Wilson fermions quark bilinears to three loops

TL;DR

This paper advances the calculation of quark current renormalization constants in lattice QCD by employing Numerical Stochastic Perturbation Theory to reach three and four loops, improving precision and comparison with non-perturbative results.

Contribution

It introduces a method to compute higher-loop renormalization constants in lattice QCD using Numerical Stochastic Perturbation Theory, surpassing traditional computational limitations.

Findings

Achieved three and four loop calculations for quark bilinear renormalization constants.

Assessed convergence properties of the perturbative series.

Compared perturbative results with non-perturbative data where available.

Abstract

Quark currents renormalization constants can in principle be safely computed in lattice perturbation theory. In practice, traditional lattice perturbative computations are quite cumbersome, so that so far only the first loop results were available. By making use of Numerical Stochastic Perturbation Theory we reached three (and with less statistical precision even four) loops, both in quenched and in unquenched theory. Convergence properties of the series can be assessed and omparison with non perturbative results (where available) can be made: high loops computations of renormalization constants can be a valuable tool for lattice QCD.