Determination of $\alpha_{S}$ beyond $NNLO$ using the event shape averages

TL;DR

This paper presents a method to determine the strong coupling constant  at N;LO precision using event shape data from multiple colliders, highlighting the limitations imposed by hadronization modeling on improving accuracy.

Contribution

The paper introduces a prescription combining  calculations up to N;LO with data-driven estimates of higher-order corrections for  extraction.

Findings

Higher-order pQCD alone cannot significantly improve  precision.

Hadronization modeling remains a major source of uncertainty.

Further progress requires advances in hadronization understanding.

Abstract

In this proceedings we discuss a prescription to extract the QCD strong coupling constant at $N^{3}LO$ precision in perturbative QCD using a combination of ${\cal{O}}(\alpha_{S}^{3})$ calculations in pQCD and estimations of the ${\cal{O}}(\alpha_{S}^{4})$ corrections from the data. The method is applied to a set of event shape averages measured in experiments at the LEP, PETRA, PEP and TRISTAN colliders. In our analysis we account for hadronization effects with models from modern Monte Carlo event generators and analytic hadronization models. We conclude that the precision of the $\alpha_{S}$ extraction cannot be improved significantly only with pQCD predictions of higher orders, and further progress in these studies requires a significant advances in the studies and modeling of hadronization process.