Scaling Rule for Nonperturbative Radiation in a Class of Event Shapes

TL;DR

The paper derives a scaling rule that links nonperturbative shape functions for a broad class of infrared-safe event shapes to the thrust shape function, grounded in NLL resummation and boosted by the eikonal interpretation of soft radiation. It separates perturbative and nonperturbative contributions below an infrared scale, yielding a simple 1/(1-a) dependence that leads to a renormalization-group-like scaling across the tau_a family. The authors test the scaling against PYTHIA, finding good agreement for moderate a and identifying potential scaling violations due to interjet correlations and coherence beyond NLL. The work provides a framework to study universality of nonperturbative corrections in jet physics and motivates data-driven checks with LEP-era measurements and future analyses.

Abstract

We discuss nonperturbative radiation for a recently introduced class of infrared safe event shape weights, which describe the narrow-jet limit. Starting from next-to-leading logarithmic (NLL) resummation, we derive an approximate scaling rule that relates the nonperturbative shape functions for these weights to the shape function for the thrust. We argue that the scaling reflects the boost invariance implicit in NLL resummation, and discuss its limitations. In the absence of data analysis for the new event shapes, we compare these predictions to the output of the event generator PYTHIA.