Estimates of Scaling Violations for Pure SU(2) LGT

TL;DR

This study examines how pure SU(2) lattice gauge theory approaches the continuum limit, comparing different scale-setting methods and analyzing systematic errors to improve understanding of scaling violations.

Contribution

It introduces a comprehensive analysis of scaling violations using multiple scale-setting techniques and systematic error assessments in SU(2) lattice gauge theory.

Findings

Cooling flow is the most computationally efficient scale-setting method.

Systematic errors are larger than statistical errors, emphasizing the importance of their control.

Different fitting forms impact the estimated approach to the continuum limit.

Abstract

We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining transition, Luescher's gradient flow, and the cooling flow to set the scale. Of those, the cooling flow turns out to be computationally most efficient. We explore systematic errors due to use of three different energy observables and two distinct reference values for the flow time, the latter obtained by matching initial scaling behavior of some energy observables to that of the deconfining transition. Another important source of systematic errors are distinct fitting forms for the approach to the continuum limit. Besides relying in the conventional way on ratios of masses, we elaborate on a form introduced by Allton, which incorporates asymptotic scaling behavior. Ultimately we find that, though still small, our systematic errors are considerably larger than our statistical errors. ~