Renormalization constants of local operators for Wilson type improved fermions

TL;DR

This paper provides both perturbative and non-perturbative calculations of renormalization constants for various quark operators in Wilson-type fermion formulations, improving accuracy by subtracting lattice artifacts and converting to MS-bar scheme.

Contribution

It offers a comprehensive set of renormalization constants for Wilson, clover, and twisted mass fermions, including perturbative calculations up to second order and non-perturbative results with artifact subtraction.

Findings

Perturbative results include one-loop and second-order lattice spacing corrections.

Non-perturbative results cover multiple pion masses and lattice spacings, with artifact subtraction.

Renormalization constants are provided in MS-bar scheme at 2 GeV.

Abstract

Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level and up to second order in the lattice spacing, is performed for a fermion action, which includes the clover term and the twisted mass parameter yielding results that are applicable for unimproved Wilson fermions, as well as for improved clover and twisted mass fermions. We consider ten variants of the Symanzik improved gauge action corresponding to ten different values of the plaquette coefficients. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations are performed for pion masses in the range of 480 MeV to 260 MeV and at three values of the lattice spacing, a, corresponding to beta=3.9, 4.05, 4.20. For each renormalization factor computed non-perturbatively we subtract its perturbative O(a^2) terms so that we eliminate part of the cut-off artifacts. The renormalization constants are converted to MS-bar at a scale of mu=2 GeV. The perturbative results depend on a large number of parameters and are made easily accessible to the reader by including them in the distribution package of this paper, as a Mathematica input file.