Linear power corrections to $e^+e^-$ shape variables in the three-jet region

TL;DR

This paper investigates linear power corrections in the three-jet region of $e^+e^-$ annihilation, revealing differences from two-jet corrections and providing explicit formulas for key event shape variables within an abelian model.

Contribution

It extends the understanding of power corrections to the three-jet region, introducing a factorized form involving a universal factor and deriving explicit corrections for specific event shapes.

Findings

Power corrections differ between two-jet and three-jet regions.

A universal factor proportional to the Milan factor governs corrections.

Explicit formulas for $C$-parameter and thrust in N-jet regions are provided.

Abstract

We use an abelian model to study linear power corrections which arise from infrared renormalons and affect event shapes in $e^+e^-$ annihilation into hadrons. While previous studies explored power corrections in the two-jet region, in this paper we focus on the three-jet region, which is the most relevant one for the determination of the strong coupling constant. We show that for a broad class of shape variables, linear power corrections can be written in a factorised form, that involves an analytically-calculable function, that characterises changes in the shape variable when a soft parton is emitted, and a constant universal factor. This universal factor is proportional to the so-called Milan factor, introduced in earlier literature to describe linear power corrections in the two-jet region. We find that the power corrections in the two-jet and in the three-jet regions are different, a result which is bound to have important consequences for the determination of the strong coupling constant from event shapes. As a further illustration of the power of the approach developed in this paper, we provide explicit analytic expressions for the leading power corrections to the $C$-parameter and the thrust distributions in the $N$-jet region for arbitrary $N$, albeit in the abelian model.