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

Abstract

We perform a nonperturbative determination of the $O(a)$-improvement coefficient ${c}_{\mathrm{SW}}$ and the critical hopping parameter ${\ensuremath{\kappa}}_{c}$ for ${N}_{f}=3$, 2, and 0 flavor QCD with the (RG) renormalization-group-improved gauge action using the Schr\"odinger functional method. In order to interpolate ${c}_{\mathrm{SW}}$ and ${\ensuremath{\kappa}}_{c}$ as a function of the bare coupling, a wide range of $\ensuremath{\beta}$ 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 ${c}_{\mathrm{SW}}$ determined for a fixed lattice size $L/a$ is used in numerical simulations.