通过菲隆求积法计算色玻璃凝聚多威尔逊线关联函数的傅里叶变换
Fourier Transforms of Color Glass Condensate Multi-Wilson-Line Correlators via Filon Quadrature
- Central China Normal University（华中师范大学）
- Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（夸克与轻子物理教育部重点实验室及粒子物理研究所，华中师范大学）
- Artificial Intelligence and Computational Physics Research Center, Central China Normal University（人工智能与计算物理研究中心，华中师范大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本研究提出菲隆型求积法，解决色玻璃凝聚中多威尔逊线关联函数傅里叶变换的高成本问题，经GPU优化后大幅缩短运行时间，可应用于次领头阶散射截面计算。
中文摘要 AI 辅助
在色玻璃凝聚（Color Glass Condensate, CGC）有效理论中计算散射截面，需要将多威尔逊线（multi-Wilson-line）关联函数从横向坐标空间变换到横向动量空间的傅里叶变换。在常见的碰撞参数无关假设下，每次变换会简化为一组汉克尔（Hankel）变换，其贝塞尔函数核在与现象学相关的动量处振荡剧烈，导致直接求积的计算成本过高。我们提出一种适用于任意被积函数的菲隆型（Filon-type）求积法，该方法在存储的坐标网格上以闭式形式积分这些振荡因子，将每个汉克尔变换简化为预计算的权重向量，将完整的嵌套变换链简化为一系列矩阵乘积。我们在超出关联极限近似的深度非弹性散射双喷注截面场景中开发并验证了该方法，其中基于指数函数近似（exprel）的四极威尔逊线关联函数重构，消除了其标准参数化中固有的数值0/0不稳定性。将该计算移植到图形处理器（GPU）上，通过自定义CUDA内核将动量空间收缩直接融合到关联函数计算中，使单个偶极输入的运行时间从多核中央处理器（CPU）上的数小时缩短至单个NVIDIA A800上的约两分钟。我们进一步将该算法推广到三次连续汉克尔变换，并针对每一步均有闭式结果的解析高斯被积函数族验证了所得的六维变换。这种通用的、与过程无关的算法可直接应用于无关联极限近似的次领头阶质子-原子核和电子-离子散射截面计算，代码可在该https URL处公开获取。
英文摘要
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.
