Lambda-parameter of lattice QCD with Symanzik improved gluon actions

TL;DR

This paper calculates the ratio of lattice to MS scale parameters in lattice QCD with Symanzik improved gluon actions, providing key renormalization constants for various action combinations.

Contribution

It introduces a comprehensive calculation of Lambda_L/Lambda_MS for a family of Symanzik improved gluon actions combined with standard fermion discretizations.

Findings

Calculated Lambda_L/Lambda_MS ratios for multiple Symanzik coefficients.

Provided Z_g renormalization constants at 1-loop level for various action combinations.

Extended the understanding of scale setting in lattice QCD with improved actions.

Abstract

We compute the ratio Lambda_L/Lambda_MS, where the scale parameter Lambda_L is associated with a lattice formulation of QCD. We consider a 3-parameter family of gluon actions, which are most frequently used for O(a) improvement a` la Symanzik. The gluon action is put togeter with standard discretizations for fermions (Wilson/clover, overlap), to provide Lambda_L for several possible combinations of fermion and gluon actions. We employ the background field technique in order to calculate the 1PI 2-point function of the background field; this leads to the coupling constant renormalization function, Z_g, at 1-loop level. Our results are obtained for an extensive range of values for the Symanzik coefficients.