Estimates of Scaling Violations for Pure SU(2) LGT

Abstract

We investigate the approach of pure SU(2) lattice gauge theory with theWilson action to its continuum limit using the deconfining transition, Lüscher’s gradient flow [1], and the cooling flow [2, 3] 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 [4], which incorporates asymptotic scaling behavior. Ultimately we find that, though still small, our systematic errors are considerably larger than our statistical errors.