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

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.

44 pages + 4 appendices, 3 figures; v2: version published in JHEP

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• A Precise Determination of ${\alpha }_s$ from the Heavy Jet Mass Distribution
• Renormalon effect of quasi-PDF in gradient flow formalism
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