Non-perturbative running of renormalization constants from correlators in coordinate space using step scaling

TL;DR

This paper investigates a non-perturbative method to compute the running of renormalization constants using coordinate space in lattice QCD, demonstrating feasibility and agreement with perturbative results.

Contribution

It introduces the use of the coordinate (X-space) renormalization scheme for step scaling in lattice QCD and assesses its practicality in small volume simulations.

Findings

Successful computation of step scaling function in X-space scheme

Good agreement with four-loop perturbative results in MSbar scheme

Feasibility demonstrated for small volume lattice simulations

Abstract

Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on-shell and gauge invariant. The step scaling method allows us to calculate the running of the renormalization constants of quark bilinear operators. We describe here the details of this calculation. The aim of this exploratory study is to identify the feasibility of the X-space scheme when used in small volume simulations required by the step scaling technique. Eventually, we translate our final results to the continuum MSbar scheme and compare against four-loop analytic formulae finding satisfactory agreement.