Nonperturbative O(a) improvement of the Wilson quark action with the renormalization-group-improved gauge action using the Schrödinger functional method

We perform a nonperturbative determination of the O(a)-improvement coefficient c{sub SW} and the critical hopping parameter {kappa}{sub c} for N{sub f}=3, 2, and 0 flavor QCD with the (RG) renormalization-group-improved gauge action using the Schroedinger functional method. In order to interpolate c{sub SW} and {kappa}{sub c} as a function of the bare coupling, a wide range of {beta} from the weak coupling region to the moderately strong coupling points used in large-scale simulations is studied. Corrections at finite lattice size of O(a/L) turned out to be large for the RG-improved gauge action, and hence we make the determination at a size fixed in physical units using a modified improvement condition. This enables us to avoid O(a) scaling violations which would remain in physical observables if c{sub SW} determined for a fixed lattice size L/a is used in numerical simulations.