{
  "abstract": "We revisit the $e^+e^- \\to ϕπ^+π^-$ reaction within the $K_1$-$\\bar{K}$-$K$ triangle dynamics framework, in which the $e^+e^-$ pair annihilates through one-photon exchange approximation to produce a $K_1\\bar{K}$ pair, followed by the $K_1 \\toϕK$ decay and the final-state $K\\bar{K} \\to π^+π^-$ rescattering. With the same theoretical formalism and model parameters, the $e^+e^- \\to ϕK^+K^-$ reaction is investigated, and it is found that the predicted total cross sections for the $e^+ e^- \\to ϕK^+ K^-$ reaction are in good agreement with the existing BESIII measurements. Our study shows that the triangle singularity in the $ϕK^+K^-$ channel is strongly suppressed, because the higher $K^+K^-$ mass threshold shifts the kinematics away from the triangle singularity condition and the phase space near the $K_1\\bar{K}$ threshold is very limited. Moreover, the interference between the tree-level and loop amplitudes eliminates the remaining signal. These combined effects naturally explain the absence of a distinct $ϕ(2170)$ signal in the $e^+ e^- \\to ϕK^+ K^-$ reaction, provide a strong test of the model, and reinforce the picture that both reactions are governed by the same underlying mechanism, in which the $ϕ(2170)$ state is produced in the $e^+ e^-$ annihilation from the $K_1$-$\\bar{K}$-$K$ triangle loop.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19951",
  "author_total": 7,
  "authors": [
    {
      "name": "Xiang Wei"
    },
    {
      "name": "Cheng Chen"
    },
    {
      "name": "Si-Wei Liu"
    },
    {
      "name": "Zu-Xin Cai"
    },
    {
      "name": "Gang Li"
    },
    {
      "name": "Xiao-Hai Liu"
    },
    {
      "name": "Ju-Jun Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffdmbymyjjs8n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19951",
  "fulltext_url": null,
  "id": "ffdmbymyjjs8n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19951",
  "language": null,
  "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",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7213600492",
  "pdf_url": "https://arxiv.org/pdf/2609.19951",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffdmbymyjjs8n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19951",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19951"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Study of the $e^+e^- \\to ϕK^+K^-$ reaction within triangle dynamics and its implications for the $ϕ(2170)$",
  "title_text": "Study of the e^+e^- → ϕK^+K^- reaction within triangle dynamics and its implications for the ϕ(2170)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/ffdmbymyjjs8n",
  "venue": "arXiv",
  "versions": []
}