Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions

TL;DR

This paper uses soft-collinear effective theory to predict angularity distributions in electron-positron annihilation, incorporating resummation and nonperturbative effects, advancing the understanding of jet substructure in QCD.

Contribution

It provides the first NLO calculations of jet and soft functions for all angularities with a<1 and demonstrates the effective theory's advantages over previous methods.

Findings

Calculated angularity distributions for all a<1 at NLL accuracy.

Presented NLO jet and soft functions for the first time.

Explored the breakdown of factorization as a approaches 1.

Abstract

Using soft-collinear effective theory (SCET), which provides a unified framework for factorization, resummation of logarithms, and incorporation of universal nonperturbative functions in hard-scattering QCD cross-sections, we present a new prediction of angularity distributions in e+e- annihilation. Angularities tau_a are an infinite class of event shapes which vary in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter a<2. We calculate angularity distributions for all a<1 to first order in the strong coupling alpha_s and resum large logarithms in these distributions to next-to-leading logarithmic (NLL) accuracy. Our expressions for the next-to-leading order (NLO) O(alpha_s) partonic jet and soft functions in the factorization theorem for angularity distributions are given for the first time. We employ a model for the nonperturbative soft function with a gap parameter which cancels the renormalon ambiguity in the partonic soft function. We explore the relation between the SCET approach to resummation and past approaches in QCD, and discuss the advantages of the effective theory approach. In addition, we draw from the NLO calculations of the jet and soft functions an intuitive lesson about how factorization breaks down in the effective theory as a->1.