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 $eta_s$ for determining the lattice spacing and tuning the $s$-quark mass accurately, by giving values for $m_{eta_s}$ (0.6858(40) GeV) and $f_{eta_s}$ (0.1815(10) GeV).
تحميل البحث