Ichep'98 #142 Consistent Measurements of S from Precise Oriented Event Shape Distributions Preliminary Delphi Collaboration

An updated analysis using about 1.5 million events recorded with the DELPHI detector in 1994 is presented. A number of IR-and collinear-safe event shape ob-servables are measured as a function of the polar angle of the thrust axis with respect to the e + e ? beam direction. The data are compared to theoretical calculations in O(2 s) including the event orientation. A combined t of s and of the renormalisation scale in O(2 s) yields an excellent description of the high statistics data. Agreement with the data requires a rather narrow selection of the values of the renormalisation scale for each observable. For these experimentally optimized scale values perfect consistency of the t values of s (M Z) is obtained for all event shape observables considered. A weighted average, taking into account correlations between the observables yields an uncertainty s (M 2 Z) = 0:0025. Taking also account of heavy quark mass eeects our preliminary result is s (M 2 Z) = 0:117 0:003. Further studies include an s determination using theoretical predictions in the next to leading log approximation (NLLA), matched NLLA and O(2 s) predictions as well as theoretically motivated optimized scale setting methods. The innuence of higher order contributions was also investigated by using the method of Pad e approximants for the estimation of the uncalculated O(3 s) contributions.