{
  "id": "2010.06947",
  "version": "v1",
  "published": "2020-10-14T10:50:55.000Z",
  "updated": "2020-10-14T10:50:55.000Z",
  "title": "Resummation methods for Master Integrals",
  "authors": [
    "Dhimiter D. Canko",
    "Nikolaos Syrrakos"
  ],
  "comment": "20 pages, 2 figures and 2 tables",
  "categories": [
    "hep-ph",
    "hep-th"
  ],
  "abstract": "We present two new beneficial methods emerging from the application of the Simplified Differential Equations approach to a canonical basis of master integrals. The first one is a method which allows for an easy determination of the boundary conditions, since it finds relations between the boundaries of the basis elements and the second one indicates how using the $x \\rightarrow 1$ limit to the solutions of a canonical basis, one can obtain the solutions to a canonical basis for the same problem with one mass less. Both methods utilise the residue matrices for the letters $\\{0,1\\}$ of the canonical differential equation. As proof of concept, we apply these methods to a canonical basis for the three-loop ladder-box with one external mass off-shell, obtaining subsequently a canonical basis for the massless three-loop ladder-box as well as its solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-14T10:50:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "master integrals",
      "canonical basis",
      "resummation methods",
      "three-loop ladder-box",
      "simplified differential equations approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}