Precise determination of the lattice spacing in full lattice QCD

This is the authors' abstract. We don't add key points for this paper.

We compare three different methods to determine the lattice spacing in lattice QCD and give results from calculations on the MILC ensembles of configurations that include the effect of u, d, and s sea quarks. It is useful, for ensemble to ensemble comparison, to express the results as giving a physical value for r₁, a parameter from the heavy quark potential. Combining the three methods gives a value for r₁ in the continuum limit of 0.3133(23)(3) fm. Using the MILC values for r₀/r₁, this corresponds to a value for the r₀ parameter of 0.4661(38) fm. One of our methods involves using the ηₛ to determine the lattice spacing and to tune the s-quark mass accurately. We give values for m_ηₛ [0.6858(40) GeV] and f_ηₛ [0.1815(10) GeV] needed to implement this. We show that the ηₛ method by itself is competitive with the r₁ method on an ensemble by ensemble basis and compare the two.