The Strong Coupling Constant from the Lattice 3-Gluon Vertex

We compute the QCD running coupling on the lattice as defined from the 3-gluon vertex. We present the results of an exploratory study at $\beta=6.0$ on a $16^4$ lattice, which show that for momenta larger than 2 \Gev, the coupling runs according to the 2-loop asymptotic formula, allowing a precise determination of the $\Lambda$ parameter. Our renormalization procedure corresponds to a momentum subtraction scheme in the continuum and, most remarkably, one does not need lattice perturbation theory to match the results to MSbar scheme. We obtain $\alpha^{\MSB}(M_Z) = 0.115 \pm 0.003 \pm 0.008$.