Abstract
We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to a = 0.015 fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of the action density E(t) close to the boundaries, the feasibility of the small flow-time expansion and the extraction of the Λ-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative β-function are visible at α ≈ 0.2. We still can extrapolate to extract roΛ.
Highlights
We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances
To simulate SU(3) Yang Mills theory on fine lattices, close to the continuum limit with lattice spacings down to a = 0.015 fm one has to avoid the freezing of the topological charge [1, 2]
The coupling g2qq(r, a) at finite lattice spacing a was derived from Wilson loops applying the analysis described in [22] with only one difference: the parallel transporters in time are the dynamical gauge fields and statistical errors are reduced by the multi-hit technique [23]
Summary
To simulate SU(3) Yang Mills theory on fine lattices, close to the continuum limit with lattice spacings down to a = 0.015 fm one has to avoid the freezing of the topological charge [1, 2] This is achieved by introducing open boundary conditions in time [3]. Deviations near the time boundaries from the plateau values are caused both by boundary conditions affecting the continuum theory and by discretisation effects The latter can be reduced by boundary improvement terms. The deviation of the action density near – but not too close to – the time boundary is used as a testing ground for the small flow-time expansion [5]. From the integration of eq (3) with the perturbative βqq we will extract the Λ-parameter and test perturbation theory from the condition that Λ is Renormalization Group Invariant
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