{
  "id": "2406.12051",
  "version": "v1",
  "published": "2024-06-17T19:44:20.000Z",
  "updated": "2024-06-17T19:44:20.000Z",
  "title": "Unregulated Divergences of Feynman Integrals",
  "authors": [
    "Wen Chen"
  ],
  "comment": "5 pages",
  "categories": [
    "hep-ph",
    "hep-th"
  ],
  "abstract": "Feynman integrals can be expanded asymptotically with respect to some small parameters at the integrand level, a technique known as the expansion by regions. A naive expansion by regions may break down due to divergences not regulated by the spacetime dimension, exemplified by the rapidity divergences. A criterion to identify unregulated divergences is provided in this article. The analysis is conducted using both parametric and Mellin-Barnes representations, leading to a consistent conclusion. Based on this analysis, it is proven that {\\it the presence of unregulated divergences implies the degeneracies of regions}, which may help to explain phenomena like the collinear anomaly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-17T19:44:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "feynman integrals",
      "explain phenomena",
      "small parameters",
      "rapidity divergences",
      "integrand level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}