Eur. Phys. J. C (2007) 51: 645-657
https://doi.org/10.1140/epjc/s10052-007-0319-2

Regular Article - Theoretical Physics

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

¹ Dipartimento di Fisica, Università di Parma and INFN, Gruppo Collegato di Parma, viale G.P. Usberti 7/a, 43100, Parma, Italy
² Sezione di Milano Bicocca, I.N.F.N., Piazza della Scienza 3, 20126, Milano, Italy
³ Faculty of Physics, University of Bielefeld, Universitätsstr., 33615, Bielefeld, Germany
⁴ ECT*, Villazzano, strada delle tabarelle 286, 38100, Trento, Italy

^* e-mail: scorzato@ect.it

Received: 25 April 2007
Published online: 6 June 2007

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 flavors 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 the 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 renormalization constants (RCs) are feasible and should not be viewed as a second choice. As a by-product, we discuss the perturbative expansion for the critical mass, for which results are also for generic n_f up to three loops, while a four-loop result is obtained for n_f=2.