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@INPROCEEDINGS{Ammer:1019543,
      author       = {Ammer, Maximilian and Durr, Stephan},
      title        = {$\mathbf{c_\textbf{{SW}}}$ at {O}ne-{L}oop {O}rder for
                      {B}rillouin {F}ermions},
      publisher    = {Sissa Medialab Trieste, Italy},
      reportid     = {FZJ-2023-05490},
      pages        = {289},
      year         = {2023},
      note         = {Proceedings of the 39th International Symposium on Lattice
                      Field Theory, 8th-13th August, 2022, Rheinische
                      $Friedrich-Wilhelms-Universit\'at$ Bonn, Bonn, Germany},
      comment      = {Proceedings of The 39th International Symposium on Lattice
                      Field Theory — PoS(LATTICE2022) - Sissa Medialab Trieste,
                      Italy, 2022. - ISBN - doi:10.22323/1.430.0289},
      booktitle     = {Proceedings of The 39th International
                       Symposium on Lattice Field Theory —
                       PoS(LATTICE2022) - Sissa Medialab
                       Trieste, Italy, 2022. - ISBN -
                       doi:10.22323/1.430.0289},
      abstract     = {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 $r=1$.},
      month         = {Aug},
      date          = {2022-08-08},
      organization  = {Lattice 2022, Bonn (Germany), 8 Aug
                       2022 - 13 Aug 2022},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      eprint       = {2210.06860},
      howpublished = {arXiv:2210.06860},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2210.06860;\%\%$},
      doi          = {10.22323/1.430.0289},
      url          = {https://juser.fz-juelich.de/record/1019543},
}