New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams
New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams
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某些一环、二环和三环费曼图的 ε 展开的新结果
DOI：
10.1016/s0550-3213(01)00095-5
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
M. Kalmykov
中科院分区：
文献类型：
--
作者：
A. I. Davydychev;M. Kalmykov
对于某些维数可调的一圈、二圈和三圈图，研究了ε-展开式的构造和结果的解析延拓问题。在一些示例中，可以计算ε-展开的任意项。对于更复杂的情况，仅得到ε中的少数高阶项。除了单圈两点图和三点图外，例子还包括两圈（主要是在壳层上）传播子型图和三圈真空图。作为副产品，建立了Clausen函数、广义对数正弦积分和某些Euler-Zagier和之间的新关系，并对辐角为1 ~ 4的超几何函数给出了一些有用的结果.
For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the ε-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the ε-expansion can be calculated. For more complicated cases, only a few higher terms in ε are obtained. Apart from the one-loop two- and three-point diagrams, the examples include two-loop (mainly on-shell) propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some new relations involving Clausen function, generalized log-sine integrals and certain Euler–Zagier sums are established, and some useful results for the hypergeometric functions of argument 1 4 are presented.