One-loop $c_\mathrm{SW}$ for Wilson and Brillouin fermions with stout smearing or Wilson flow

Abstract

We present results for the one-loop value of the improvement coefficient $c_\mathrm{SW}$ for Wilson and Brillouin fermions subject to stout smearing or Wilson flow, in combination with Wilson or Symanzik glue. To this end we use a recently developed method that allows one to modify an existing perturbative calculation, like the one for $c_\mathrm{SW}^{(1)}$, to include stout smearing or Wilson flow at arbitrary stout parameters ($\varrho$, $n_\mathrm{stout}$) or flow times $t/a^2$, respectively. Our results indicate that already a small amount of smoothing makes the perturbative series well behaved, suggesting that a non-perturbatively determined $c_\mathrm{SW}$ might be close to its one-loop value for couplings $g_0^2\simeq 1$.