从Drell-Yan数据中符号提取非微扰横向动量依赖分布
Symbolic Extraction of Non-Perturbative Transverse-Momentum-Dependent Distributions from Drell-Yan Data
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中文总结 AI 辅助
该研究从Drell-Yan数据中，通过神经网络拟合与符号回归结合的方法提取非极化夸克的非微扰横向动量依赖分布函数，得到含9个自由常数的封闭形式函数，展示了符号回归在连接机器学习与解析参数化方面的作用，为非微扰QCD特征发现开辟路径。
中文摘要 AI 辅助
我们提出了一种非极化夸克的非微扰横向动量依赖（TMD）部分子分布函数的解析参数化方法，该方法通过神经网络拟合和符号回归相结合，从Drell-Yan数据中提取。利用因子分解神经网络直接针对固定靶、Tevatron、RHIC和LHC实验的实验截面数据进行训练，达到次下下领先对数精度，随后对每个网络组件应用符号回归以发现紧凑的解析表达式。最终公式从表达式复杂度和实验χ²空间中的帕累托前沿中选择，得到一个具有9个自由数值常数的封闭形式非微扰函数，在482个数据点上实现χ²/ndf = 1.040。即使在偏向零的稀疏先验下，非平凡的x - bT交叉项也被保留，表明纵向动量分数和横向动量之间存在轻微但真实的相关性。这项工作表明符号回归是连接灵活的机器学习拟合和可解释的解析TMD参数化的可行工具，并为数据驱动发现非微扰QCD的特定特征开辟了一条系统路径。
英文摘要
We present an analytical parametrization of the non-perturbative transverse-momentum-dependent (TMD) parton distribution function of unpolarized quarks, extracted from Drell-Yan data using a combination of neural-network fitting and symbolic regression. A factorized neural network is trained directly against experimental cross-section data from fixed-target, Tevatron, RHIC, and LHC experiments at next-to-next-to-next-to-leading logarithmic accuracy, and symbolic regression is subsequently applied to each network component to discover compact analytical expressions. The final formula is selected from a Pareto front in the space of expression complexity and experimental $χ^2$, yielding a closed-form non-perturbative function with 9 free numerical constants that achieves $χ^2/\mathrm{ndf}=1.040$ over 482 data points. A non-trivial $x$-$b_T$ cross term is retained even under a sparsity prior that biases it toward zero, indicating a mild but genuine correlation between the longitudinal momentum fraction and the transverse momentum. This work demonstrates that symbolic regression is a viable tool for bridging flexible machine-learning fits and interpretable analytical TMD parametrizations, and opens a systematic path toward data-driven discovery of specific features of non-perturbative QCD.
