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

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 $c_{\mathrm{SW}}=c_{\mathrm{SW}}^{(0)}+g_0^2{c}_{\mathrm{SW}}^{(1)}+\mathcal{O}(g_0^4)$. 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 Lüscher-Weisz gluons. Numerically its value is found to be about half that of the Wilson action.

Comments: 23 pages, 6 figures, 10 tables, Version 2: matches published version