Running Coupling Constant from Position-Space Current-Current Correlation Functions in Three-Flavor Lattice QCD
Salvatore Calì, Krzysztof Cichy, Piotr Korcyl, Jakob Simeth
Abstract
In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), ${\ensuremath{\alpha}}_{s}^{\overline{\mathrm{MS}}}(\ensuremath{\mu})$, for $\overline{\mathrm{MS}}$ renormalization scales $\ensuremath{\mu}\ensuremath{\in}(1,2)\text{ }\text{ }\mathrm{GeV}$. 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 $\mathrm{\ensuremath{\Lambda}}$ parameter and obtain ${\mathrm{\ensuremath{\Lambda}}}_{\overline{\mathrm{MS}}}^{{N}_{f}=3}=342\ifmmode\pm\else\textpm\fi{}17\text{ }\text{ }\mathrm{MeV}$, 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.