Two-loop diagrams in nonrelativistic QCD with elliptics

We consider two-loop two-, three-, and four-point diagrams with elliptic subgraphs involving two different masses, m and M. Such diagrams generally arise in matching procedures within nonrelativistic QCD and QED and are relevant, e.g., for top-quark pair production at threshold and parapositronium decay. We present the obtained results in several different representations: series solution with binomial coefficients, integral representation, and representation in terms of generalized hypergeometric functions. The results are valid up to terms of O(epsilon) in d = 4 - 2 epsilon space-time dimensions. In the limit of equal masses, m = M, the obtained results are written in terms of elliptic constants with explicit series representations. (C) 2019 The Authors. Published by Elsevier B.V