2018 Impact factor 4.843
Particles and Fields
Eur. Phys. J. C 14, 557-584
DOI 10.1007/s100520000354

Consistent measurements of $\bf {\alpha_s}$
from precise oriented event shape distributions

The DELPHI Collaboration

P.Abreu22

22 LIP, IST, FCUL - Av. Elias Garcia, 14-1o, 1000 Lisboa Codex, Portugal

Received: 8 October 1999 / Revised version: 26 January 2000 /
Published online: 18 May 2000 - © Springer-Verlag 2000

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

\begin{eqnarray*}\small
{
\rm\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.)
\pm 0.0008 (scale) \pm 0.0007 (mass).
}
\end{eqnarray*}


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.


Copyright Società Italiana di Fisica, Springer-Verlag 2000