{
  "abstract": "We study the $I^G(J^{PC})=0^+(1^{++})$ $K\\bar Kπ$ system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the $f_1(1285)$ and $f_1(1420)$ resonances. The coupled $πa_0$-$K\\bar K^*$ amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the $0^+(1^{++})$ component of the BESIII $K^0_SK^0_Sπ^0$ invariant-mass distribution in the $J/ψ\\toγ(K^0_SK^0_Sπ^0)$ decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: \\begin{align} \\sqrt{s_{f_1(1285)}}&= \\left(1277\\pm2\\pm1\\right) -\\mathrm{i}\\left(12\\pm1\\pm0\\right)\\text{MeV}\\,,\\notag\\\\ \\sqrt{s_{f_1(1420)}}&= \\left(1435\\pm2\\pm7\\right) -\\mathrm{i}\\left(40\\pm2\\pm1\\right)\\text{MeV}\\,.\\notag \\end{align} The pole trajectories indicate that the $f_1(1285)$ originates from dressing a bare state introduced in the potential. In contrast, the $f_1(1420)$ is predominantly dynamically generated, and a single-channel analysis traces it to an $S$-wave $K\\bar K^*$ quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the $f_1(1285)$. This additional pole is generated by the $P$-wave $πa_0$ contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Commun. Theor. Phys. 78 (2026) 125202",
  "arxiv": "2606.19040",
  "author_total": 5,
  "authors": [
    {
      "name": "Tao-Ran Hu"
    },
    {
      "name": "Hai-Long Fu"
    },
    {
      "name": "Feng-Kun Guo"
    },
    {
      "name": "Ulf-G. Meißner"
    },
    {
      "name": "Xu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nxvgqyf2hvt4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.19040",
  "fulltext_url": null,
  "id": "7nxvgqyf2hvt4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.19040",
  "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-ex"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "nucl-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.19040",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nxvgqyf2hvt4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2606.19040",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.19040"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Three-body unitary determination of the $f_1(1285)$ and $f_1(1420)$ pole positions",
  "title_text": "Three-body unitary determination of the f_1(1285) and f_1(1420) pole positions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/7nxvgqyf2hvt4",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1088/1572-9494/aea06c",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}