{
  "abstract": "We investigate the phenomenological consequences of a genuine three-body holonomy in a relativistic Dirac system in one spatial dimension. After removing the center-of-mass coordinate, the triple-coincidence point punctures the two-dimensional relative configuration space and permits a nontrivial $U(1)$ winding phase, whereas the pairwise Sakamoto--Munakata--Ino contact interactions give trivial net matching around this point. At fixed intrinsic parity, the six particle-ordering sectors reduce to a three-dimensional cyclic space. A Hermitian $C_3$-invariant effective mass operator admits a Peierls-type realization in which the gauge-invariant phase around the three links equals the three-body holonomy $θ_3$. Its eigenvalues are $$ M^{[k]}=M_0+2Δ\\cos\\!\\left(\\frac{θ_3+2πk}{3}\\right), \\qquad k=0,1,2. $$ The holonomy lifts the conjugate-channel degeneracy and can generate a parametrically light branch through cancellation between the common mass and the holonomy-induced shift. We further allow cyclic-symmetry breaking and consider a general Hermitian three-state mass matrix. Exact elimination of two heavy states by the Schur complement yields a low-energy correction containing the rephasing-invariant loop product $\\mathrm{Re}(t_{12}t_{23}t_{31})\\propto\\cosθ_3$. Thus, even when only one branch is kinematically accessible, its effective mass can retain finite memory of the complete three-state loop. The complementary invariant $\\mathrm{Im}(t_{12}t_{23}t_{31})\\propto\\sinθ_3$ is phase sensitive but does not alone imply CP violation. The construction provides a low-dimensional phenomenological proof of concept for family-like triplication, mass hierarchy, and infrared memory, rather than a microscopic theory of Standard Model fermion generations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24022",
  "author_total": 1,
  "authors": [
    {
      "name": "Tadashi YOSHIKAWA"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gcgz4vwwf6nq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24022",
  "fulltext_url": null,
  "id": "0gcgz4vwwf6nq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24022",
  "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-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7214052904",
  "pdf_url": "https://arxiv.org/pdf/2609.24022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gcgz4vwwf6nq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.24022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24022"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Three-Body Holonomy as a Toy-Model Mechanism for Family Triplication and Mass Hierarchy in (1+1) Dimensions",
  "title_text": "Three-Body Holonomy as a Toy-Model Mechanism for Family Triplication and Mass Hierarchy in (1+1) Dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/0gcgz4vwwf6nq",
  "venue": "arXiv",
  "versions": []
}