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

Abstract

We give a factorization formula for the e[superscript +]e[superscript -] thrust distribution dσ/dτ with τ=1-T based on the soft-collinear effective theory. The result is applicable for all τ, i.e. in the peak, tail, and far-tail regions. The formula includes O(α[subscript s][superscript 3]) fixed-order QCD results, resummation of singular partonic α[subscript s][superscript j]ln⁡[superscript k](τ)/τ terms with N[superscript 3]LL 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 Ω[subscript 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 α[subscript s](m[subscript Z]) and the first moment Ω[subscript 1] suffices. We use a short-distance scheme to define Ω1, called the R-gap scheme, thus ensuring that the perturbative dσ/dτ does not suffer from an O(Λ[subscript QCD]) renormalon ambiguity. We find α[subscript s](m[subscript Z])=0.1135±(0.0002)[subscript expt]±(0.0005)[subscript hadr]±(0.0009)[subscript pert], with χ2/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 αs is significantly decreased compared to earlier analyses by our two-parameter fit, which determines Ω[subscript 1]=0.323 GeV with 16% uncertainty.