论文标题
$ \ mathbf {c_ \ textbf {sw}} $以brillouin fermions的一环订单
$\mathbf{c_\textbf{SW}}$ at One-Loop Order for Brillouin Fermions
论文作者
论文摘要
像威尔逊一样的狄拉克运算符可以用$ d =γ_μ\nabla_μ-\ frac {ar} {2}Δ$编写。对于Wilson Fermions，使用了标准的两点衍生物$ \nabla_μ^{（\ Mathrm {std}）} $和9点laplacian $δ^{（\ m athrm {std}}} $。对于Brillouin fermions，这些由改进的离散化取代$ \nabla_μ^{（\ Mathrm {iso}）} $和$Δ^^{（\ Mathrm {bri}）} $，分别具有54-和81点模具。我们在布里鲁因动作的晶格扰动理论中得出了Feynman规则，并将其应用于改进系数$ {c_ \ mathrm {sw}} $的计算，与威尔逊案相似，它具有形式的扰动扩展$ {c_ \ mathrm {sw}} = 1+ {c_ \ mathrm {sw}}}}^{（1）} g_0^2+\ mathcal {o}（g_0^4）$。对于$ n_c = 3 $，我们找到$ {c_ \ mathrm {sw}}^{（1）} _ \ mathrm {brillouin} = 0.12362580（1）$，与$ {C_ \ Mathrm {sw}}}}^{（1）}^{（1）} _ \ MathRM} 0.26858825（1）$，均以$ r = 1 $。
Wilson-like Dirac operators can be written in the form $D=γ_μ\nabla_μ-\frac {ar}{2} Δ$. For Wilson fermions the standard two-point derivative $\nabla_μ^{(\mathrm{std})}$ and 9-point Laplacian $Δ^{(\mathrm{std})}$ are used. For Brillouin fermions these are replaced by improved discretizations $\nabla_μ^{(\mathrm{iso})}$ and $Δ^{(\mathrm{bri})}$ 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 $r=1$.
