AI 中文总结
该研究提出物理信息神经网络框架，结合共线改进的Balitsky-Kovchegov演化方程，无偏数据驱动确定色玻璃凝聚中核胶子偶极振幅，重现实验数据并预测碰撞可观测量，为核结构研究提供新方法。
AI 中文摘要
胶子饱和限制了小Bjorken-x下部分子密度的增长，且预计在重核中表现最为显著。然而，长期以来对核胶子偶极振幅的定量提取一直依赖参数化的初始条件，这引入了不受控的模型依赖性，掩盖了真实的核效应。我们提出一种物理信息神经网络框架，将共线改进的Balitsky-Kovchegov演化方程直接嵌入训练目标，使得无需假设初始条件的函数形式，即可从数据中确定 impact 参数平均的偶极振幅。将该框架应用于 forward 强子核修正因子和相干J/ψ光生数据，我们在整个训练过程中强制QCD演化和动量空间正性的条件下，提取了x₀=0.01处²⁰⁸Pb的偶极振幅。演化后的振幅在可用运动学范围内重现了测量的截面，并给出饱和标度比Q_{s0,Pb}²/Q_{s0,p}²=3.17⁺⁰.¹⁷₋₀.₁₀，与简单几何标度一致。提取的Pb初始条件可由McLerran-Venugopalan型形式很好地描述，这与质子形成对比，反映了大核更高的色荷密度。利用同一振幅，我们预测了pp、pPb和Pb p碰撞中横动量比的快度依赖性，发现其与最近LHCb在低多重数下的测量结果吻合，且无需任何与系统相关的参数。本工作首次在饱和区实现了核结构的无偏、数据驱动确定，并建立了将非线性演化方程嵌入受动力学约束可观测量的机器学习提取的通用策略。
英文摘要
Gluon saturation limits the growth of parton densities at small Bjorken-$x$ and is expected to be most pronounced in heavy nuclei. Yet quantitative extractions of the nuclear gluon dipole amplitude have long relied on parametrized initial conditions, introducing uncontrolled model dependence that obscures genuine nuclear effects. We introduce a physics-informed neural-network framework that embeds the collinearly improved Balitsky-Kovchegov evolution equation directly into the training objective, allowing the impact-parameter-averaged dipole amplitude to be determined from data without assuming a functional form for its initial condition. Applying this framework to forward-hadron nuclear-modification-factor and coherent $J/ψ$ photoproduction data, we extract the $^{208}$Pb dipole amplitude at $x_0=0.01$ with QCD evolution and momentum-space positivity enforced throughout training. The evolved amplitude reproduces the measured cross sections across the available kinematic range and yields a saturation-scale ratio $Q_{s0,\mathrm{Pb}}^2/Q_{s0,p}^2 = 3.17^{+0.17}_{-0.10}$, consistent with simple geometric scaling. The extracted Pb initial condition is well described by a McLerran-Venugopalan-type form, in contrast to the proton, reflecting the higher color-charge density of a large nucleus. Using the same amplitude, we predict the rapidity dependence of the transverse-momentum ratio in $pp$, $p$Pb, and Pb$p$ collisions, finding agreement with recent LHCb measurements at low multiplicity without any system-dependent parameters. This work provides the first unbiased, data-driven determination of nuclear structure in the saturation regime and establishes a general strategy for embedding nonlinear evolution equations into machine-learning extractions of dynamically constrained observables.
