Ghost-gluon running coupling, power corrections and the determination of $\Lambda_{\bar {\rm MS}}$

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 $\Lambda_{\bar{\rm MS}}$ from the lattice computation of the running coupling constant. We show a good agreement between the different methods which have been used to estimate $\Lambda_{\bar{\rm MS}}^{N_f=0}$. We argue that $\Lambda_{\bar{\rm MS}}$ or the strong coupling constant computed with different lattice spacings may be used to estimate the lattice spacing ratio.