Precision thrust cumulant moments at N³LL

We consider cumulant moments (cumulants) of the thrust distribution using predictions of the full spectrum for thrust including O(α3s) fixed order results, resummation of singular N3LL logarithmic contributions, and a class of leading power corrections in a renormalon-free scheme. From a global fit to the first thrust moment we extract the strong coupling and the leading power correction matrix element Ω1. We obtain αs(mZ)=0.1140±(0.0004)exp±(0.0013)hadr±(0.0007)pert, where the 1-σ uncertainties are experimental, from hadronization (related to Ω1) and perturbative, respectively, and Ω1=0.377±(0.044)exp±(0.039)pert  GeV. The nth thrust cumulants for n≥2 are completely insensitive to Ω1, and therefore a good instrument for extracting information on higher order power corrections, Ω′n/Qn, from moment data. We find (Ω˜′2)1/2=0.74±(0.11)exp±(0.09)pert  GeV.