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arXiv · 1504.03255

The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case

Luise Adams·Christian Bogner·Stefan Weinzierl
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Abstract

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 ${\mathcal O}(\varepsilon^0)$-part and the ${\mathcal O}(\varepsilon^1)$-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 ${\mathcal O}(\varepsilon^1)$-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.

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Luise Adams, Christian Bogner, Stefan Weinzierl. 2015-04-13. The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case. https://arxiv.org/abs/1504.03255

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