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), $alpha^{overline{mathrm{MS}}}_s(mu)$, for $overline{mathrm{MS}}$ 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 $Lambda$-parameter and obtain $Lambda_{overline{mathrm{MS}}}^{N_f=3} = 342 pm 17$ 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.