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 $\mathrm{\Lambda }$ 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 ${\alpha }^{\text{MSB}}(M_Z)=0.115\pm 0.003\pm 0.008$.