Calculation of $c_\mathrm{SW}$ at one-loop order for Brillouin fermions

TL;DR

This paper calculates the one-loop correction to the Sheikholeslami-Wohlert coefficient for Brillouin fermions, showing it is roughly half of that for Wilson fermions, using lattice perturbation theory.

Contribution

It provides the first one-loop calculation of $c_ ext{SW}$ for Brillouin fermions, including Feynman rules and numerical results.

Findings

One-loop $c_ ext{SW}$ for Brillouin fermions is about half of Wilson's.

Derived Feynman rules for Brillouin action in lattice perturbation theory.

Numerical values obtained using plaquette and Lüscher-Weisz gluons.

Abstract

The Brillouin action is a Wilson-like lattice fermion action with a 81-point stencil, which was found to ameliorate the Wilson action in many respects. The Sheikholeslami-Wohlert coefficient $c_\mathrm{SW}$ of the clover improvement term has a perturbative expansion $c_\mathrm{SW}=c_\mathrm{SW}^{(0)}+g_0^2c_\mathrm{SW}^{(1)}+\mathcal{O}(g_0^4)$. At tree-level $c_\mathrm{SW}^{(0)}=r$ holds for Wilson and Brillouin fermions alike. We present the Feynman rules for the Brillouin action in lattice perturbation theory, and employ them to calculate the one-loop coefficient $c_\mathrm{SW}^{(1)}$ with plaquette or L\"uscher-Weisz gluons. Numerically its value is found to be about half that of the Wilson action.