发表机构
Indian Institute of Technology Gandhinagar; Tata Institute of Fundamental Research; National Institute of Science Education and Research（印度理工学院甘地纳加尔分校; 塔塔基础研究所; 国家科学教育与研究学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过随机框架将重夸克动量扩散与托马斯进动引起的自旋旋转耦合，推导出自旋-动量福克-普朗克方程，建立自旋弛豫时间与动量扩散系数的直接关系，并利用多种方法计算了粲、底夸克的自旋弛豫时间。
AI 中文摘要
夸克-胶子等离子体中的重夸克自旋动力学为探测重夸克与介质之间的相互作用提供了潜在手段。我们发展了一个随机框架，其中导致重夸克扩散的随机动量冲击通过托马斯进动也引发自旋旋转。从托马斯-巴格曼-米歇尔-泰莱格迪方程和重夸克动量的朗之万方程出发，我们推导出一个新颖的自旋-动量耦合福克-普朗克方程。在重夸克极限下，当动量比自旋更快达到平衡时，动量自由度可以被积分掉，从而得到自旋取向的旋转福克-普朗克方程。这建立了自旋弛豫时间$\tau_{s}$中托马斯进动贡献与重夸克动量扩散系数$\kappa$之间的直接关系。在非相对论极限下，我们发现$\tau_s=2\tau_p(m_Q/T)^2$，其中$\tau_p$是动量弛豫时间。利用近期从格点QCD、强耦合估计、$T$-矩阵计算以及重味现象学得到的$\kappa$测定值，我们获得了粲夸克和底夸克对应的托马斯进动对自旋弛豫时间的贡献。在与重离子碰撞相关的温度范围内，相对论运动学仅对结果产生适度修正，而不确定性主要由$\kappa$主导。我们强调，该结果代表托马斯进动对重夸克自旋弛豫的贡献；与色磁场直接耦合提供了额外的通道。
英文摘要
Heavy-quark spin dynamics in the quark-gluon plasma provides a potential probe of the interaction between heavy quarks and the medium. We develop a stochastic framework in which the random momentum kicks responsible for heavy-quark diffusion also induce spin rotation through Thomas precession. Starting from the Thomas-Bargmann-Michel-Telegdi equation and a Langevin equation for heavy-quark momentum, we derive a novel coupled spin-momentum Fokker-Planck equation. In the heavy-quark limit, where momentum equilibrates faster than spin, the momentum degrees of freedom can be integrated out, yielding a rotational Fokker-Planck equation for the spin orientation. This establishes a direct relation between the Thomas precession contribution to the spin-relaxation time $τ_{s}$ and the heavy-quark momentum-diffusion coefficient $κ$. In the non-relativistic limit, we find $τ_s=2τ_p(m_Q/T)^2$, with $τ_p$ being the momentum relaxation time. Using recent determinations of $κ$ from lattice QCD, strong-coupling estimates, $T$-matrix calculations, and heavy-flavor phenomenology, we obtain the corresponding Thomas precession contribution to spin relaxation times for charm and bottom quarks. Relativistic kinematics modify the result by only a modest amount over the temperature range relevant for heavy-ion collisions, while the uncertainty is dominated by that of $κ$. We emphasize that the result represents the Thomas precession contribution to heavy-quark spin relaxation; direct coupling to the chromomagnetic field provides an additional channel.
Comments8 pages, 1 figure
