{
  "abstract": "We revisit single-inclusive gluon production in the dilute--dilute limit of the Color Glass Condensate and show that $k_\\perp$-factorization is only the zeroth order of a systematic gradient expansion in the transverse positions of the two colliding sources, organized in powers of $1/(Q_sR)$, with $Q_s$ the saturation scale and $R$ the size over which the sources vary. Collecting terms order by order builds a ladder of scalar and tensor structures from the local distributions and their transverse derivatives, yielding an extended $k_\\perp$-factorized formula that retains the spatial dependence of the sources and, through kinetic moments of the spectrum, the energy-momentum tensor. Repeating the expansion from a real-time computation of the classical Glasma fields in the future light cone reproduces the momentum-space result in the eikonal limit, but additionally retains coherent interference between amplitude and conjugate. This adds terms to the ladder (flow responses, chromo-electric--magnetic interference, and a longitudinal energy flux) further suppressed by powers of the large outgoing momentum $|\\pp|\\gg Q_s$. The hierarchy thus reveals momentum-space anisotropies present in the initial state before any hydrodynamic evolution, which leading $k_\\perp$-factorization misses by construction. Since each order is a local operator on the same unintegrated distributions, these corrections can be added directly to existing saturation-based initial-state models, giving a dynamically generated initial momentum anisotropy and a more faithful early-time energy-momentum tensor without abandoning the tractable factorized form. Set by gradients of the transverse density profiles, they grow towards more dilute, fluctuation-dominated systems, e.g. light-ion collisions. Phenomenological consequences will be developed in a companion paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07847",
  "author_total": 1,
  "authors": [
    {
      "name": "Oscar Garcia-Montero"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czdx53jj64pgm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07847",
  "fulltext_url": null,
  "id": "czdx53jj64pgm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07847",
  "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"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|High-Energy Particle Collisions Research"
    ]
  ],
  "openalex": "W7212035594",
  "pdf_url": "https://arxiv.org/pdf/2609.07847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czdx53jj64pgm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07847"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Initial momentum anisotropies in the kT-factorization of the CGC I: Gradient Expansion",
  "title_text": "Initial momentum anisotropies in the kT-factorization of the CGC I: Gradient Expansion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/czdx53jj64pgm",
  "venue": "arXiv",
  "versions": []
}