{
  "abstract": "The near-threshold $T_{cc}^{+}$ is a clean testing ground for how constituent-level colour structure connects to hadronic scattering. We report three results and state what each does and does not establish. (i)~\\emph{Colour algebra.} In the two-dimensional colour-singlet basis of $cc\\bar u\\bar d$, a general pairwise colour operator has direct $DD^*$ matrix element $V_{MM}=-\\tfrac43(v_{13}+v_{24})$, containing only the two intra-meson coefficients, while meson--hidden-colour mixing is $V_{MH}^{\\rm off}=\\tfrac{\\sqrt2}{3}Δ_v$ with $Δ_v=v_{14}+v_{23}-v_{12}-v_{34}$; uniform edges give no mixing. The projection is exact within this basis and is checked numerically on 10\\,000 random edge assignments. A same-Hamiltonian decomposition shows that it re-expresses the central colour operator ($116.46$ MeV off-diagonal) rather than adding an independent dynamical input. (ii)~\\emph{Negative dynamical results.} For Coulomb-type Gaussian edges the hidden-colour diagonal lies below the meson diagonal, so the attractive second-order shift $-2Δ_v^2/(9Δ_H)$ does not apply. In a Gaussian constituent Hamiltonian calibrated to $M_D$ and $M_{D^*}$, the lowest compact level lies $148.6$ MeV above its model $DD^*$ threshold (iii)~\\emph{Pion-mass test.} Couplings fixed at the $m_π\\simeq280$ MeV lattice pole ($-5.2$ MeV) are carried to $m_π\\simeq391$ MeV by changing only the reduced mass and compact-sector gap, both refitted to the lattice $D$ and $D^*$ masses. A one-channel separable Lippmann--Schwinger benchmark ($Λ=650$ MeV, $μ=967.7$ MeV, $C_G\\simeq-36.15~\\mathrm{GeV}^{-2}$) is calibrated to the $5.2$ MeV pole and serves only as a regulator-sensitivity study. We do not reproduce the complex lattice pole or perform a full coupled-channel calculation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39787",
  "author_total": 2,
  "authors": [
    {
      "name": "M. Monemzadeh"
    },
    {
      "name": "N. Tazimi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7d3djgapvys20.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39787",
  "fulltext_url": null,
  "id": "7d3djgapvys20",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39787",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39787",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7d3djgapvys20.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39787",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39787"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "From Colour--Casimir Recoupling to Near-Threshold Scattering: Algebraic Diagnostics and a Pion-Mass Test for the $T_{cc}^{+}$ Channel",
  "title_text": "From Colour--Casimir Recoupling to Near-Threshold Scattering: Algebraic Diagnostics and a Pion-Mass Test for the T_cc^+ Channel",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/7d3djgapvys20",
  "venue": "arXiv",
  "versions": []
}