High-loop perturbative renormalization constants for Lattice QCD (I): finite constants for Wilson quark currents

We present a high order perturbative computation of the renormalization constants ZV , ZA and of the ratio ZP/ZS for Wilson fermions. The computational setup is the one provided by the RI’-MOM scheme. Threeand four-loop expansions are made possible by Numerical Stochastic Perturbation Theory. Results are given for various numbers of flavours and/or (within a finite accuracy) for generic nf up to three loops. For the case nf = 2 we also present four-loop results. Finite size effects are well under control and the continuum limit is taken by means of hypercubic symmetric Taylor expansions. The main indetermination comes from truncation errors, which should be assessed in connection with convergence properties of the series. The latter is best discussed in the framework of Boosted Perturbation Theory, whose impact we try to assess carefully. Final results and their uncertainties show that high-loop perturbative computations of Lattice QCD RC’s are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, also for which results are for generic nf up to three loops, while a four-loop result is obtained for nf = 2.