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.

Precision QCD at FCC-ee

“…Similar remarks apply to analytic calculations: how precisely hadronization corrections are modeled and constrained through different orders in resummed perturbation theory is currently a very active field, in particular with respect to the three-jet limit see e.g. [6][7][8][9], and might turn out to be equally inspired by event generators or used vice-versa.…”