A New Way to Set the Energy Scale in Lattice Gauge Theories and its Application to the Static Force and $\alpha_s$ in SU(2) Yang--Mills Theory

TL;DR

This paper introduces a new hadronic scale based on the static quark force in SU(2) gauge theory, enabling precise scale setting and continuum extrapolation for the static force and running coupling calculations.

Contribution

It proposes a novel scale $R_0$ derived from the static force, facilitating accurate scale setting and continuum limit extrapolation in lattice gauge theories.

Findings

$R_0$ provides a reliable scale for lattice calculations.

Continuum extrapolation of $F(r)$ and the running coupling is achieved.

One-loop Symanzik improvement reduces lattice artifacts.

Abstract

We introduce a hadronic scale $R_0$ through the force $F(r)$ between static quarks at intermediate distances $r$. The definition $F(R_0)R_0^2=1.65$ amounts to $R_0 \simeq 0.5$~fm in phenomenological potential models. Since $R_0$ is well defined and can be calculated accurately in a Monte Carlo simulation, it is an ideal quantity to set the scale. In SU(2) pure gauge theory, we use new data (and $R_0$ to set the scale) to extrapolate $F(r)$ to the continuum limit for distances $r=0.18$~fm to $r=1.1$~fm. Through $R_0$ we determine the energy scale in the recently calculated running coupling, which used the recursive finite size technique to reach large energy scales. Also in this case, the lattice data can be extrapolated to the continuum limit. The use of one loop Symanzik improvement is seen to reduce the lattice spacing dependence significantly. Warning: The preprint is not completely fresh, but maybe you haven't seen it...