In perturbation theory, the spectral densities of two-point functions develop nonintegrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they become stronger when one rearranges the perturbative expansion in terms of the running quark mass. In this paper, we discuss the proper way to handle such singularities.

中文翻译：

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微扰理论中两点函数的不可积阈值奇异性

在微扰理论中，两点函数的谱密度在较高阶上发展出不可积分的阈值奇点。在QCD中，当根据极夸克质量计算图时，会出现这种奇点，而当根据运行的夸克质量重新排列扰动展开时，这些奇点会变得更强。在本文中，我们讨论了处理此类奇点的正确方法。