Thrust at N3LL with power corrections and a precision global fit for αs(mZ)

We give a factorization formula for the e(+)e-thrust distribution d sigma/d tau with tau = 1 - T based on the soft-collinear effective theory. The result is applicable for all tau, i.e. in the peak, tail, and far-tail regions. The formula includes O(alpha(3)(s)) fixed-order QCD results, resummation of singular partonic alpha(j)(s)ln(k)(tau)/tau terms with (NLL)-L-3 accuracy, hadronization effects from fitting a universal nonperturbative soft function defined with field theory, bottom quark mass effects, QED corrections, and the dominant top mass dependent terms from the axial anomaly. We do not rely on Monte Carlo generators to determine nonperturbative effects since they are not compatible with higher order perturbative analyses. Instead our treatment is based on fitting nonperturbative matrix elements in field theory, which are moments Omega(i) of a nonperturbative soft function. We present a global analysis of all available thrust data measured at center-of-mass energies Q = 35-207 GeV in the tail region, where a two-parameter fit to alpha(s)(m(Z)) and the first moment Omega(1) suffices. We use a short-distance scheme to define Omega(1), called the R-gap scheme, thus ensuring that the perturbative d sigma/d tau does not suffer from an O(Lambda(QCD)) renormalon ambiguity. We find alpha(s)(m(Z)) = 0.1135 +/- (0.0002)(expt) +/- (0.0005)(hadr) +/- (0.0009)(pert), with chi(2)/dof = 0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. The hadronization uncertainty in alpha(s) is significantly decreased compared to earlier analyses by our two-parameter fit, which determines Omega(1) = 0.323 GeV with 16% uncertainty.