Note on Rome-Southampton renormalization with smeared gauge fields

We have calculated continuum-limit step scaling functions of bilinear and four-fermion operators renormalized in a Rome-Southampton scheme using various smearing prescriptions for the gauge field. Also, for the first time, we have calculated nonperturbative anomalous dimensions of operators renormalized in a Rome-Southampton scheme. The effect of such smearing first enters connected fermionic correlation functions via radiative corrections. We use off-shell renormalization as a probe, and observe that the upper edge of the Rome-Southampton window is reduced by link smearing. This can be interpreted as arising due to the fermions decoupling from the high-momentum gluons and we observe that the running of operators with the scale at large lattice momenta shows enhanced lattice artifacts. We find that the effect is greater for HEX smearing than for Stout smearing, but that in both cases additional care must be taken when using off-shell renormalization with smeared gauge fields compared to thin-link simulations.