AI 中文总结
该研究采用归一化流模型推断手性有效场论中两体低能常数的联合概率分布，所得分布可重现中子-质子散射相移，揭示了低能常数的非高斯相关性，为构建受实验约束的核相互作用统计集成提供了通用框架。
AI 中文摘要
近期，从头算核理论、机器学习与贝叶斯推断的进展，结合日益精确的核实验与天体物理观测，为核相互作用的基础描述提供了更可靠的约束。尽管成熟的非线性回归方法可在固定分辨率尺度下识别低能常数的最佳拟合集，但它们对这些常数的完整潜在概率分布的揭示有限。因此，核理论领域剩余的核心挑战是表征跨分辨率尺度的核力完整概率分布。本研究采用归一化流（一类表达性生成式机器学习模型），推断手性有效场论中两体低能常数（LECs）在宽分辨率尺度范围内的联合概率分布。结果表明，所得LEC分布可准确重现实验上的中子-质子散射相移分布；此外，研究还揭示了LECs之间存在强非高斯相关性，表明不同短程核动力学之间存在非平凡的相互作用。本研究建立了一种构建核相互作用统计集成的通用框架，该框架可通过未来的核实验与天体物理观测进行系统约束。
英文摘要
Recent advances in ab initio nuclear theory, machine learning, and Bayesian inference, coupled with increasingly precise nuclear experiments and astrophysical observations, have enabled more robust constraints on fundamental descriptions of the nuclear interaction. Although well-established nonlinear regression methods can identify best-fit sets of low-energy constants at fixed resolution scale, they provide limited insight into the full underlying probability distributions of those constants. A central remaining challenge in nuclear theory is therefore to characterize full probability distributions of nuclear forces across resolution scales. In this work, we employ normalizing flows, a class of expressive generative machine learning models, to infer the joint probability distribution of two-body low-energy constants (LECs) in chiral effective field theory over a wide range of resolution scales. The resulting LEC distributions are shown to accurately reproduce experimental neutron-proton scattering phase-shift distributions. Furthermore, strong non-Gaussian correlations among LECs are revealed, indicating a nontrivial interplay among distinct short-range nuclear dynamics. This work establishes a general framework for constructing statistical ensembles of nuclear interactions that can be systematically constrained by future nuclear experiments and astrophysical observations.
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