High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n_f=4 Wilson fermions

Abstract

This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main point of interest are results for the regularization defined by Iwasaki gauge action and n_f=4 Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for Twisted Mass QCD: being defined in the chiral limit, renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of Boosted Perturbation Theory and the disentanglement of irrelevant and finite volume contributions. Discussing these issues we consider ont only the new results of this paper, but also those for the regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions, which we presented in a recent paper of ours. We finally comment to which extent the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme.