{
  "abstract": "We calculate the one- and two-loop running couplings for a massless photon coupled to dyons, including CP violating couplings. The electric and magnetic source vertices in the most general theory form a real coupling matrix $C$, while a current-current interaction depends on $C^T C$ and the quantized determinant $\\det C$. These determine, respectively, the continuously running Coulombic interactions and the fixed antisymmetric Dirac--Schwinger--Zwanziger charge quantization condition which also determines pairwise helicity. The running preserves $\\det C$, showing that the electric and magnetic couplings run inversely while every pairwise helicity remains constant. We comment on how the running of the CP-odd coupling $θ$ relates to physical CP violation, which also depends on the spectrum, mass phases, and threshold corrections. We also show that an invertible field redefinition moves the CP-odd coupling between the current source terms and the photon kinetic terms; these are two descriptions of the same local interaction. Finally, we show that the result agrees with the Argyres--Douglas $β$ function ansatz.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07016",
  "author_total": 3,
  "authors": [
    {
      "name": "Joshua Newey"
    },
    {
      "name": "John Terning"
    },
    {
      "name": "Christopher B. Verhaaren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kke8q160erf0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07016",
  "fulltext_url": null,
  "id": "6kke8q160erf0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07016",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kke8q160erf0.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.07016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07016"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Running Couplings in CP Violating Abelian Theories",
  "title_text": "Running Couplings in CP Violating Abelian Theories",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:39Z",
  "url": "https://research.draconitic.com/paper/6kke8q160erf0",
  "venue": "arXiv",
  "versions": []
}