Quark action for very coarse lattices

We investigate a tree-level O(a(3))-accurate action, D234c, on coarse lattices. For the improvement terms we use tadpole-improved coefficients, with the tadpole contribution measured by the mean link in the Landau gauge. We measure the hadron spectrum for quark masses near that of the strange quark. We find that D234c shows much better rotational invariance than the Sheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to smaller finite-lattice-spacing errors than plaquette tadpole improvement. We obtain accurate ratios of lattice spacings using a convenient "Galilean quarkonium" method. We explore the effects of possible O(a(s)) changes to the improvement coefficients, and find that the two leading coefficients can be independently tuned: hadron masses are most sensitive to the clover coefficient C-F, while hadron dispersion relations are most sensitive to the third derivative coefficient C-3. Preliminary nonperturbative tuning of these coefficients yields values that are consistent with the expected size of perturbative corrections. [S0556-2821(98)06315-2].