Thrust at NNNLL with Power Corrections and a Precision Global Fit for alpha_s(m_Z)

We give a factorization formula for the e+e- thrust distribution dsigma/dtau with tau=1-T based on 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(alphas^3) fixed-order QCD results, resummation of singular partonic alphas^j ln^k(tau)/tau terms with N^3LL accuracy, hadronization effects from fitting a universal nonperturbative soft function defined in 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 to 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 dsigma/dtau does not suffer from an O(Lambda_QCD) renormalon ambiguity. We find alphas(mZ)=0.1135 \pm (0.0002)_{expt} \pm (0.0005)_{hadr} \pm (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 alphas is significantly decreased compared to earlier analyses by our two parameter fit, which determines Omega_1=0.323 GeV with 16% uncertainty