Heavy Wilson quarks and O( a ) improvement: nonperturbative results for b g

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, g̃_0^2=g_0^2(1+b_gam_q) , and the determination of b_g(g_0^2) 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 α s ( m Z ) [ 1 ]. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.