Consistent measurements of \(\alpha_s\) from precise oriented event shape distributions

Abstract

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 \(\rm \alpha_s(M_Z^2) = 0.1174 \pm 0.0026 \). The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is

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 Padé approximants. Average \(\alpha_s\) values derived from the different approaches are in good agreement.