Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD

In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), ${\alpha }_s^{\overline{\mathrm{M}\mathrm{S}}}(\mu )$, for $\overline{\mathrm{M}\mathrm{S}}$ renormalization scales $\mu \in (1,2)$ GeV. The computation uses gauge field configuration ensembles with $\mathcal{O}(a)$-improved Wilson-clover fermions generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach is based on current-current correlation functions and has never been applied before in this context. We convert the results perturbatively to the QCD $\mathrm{\Lambda }$-parameter and obtain $\Lambda_{\overline{$\mathrm{M}\mathrm{S}$}}^{N_f=3} = 342 \pm 17$ MeV, which agrees with the world average published by the Particle Data Group and has competing precision. The latter was made possible by a unique combination of state-of-the-art CLS ensembles with very fine lattice spacings, further reduction of discretization effects from a dedicated numerical stochastic perturbation theory simulation, combining data from vector and axial-vector channels and matching to high-order perturbation theory.