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

TL;DR

This paper calculates the one-loop improvement coefficient $c_ ext{SW}$ for Wilson and Brillouin fermions with stout smearing or Wilson flow, showing smoothing improves perturbative series and aiding non-perturbative estimates.

Contribution

It introduces a method to include stout smearing or Wilson flow effects into existing perturbative calculations of $c_ ext{SW}$ for Wilson-type fermions.

Findings

Small smoothing leads to well-behaved perturbative series.

Non-perturbative $c_ ext{SW}$ might be close to one-loop value at moderate couplings.

Method allows flexible inclusion of smearing and flow parameters in calculations.

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 $g_0^2\simeq 1$.