{
  "abstract": "The long-standing upward shift of the extracted $ψ(4160)$ mass, from about $4.16$~GeV to $4.19$~GeV in later analyses, remains a puzzling issue in charmonium spectroscopy. In our previous study, this problem was investigated through the $B^+\\to K^+μ^+μ^-$ process within an unquenched charmonium framework, where the lower-mass $ψ(4160)$ assignment was found to be compatible with the data. Here we revisit the BESII $R$-value data, which played an important role in the historical extraction of the higher $ψ(4160)$ mass, and provide an independent examination. In contrast to the conventional quenched picture with $ψ(4040)$, $ψ(4160)$, and $ψ(4415)$, the unquenched vector-charmonium spectrum contains six states: $ψ(4040)$, $ψ(4160)$, $ψ(4220)$, $ψ(4380)$, $ψ(4415)$, and $ψ(4500)$. Including these states together with the near-threshold $ψ(3770)$, we find that the BESII $R$-value line shape can be well reproduced over the full energy range while retaining the lower-mass $ψ(4160)$ assignment. The enhancement around $4.19$~GeV then arises from the coherent interplay among the nearby $ψ(4040)$, $ψ(4160)$, and $ψ(4220)$ amplitudes, rather than requiring an upward shift of the $ψ(4160)$ mass itself. The additional higher states also naturally describe the line-shape structure in the $4.4$~GeV region. We further show that the seven-resonance coherent amplitude contains six complex zeros, yielding $2^6=64$ mathematically equivalent solutions with identical line shapes but substantially different di-electron widths and relative phases. Comparing these solutions with available experimental information and representative unquenched charmonium predictions, we provide a qualitative assessment of their phenomenological consistency and highlight several solutions that appear more compatible with present information.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19673",
  "author_total": 2,
  "authors": [
    {
      "name": "Tian-Cai Peng"
    },
    {
      "name": "Xiang Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1r4tf3wayq183.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19673",
  "fulltext_url": null,
  "id": "1r4tf3wayq183",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19673",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ex"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7213602107",
  "pdf_url": "https://arxiv.org/pdf/2609.19673",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1r4tf3wayq183.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19673",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19673"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    }
  ],
  "title": "Clarifying the puzzling mass shift of the $ψ(4160)$ via a reanalysis of $R$-value data with unquenched charmonium spectroscopy",
  "title_text": "Clarifying the puzzling mass shift of the ψ(4160) via a reanalysis of R-value data with unquenched charmonium spectroscopy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/1r4tf3wayq183",
  "venue": "arXiv",
  "versions": []
}