Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow

Abstract

A parametrization of the lattice spacing ($a$) in terms of the bare coupling ($\beta$) for the SU(3) Yang--Mills theory with the Wilson gauge action is given in a wide range of~$\beta$. The Yang--Mills gradient flow with respect to the flow time~$t$ for the dimensionless observable, $t\frac{d}{dt}{t}^2⟨E(t)⟩$, is utilized to determine the parametrization. With fine lattice spacings ($6.3\le \beta \le 7.5$) and large lattice volumes ($N_{\mathrm{s}}=64$--$128$), the discretization and finite-volume errors are significantly reduced to the same level as the statistical error.

Comments: 20 pages, 7 figures