Radiative corrections to the lattice gluon action for highly improved staggered quarks and the effect of such corrections on the static potential

We perform a perturbative calculation of the influence of dynamical highly improved staggered quark fermions on the perturbative improvement of the gluonic action in the same way as we have previously done for asqtad fermions. We find the fermionic contributions to the radiative corrections in the Lüscher-Weisz gauge action to be somewhat larger for highly improved staggered quark fermions than for asqtad. Using one-loop perturbation theory as a test, we estimate that omission of the fermion-induced radiative corrections in dynamical asqtad simulations will give a measurable effect. The one-loop result gives a systematic shift of about $-0.6\%$ in ${\widehat{r}}_1$ on the coarsest asqtad improved staggered ensembles. This is the correct sign and magnitude to explain the scaling violations seen in ${\Phi }_B=f_B\sqrt{M_B}$ on dynamical lattice ensembles.