{
  "abstract": "A parton density depends on the renormalization scheme, and any two schemes are connected by a transformation that preserves the DGLAP form of the evolution. In Mellin space such a transformation acts on the evolution kernels as a gauge transformation, and we take this point of view throughout the discussion. For the unpolarized densities we first ask which transformations also preserve the charge-conjugation and flavor symmetries of the evolution kernels and the momentum and valence number sum rules. The symmetries reduce the transformation to a few blocks, and the sum rules constrain only two Mellin moments, where they leave a single freedom, the split of momentum between the quark singlet and the gluon, and freeze the valence numbers. The resulting classification is complete, because with asymptotic freedom as a boundary condition a change of scheme is determined by its action on the kernels. Inside this group, the transformations that preserve positivity form a semigroup, and the same argument covers the polarized densities. A transformation that fails only the sum rules is not lost either, since a normalization that the sum rules themselves determine repairs it, and we use this to define collinear densities as integrals of transverse-momentum-dependent densities without giving up the sum rules. We then use the same gauge freedom to solve the evolution. Gauging the kernel away reduces DGLAP at any order to a single second-order linear equation plus a quadrature, and it organizes the estimate of missing higher orders in a way that respects the sum rules exactly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18627",
  "author_total": 1,
  "authors": [
    {
      "name": "Tommaso Rainaldi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfns9z828wnhy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18627",
  "fulltext_url": null,
  "id": "dfns9z828wnhy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18627",
  "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"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7213493135",
  "pdf_url": "https://arxiv.org/pdf/2609.18627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfns9z828wnhy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.18627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18627"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Scheme transformations as the gauge group of DGLAP: sum rules, classification and solution",
  "title_text": "Scheme transformations as the gauge group of DGLAP: sum rules, classification and solution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/dfns9z828wnhy",
  "venue": "arXiv",
  "versions": []
}