Global Fit of alpha_s(m_Z) to Thrust at NNNLL Order with Power Corrections

Abstract

From soft-collinear effective theory one can derive a factorization formula for the e+e- thrust distribution dsigma/dtau with tau = 1-T that is applicable for all tau. The formula accommodates available O(alpha_s^3) fixed-order QCD results, resummation of logarithms at NNNLL order, a universal nonperturbative soft function for hadronization effects, factorization 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 carried out for alpha_s(m_Z) and Omega_1, the first moment of the soft function. To obtain small theoretical errors it is essential to define Omega_1 in a short-distance scheme, free of an O(Lambda_QCD) renormalon ambiguity. We find alpha_s(m_Z) = 0.1135 +- (0.0002)_expt +- (0.0005)_Omega_1 +- (0.0009)_pert with chi^2/dof = 0.9.

Figures (3)

• Figure 1: (a) Ingredients for primed and unprimed orders used in our analysis. The numbers give the loop orders for the cusp and non-cusp anomalous dimensions, matching/matrix element contributions, the $\alpha_s$-running, the nonsingular distribution, the gap-anomalous dimensions, and the perturbative $R$-scheme subtractions $\delta$ for our scheme for $\Omega_1$. The 4-loop cusp anomalous dimension required at N${}^3$LL${}^\prime$ order is estimated from Padé approximants. The associated uncertainty is negligible. (b) Central values and theory uncertainties for the fits at the different orders with and without the gap and renormalon subtractions. html:<A name="ref-fig:orderserrors">html:</A> LAB: fig:orderserrors
• Figure 2: Plots of $\Omega_1$ vs $\alpha_s(m_Z)$. (a) Includes perturbation theory, resummation of the logs, the soft model function and $\Omega_1$ with renormalon subtractions at $\mu_R=2$ GeV. (b) As (a) but in a scheme $\bar{\Omega}_1$ without a gap, which gives perturbative results without the corresponding renormalon subtractions. The shaded regions indicate the theory errors at NLL${}^\prime$ (brown), NNLL (magenta), NNLL${}^\prime$ (green), N${}^3$LL (blue), N${}^3$LL${}^\prime$ (red). The dark red ellipses in (a) and (b) represent the $(\chi^2_{\rm min}+1$) error ellipses for the combined theoretical, experimental and hadronization uncertainties. The ellipse in (a) is displayed again in Fig. 3b. The best fit points at N${}^3$LL${}^\prime$ with gap and renormalon subtractions shown in red in (a) each have $\chi^2/{\rm dof}\simeq 0.90$. html:<A name="ref-fig:M1alphagap">html:</A> LAB: fig:M1alphagap
• Figure 3: (a) ($\chi^2_{\rm min}+1$)-ellipse for the central fit at N${}^3$LL${}^\prime$ order obtained from the experimental correlation matrix with default values for the theory scan parameters. (b) ($\chi^2_{\rm min}+1$)-ellipses of central fits for many different $\tau$-ranges in the tail region. The exponents display the number of data bins for each fit. The big red ellipse is the combined experimental and theoretical error ellipse that should be understood as 1-sigma for $\alpha_s(m_Z)$. html:<A name="ref-fig:ellipsedatasets">html:</A> LAB: fig:ellipsedatasets