Non-perturbative decoupling of heavy quarks and the determination of alpha_s(m_Z)

The strong coupling is one of the fundamental parameters of the Standard Model and its precise determination from experiment is an important goal in itself.  A controlled error around half a percent would also greatly benefit phenomenology of Higgs physics and inform attempts at ultraviolet completions of the Standard Model. In this talk, I will first discuss how alpha_s can be determined from experimental input in principle, and why lattice QCD is in the best position to achieve high precision with controlled errors. In particular, the explicit inclusion of charm and bottom sea quarks in the numerical simulations is not necessary, as non-perturbative tests of matching across quark thresholds have shown the perturbative description to be very accurate, even for the charm quark. This prepares the ground for discussing the new decoupling method deployed by the ALPHA collaboration, whereby 3-flavour QCD is non-perturbatively matched to Yang-Mills theory, by the simultaneous decoupling of 3 fictitious, mass degenerate heavy quarks. This allows for essential parts of the simulations to be performed in Yang-Mills theory and to thus leverage the higher precision that can be achieved there. The recent result, alpha_s(m_Z) = 0.11823(84), has a 0.7 percent uncertainty which is still statistics dominated, and there appears to be a clear path to a further reduction of the error.