Characterising hadronisation across the phase space

TL;DR

This paper refines the understanding of non-perturbative hadronisation corrections in two-jet event shapes by including effects of multiple soft gluon emissions, improving accuracy across different phase space regions.

Contribution

It introduces a comprehensive method to account for additional soft wide-angle gluon emissions in hadronisation corrections, extending previous two-parton approximations.

Findings

Identifies missing correction from soft wide-angle gluon emissions.

Provides a unified treatment valid for both two-jet and three-jet regions.

Enhances the precision of non-perturbative shift calculations.

Abstract

Leading hadronisation corrections to two-jet global event shapes amount to a shift in the corresponding perturbative distributions. It has been recently established that this shift depends significantly on the value of the considered event shape. These analyses consider perturbative configurations with only three partons emitting an ultra-soft non-perturbative gluon. These are dominant in the three-jet region. However, multiple soft and/or collinear emissions need to be considered to accurately describe event shape distributions near their Sudakov peak. In this region, non-perturbative shifts are usually computed by considering only two hard emitters. In this paper, we find that this approximation misses an important correction to the shift due to the emission of an additional soft wide-angle gluon. We then compute its contribution, and embed it in a general treatment for the shift that is valid in both the two-jet and three-jet regions.