularities reveal multi-operator energy-flow correlations, using both conventional QCD factorization and soft-collinear effective theory (SCET) with careful double-counting eliminations (zero-bin/eikonal subtractions). The authors introduce a momentum-flow operator formalism to connect shape functions to energy flow and derive explicit universality coefficients for C-parameter and angularities, highlighting how cumulants of energy flow encode nonperturbative dynamics. The results provide a framework to extract hadronization information from data and to test the underlying QCD dynamics governing event shapes, with practical implications for precision QCD studies and jet phenomenology.

Abstract

The distributions of two-jet event shapes contain information on hadronization in QCD. Near the two-jet limit, these distributions can be described by convolutions of nonperturbative event shape functions with the same distributions calculated in resummed perturbation theory. The shape functions, in turn, are determined by correlations of momentum flow operators with each other and with light-like Wilson lines, which describe the coupling of soft, wide-angle radiation to jets. We observe that leading power corrections to the mean values of event shapes are determined by the correlation of a single momentum flow operator with the relevant Wilson lines. This generalizes arguments for the universality of leading power corrections based on the low-scale behavior of the running coupling or resummation. We also show how a study of the angularity event shapes can provide information on correlations involving multiple momentum flow operators, giving a window to the system of QCD dynamics that underlies the variety of event shape functions. In deriving these results, we review, develop and compare factorization techniques in conventional perturbative QCD and soft-collinear effective theory (SCET). We give special emphasis to the elimination of double counting of momentum regions in these two formalisms.