{
  "abstract": "We construct a dispersive representation of the relativistic $3\\to 3$ scattering amplitude for three identical spinless particles in the $S$-wave. The two-particle subenergy, instead of the total energy, is used as the dispersive variable. This choice keeps the physical dispersive contour free of the kinematical cuts that complicate total-energy dispersion relations. By separating discontinuities across the two-particle subenergy cuts from that across the three-body cut, we derive a linear integral equation with one-particle exchange as the driving term. We further show that the solution satisfies three-body unitarity as a consequence of two-body unitarity, analyticity, and crossing symmetry. For pair-wise interactions, this representation can be rewritten into the form used for isobar-spectator scattering. Finally, we give prescriptions for contour deformation and the subtraction of poles in the two-body subsystem amplitudes, which continue the amplitude onto adjacent unphysical Riemann sheets and thus provide direct access to the analytic structure relevant for three-body resonance poles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00985",
  "author_total": 2,
  "authors": [
    {
      "name": "Xu Zhang"
    },
    {
      "name": "Feng-Kun Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/er13pv84401vh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00985",
  "fulltext_url": null,
  "id": "er13pv84401vh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00985",
  "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-lat"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7206190951",
  "pdf_url": "https://arxiv.org/pdf/2609.00985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/er13pv84401vh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.00985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00985"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Amplitude structure of $3\\to 3$ scattering in a Mandelstam variable representation",
  "title_text": "Amplitude structure of 3→ 3 scattering in a Mandelstam variable representation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/er13pv84401vh",
  "venue": "arXiv",
  "versions": []
}