We use lattice QCD simulations, with MILC configurations (including vacuum polarization from $u$, $d$, and $s$ quarks), to update our previous determinations of the QCD coupling constant. Our new analysis uses results from 6 different lattice spacings and 12 different combinations of sea-quark masses to significantly reduce our previous errors. We also correct for finite-lattice-spacing errors in the scale setting, and for nonperturbative chiral corrections to the 22 short-distance quantities from which we extract the coupling. Our final result is ${\alpha }_V(7.5\mathrm{GeV},n_f=3)=0.2120(28)$, which is equivalent to ${\alpha }_{\overline{\mathrm{MS}}}(M_Z,n_f=5)=0.1183(8)$. We compare this with our previous result from Wilson loops, which differs by one standard deviation.

• Received 15 September 2008

DOI:https://doi.org/10.1103/PhysRevD.78.114507