The continuum limit of the quark mass step scaling function in quenched lattice QCD

TL;DR

This paper non-perturbatively determines the quark mass running over various scales in quenched lattice QCD, confirming the continuum limit's uniqueness and providing precise ratios of invariant to renormalized quark masses.

Contribution

It presents the first non-perturbative calculation of the step scaling function in quenched lattice QCD with both Wilson and Clover actions, including a perturbative analysis of discretisation effects.

Findings

Continuum results are regularisation independent.

High-accuracy ratio of invariant to renormalized quark mass obtained.

Evidence for the uniqueness of the continuum limit.

Abstract

The renormalisation group running of the quark mass is determined non-perturbatively for a large range of scales, by computing the step scaling function in the Schroedinger Functional formalism of quenched lattice QCD both with and without O(a) improvement. A one-loop perturbative calculation of the discretisation effects has been carried out for both the Wilson and the Clover-improved actions and for a large number of lattice resolutions. The non-perturbative computation yields continuum results which are regularisation independent, thus providing convincing evidence for the uniqueness of the continuum limit. As a byproduct, the ratio of the renormalisation group invariant quark mass to the quark mass, renormalised at a hadronic scale, is obtained with very high accuracy.