发表机构
School of Mathematics and Physics, China University of Geosciences (Wuhan); Institute of Physics and Technology, University of Bergen（中国地质大学（武汉）数学与物理学院; 卑尔根大学物理与技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过 (3+1) 维流体动力学分析 48 个 Pb-Pb 初始态，发现纵向超子极化与冻结出射偏心率相关，提出紧凑关系描述其变化，并利用 ALICE 数据反演验证，表明纵向极化可约束解耦时的空间各向异性。
AI 中文摘要
纵向超子极化由解耦时的速度梯度产生，但其与演化碰撞几何的定量联系尚不清楚。我们使用 (3+1) 维理想流体动力学和等温局域平衡自旋方案分析了 48 个 Pb-Pb 初始态。正的运动剪切贡献与冻结出射偏心率 $\u03b5_{2,\mathrm{fo}}$ 相关，而负的运动涡度贡献的大小则共同依赖于椭圆流 $v_2$ 和偏心率存活分数 $S_\u03b5=\u03b5_{2,\mathrm{fo}}/\u03b5_{2,\mathrm{init}}$。它们的竞争遵循 $R\simeq0.84(\u03b5_{2,\mathrm{fo}}/v_2)^{0.47}$，其总和由 $P_{z,s2}^{\mathrm{ILE}}\simeq0.0404v_2S_\u03b5 [0.850(\u03b5_{2,\mathrm{fo}}/v_2)^{1/2}-1]$ 描述。这一紧凑关系描述了 48 态扫描中 87% 的变化。在其系数固定后，它描述了 12 个新计算的初始态中 86% 的变化，包括四个在先前未采样的 $b_0=0.685$ 处的态。使用 ALICE 极化数据的原理验证反演返回了模型拟合域内的冻结出射偏心率。这些结果表明，纵向极化可以约束解耦时剩余的空间各向异性，补充了椭圆流携带的动量空间信息。
英文摘要
Longitudinal hyperon polarization is generated by velocity gradients at decoupling, but its quantitative connection to the evolving collision geometry has remained unclear. We analyze 48 Pb-Pb initial states with (3+1)-dimensional ideal hydrodynamics and the isothermal local-equilibrium spin prescription. The positive kinematic-shear contribution correlates with the freeze-out eccentricity $ε_{2,\mathrm{fo}}$, whereas the magnitude of the negative kinematic-vorticity contribution depends jointly on elliptic flow $v_2$ and the eccentricity survival fraction $S_ε=ε_{2,\mathrm{fo}}/ε_{2,\mathrm{init}}$. Their competition follows $R\simeq0.84(ε_{2,\mathrm{fo}}/v_2)^{0.47}$, and their sum is described by $P_{z,s2}^{\mathrm{ILE}}\simeq0.0404v_2S_ε[0.850(ε_{2,\mathrm{fo}}/v_2)^{1/2}-1]$. This compact relation describes $87\%$ of the variation across the 48-state scan. After its coefficients were fixed, it describes $86\%$ of the variation across 12 newly calculated initial states, including four at the previously unsampled $b_0=0.685$. A proof-of-principle inversion using ALICE polarization data then returns freeze-out eccentricities inside the model fit domain. These results show that longitudinal polarization can constrain the spatial anisotropy remaining at decoupling, complementing the momentum-space information carried by elliptic flow.
