Non-perturbative renormalization of lattice operators in coordinate space

TL;DR

This paper introduces a novel non-perturbative renormalization technique for lattice operators using coordinate space correlation functions, demonstrating its application to Wilson and Neuberger fermions and matching with perturbative schemes.

Contribution

It provides the first numerical implementation of a coordinate space non-perturbative renormalization method for lattice operators, including practical applications and feasibility studies.

Findings

Successful computation of renormalization constants for bilinear quark operators.

Matching with MS-bar scheme at next-to-leading order.

Feasibility demonstrated for Neuberger fermions.

Abstract

We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute the renormalization constants of bilinear quark operators for the non-perturbative O(a)-improved Wilson action in the quenched approximation. The matching with perturbative schemes, such as MS-bar, is computed at the next-to-leading order in continuum perturbation theory. A feasibility study of this technique with Neuberger fermions is also presented.