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. We also discuss how to use the $η_s$ for determining the lattice spacing and tuning the $s$-quark mass accurately, by giving values for $m_{η_s}$ (0.6858(40) GeV) and $f_{η_s}$ (0.1815(10) GeV).

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