{
  "id": "2008.04823",
  "version": "v1",
  "published": "2020-08-11T16:16:21.000Z",
  "updated": "2020-08-11T16:16:21.000Z",
  "title": "Decomposition of Feynman Integrals by Multivariate Intersection Numbers",
  "authors": [
    "Hjalte Frellesvig",
    "Federico Gasparotto",
    "Stefano Laporta",
    "Manoj K. Mandal",
    "Pierpaolo Mastrolia",
    "Luca Mattiazzi",
    "Sebastian Mizera"
  ],
  "comment": "51 Pages",
  "categories": [
    "hep-th",
    "hep-ph"
  ],
  "abstract": "We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-11T16:16:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "feynman integrals",
      "direct decomposition",
      "master integrals",
      "generic multi-loop integrals",
      "perform explicit computations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}