论文标题
Yang-Mills理论中的两循环理性术语
Two-Loop Rational Terms in Yang-Mills Theories
论文作者
论文摘要
$ d $尺寸中的散射幅度涉及特定的术语，这些术语源自紫外线与$ d-4 $ d-4 $尺寸零件的相互作用。可以通过一组有限的与过程无关的有理反应来控制此类贡献，这使得可以使用数值工具来计算循环幅度，这些工具可以在四个维度中构造循环分子。基于两循环有理反应的一般特性的最新研究[1]，在本文中，我们研究了它们对重量级化方案选择的依赖性。我们确定了一种非平凡的方案依赖性形式，该形式源自质量和田间重态度与$ d-4 $尺寸零件的相互作用，我们证明它可以通过一种新型的单循环反应来控制。这可以确保可以在通用的肾拟态化常数方面一劳永逸地得出给定的肾上腺素理论的两循环理性反应，这可以使后验适应任何方案。使用这种方法，我们介绍了Yang-Mills理论中完整的两循环合理反对者的第一个计算。结果适用于su（n）和u（1）量表理论，耦合到$ n_ {f} $ fermions，并带有任意群众。
Scattering amplitudes in $D$ dimensions involve particular terms that originate from the interplay of UV poles with the $D-4$ dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the $D-4$ dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to $n_{f}$ fermions with arbitrary masses.
