Ghost-gluon running coupling, power corrections and the determination of ${\Lambda }_{\overline{\mathrm{MS}}}$

Abstract

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