$a_S$ from the ALPHA collaboration (part I)

The recent determination of αs(mZ) =0.11852(84)by the ALPHA collaboration [1] distinguishes itself by the very good control of perturbative truncation and other systematic errors. A variety of tools and methods had to be deployed to enable this result. In this contribution I will give a short account of the step-scaling method and its application to QCD couplings in finite volume renormalization schemes. Tracing the running couplings non-perturbatively between scales μ0 and 32μ0(corresponding roughly to the range 4–128 GeV) leads to the intermediate result Λ(3)MS/μ0=0.0791(19)in 3-flavour QCD. By computing this ratio in variety of ways, using perturbation theory in different schemes and at different energy scales at intermediate stages, gives us confidence in the error estimate and also enables a number of useful tests of perturbation theory. The remaining steps required for αs(mZ)will be discussed by Mattia Dalla Brida in these proceedings [2].