{
  "abstract": "The transverse shape of the proton's small-$x$ gluon distribution is determined from exclusive $J/ψ$ photoproduction at HERA. We derive analytic expressions for the coherent and incoherent diffractive cross sections in the hotspot model at leading twist, enabling a global fit to all 104 available H1 and ZEUS data points, with $|t|<30~{\\rm GeV}^2$ and $40\\leq W\\leq 251~{\\rm GeV}$, with $χ^2/{\\rm ndf}=0.72$. The gluonic hotspots are resolved into a core of size 0.088(10) fm surrounded by an exponential halo of range 0.20(2) fm, matching the penetration depth of lattice flux tubes. This shape is stable over $\\xpom$ and over the assumed number of hotspots in the range $5\\leq N_{hs}\\leq 12$. We find the Ginzburg-Landau parameter of the QCD vacuum to be $κ=2.7(7)$, which corresponds to fluxtube geometry in a type-II dual superconductor. The calculated QCD string-tension from the extracted parameter values is in agreement with theoretical calculations on the lattice. The gluonic geometry evolves only through a slow transverse diffusion of the hotspot centers with $α'_{\\rm eff.}=0.060(19)~{\\rm GeV}^{-2}$, while the incoherent cross section at small $|t|$ is dominated by shot-noise fluctuations at the order of a few gluons per hotspot.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.14955",
  "author_total": 2,
  "authors": [
    {
      "name": "Tobias Toll"
    },
    {
      "name": "Nahid Vasim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab32n961x8ppp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.14955",
  "fulltext_url": null,
  "id": "ab32n961x8ppp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.14955",
  "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": "W7169604531",
  "pdf_url": "https://arxiv.org/pdf/2607.14955",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab32n961x8ppp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2607.14955",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.14955"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Determining the Proton's Gluon Cloud Geometry from HERA Data",
  "title_text": "Determining the Proton's Gluon Cloud Geometry from HERA Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/ab32n961x8ppp",
  "venue": "arXiv",
  "versions": []
}