Ghost-gluon running coupling, power corrections, and the determination of Λ MS ¯

We compute a formula including operator-product expansion power corrections to describe the running of a QCD coupling nonperturbatively defined through the ghost and gluon dressing functions. This turns out to be rather accurate. We propose the ``plateau'' procedure to compute ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$ from the lattice computation of the running coupling constant. We show a good agreement between the different methods which have been used to estimate ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}^{{N}_{f}=0}$. We argue that ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}$ or the strong coupling constant computed with different lattice spacings may be used to estimate the lattice spacing ratio.