{
  "abstract": "Spontaneous symmetry breaking (SSB) is conventionally understood through static vacuum selection in low-energy approximations. However, the nonperturbative dynamical pathways connecting symmetric configurations to asymmetric states remain an open question. In this paper, we propose an operator-theoretic framework that characterizes $Z_{2}$ symmetry breaking in scalar field theory through spectral branching. Specifically, we identify an effective invariant manifold of the nonlinear Klein-Gordon equation termed the \"symmetric dual breather mode,\" whose phase-space geometry is traced using a $t$-dependent finite-dimensional representation. Our analysis demonstrates that static SSB represents merely a small-amplitude limit ($A \\ll ϕ_{v1}$). As the amplitude increases into the heteroclinic regime ($A > ϕ_{v1}$), the field dynamically overflows the central barrier, yielding a vanishing time-averaged order parameter ($\\langle ϕ\\rangle = 0$) and driving a geometric curvature cancellation ($\\langle V''(ϕ) \\rangle_{t} \\to 0$). Governed by a universal scaling function $\\mathfrak{F}(y)$, the logarithmic period divergence near the heteroclinic boundary naturally generates sub-eV effective mass scales without fine-tuning bare parameters. Furthermore, this dynamic barrier overflow naturally favors Majorana-like self-conjugate states over Dirac-type states. Additionally, nonlinear phase interference along the heteroclinic channel induces asymmetric phase-space contraction, decoupling the right-handed mode and dynamically giving rise to the left-handed Weyl equation. These results bridge nonperturbative wave dynamics, topological mass suppression, chiral selection, and the dynamic origin of active neutrino masses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15990",
  "author_total": 2,
  "authors": [
    {
      "name": "Yoritaka Iwata"
    },
    {
      "name": "Yasuhiro Takei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1a97791wr9pwb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15990",
  "fulltext_url": null,
  "id": "1a97791wr9pwb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15990",
  "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"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "nlin.PS"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7221807280",
  "pdf_url": "https://arxiv.org/pdf/2610.15990",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1a97791wr9pwb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15990",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15990"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.PS",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Symmetric Dual Breather Modes as a Dynamic Origin of Tiny Particle Masses",
  "title_text": "Symmetric Dual Breather Modes as a Dynamic Origin of Tiny Particle Masses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/1a97791wr9pwb",
  "venue": "arXiv",
  "versions": []
}