CoLoRFulNNLO at work: A determination of $\alpha_S$

The most precise determination of fundamental parameters of the Standard Model is very important. One such fundamental parameter is the strong coupling of QCD. Its importance can be gauged by taking a look at the various experiments and configurations where it was measured, for an up to date summary see Ref. [1]. The precise measurement of such a parameter is two-fold difficult. First, high quality data with small and well-controlled uncertainties are needed. Second, high precision calculations are needed from the theory side such that theoretical uncertainties are small as well. In a theoretical prediction based on calculation in perturbation theory the uncertainty has two main sources: the omission of higher-order terms which are estimated by the renormalization scale and the numerical stability of the integrations. While the dependence on unphysical scales can be, in principle, decreased by including more and more higher-order contributions in the prediction the numerical uncertainty can be intrinsic to the method used to obtain the theoretical prediction. Beside this, the way of comparison of experiment with theory is also affected by another uncertainty. While an experiment measures color-singlet objects, hadrons, the predictions are made in QCD for colorful ones, partons. The assumption of local partonhadron duality ensures a correspondence between these two up to non-perturbative effects. Non-perturbative effects are power corrections in nature going with some negative power of the collision energy. This means that for an accurate comparison 1) either these effects should be estimated and taken into account 2) or the experiment should have a high enough energy that these contributions become negligible compared to other effects 3) or an observable has to be chosen which is not sensitive to these effects.