State-of-the-Art Predictions for C-parameter and a Determination of α_s

Abstract

The C-parameter event-shape distribution for $e^{+}{e}^{-}$ annihilation into hadrons is computed in the framework of SCET including input from fixed-order perturbation theory. We calculate all missing ingredients for achieving N³LL resummation accuracy in the cross section, which is then matched onto $O({\alpha }_s^3)$ fixed-order results. Hadronization power corrections are incorporated as a convolution with a nonperturbative shape function. Wide-angle soft radiation effects introduce an $O({\mathrm{\Lambda }}_{QCD})$ renormalon ambiguity in the cross section, which we cure by switching to the Rgap short-distance scheme. We also include hadron mass effects, but find their effect is rather small. Performing fits to the tail of the C-parameter distribution for many center of mass energies we find that the strong coupling constant is ${\alpha }_s(m_Z)=0.1121\pm 0.0015$, with ${\chi }^2/\mathrm{dof}=0.99$.