利用深度神经网络提取π介子的非极化夸克与胶子广义部分子分布
Extraction of Pion Unpolarized Quark and Gluon Generalized Parton Distributions using Deep Neural-Networks
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中文总结 AI 辅助
本研究采用物理信息神经网络（PINN）结合JAM21、xFitter的PDF及实验、格点QCD数据，提取π介子的非极化夸克与胶子广义部分子分布，得到与格点结果吻合的分布，为强子断层扫描提供新途径。
中文摘要 AI 辅助
我们利用来自JAM21和xFitter分析的部分子分布函数（PDFs）、π介子电磁形状因子（EMFF）的实验测量结果，以及格点量子色动力学（QCD）结果，通过深度神经网络（DNN）对π介子的非极化夸克与胶子广义部分子分布（GPDs）进行提取。GPDs采用物理信息神经网络（PINN）进行参数化，该网络结合了已知的PDF行为、指数形式的动量转移依赖关系以及可训练的神经网络（NN）组件。网络参数通过最小化基于χ²的损失函数确定。对于价夸克GPDs，损失函数包含EMFF、平方EMFF、电荷归一化约束以及正则化项的贡献；对于胶子GPDs，损失函数则包含胶子引力形状因子的约束以及正则化项。该框架可实现灵活的非参数化提取，同时保留必要的理论与唯象学约束。通过采用全部可用的PDF副本集合，我们在纵向动量分数和动量转移的宽运动学范围内量化了提取的GPDs的不确定性，不确定性带对应1σ置信区间。提取的价夸克GPDs与现有格点QCD计算结果吻合良好。本研究表明，基于DNN的方法为提取π介子GPDs及探测π介子的多维内部结构提供了灵活且鲁棒的框架，为未来强子断层扫描研究提供了有前景的途径。
英文摘要
We present a deep neural-network (DNN) extraction of the pion unpolarized quark and gluon generalized parton distributions (GPDs) using the corresponding parton distribution functions (PDFs) from the JAM21 and xFitter analysis, together with experimental measurements of the pion electromagnetic form factor (EMFF) and lattice quantum chromodynamics (QCD) results. The GPDs are parameterized using a physics-informed neural-network (PINN) that incorporates the known PDF behavior, an exponential momentum-transfer dependence, and a trainable neural network (NN) component. The network parameters are determined by minimizing a $χ^2$-based loss function. For the valence-quark GPDs, the loss function includes contributions from the EMFF, squared EMFF, charge-normalization constraints, and regularization terms. For the gluon GPDs, it incorporates constraints from the gluon gravitational form factors together with regularization. This framework enables a flexible, nonparametric extraction while preserving the essential theoretical and phenomenological constraints. By employing the full ensemble of available PDF replicas, we quantify the uncertainties of the extracted GPDs over a broad kinematic range in the longitudinal momentum fraction and momentum transfer, with the uncertainty bands corresponding to the $1σ$ confidence interval. The extracted valence-quark GPDs are found to be in good agreement with available lattice-QCD calculations. Our study demonstrates that DNN-based methods provide a flexible and robust framework for extracting pion GPDs and probing the multidimensional internal structure of the pion, offering a promising avenue for future investigations of hadron tomography.
