{
  "abstract": "The conventional strong $CP$ problem arises from the tension between an unrestricted physical parameter $\\barθ$ and the experimental constraint $\\lvert\\barθ\\rvert\\lesssim10^{-10}$. In the standard formulation, a global topological classification of gauge-field configuration space leads to integer-valued sectors, $θ$-vacua, and $θ$ as a physical vacuum angle. Alternatively, a physical flavor-singlet pseudoscalar phase may be introduced through the quark mass matrix. The axial anomaly relates these descriptions through the invariant combination $\\barθ=θ+\\arg\\det M$. We ask the logically prior question of whether known physical principles or observables require the introduction of an independent physical flavor-singlet $CP$-violating parameter in QCD. We distinguish consequences of local gauge invariance and causal locality from those requiring additional global assumptions or the introduction of a physical flavor-singlet $CP$-violating parameter. For constant $θ$, the topological charge density is a total four-divergence with no local variational response to compactly supported field variations, and a nonzero $θ$ coupling is not required by perturbative renormalization. No established QCD phenomenology requires a physical $\\barθ$ parameter. Without such a parameter, the topological susceptibility, axial anomaly, 't~Hooft vertex, Leutwyler--Smilga and Witten--Veneziano relations, standard lattice QCD results, semiclassical instanton solutions, and established phenomenological successes of QCD all remain. Nothing prevents the introduction of $\\barθ$ as an independent physical parameter, which is consistent with these same QCD results. In this sense, establishing that the strong $CP$ problem is an \\emph{unavoidable} feature of QCD requires showing why a physical $\\barθ$ parameter is \\emph{required}, rather than merely allowed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10272",
  "author_total": 1,
  "authors": [
    {
      "name": "Anthony G. Williams"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6hsndrdbve7jd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10272",
  "fulltext_url": null,
  "id": "6hsndrdbve7jd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10272",
  "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"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7168279351",
  "pdf_url": "https://arxiv.org/pdf/2607.10272",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6hsndrdbve7jd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2607.10272",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10272"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "On the Origins of the Strong CP Problem",
  "title_text": "On the Origins of the Strong CP Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/6hsndrdbve7jd",
  "venue": "arXiv",
  "versions": []
}