Accurate Determinations of ${\alpha }_s$ from Realistic Lattice QCD

Abstract

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 $\order(a^2)$-accurate QCD action. We use 28~different (but related) short-distance quantities to obtain ${\alpha }_{\overline{\mathrm{MS}}}^{(5)}(M_Z)=0.1170(12)$.

4 pages, 2 figures, 1 table. The revised version differs from the original because we now use 4-loop beta functions (rather than 3-loop). This shifts the answer a little (mostly from the evolution from the lattice scale to M_z -- lattice results aren't very different) and reduces the error slightly

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