经典弱场极限下色玻璃凝聚态的解析解与近似解
Analytic and Approximate Solutions to Color Glass Condensate in the Classical Weak-Field Limit
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中文总结 AI 辅助
研究弱场极限下色荷片碰撞后经典胶子场相关问题，基于胶子分布一般表达式推导能量动量张量时间依赖性，探讨MV模型和iG模型情况，给出解析解、级数展开等，揭示长时间行为普遍性及相关模型特性。
中文摘要 AI 辅助
我们讨论了在弱场极限下，光锥上色荷片碰撞后经典胶子场的两点函数和能量动量张量。这种设置产生的经典场被认为可以近似大能量下重核碰撞后产生的胶子物质的行为。我们的讨论基于原子核中胶子分布的一般表达式，其中包含McLerran-Venugopalan（MV）模型作为特殊情况。我们推导了这种一般情况下能量动量张量的时间依赖性。我们表明，长时间行为是普遍的，即与胶子分布的具体模型无关，例如对于能量密度、横向压力和纵向压力$\epsilon、P_T \sim 1/\tau$和$P_L \sim 1/\tau^3$，其中$\tau$是纵向固有时间。随后，我们关注两个特殊情况，MV模型和一个提出的具有改进的紫外（UV）和红外（IR）行为的改进高斯（iG）模型，后者受Lam和Mahlon早期工作的启发。我们明确讨论了两个模型中能量动量张量的时间依赖性。在MV模型的情况下，对于无限碰撞的原子核，可以根据特殊函数给出能量动量张量的封闭形式解析解。能量动量张量的分量形式为$\sim C (m\tau)^{-n} H(m\tau)$，其中$n$是整数幂，$m$是红外截止，$H$是具有恒定渐近值的Meijer-G函数的线性组合，$C$是已知常数。对于iG模型，我们获得了小时间和大时间的可靠级数展开，并表明在UV极限下定性地恢复了MV模型。我们简要评论了胶子场携带的角动量的影响。
英文摘要
We discuss two-point functions and the energy momentum tensor of the classical gluon field after the collision of sheets of color charges on the light cone in the weak-field limit. The classical fields created by such a setup is thought to approximate the behavior of the gluon matter created right after the collision of heavy nuclei at large energies. Our discussion is based on a general expression for the gluon distribution in a nucleus, which contains the McLerran-Venugopalan (MV) Model as a special case. We derive the time-dependence of the energy momentum tensor in this general scenario. We show that the large-time behavior is universal, i.e.\ independent of the specific model for the gluon distribution, e.g.\ for energy density, transverse pressure and longitudinal pressure $ε, P_T \sim 1/τ$ and $P_L \sim 1/τ^3$, where $τ$ is longitudinal proper time. Subsequently, we focus on two special cases, the MV model and a proposed improved Gaussian (iG) model with improved ultraviolet (UV) and infrared (IR) behavior, the latter inspired by earlier work by Lam and Mahlon. We explicitly discuss the time dependence of the energy momentum tensor in both models. In the case of the MV-model, for infinite colliding nuclei, it is possible to give closed-formed analytic solutions for the energy momentum tensor in terms of special functions. Components of the energy momentum tensor take the form $\sim C (mτ)^{-n} H(mτ)$, where $n$ is an integer power, $m$ is the infrared cutoff, $H$ is a linear combination of Meijer-G functions with constant asymptotic value, and $C$ is a known constant. For the iG-model, we obtain reliable series expansions for both small and large times and show that the MV-model is recovered qualitatively in the UV limit. We briefly comment on implications for the angular momentum carried by the gluon field.
