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arXiv 0902.2656hep-ph
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FORM扇区分解的新实现

New implementation of the sector decomposition on FORM

Takahiro Ueda, Junpei Fujimoto

备注：
5 pages, uses PoS.cls, proceedings of ACAT 2008, Erice, Italy, Nov. 3-7, 2008
发表信息：
PoS ACAT08:120,2008
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摘要：

扇形分解技术可以分离积分的参数化表示中的发散项，是计算Feynman环积分的一个非常有用的工具。它用于验证多圈积分的解析结果在欧几里德区域，或在某些情况下，实际使用的物理区域，通过与其他方法相结合处理阈值。在多环积分扇形分解的中间阶段，常常需要处理包含大量项的极大表达式。符号处理系统FORM就是为处理这种庞大的表达式而设计的，它具有很强的优越性，本文讨论了在FORM上实现扇区分解算法。一些具体的例子，包括多回路图的情况下，也显示。

英文摘要：

Nowadays the sector decomposition technique, which can isolate divergences from parametric representations of integrals, becomes a quite useful tool for numerical evaluations of the Feynman loop integrals. It is used to verify the analytical results of multi-loop integrals in the Euclidean region, or in some cases practically used in the physical region by combining with other methods handling the threshold. In an intermediate stage of the sector decomposition for the multi-loop integrals, one often has to handle enormously large expressions containing tons of terms. The symbolic manipulation system FORM is originally designed to treat such huge expressions and has a strong advantage for it. In this talk, the implementation of the sector decomposition algorithm on FORM is discussed. A number of concrete examples including cases of multi-loop diagrams are also shown.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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