{
  "abstract": "A bstract : 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.\n\nAs 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, which are included in the accompanying supplementary material. 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": [
    "Graduate School of China Academy of Engineering Physics",
    "Chinese Academy of Sciences",
    "Hangzhou Institute for Advanced Study and ICTP-AP, UCAS"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Fan Zhu",
      "orcid": "0009-0007-2188-4393"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Song He",
      "orcid": "0000-0002-9534-3844"
    },
    {
      "affs": [
        2
      ],
      "name": "Zhenqi Han",
      "orcid": "0009-0008-3656-8868"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75sa8a4bv620k.bib",
  "cited_by": 0,
  "doi": "10.1007/jhep10(2026)221",
  "fulltext_url": "https://doi.org/10.1007/JHEP10(2026)221",
  "id": "75sa8a4bv620k",
  "issns": [
    "1029-8479"
  ],
  "landing_url": "https://link.springer.com/article/10.1007/JHEP10(2026)221",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QC770-798"
    ],
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      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
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  "openalex": "W7166532721",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/JHEP10(2026)221.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/75sa8a4bv620k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "10.1007/jhep10(2026)221",
      "source": "crossref",
      "url": "https://link.springer.com/article/10.1007/JHEP10(2026)221"
    },
    {
      "first_seen": "2026-10-30T13:45:36Z",
      "native_id": "9881da9d7ae343f1a5ed763ac0d9990b",
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      "url": "https://doi.org/10.1007/jhep10(2026)221"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Particle physics theoretical and experimental studies",
      "subfield": "high-energy"
    }
  ],
  "title": "Planar loop integrands from cuts in D dimensions",
  "title_text": "Planar loop integrands from cuts in D dimensions",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:45:36Z",
  "url": "https://research.draconitic.com/paper/75sa8a4bv620k",
  "venue": "Journal of High Energy Physics",
  "versions": []
}