Consistent Measurements of $\alpha_{s}$ from Precise Oriented Event Shape Distributions

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 0:0006(exp:) 0:0013(hadr:) 0:0008(scale) 0:0007(mass). Further studies include an s determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and O(\alpha^{2}_{s}) predictions as well as theoretically motivated optimized scale setting methods. The in uence of higher order contributions was also investigated by using the method of Pad e approximants. Average s values derived from the different approaches are in good agreement.