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From soft-collinear effective theory one can derive a factorization formula for the e + e − thrust distribution dσ/dτ with τ = 1 − T that is applicable for all τ. The formula accommodates available O(α 3 s ) fixed-order QCD results, resummation of logarithms at N 3 LL order, a universal nonperturbative soft function for hadronization effects, factoriza tion of nonperturbative effects in subleading power contributions, bottom mass effects and QED corrections. We emphasize that the use of Monte Carlos to estimate hadronization effects is not compatible with high-precision, high-order analyses. We present a global analysis of all available e + e − thrust data measured at Q = 35 to 207 GeV in the tail region, where a two-parameter fit can be car ried out for αs(mZ) and Ω1, the first moment of the soft function. To obtain small theoretica l errors it is essential to define Ω1 in a short-distance scheme, called the R-gap scheme, free of an O(ΛQCD) renormalon ambiguity. We find αs(mZ) = 0.1135 ± (0.0002)expt ± (0.0005)Ω1 ± (0.0009)pert with χ 2 /dof = 0.9.

Thrust distribution at N^3LL with power corrections and precision determination of alpha_s