发表机构
Center for Theoretical Physics — A Leinweber Institute, Massachusetts Institute of Technology; Kavli Institute for Theoretical Physics, University of California, Santa Barbara（麻省理工学院理论物理中心——莱因韦伯研究所; 加州大学圣塔芭芭拉分校卡弗里理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明相对论性重夸克在违反爱因斯坦关系时仍能平衡，通过弱耦合非阿贝尔等离子体的高阶计算揭示非高斯核的关键作用，并指出强耦合下幸存者偏差导致显著增强，为第一性原理唯象描述奠定基础。
AI 中文摘要
相对论性重夸克即使在其微观阻力和动量扩散违反爱因斯坦关系的情况下也能达到平衡。我们研究了平衡如何作为耦合强度的函数进行，并与简化的福克-普朗克模型进行了比较。为此，我们给出了弱耦合非阿贝尔等离子体中动量传递核在严格$\mathcal{O}(g^4)$阶下的详细计算，并在逆重夸克质量的前导阶下研究了由此产生的动力学。超越前导对数，其非高斯结构在平衡过程中起着关键作用。我们仔细研究了演化核的解析结构，确定了动量传递累积量的大阶渐近行为，并展示了核的有界解析域如何在动量传递概率层面固定不对称指数尾。强耦合$\mathcal{N}=4$超对称杨-米尔斯理论也具有近似高斯的核和指数尾，但在核的奇点性质以及输运系数和尾指数的速度依赖性方面有所不同。这些差异具有不同的动力学后果：对于所研究的参数，在极弱耦合下，陡峭下降谱中相对论性群体的持续存在主要由阻力单独解释，而在强耦合下，涨落引起的幸存者偏差产生了较大的相对增强。尽管如此，弱耦合和强耦合之间共享的定性结构为基于第一性原理场论的重夸克实用唯象描述指明了道路。
英文摘要
Relativistic heavy quarks equilibrate even when their microscopic drag and momentum diffusion violate the Einstein relation. We investigate how equilibration proceeds as a function of the coupling and compared to simplified Fokker-Planck models. To do this, we present a detailed calculation of the momentum-transfer kernel in weakly coupled non-Abelian plasmas through strict $\mathcal{O}(g^4)$, and study the resulting dynamics at leading order in the inverse heavy-quark mass. Beyond leading logarithm, its non-Gaussian structure plays a crucial role in equilibration. We examine closely the analytic structure of the evolution kernel, determine the large-order asymptotics of the momentum-transfer cumulants, and show how the kernel's bounded analytic domain fixes asymmetric exponential tails at the level of the momentum transfer probability. Strongly coupled $\mathcal{N}=4$ SYM also features an approximately Gaussian core and exponential tails, but differs in the nature of the kernel's singularities and the velocity dependence of the transport coefficients and tail exponents. These differences have distinct dynamical consequences: for the parameters studied, the persistence of the relativistic population in steeply falling spectra is largely explained by drag alone at very weak coupling, whereas fluctuation-induced survivor bias produces a large relative enhancement at strong coupling. Nevertheless, the shared qualitative structure between weak and strong coupling points the way towards a practical phenomenological description of heavy quarks anchored in first-principles field theory.
Comments81 pages, 13 figures
