Abstract
AbstractWe study the perturbative behavior of the Yang-Mills gradient flow in the Schrödinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set ofNf= 2 gauge field ensembles in a physical volume ofL~ 0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.
Highlights
Lattice simulation, the idea of finite-size scaling exploits the size of a finite volume world as renormalization scale
We study the perturbative behavior of the Yang-Mills gradient flow in the Schrodinger Functional, both in the continuum and on the lattice
On a set of Nf = 2 gauge field ensembles in a physical volume of L ∼ 0.4 fm we demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision
Summary
We would like to start this section by recalling the original proposal of using the Wilson flow and the energy density as a definition for a coupling in gauge theories [18]. Later it will become clear what role the SF setup plays
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