OPE and Powers corrections on the QCD coupling constant

Abstract

The running coupling constant can be estimated by computing gluon two- and three-point Green functions from the lattice. Computing in lattice implies working in a fixed gauge sector (Landau). An source of systematic uncertainty is then the contribution of non gauge-invariant condensates, as $<A^2 >$, generating power corrections that might still be important at very high energies. We study the impact of this gluon condensate on the analysis of gluon propagator and vertex lattice data and on the estimate of $\Lambda_{\bar{\rm MS}}$. We finally try a qualitative description of this gluon condensate through the instanton picture