Universality of the Nf=2 Running Coupling

TL;DR

This study examines the universality of the Nf=2 running coupling in lattice QCD by calculating the step scaling function using RG improved gauge actions at different couplings, confirming consistency with previous results.

Contribution

It provides a detailed comparison of the step scaling function using RG improved and plaquette gauge actions, demonstrating universality in the continuum limit.

Findings

Agreement with previous results within errors at both couplings

Errors reduced by 2% at weak coupling and 22% at strong coupling with combined fits

Scaling behaviors are affected by O(a) improvement coefficients

Abstract

We investigate universality of the Nf=2 running coupling in the Sch\"odinger functional scheme, by calculating the step scaling function in lattice QCD with the renorm alization group (RG) improved gauge action at both weak(u=0.9796) and strong(u=3.3340) couplings, where u=\bar{g}^2_SF with \bar{g}_SF being the running coupling in this scheme. In our main calculations, we use the tree-level value for O(a) improvement coefficients of boundary gauge fields. In addition we employ the 1-loop value for them in order to see how scaling behaviours are affected by them. In the continuum limit, the step scaling function obtained from the RG improved gauge actions agrees with the previous result obtained from the plaquette action within errors at both couplings, though errors of our result are larger. Combined fits using all data with the RG improved action as well as the plaquette action reduce errors in the continuum limit by 2% at the weak coupling and 22% at the strong coupling.