{
  "id": "1907.04638",
  "version": "v1",
  "published": "2019-07-10T11:58:35.000Z",
  "updated": "2019-07-10T11:58:35.000Z",
  "title": "Two-loop diagrams in non-relativistic QCD with elliptics",
  "authors": [
    "B. A. Kniehl",
    "A. V. Kotikov",
    "A. I Onishchenko",
    "O. L. Veretin"
  ],
  "comment": "31 pages, 2 figures",
  "categories": [
    "hep-ph",
    "hep-th"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-10T11:58:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-relativistic qcd",
      "two-loop diagrams",
      "explicit series representation",
      "elliptic constants",
      "equal masses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}