Fourier Transforms of Color Glass Condensate Multi-Wilson-Line Correlators via Filon Quadrature
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.
Related
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- Bootstrapping Wilson lines in Critical Bosonic QED3 Part 1: Large-N endpoint correlators and CFT data
- Conditioning-Free Non-Uniform Quantum Fourier and Chebyshev Transforms
- Efficient Quantum Fourier Transforms For Semisimple Algebras
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BibTeX
@misc{duan2026fourier,
title = {{Fourier Transforms of Color Glass Condensate Multi-Wilson-Line Correlators via Filon Quadrature}},
author = {Haowu Duan and Si-Wei Dai and Cong Yi and Wenbin Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.18589},
eprint = {2608.18589},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18589},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fourier Transforms of Color Glass Condensate Multi-Wilson-Line Correlators via Filon Quadrature
AU - Haowu Duan
AU - Si-Wei Dai
AU - Cong Yi
AU - Wenbin Zhao
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2608.18589
UR - https://arxiv.org/abs/2608.18589
AB - 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.
ER -