Renormalization in lattice QCD: Some three-loop results

We calculate the third coefficient of the lattice beta function in QCD with Wilson fermions, extending the pure gauge results of Luscher and Weisz; we show how this coefficient modifies the scaling function on the lattice. We also calculate the three-loop average plaquette in the presence of Wilso n fermions. This allows us to compute the lattice scaling function both in the standard and energy schemes. Finally, we show how to perform a resummation, to all orders in perturbatio n theory, of a certain class of gauge invariant diagrams in Lattice QCD. Th ese diagrams are often largely responsible for lattice artifacts. Our resum mation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corres ponding nonperturbative estimates.