Consistent Measurements of alpha_s from Precise Oriented Event Shape Distributions

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 $\mathcal{O}({\alpha }_s^2)$ including the event orientation. A combined fit of ${\alpha }_s$ and of the renormalization scale $x_{\mu }$ in $\mathcal{O}({\alpha }_s^2$) 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 $\mathcal{O}({\alpha }_s^2$) 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.

48 pages

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