Precise determination of the lattice spacing in full lattice QCD

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 r(1), a parameter from the heavy quark potential. Combining the three methods gives a value for r(1) in the continuum limit of 0.3133(23)(3) fm. Using the MILC values for r(0)/r(1), this corresponds to a value for the r(0) parameter of 0.4661(38) fm. One of our methods involves using the eta(s) to determine the lattice spacing and to tune the s-quark mass accurately. We give values for m(eta s) [0.6858(40) GeV] and f(eta s) [0.1815(10) GeV] needed to implement this. We show that the eta(s) method by itself is competitive with the r(1) method on an ensemble by ensemble basis and compare the two.