Two-loop diagrams in non-relativistic QCD with elliptics

Abstract

In this paper we consider two-loop two-, three- and four-point diagrams with elliptic structure in the case of two different masses $m$ and $M$. The latter diagrams generally arise within NRQCD matching procedures and are relevant for parapositronium decay and top pair production at threshold. 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 $\mathcal{O}(\epsilon )$ terms 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 representation.

Comments: 31 pages, 2 figures, matches journal version