We report on a scale determination with gradient-flow techniques on the Nf=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, t0,imp and w0,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(+8-5) fm and w0=0.1714(+15-12) 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.
ASJC Scopus subject areas
- Nuclear and High Energy Physics