Precision Determination of $\alpha_s$ from Lattice QCD

Abstract

We present an overview of the recent lattice determination of the QCD coupling $\alpha_s$ by the ALPHA Collaboration. The computation is based on the non-perturbative determination of the $\Lambda$-parameter of $N_{\rm f}=3$ QCD, and the perturbative matching of the $N_{\rm f}=3$ and $N_{\rm f}=5$ theories. The final result: $\alpha_s(m_Z)=0.11852(84)$, reaches sub-percent accuracy.