{
  "abstract": "We discuss the tension one encounters in trying to solve, simultaneously, the $U(1)$ and strong-$CP$ problems in QCD with light quarks and a small $\\barθ$ angle within QCD itself. We do so by considering the low-energy expansion of a $1$PI effective action $Γ$, a functional of a properly chosen set of gauge-invariant (composite) operators. After enforcing Ward-identity constraints on $Γ$, we prove, under minor assumptions, that $CP$ violation at small non-vanishing $\\barθ$ can be avoided only if the anomaly-induced contribution to the pseudoscalar mass matrix is completely negligible when compared to its non-anomalous counterpart - that is, only if the $U(1)$ problem is not solved. The topological susceptibility in QCD and a precise generalization of the one in pure Yang-Mills theory emerge as the most important players in establishing the above tension and in determining the corrections to various known results at leading order in $\\barθ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28253",
  "author_total": 5,
  "authors": [
    {
      "name": "Paolo Di Vecchia"
    },
    {
      "name": "Francesco Sannino"
    },
    {
      "name": "Graham M. Shore"
    },
    {
      "name": "Gabriele Veneziano"
    },
    {
      "name": "Shimon Yankielowicz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0dhrjjxfg1x9a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28253",
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  "id": "0dhrjjxfg1x9a",
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  "landing_url": "https://arxiv.org/abs/2608.28253",
  "language": "en",
  "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",
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  "openalex": "W7204752185",
  "pdf_url": "https://arxiv.org/pdf/2608.28253",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0dhrjjxfg1x9a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28253",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28253"
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    {
      "first_seen": "2026-10-30T12:17:31Z",
      "native_id": "hal-05742552",
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      "url": "https://hal.science/hal-05742552v1"
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  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Revisiting the $U(1)$-$CP$ tension in QCD from a 1PI-action perspective",
  "title_text": "Revisiting the U(1)-CP tension in QCD from a 1PI-action perspective",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:31Z",
  "url": "https://research.draconitic.com/paper/0dhrjjxfg1x9a",
  "venue": "arXiv",
  "versions": []
}