AI 中文总结
该研究提出物理信息型深度神经网络方法，从Drell-Yan数据提取$b_T$空间非极化TMDPDFs，通过特定微扰处理与稳健性测试得到验证，为相关物理研究提供基准与可识别性研究支持。
AI 中文摘要
我们提出一种物理信息型深度神经网络方法，用于从Drell-Yan数据中提取 impact-parameter 空间内的非极化横向动量依赖部分子分布函数（TMDPDFs）。微扰贡献通过重求和$W$项计算，采用$\text{N}^3\text{LL}$演化、严格NLO硬散射和算符乘积展开匹配，以及小$b_T$和大$b_T$处的平滑轮廓标度。一个紧凑的特征-wise 线性调制网络仅学习共享的非微扰因子$F_{\text{NP}}(x,b_T)$；共线PDFs、硬因子、演化核、匹配系数和傅里叶-贝塞尔变换保持固定。主要结果是得到平滑的轻味$b_T$空间TMD集合及其截面级验证。所报告的$k_T$分布是正则化的有限$b_T$汉克尔变换，而非独立的动量空间拟合。作为单独的稳健性测试，对延伸至$q_T/Q\backsimeq0.30$的24个额外Tevatron点应用平滑的有限$Y$过渡；标称的329点拟合保持不变，且当$F_{\text{NP}}$固定而过渡轮廓变化时，结果仍稳定。一个独立的122-bin Tevatron $\text{N}^3\text{LL}+\text{NNLO}$ $W+Y$网格提供直接的微扰基准。使用指定的非LHCb有限$Y$输入的单独$W+Y$候选物被保留作为可识别性研究。
英文摘要
We present a physics-informed deep-neural-network extraction of unpolarized transverse-momentum-dependent parton distribution functions (TMDPDFs) in impact-parameter space from Drell--Yan data. The perturbative contribution is computed with a resummed $W$ term using $\mathrm{N}^{3}\mathrm{LL}$ evolution, strict-NLO hard and operator-product-expansion matching, and smooth profile scales at small and large $b_T$. A compact feature-wise linear modulation network learns only a shared nonperturbative factor $F_{NP}(x,b_T)$; the collinear PDFs, hard factor, evolution kernel, matching coefficients, and Fourier--Bessel transform remain fixed. The primary result is a smooth light-flavor $b_T$-space TMD ensemble and its cross-section-level validation. The reported $k_T$ distributions are regularized finite-$b_T$ Hankel transforms, not independent momentum-space fits. As a separate robustness test, a smooth finite-$Y$ transition is applied to 24 additional Tevatron points extending to $q_T/Q\simeq0.30$. The nominal 329-point fit is unchanged, and the results remain stable when $F_{\rm NP}$ is held fixed while the transition profile is varied. An independent 122-bin Tevatron $\mathrm{N}^{3}\mathrm{LL}+\mathrm{NNLO}$ $W+Y$ grid provides a direct perturbative benchmark. A separate $W+Y$ candidate using the specified non-LHCb finite-$Y$ inputs is retained as an identifiability study.
