Power Corrections to Event Shapes with Mass-Dependent Operators

TL;DR

This paper introduces a new operator dependent on transverse velocity to describe hadron mass effects on event-shape power corrections, revealing universality classes and nonperturbative parameters influencing these corrections.

Contribution

It develops a mass-dependent operator framework and identifies universality classes for event-shape power corrections, with a method to determine many corrections from two nonperturbative parameters.

Findings

Power corrections depend on a transverse velocity operator.

Universality classes link event shapes with common nonperturbative parameters.

Models in Pythia 8 and Herwig++ reproduce the universality and anomalous dimension effects.

Abstract

We introduce an operator depending on the "transverse velocity" r that describes the effect of hadron masses on the leading 1/Q power correction to event-shape observables. Here, Q is the scale of the hard collision. This work builds on earlier studies of mass effects by Salam and Wicke and of operators by Lee and Sterman. Despite the fact that different event shapes have different hadron mass dependence, we provide a simple method to identify universality classes of event shapes whose power corrections depend on a common nonperturbative parameter. We also develop an operator basis to show that at a fixed value of Q, the power corrections for many classic observables can be determined by two independent nonperturbative matrix elements at the 10% level. We compute the anomalous dimension of the transverse velocity operator, which is multiplicative in r and causes the power correction to exhibit non-trivial dependence on Q. The existence of universality classes and the relevance of anomalous dimensions are reproduced by the hadronization models in Pythia 8 and Herwig++, though the two programs differ in the values of their low-energy matrix elements.