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

Krzysztof Cichy,Karl Jansen,Piotr Korcyl

doi:10.1016/j.nuclphysb.2016.09.015

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 MS‾ scheme and compare against four-loop analytic formulae finding satisfactory agreement.

Highlights

In lattice Monte Carlo simulations of QCD, connecting the high energy regime where perturbation theory can be safely applied, to the low energy regime of large volume simulationsK
Due to the known difficulties of perturbation theory for QCD in a small periodic box, we look at correlation functions at very short distances compared to the physical extent of the simulated box
We fix Lto 8, 16, 24 and 32 and find the corresponding lattice spacing such that the spatial extent is always equal to L1

Summary

Introduction

In lattice Monte Carlo simulations of QCD, connecting the high energy regime where perturbation theory can be safely applied, to the low energy regime of large volume simulationsK. In lattice Monte Carlo simulations of QCD, connecting the high energy regime where perturbation theory can be safely applied, to the low energy regime of large volume simulations. The latter says that the relevant physical distances at which we evaluate our observables should be sufficiently small, we are limited by the discretization errors. [1,2,3,4] It is called step scaling and consists in performing several simulations at a smaller and smaller lattice spacing as well as smaller and smaller volumes starting at the coarse, large volume level and repeating the procedure until the mentioned high energy regime of the theory can be reached

Objectives

Results

Discussion

Conclusion