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 $\mathcal{O}({\alpha }_s^3)$ fixed-order QCD results, resummation of singular partonic ${\alpha }_s^j{ln}^k(\tau )/\tau$ terms with ${\mathrm{N}}^3\mathrm{LL}$ 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 ${\Omega }_i$ of a nonperturbative soft function. We present a global analysis of all available thrust data measured at center-of-mass energies $Q=35–207\mathrm{GeV}$ 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 $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ renormalon ambiguity. We find ${\alpha }_s(m_Z)=0.1135\pm (0.0002{)}_{\mathrm{expt}}\pm (0.0005{)}_{\mathrm{hadr}}\pm (0.0009{)}_{\mathrm{pert}}$, with ${\chi }^2/\mathrm{dof}=0.91$, 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 ${\Omega }_1=0.323\mathrm{GeV}$ with 16% uncertainty.

Close

PrevNext

View figure in article

• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
•