e⁺e⁻→Ω⁻Ω⁺的近阈截面：重味再散射与物理引导深度学习
The near-threshold cross section of $e^+e^- \to Ω^-\barΩ^+$: Heavy-flavor rescattering and physics-informed deep learning
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中文总结 AI 辅助
本研究结合耦合道框架、模拟推理与物理引导神经网络，分析e⁺e⁻→Ω⁻Ω⁺近阈截面，发现D_s⁻D_s⁺阈值下存在零宽度极点，对应动态产生的D_s⁻D_s⁺束缚态。
中文摘要 AI 辅助
BESIII合作组近期对e⁺e⁻→Ω⁻Ω⁺截面的精确测量，为探究复杂的强子再散射机制提供了宝贵契机。本研究采用包含ΩΩ、ΞΞ与D_sD_s相互作用的耦合道框架，探究D_sD_s阈值附近的潜在结构；驱动势来自满足重夸克自旋对称性、手征对称性与隐定域对称性的有效拉格朗日量，散射振幅通过Bethe-Salpeter方程的在壳因子化实现幺正化。为超越局域拟合并刻画理论不确定性，本研究采用两步机器学习框架：第一步，基于混合密度网络的模拟推理，映射有效耦合的全局贝叶斯后验；第二步，为识别非微扰阈值动力学且避免多黎曼面上传统求根的不稳定性，采用柯西-黎曼物理引导神经网络（PINN），该网络强制数学解析性，将实轴振幅平滑延拓至复能量平面。研究分离出质量M=3.847 GeV、衰变宽度为零的极点，其位于D_s⁻D_s⁺阈值下方89 MeV处；对应的S矩阵残差显示其与D_sD_s道的耦合占绝对主导，表明该阈值动力学由动态产生的D_s⁻D_s⁺束缚态驱动。
英文摘要
Recent precision measurements of the $e^+e^- \to Ω^-\barΩ^+$ cross section by the BESIII collaboration provide a valuable opportunity to probe complex hadronic rescattering mechanisms. In this work, we investigate a potential structure near the $D_s\bar{D}_s$ threshold using a coupled-channel framework incorporating $Ω\barΩ$, $Ξ\barΞ$, and $D_s\bar{D}_s$ interactions. The driving potentials are derived from effective Lagrangians respecting heavy quark spin symmetry, chiral symmetry, and hidden local symmetry, and the scattering amplitude is unitarized via the on-shell factorization of the Bethe-Salpeter equation. To go beyond local fits and map theoretical uncertainties, we use a two-step machine-learning framework. First, Simulation-Based Inference with a Mixture Density Network maps the global Bayesian posterior of the effective couplings. Second, to identify the non-perturbative threshold dynamics without the instabilities of traditional root-finding across multiple Riemann sheets, we employ a Cauchy-Riemann Physics-Informed Neural Network (PINN). The network enforces mathematical analyticity, smoothly continuing the real-axis amplitude into the complex energy plane. We isolate a pole at $M = 3.847$ GeV with zero decay width, sitting $89$~MeV below the $D_s^-\bar{D}_s^+$ threshold. The corresponding S-matrix residues show an overwhelming coupling to the $D_s\bar{D}_s$ channel, indicating that the threshold dynamics are driven by a dynamically generated $D_s^-\bar{D}_s^+$ bound state.
