Papers › Gradient flow and scale setting on MILC HISQ ensembles
Gradient flow and scale setting on MILC HISQ ensembles
MILC Collaboration, A. Bazavov, C. Bernard, N. Brown, C. DeTar, J. Foley, Steven Gottlieb, U. M. Heller, J. Komijani, J. Laiho, L. Levkova, R. L. Sugar, D. Toussaint, R. S. Van de Water
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We report on a scale determination with gradient-flow techniques on the N_f=2+1+1 highly improved staggered quark ensembles generated by the MILC Collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales √(t₀)/a and w₀/a and their tree-level improvements, √(t_(0,imp)) and w_(0,imp), are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density E. Using a combination of continuum chiral-perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales √(t₀) = 0.1416(₋₅⁺⁸) fm and w₀ = 0.1714(₋₁₂⁺¹⁵) fm, where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of w₀ and √(t₀) is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass dependence of √(t₀) and w₀, which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of ⟨E(t) ⟩. For long flow times, the autocorrelation length of ⟨E ⟩ appears to be comparable to that of the topological charge.
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