{
  "abstract": "Integrating scattering amplitudes over the forward direction, and consequently the unitarity constraints one extracts from such integrals, can appear ambiguous in theories with long-range forces. Standard techniques for bounding EFT couplings then typically produce bounds that depend on an arbitrary infrared scale. We study a non-relativistic model in which the standard techniques produce such an ambiguous bound, but which is simple enough that the exact bound can also be derived non-perturbatively and shown to involve no infrared scale. We then show how to derive bounds perturbatively, with no infrared scale entering at any stage. This requires two ingredients: accounting for the modified distributional structure of long-range amplitudes, and using distorted-wave perturbation theory (DWPT), which treats the Coulomb dynamics exactly. Together they give amplitudes with well-defined partial-wave projections and no spurious infrared divergences. Interpreting the model as an EFT with an ultraviolet cutoff $Λ_{\\rm EFT}$, we derive cutoff-dependent bounds valid for arbitrary UV completions. Taking $Λ_{\\rm EFT}\\to\\infty$ at each order yields bounds that rapidly converge to the exact bound, reaching $0.002\\%$ accuracy at fourth order in the expansion. Finally, we demonstrate that every order of the DWPT expansion resums infinitely many Feynman diagrams of short-range perturbation theory, which individually evaluate to multiple polylogarithms and complete elliptic integrals, into a compact expression. At the orders we compute, no integration is even required, suggesting that DWPT may offer a simpler representation of scattering amplitudes than standard perturbation theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16896",
  "author_total": 1,
  "authors": [
    {
      "name": "Luke Lippstreu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f8jf5y92vdq6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16896",
  "fulltext_url": null,
  "id": "8f8jf5y92vdq6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16896",
  "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-th"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7213403021",
  "pdf_url": "https://arxiv.org/pdf/2609.16896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8f8jf5y92vdq6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16896"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Unitarity and the Forward Direction in Theories with Long-Range Forces",
  "title_text": "Unitarity and the Forward Direction in Theories with Long-Range Forces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/8f8jf5y92vdq6",
  "venue": "arXiv",
  "versions": []
}