Precise determination of the lattice spacing in full lattice QCD

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Abstract
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 $\eta${}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 r1 method on an ensemble by ensemble basis and compare the two.
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