初始动量各向异性在CGC的kT-因子化中 I：梯度展开
Initial momentum anisotropies in the kT-factorization of the CGC I: Gradient Expansion
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- Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela（加利西亚高能物理研究所，圣地亚哥德孔波斯特拉大学）
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中文总结 AI 辅助
本文通过梯度展开扩展CGC的kT-因子化，揭示初始动量各向异性，为初始状态模型提供动态修正。
中文摘要 AI 辅助
我们重新审视了色玻璃凝聚体中稀薄-稀薄极限下的单举胶子产生，并表明$k_\perp$-因子化只是两个碰撞源横向位置系统梯度展开的零阶项，该展开按$1/(Q_sR)$的幂次组织，其中$Q_s$为饱和尺度，$R$为源变化的尺度。逐阶收集各项，从局部分布及其横向导数构建标量和张量结构的阶梯，从而得到一个扩展的$k_\perp$-因子化公式，该公式保留了源的空间依赖性，并通过谱的动力学矩保留了能量-动量张量。从未来光锥中经典Glasma场的实时计算重复该展开，在eikonal极限下重现了动量空间结果，但额外保留了振幅与其共轭之间的相干干涉。这为阶梯增加了项（流动响应、色电-磁干涉和纵向能量通量），这些项进一步受到大出射动量$|\pp|\gg Q_s$的幂次抑制。因此，该层级揭示了在任何流体动力学演化之前初始状态中存在的动量空间各向异性，而领先阶$k_\perp$-因子化在构造上会遗漏这些各向异性。由于每一阶都是同一未积分分布上的局域算符，这些修正可以直接添加到现有的基于饱和的初始状态模型中，从而在不放弃可处理的因子化形式的情况下，动态生成初始动量各向异性和更真实的早期能量-动量张量。由横向密度分布的梯度决定，这些修正向更稀薄、涨落主导的系统（例如轻离子碰撞）增长。唯象学后果将在配套论文中阐述。
英文摘要
We revisit single-inclusive gluon production in the dilute--dilute limit of the Color Glass Condensate and show that $k_\perp$-factorization is only the zeroth order of a systematic gradient expansion in the transverse positions of the two colliding sources, organized in powers of $1/(Q_sR)$, with $Q_s$ the saturation scale and $R$ the size over which the sources vary. Collecting terms order by order builds a ladder of scalar and tensor structures from the local distributions and their transverse derivatives, yielding an extended $k_\perp$-factorized formula that retains the spatial dependence of the sources and, through kinetic moments of the spectrum, the energy-momentum tensor. Repeating the expansion from a real-time computation of the classical Glasma fields in the future light cone reproduces the momentum-space result in the eikonal limit, but additionally retains coherent interference between amplitude and conjugate. This adds terms to the ladder (flow responses, chromo-electric--magnetic interference, and a longitudinal energy flux) further suppressed by powers of the large outgoing momentum $|\pp|\gg Q_s$. The hierarchy thus reveals momentum-space anisotropies present in the initial state before any hydrodynamic evolution, which leading $k_\perp$-factorization misses by construction. Since each order is a local operator on the same unintegrated distributions, these corrections can be added directly to existing saturation-based initial-state models, giving a dynamically generated initial momentum anisotropy and a more faithful early-time energy-momentum tensor without abandoning the tractable factorized form. Set by gradients of the transverse density profiles, they grow towards more dilute, fluctuation-dominated systems, e.g. light-ion collisions. Phenomenological consequences will be developed in a companion paper.
