Determination of the Strong Coupling Constant by the ALPHA Collaboration

A high precision determination of the strong coupling constant in the MS scheme at the Z-mass scale, using low energy quantities, namely pion/kaon decay constants and masses, as experimental input is presented. The computation employs two different massless finite volume renormalization schemes to non-perturbatively trace the scale dependence of the respective running couplings from a scale of about 200 MeV to 100 GeV. At the largest energies perturbation theory is reliable. At high energies the Schrödinger-Functional scheme is used, while the running at low and intermediate energies is computed in a novel renormalization scheme based on an improved gradient flow. Large volume N_f = 2 + 1 QCD simulations by CLS are used to set the overall scale. The result is compared to world averages by FLAG and the PDG.