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

2015/04/13 by Luise Adams, Adams, Luise, Christian Bogner +3 · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.1504.03255

Abstract

We present the result for the finite part of the two-loop sunrise integral\nwith unequal masses in four space-time dimensions in terms of the mathcal\nO(\ε⁰)-part and the mathcal O(\ε¹)-part of the\nsunrise integral around two space-time dimensions. The latter two integrals are\ngiven in terms of elliptic generalisations of Clausen and Glaisher functions.\nInteresting aspects of the result for the mathcal O(\ε¹)-part of\nthe sunrise integral around two space-time dimensions are the occurrence of\ndepth two elliptic objects and the weights of the individual terms.\n

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