Fits of $\alpha_s$ from event-shapes in the three-jet region: extension to all energies

TL;DR

This paper extends previous analyses by fitting the strong coupling constant $oldsymbol{ ext{α}_s}$ using event-shape data across a wide energy range, improving the understanding of perturbative and non-perturbative effects in three-jet regions.

Contribution

It introduces a comprehensive fit of $oldsymbol{ ext{α}_s}$ incorporating data from multiple energies and revises the treatment of theoretical uncertainties, enhancing the precision of $oldsymbol{ ext{α}_s}$ determination.

Findings

Best fit $oldsymbol{ ext{α}_s(M_Z)}=0.1181$ with detailed uncertainties.

Including multiple energies helps disentangle perturbative and non-perturbative effects.

The fit confirms consistency with previous measurements of $oldsymbol{ ext{α}_s}$.

Abstract

This work is an extension of a previous publication [1] where we fitted the strong coupling $\alpha_s$ together with the non-perturbative parameter $\alpha_0$ from event-shape and jet-shape distributions using power corrections computed in the three-jet region. In ref. [1] only ALEPH data at the $Z$-pole were used in the fit. Here, instead, we include a large data sample from various $e^+e^-$ experiments at energies ranging from 22 to 207 GeV and revisited the treatment of theoretical uncertainties. We find that the inclusion of different energies, while not changing the central fit result considerably, helps to disentangle the dependence of perturbative and non-perturbative corrections. Our best fit result is $\alpha_s(M_Z) = 0.1181 (+0.0002 -0.0005) (+0.0018 -0.0021)$, where the first error includes experimental uncertianties and the second one includes uncertainties associated with scale variation, mass effects, fit limits, non-perturbative schemes and non-perturbative uncertainties.