Nonperturbative $O(a)$ improvement of the Wilson quark action with the RG-improved gauge action using the Schr\"odinger functional method

TL;DR

This paper nonperturbatively determines the $O(a)$-improvement coefficient and critical hopping parameter for various flavors of QCD using the Schr"odinger functional method with an RG-improved gauge action, ensuring more accurate lattice simulations.

Contribution

It introduces a nonperturbative method to determine $c_{SW}$ and $\kappa_c$ across a wide coupling range, accounting for finite size effects to improve lattice QCD accuracy.

Findings

Large finite size corrections at fixed lattice size were identified.

Determined $c_{SW}$ and $\kappa_c$ as functions of the bare coupling.

Method reduces $O(a)$ scaling violations in physical observables.

Abstract

We perform a nonperturbative determination of the $O(a)$-improvement coefficient $c_{\rm SW}$ and the critical hopping parameter $\kappa_c$ for $N_f$=3, 2, 0 flavor QCD with the RG-improved gauge action using the Schr\"odinger functional method. In order to interpolate $c_{\rm SW}$ and $\kappa_c$ 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 $c_{\rm SW}$ determined for a fixed lattice size $L/a$ is used in numerical simulations.