论文标题
非平凡的一环递归还原关系
Nontrivial One-loop Recursive Reduction Relation
论文作者
论文摘要
在ARXIV：2204.03190中，我们提出了一种通用方法，可以减少具有张量结构和更高功率传播器的单环积分。但是该方法非常冗余，因为它在解决某些张量积分时不会利用较低等级情况的结果。最近，我们发现了一个显着的递归关系ARXIV：2203.16881,2205.03000，其中张量积分还原为较低的积分，而\ textit {soulower {sower tenter}与积分相对应，而一个或多个传播器被取消。但是，较低项的表达尚不清楚。在本文中，我们得出了非统一和退化病例的这种非平凡的递归关系，并为较低的术语提供了明确的表达，从而简化并加快了还原过程。
In arXiv:2204.03190, we proposed a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. But the method is quite redundant as it does not utilize the results of lower rank cases when addressing certain tensor integrals. Recently, we found a remarkable recursion relation arXiv:2203.16881,2205.03000, where a tensor integral is reduced to lower-rank integrals and \textit{lower terms} corresponding to integrals with one or more propagators being canceled. However, the expression of the lower terms is unknown. In this paper, we derive this non-trivial recursion relation for non-degenerate and degenerate cases and provides an explicit expression for the lower terms, thus simplifying and speeding up the reduction process.
