Effectiveness of NonperturbativeO(a)Improvement in Lattice QCD

The ALPHA Collaboration has determined the $O\left(a\right)$ improved Wilson quark action for lattice spacings $a\le 0.1$ fm, in the quenched approximation. We extend this result to coarser lattices, $a\le 0.17\mathrm{fm}$, and calculate the hadron spectrum on them. The large range of lattice spacings obtained by combining our results with earlier ones on finer lattices allows us to present a convincing demonstration of the efficiency of nonperturbative $O\left(a\right)$ improvement. We find that scaling violations of the hadron masses studied drop from 30%–40% for the unimproved Wilson action on the coarsest lattice to only 2%–3%.