标题： 任意自旋粒子在全域平衡下的精确极化 显示英文标题

标题： Exact Polarization of Particles of Any Spin at Global Equilibrium

摘要： $\Lambda$粒子的极化提供了研究重离子碰撞中形成的夸克-胶子等离子体中流体力学梯度的独特机会。然而，通常用于计算极化的理论公式只是在热涡度下的线性阶展开，并忽略了高阶修正。这里，我展示了在全局平衡下对（常数）热涡度的所有阶精确计算，得到了任意自旋质量粒子的自旋密度矩阵和极化矢量的解析形式。最后，我将这些结果扩展到局域平衡，并通过数值计算 \( 3+1 \) 流体动力学模拟中的极化矢量来评估它们的经验影响。 显示英文摘要

摘要： The polarization of the $\Lambda$ particle offers the unique opportunity to study the hydrodynamic gradients in the Quark-Gluon Plasma formed in heavy-ion collisions. However, the theoretical formula commonly used to calculate polarization is only a linear order expansion in thermal vorticity and neglects higher-order corrections. Here, I present an exact calculation to all orders in (constant) thermal vorticity at global equilibrium, obtaining the analytic form of the spin density matrix and the polarization vector for massive particles of any spin. Finally, I extend these results to local equilibrium and assess their phenomenological impact by numerically calculating the polarization vector in a 3+1 hydrodynamic simulation.