With Wilson quarks, on-shell O(a) improvement of the lattice QCD action is achieved by including the Sheikholeslami-Wohlert term and two further operators of mass dimension 5, which amount to a mass-dependent rescaling of the bare parameters. We here focus on the rescaled bare coupling, \( {\tilde{g}}_0^2={g}_0^2\left(1+{b}_{\textrm{g}}a{m}_{\textrm{q}}\right) \) , and the determination of \( {b}_{\textrm{g}}\left({g}_0^2\right) \) which is currently only known to 1-loop order of perturbation theory. We derive suitable improvement conditions in the chiral limit and in a finite space-time volume and evaluate these for different gluonic observables, both with and without the gradient flow. The choice of β-values and the line of constant physics are motivated by the ALPHA collaboration’s decoupling strategy to determine αs(mZ) [1]. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.
