标题： 从QCD薛定谔泛函的运行耦合——一项一环分析 显示英文标题

标题： The running coupling from the QCD Schrödinger functional -- a one-loop analysis

摘要： 从薛定谔泛函出发，我们在QCD中给出了耦合常数的一个非微扰定义。 反夸克场的空间边界条件被选取为使得经典背景场中的无质量Dirac算符具有一个较大的最小特征值。 在一阶微扰论中，我们确定了匹配系数到$\MSbar$-方案，并讨论了$\beta$-函数中的夸克质量效应。 达到这一精度，我们也计算了Symanzik改善系数，以消除由边界引起的$\Oa$晶格伪影。 对于合理的晶格分辨率和标准Wilson作用量，发现晶格伪影仅弱依赖于晶格间距$a$；而当使用Sheikholeslami和Wohlert的改善作用量时，这些伪影会迅速消失。 显示英文摘要

摘要： Starting from the Schr\"odinger functional, we give a non-perturbative definition of the running coupling constant in QCD. The spatial boundary conditions for the quark fields are chosen such that the massless Dirac operator in the classical background field has a large smallest eigenvalue. At one-loop order of perturbation theory, we determine the matching coefficient to the $\MSbar$-scheme and discuss the quark mass effects in the $\beta$-function. To this order, we also compute the Symanzik improvement coefficient necessary to remove the $\Oa$ lattice artefacts originating from the boundaries. For reasonable lattice resolutions and the standard Wilson action, lattice artefacts are found to be only weakly dependent on the lattice spacing $a$, while they vanish quickly with the improved action of Sheikholeslami and Wohlert.