{
  "abstract": "In high-energy physics, short-lived resonances appearing in scattering processes are described by energy-dependent spectral functions. The relativistic Breit--Wigner distribution (rBW), obtained as a relativistic extension of the standard Breit--Wigner form, is commonly employed owing to its simplicity. However, when the lower-energy threshold lies sufficiently close to the resonance peak, sizable deviations from the rBW line shape are expected. The Sill distribution provides a simple way to incorporate the physical threshold while preserving exact normalization, but in its original formulation it is inherently restricted to $s$-wave decays. Here, we extend the Sill distribution to arbitrary partial waves. The correct $\\ell$-wave threshold behaviour is implemented while exact normalization is retained through a simple modification of the mass term of the propagator. As a benchmark, the $p$-wave Sill provides a very good description of the $Δ(1232)^{++}$ line shape up to 1.35 GeV and simultaneously reproduces its on-shell mass and width and its complex pole position, in agreement with independent determinations compiled by the PDG.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20975",
  "author_total": 2,
  "authors": [
    {
      "name": "Krzysztof Kyzioł"
    },
    {
      "name": "Francesco Giacosa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bt490xs9y5cc7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20975",
  "fulltext_url": null,
  "id": "bt490xs9y5cc7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20975",
  "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-ex"
    ],
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7222654445",
  "pdf_url": "https://arxiv.org/pdf/2610.20975",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bt490xs9y5cc7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.20975",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20975"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "The Sill distribution for all partial waves",
  "title_text": "The Sill distribution for all partial waves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:50Z",
  "url": "https://research.draconitic.com/paper/bt490xs9y5cc7",
  "venue": "arXiv",
  "versions": []
}