{
  "abstract": "The Low-Burnett-Kroll theorem (extended to non-abelian gauge theory) states that the tree-level emission amplitude of a soft gauge boson from an arbitrary hard process can be expressed in terms of the non-radiative amplitude including the next-to-soft term. Reformulating the soft theorem in the framework of an on-shell effective theory leads to a natural gauge-invariant split into an external and internal emission process to any order in the soft expansion. In this framework, we derive a compact expression for the all-order external emission amplitude expressed in terms of the non-radiative amplitude, and express the local emission amplitude through a single gauge-invariant operator at every order beyond the next-to-soft one. For scalar QCD, we compare the number of Lorentz- and $SU(3)$-invariant amplitudes for the radiative and non-radiative hard process with an arbitrary number of scalar quarks and antiquarks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10069",
  "author_total": 3,
  "authors": [
    {
      "name": "Martin Beneke"
    },
    {
      "name": "Maria Santana"
    },
    {
      "name": "Michel Stillger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bgbf5pavj586.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10069",
  "fulltext_url": null,
  "id": "7bgbf5pavj586",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10069",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7212137887",
  "pdf_url": "https://arxiv.org/pdf/2609.10069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bgbf5pavj586.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10069"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "On the universality of soft emission beyond the next-to-soft order",
  "title_text": "On the universality of soft emission beyond the next-to-soft order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/7bgbf5pavj586",
  "venue": "arXiv",
  "versions": []
}