%0 Conference Paper
%A Ammer, Maximilian
%A Durr, Stephan
%T $\mathbf{c_\textbf{SW}}$ at One-Loop Order for Brillouin Fermions
%I Sissa Medialab Trieste, Italy
%M FZJ-2023-05490
%P 289
%D 2023
%Z Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universit\'at Bonn, Bonn, Germany
%< Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022) - Sissa Medialab Trieste, Italy, 2022. - ISBN - doi:10.22323/1.430.0289
%X Wilson-like Dirac operators can be written in the form $D=\gamma_\mu\nabla_\mu-\frac {ar}{2} \Delta$. 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 ${c_\mathrm{SW}}=1+{c_\mathrm{SW}}^{(1)}g_0^2+\mathcal{O}(g_0^4)$. For $N_c=3$ we find ${c_\mathrm{SW}}^{(1)}_\mathrm{Brillouin} =0.12362580(1) $, compared to ${c_\mathrm{SW}}^{(1)}_\mathrm{Wilson} = 0.26858825(1)$, both for $r=1$.
%B Lattice 2022
%C 8 Aug 2022 - 13 Aug 2022, Bonn (Germany)
Y2 8 Aug 2022 - 13 Aug 2022
M2 Bonn, Germany
%F PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
%9 Contribution to a conference proceedingsContribution to a book
%R 10.22323/1.430.0289
%U https://juser.fz-juelich.de/record/1019543