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

TL;DR

This paper computes high-order perturbative renormalization constants for Wilson fermions in Lattice QCD using Numerical Stochastic Perturbation Theory, demonstrating the feasibility of high-loop calculations and analyzing their uncertainties.

Contribution

It provides the first high-loop (up to four loops) perturbative results for renormalization constants in Lattice QCD with Wilson quarks, including finite size effects and convergence analysis.

Findings

High-loop renormalization constants are computationally feasible.

Results include three- and four-loop expansions for various flavors.

Uncertainties are mainly from truncation errors, assessed via Boosted Perturbation Theory.

Abstract

We present a high order perturbative computation of the renormalization constants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The computational setup is the one provided by the RI'-MOM scheme. Three- and 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 n_f up to three loops. For the case n_f=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 n_f up to three loops, while a four-loop result is obtained for n_f=2.