3 (and even 4) loops renormalization constants for Lattice QCD

We compute renormalization constants for Lattice QCD by means of Numerical Stochastic Perturbation Theory. As an example we discuss Wilson quark bilinears and in particular the “gold plated” case of Zp/Zs for which we can evaluate the perturbative series up to four loops. By making use of the knowledge of anomalous dimension up to 3 loops in the RI'-MOM scheme, the generic bilinears ca be computed to the same (3rd) order. Finite volume effects are carefully assessed and the continuum limit of the computation is taken in a clean way. The convergence properties of the series can be assessed and a comparison with non-perturbative evaluations of the same quantities can be done. In the end, Lattice Perturbation Theory to high loops is a valuable tool to evaluate renormalization constants for lattice QCD with a very high precision.