# Two-loop diagrams in non-relativistic QCD with elliptics

## TL;DR

This paper computes complex two-loop Feynman diagrams with elliptic structures in non-relativistic QCD, providing multiple representations and explicit results relevant for particle decay and production processes.

## Contribution

It introduces new methods for evaluating two-loop diagrams with elliptic structures in NRQCD, including series, integral, and hypergeometric function representations.

## Key findings

- Results valid up to ( ext{epsilon}) in 4-2 dimensions
- Explicit series in elliptic constants for equal masses
- Applicable to parapositronium decay and top pair production

## 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 $\mathcal{O}(\varepsilon)$ terms in $d=4-2\varepsilon$ 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.