We report on an estimate of alpha_s, renormalised in the MSbar scheme at the tau and Z^0 mass scales, by means of lattice QCD. Our major improvement compared to previous lattice calculations is that, for the first time, no perturbative treatment at the charm threshold has been required since we have used statistical samples of gluon fields built by incorporating the vacuum polarisation effects of u/d, s and c sea quarks. Extracting alpha_s in the Taylor scheme from the lattice measurement of the ghost-ghost-gluon vertex, we obtain alpha_s^{MSbar}(m^2_Z)=0.1200(14) and alpha_s^{MSbar}(m^2_tau)=0.339(13).
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