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

摘要

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(epsilon(0))-part and the O(epsilon(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 O(epsilon(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. (C) 2015 AIP Publishing LLC.