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arXiv · 1907.04638

Two-loop diagrams in non-relativistic QCD with elliptics

B. A. Kniehl·A. V. Kotikov·A. I Onishchenko·O. L. Veretin
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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.

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B. A. Kniehl, A. V. Kotikov, A. I Onishchenko, O. L. Veretin. 2019-07-10. Two-loop diagrams in non-relativistic QCD with elliptics. https://doi.org/10.1016/j.nuclphysb.2019.114780

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