The perturbative gradient flow at higher orders

本文给出了M.到目前为止，Lüscher在2010年的研究主要是在格点规范理论的框架内进行的。本工程采用摄动法处理。在某种程度上，两种方法的比较和结合所产生的潜力已经在文献中指出。例如，它提供了一种新的可能性，从非微扰晶格数据中推导出微扰区域中的强耦合常数的值。然而，它们是基于一种相当实用的、计算机密集型的方法。这个建议的目标之一是发展一个系统的方法在梯度流形式主义的微扰计算。使用这种设置，现象学上相关的量将被计算到微扰理论中的高阶（主要是NNLO）。

The gradient flow formalism as defined by M. Lüscher in 2010 has been considered mostly within the framework of lattice gauge theory up to now. In this project, it shall be treated with perturbative methods. To some extent, the potential resulting from the comparison and the combination of both approaches has already been pointed out in the literature. For example, it offers a new possibility to derive a value for the strong coupling constant in the perturbative regime from non-perturbative lattice data.First results in this direction have already been obtained by the applicant. However, they were based on a rather pragmatic, computer intensive approach. One of the goals of this proposal is the development of a systematic method for perturbative calculations in the gradient-flow formalism. Using this setup, phenomenologically relevant quantities shall be calculated to higher orders in perturbation theory (mostly NNLO).