TY  - CONF
AU  - Ammer, Maximilian
AU  - Durr, Stephan
TI  - $\mathbf{c_\textbf{SW}}$ at One-Loop Order for Brillouin Fermions
PB  - Sissa Medialab Trieste, Italy
M1  - FZJ-2023-05490
SP  - 289
PY  - 2023
N1  - Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universit\'at Bonn, Bonn, Germany
AB  - 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 $r=1$.
T2  - Lattice 2022
CY  - 8 Aug 2022 - 13 Aug 2022, Bonn (Germany)
Y2  - 8 Aug 2022 - 13 Aug 2022
M2  - Bonn, Germany
LB  - PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
DO  - DOI:10.22323/1.430.0289
UR  - https://juser.fz-juelich.de/record/1019543
ER  -