One-loop matching and running with covariant derivative expansion
One-loop matching and running with covariant derivative expansion
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DOI：
10.1007/jhep01(2018)123
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发表时间：
2016-04
影响因子：
5.4
通讯作者：
B. Henning;Xiaochuan Lu;H. Murayama
中科院分区：
文献类型：
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作者：
B. Henning;Xiaochuan Lu;H. Murayama
我们开发的工具进行有效场理论（EFT）的计算在一个明显的规范协变的方式。我们澄清如何功能的方法占单回路图产生的交换重和轻领域，最近出现了一些混乱的文献。为了有效地评估包含这些“混合”单循环项的功能轨迹，我们开发了一种新的协变导数展开（CDE）技术，该技术能够评估比以前的方法更广泛的一类轨迹。该技术在附录中有详细说明，因此可以独立于本文的其余部分阅读。我们回顾了著名的匹配过程，以一个循环的顺序与功能的方法。我们在这个故事中增加的是，展示如何将来自只涉及重传播子的图的单圈项与来自混合重传播子和轻传播子的图的单圈项分离。这是使用非局部有效作用来完成的，其物理上连接到“整合出”重场的概念。最后，我们展示了如何使用CDE在EFT中进行运行分析，即获得异常维数矩阵。我们证明了几个明确的例子计算的方法。
We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, ie to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.