SU（3）规范理论中薛定谔泛函的O（a）修正格点结构
An O(a) modified lattice set-up of the Schrödinger functional in SU(3) gauge theory
摘要：
在交错夸克格点上建立QCD薛定谔泛函（SF），要求格点在空间方向上的点数为偶数$L/a$，而格点的欧氏时间范围$T/a$必须为奇数。然后，识别唯一的重正化尺度$L=T$仅可能达到O（$a$）个晶格伪影。在这篇文章中，我们在纯SU（3）规范理论中研究了这种晶格，在那里我们也可以与标准设置进行比较。我们认为SF耦合是从SU（3）阿贝尔和空间恒定背景场的变化中获得的。现有的O（$a$）边界反项可以消除O（$a$）晶格伪影。然而，它的系数，$\ct$，从它的标准值在树的水平上不同，所以首先需要重新确定诱导的背景规范场。对耦合的微扰单回路校正允许将$\ct$确定为单回路阶。几个数值模拟的服务，以证明剩余的截止效应的步骤缩放功能是小的，在这两种情况下，$T=L\pm a$和可比的标准情况下与$T=L$。
英文摘要：
The set-up of the QCD Schrödinger functional (SF) on the lattice with staggered quarks requires an even number of points $L/a$ in the spatial directions, while the Euclidean time extent of the lattice, $T/a$, must be odd. Identifying a unique renormalisation scale, $L=T$, is then only possible up to O($a$) lattice artefacts. In this article we study such lattices in the pure SU(3) gauge theory, where we can also compare to the standard set-up. We consider the SF coupling as obtained from the variation of an SU(3) Abelian and spatially constant background field. The O($a$) lattice artefacts can be cancelled by the existing O($a$) boundary counterterm. However, its coefficient, $\ct$, differs at the tree-level from its standard value, so that one first needs to re-determine the induced background gauge field. The perturbative one-loop correction to the coupling allows to determine $\ct$ to one-loop order. A few numerical simulations serve to demonstrate that residual cutoff effects in the step scaling function are small in both cases, $T=L\pm a$ and comparable to the standard case with $T=L$.
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