{
  "abstract": "Calculating cross sections in the Color Glass Condensate effective theory requires Fourier transforms of multi-Wilson-line correlators from transverse coordinate space to transverse momentum space. Under the common assumption of impact-parameter independence, each transform reduces to a set of Hankel transforms whose Bessel-function kernels oscillate rapidly at phenomenologically relevant momenta, making direct quadrature prohibitively expensive. We present a Filon-type quadrature, applicable to any integrand, that integrates these oscillatory factors in closed form on the stored coordinate grid, reducing each Hankel transform to a precomputed weight vector and the full nested transform chain to a sequence of matrix products. We develop and validate the method on the deep inelastic scattering dijet cross section beyond the correlation-limit approximation, where an exprel-based reformulation of the quadrupole Wilson-line correlator removes a numerical $0/0$ instability inherent to its standard parametrization. Porting the calculation to the Graphics Processing Unit (GPU), with custom CUDA kernels that fuse the momentum-space contraction directly into the correlator evaluation, brings the runtime for one dipole input down to about two minutes on a single NVIDIA A800, from several hours on a multi-core Central Processing Unit (CPU). We further generalize the algorithm to three sequential Hankel transforms and validate the resulting six-dimensional transform against an analytic Gaussian integrand family with closed-form results at every stage. This general, process-independent algorithm is directly applicable to next-to-leading-order proton-nucleus and electron-ion scattering cross-section calculations performed without the correlation-limit approximation. The code is publicly available at https://github.com/CCNU-CGC-py/FFT_filon.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18589",
  "author_total": 4,
  "authors": [
    {
      "name": "Haowu Duan"
    },
    {
      "name": "Si-Wei Dai"
    },
    {
      "name": "Cong Yi"
    },
    {
      "name": "Wenbin Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5djfazdyh7h3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18589",
  "fulltext_url": null,
  "id": "5djfazdyh7h3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18589",
  "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"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2608.18589",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5djfazdyh7h3c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2608.18589",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18589"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Fourier Transforms of Color Glass Condensate Multi-Wilson-Line Correlators via Filon Quadrature",
  "title_text": "Fourier Transforms of Color Glass Condensate Multi-Wilson-Line Correlators via Filon Quadrature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/5djfazdyh7h3c",
  "venue": "arXiv",
  "versions": []
}