Step scaling in coordinate space: running of the quark mass

TL;DR

This paper investigates the step scaling method in coordinate space for renormalization constants, demonstrating its effectiveness in non-perturbative quark mass running from high to low energies within the quenched approximation.

Contribution

It provides a benchmark study of step scaling in coordinate space, validating its use for non-perturbative quark mass evolution across a wide energy range.

Findings

Non-perturbative quark mass running matches 4-loop predictions.

Step scaling is feasible and effective in X-space.

The study discusses advantages and potential issues of the method.

Abstract

We perform a benchmark study of the step scaling procedure for the ratios of renormalization constants extracted from position space correlation functions. We work in the quenched approximation and consider the pseudoscalar, scalar, vector and axial vector bilinears. The pseudoscalar/scalar cases allow us to obtain the non-perturbative running of the quark mass over a wide range of energy scales - from around 17 GeV to below 1.5 GeV - which agrees well with the 4-loop prediction of continuum perturbation theory. We find that step scaling is feasible in X-space and we discuss its advantages and potential problems.