SU(3) Yang Mills at small distances and fine lattices
We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to a=0.015fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behavior of the action density E(t) close to the boundaries, the feasibility of the small flow time expansion and the extraction of the $\Lambda$-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative $\beta$-function are visible at $\alpha \approx 0.2$. We still can extrapolate to extract $\Lambda \times r_0$.
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Standard Model Parameters and Renormalization