Determining fundamental parameters of QCD on the lattice

The natural choice for the fundamental parameters of QCD are the renormalization group invariant (RGI) quark masses, Mi, i = u, d, ..., and the Λ-parameter. The RGI masses do not depend on a renormalization scheme and the scheme dependence of the Λ-parameter is exactly given by a one-loop coefficient. These quantities are in principle free of perturbative uncertainties. Their determination from low energy hadron data is a relevant mission for lattice QCD. Before entering details, we discuss a few aspects of more conventional determinations of α (and Λ). One considers experimental observables Oi depending on an overall energy scale q and possibly some additional kinematical variables denoted by y. The observables can be computed in a perturbative series which is usually written in terms of the MS coupling αMS = ḡ 2 MS /4π, 2 (μ = q)