Scaling rule for nonperturbative radiation in a class of event shapes

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.