Status of the Lambda Lattice Scale for the SU(3) Wilson gauge action

With the emergence of the Yang-Mills gradient flow technique there is renewed interest in the issue of scale setting in lattice gauge theory. Here I compare for the SU(3) Wilson gauge action non-perturbative scale functions of Edwards, Heller and Klassen (EHK), Necco and Sommer (NS), both relying on Sommer's method using the quark potential, and the scale function derived by Bazavov, Berg and Velytsky (BBV) from a deconfining phase transition investigation by the Bielefeld group. It turns out that the scale functions are based on mutually inconsistent data, though the BBV scale function is consistent with the EHK data when their low $β$ ($β=5.6$) data point is removed. Besides, only the BBV scale function is consistent with three data points calculated from the gradient flow by Lüscher. In the range for which data exist the discrepancies between the scale functions are only up to $\pm 2$\% of their values, but clearly visible within the statistical accuracy.

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