Next-to-leading power corrections to the event shape variables

TL;DR

This paper analyzes the origin of next-to-leading power corrections in event shape variables thrust and c-parameter at NLO, comparing exact calculations with approximation methods to understand their differences.

Contribution

It provides a detailed comparison between exact NLO calculations and eikonal approximation methods for power corrections in event shapes.

Findings

Exact and approximate results expressed with elliptic integrals.

Near elastic limit, c-parameter shows patterns similar to thrust.

Differences between methods are assessed both analytically and numerically.

Abstract

We investigate the origin of next-to-leading power corrections to the event shapes thrust and $c$-parameter, at next-to-leading order. For both event shapes we trace the origin of such terms in the exact calculation, and compare with a recent approach involving the eikonal approximation and momentum shifts that follow from the Low-Burnett-Kroll-Del Duca theorem. We assess the differences both analytically and numerically. For the $c$-parameter both exact and approximate results are expressed in terms of elliptic integrals, but near the elastic limit it exhibits patterns similar to the thrust results.