Speaker
Description
Wilson-like Dirac operators can be written in the form $D=\gamma_\mu\nabla_\mu-\frac 12 \Delta$. For Wilson fermions the standard two-point derivative $\nabla_\mu^\mathrm{std}$ and 9-point Laplacian $\Delta^\mathrm{std}$ are used. For Brillouin fermions these are replaced by improved discretizations $\nabla_\mu^\mathrm{iso}$ and $\Delta^\mathrm{bri}$ which have 54- and 81-point stencils respectively. We derive the Feynman rules in lattice perturbation theory for the Brillouin action and apply them to the calculation of the improvement coefficient $c_\mathrm{SW}$, which, similar to the Wilson case, has a perturbative expansion of the form $ c_\mathrm{SW}=1+{c_\mathrm{SW}}^{(1)}g_0^2+\mathcal{O}(g_0^4)$.
We find ${c_\mathrm{SW}}^{(1)}_\mathrm{Brillouin}=0.16182118(1)$ compared to ${c_\mathrm{SW}}^{(1)}_\mathrm{Wilson}=0.26858825(1)$.
