The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
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DOI：
10.1063/1.4926985
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发表时间：
2015-04
影响因子：
1.3
通讯作者：
Luise Adams;C. Bogner;S. Weinzierl
中科院分区：
文献类型：
--
作者：
Luise Adams;C. Bogner;S. Weinzierl
我们用围绕两个时空维度的日出积分的 O(e0) 部分和 O(e1) 部分给出了四个时空维度上不等质量的二环日出积分的有限部分的结果。后两个积分是根据 Clausen 和 Glaisher 函数的椭圆推广给出的。围绕两个时空维度的日出积分的 O(e1) 部分结果的有趣方面是深度为 2 的椭圆形物体的出现以及各个项的权重。
We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the O(e0)-part and the O(e1)-part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the O(e1)-part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.