{
  "abstract": "We present a direct reconstruction formula for planar loop integrands from $D$-dimensional generalized unitarity cuts in any colored theory. The reconstruction combinatorics is separated from the theory-dependent tree amplitudes entering the cuts: for the $L$-loop $n$-point color-ordered amplitude, the integrand is expressed as a sum over admissible non-scaleless scalar graphs dressed by corresponding cuts in $D$ dimensions; the coefficients are given by the universal Möbius-inversion formula of the refinement poset, or equivalently one minus the Euler characteristics of associated complexes. As an application we write down closed-formulas for loop integrands in pure Yang--Mills theory, where the required cuts are generated by gluing $D$-dimensional tree amplitudes and summing over internal gluon states. We also use the two-loop five-point case as a validation, comparing with known integrand data and after integration-by-parts reduction, with known integrated helicity amplitudes. The same framework also produces compact cut-organized data for larger examples, including the two-loop six-point and three-loop four-point cases. We also describe the corresponding simplification in maximally supersymmetric Yang--Mills theory, where the absence of bubble and triangle subgraphs reduces the relevant cut poset substantially.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.28052",
  "author_total": 3,
  "authors": [
    {
      "name": "Fan Zhu"
    },
    {
      "name": "Song He"
    },
    {
      "name": "Zhenqi Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x6bzk4w27zyx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.28052",
  "fulltext_url": null,
  "id": "5x6bzk4w27zyx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.28052",
  "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-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.28052",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x6bzk4w27zyx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2606.28052",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.28052"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Planar loop integrands from cuts in $D$ dimensions",
  "title_text": "Planar loop integrands from cuts in D dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:03Z",
  "url": "https://research.draconitic.com/paper/5x6bzk4w27zyx",
  "venue": "arXiv",
  "versions": []
}