{
  "abstract": "We initiate the study of two-to-two scattering amplitudes involving two distinct scalar particles in $d = 4$ spacetime dimensions using the primal S-matrix bootstrap. We impose a $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ global symmetry under which the two particles are the lightest ones carrying charges $(-,+)$ and $(+,-)$, guaranteeing their absolute stability and absence of triangular anomalous thresholds. For unequal masses, the presence of a pseudo-physical cut whose discontinuity is not directly constrained by physical unitarity qualitatively changes the bootstrap problem. We find several observables to be unbounded, while others obey non-trivial one-sided bounds or become bounded once another observable is fixed. In the equal-mass limit, where the pseudo-physical region disappears, two-sided bounds are recovered. As a proof of concept, we show that supplying information about the pseudo-physical discontinuity through an Omnès parametrisation also restores boundedness. Our results provide a starting point for future studies of physical processes such as pion-kaon and pion-nucleon scattering.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09282",
  "author_total": 4,
  "authors": [
    {
      "name": "Gabriele Ferretti"
    },
    {
      "name": "Denis Karateev"
    },
    {
      "name": "Alessandro Piazza"
    },
    {
      "name": "Marco Serone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bhy9rmyztwhda.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09282",
  "fulltext_url": null,
  "id": "bhy9rmyztwhda",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09282",
  "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",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7212123173",
  "pdf_url": "https://arxiv.org/pdf/2609.09282",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bhy9rmyztwhda.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09282",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09282"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Bounds on scattering amplitudes of non-identical scalar particles in 4d",
  "title_text": "Bounds on scattering amplitudes of non-identical scalar particles in 4d",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/bhy9rmyztwhda",
  "venue": "arXiv",
  "versions": []
}