Accurate Determinations ofαsfrom Realistic Lattice QCD

We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to (1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations), (2) include third-order terms in perturbation theory, (3) systematically estimate fourth and higher-order terms, (4) use an unambiguous lattice spacing, and (5) use an $\mathcal{O}(a^2)$-accurate QCD action. We use 28 different (but related) short-distance quantities to obtain ${\alpha }_{\overline{\mathrm{MS}}}^{(5)}(M_Z)=0.1170(12)$.