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

TL;DR

This paper compares various non-perturbative scale functions for SU(3) Wilson gauge action, highlighting inconsistencies and the partial agreement with gradient flow data, which impacts scale setting in lattice gauge theory.

Contribution

It provides a comparative analysis of different scale functions, identifying their mutual inconsistencies and their relation to gradient flow results.

Findings

Scale functions are mutually inconsistent based on available data.

BBV scale function aligns with gradient flow data when low β point is excluded.

Discrepancies among scale functions reach up to ±2% within existing data range.

Abstract

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 $\beta$ ($\beta=5.6$) data point is removed. Besides, only the BBV scale function is consistent with three data points calculated from the gradient flow by L\"uscher. 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.