{
  "abstract": "We study the Sudakov form factor and the four-point scattering amplitude on the Coulomb branch of planar $\\mathcal{N}=4$ SYM as functions of the Coulomb-branch parameters and kinematic invariants. This setup provides a controlled probe of the interpolation between on- and off-shell regimes of infrared-sensitive quantities in gauge theories. We identify a novel scaling limit in which both observables exhibit double-logarithmic behavior governed by a walking anomalous dimension. As the mass scales are varied, this walking anomalous dimension interpolates between the cusp anomalous dimension of the on-shell regime and the octagon anomalous dimension of the off-shell regime. Based on the explicit two-loop result and the expected all-order structure, we propose an all-loop form for the walking anomalous dimension both for the form factor and for the four-point scattering amplitude. These all-loop expressions depend on new, presently unknown functions of the 't Hooft coupling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.16034",
  "author_total": 5,
  "authors": [
    {
      "name": "Luis F. Alday"
    },
    {
      "name": "Elisabetta Armanini"
    },
    {
      "name": "Andrei V. Belitsky"
    },
    {
      "name": "Kelian Häring"
    },
    {
      "name": "Alexander Zhiboedov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94drgy3b93h45.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.16034",
  "fulltext_url": null,
  "id": "94drgy3b93h45",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.16034",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7161607707",
  "pdf_url": "https://arxiv.org/pdf/2605.16034",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94drgy3b93h45.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2605.16034",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.16034"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Walking Sudakov: From Cusp to Octagon",
  "title_text": "Walking Sudakov: From Cusp to Octagon",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/94drgy3b93h45",
  "venue": "arXiv",
  "versions": []
}