Consistent Measurements of alpha_s from Precise Oriented Event Shape Distributions

TL;DR

This paper presents a precise measurement of the strong coupling constant alpha_s at the Z boson mass scale using event shape distributions from DELPHI data, incorporating various theoretical approaches and detailed uncertainty analysis.

Contribution

It provides a comprehensive analysis of alpha_s using multiple event shape observables and theoretical models, including next-to-leading log approximation and Padé approximants, with a focus on consistency and uncertainty reduction.

Findings

Measured alpha_s(M_Z^2) = 0.1180 ± 0.0016 combining experimental, hadronic, scale, and mass uncertainties.

Achieved excellent agreement between different theoretical approaches for alpha_s determination.

Demonstrated the effectiveness of using oriented event shape distributions for precise alpha_s measurements.

Abstract

An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is $\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.) \pm 0.0008 (scale) \pm 0.0007 (mass)$. Further studies include an $\alpha_s$ determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and $\cal O(\alpha_s^2$) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Pad\'{e} approximants. Average $\alpha_s$ values derived from the different approaches are in good agreement.