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

Abstract

In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), ${\alpha }_s^{\overline{\mathrm{MS}}}(\mu )$, 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.

Matches version accepted for publication in Physical Review Letters. Extensive supplemental material added. Main manuscript: 6 pages, 4 figures. Supplemental material: 11 pages, 8 figures