论文标题
不对称横向动量在不均匀培养基中扩大
Asymmetric transverse momentum broadening in an inhomogeneous medium
论文作者
论文摘要
高能重型离子碰撞中的梯度喷射断层扫描采用了不均匀培养基中传播Parton的不对称横向动量扩大。在培养基中传播的Parton的Wigner分布演变的路径积分描述中研究了这种拓宽。超越了多个散射的敌军近似值，横向方向的进化算子可以表示为在巨大粒子的所有经典轨迹上的功能积分，而光动量动量$ω$作为其质量。随着Wilson线相关功能的偶极近似，带有轻度时间的时间$ t $的演变取决于喷气运输系数$ \ hat Q $随时间和时间而变化的。在具有恒定$ \ hat Q_0 $的统一介质中，对Wigner分布的分析解决方案在横向动量中成为典型的漂移高斯，并与扩散宽度$ \ sqrt {\ hat q_0t} $和$ \ sqrt {\ hat q_0t} $和$ \ sqrt {\ hat q_0t q_0t^3/3ω^2} $相应。如果在均匀培养基上具有空间宽度$σ$的简单高斯横向不均匀性，则可以通过半分析来计算最终的不对称动量分布。发现特征在于不对称分布的喷气梯度断层扫描定义的横向不对称性与在不均匀性域内的繁殖部分的初始横向位置线性相关。它随着Parton Energy $ω$的减小，最初随传播时间的增加而增加，并且当扩散距离大得多，远大于不均匀性的大小或$ t^3 \ gg3Ω^2σ^2/\ hat q_0 $。由于空间中漂移的扩散被忽略，由于不均匀性引起的横向动量扩大，与持续增加的时间相反。
Gradient jet tomography in high-energy heavy-ion collisions utilizes the asymmetric transverse momentum broadening of a propagating parton in an inhomogeneous medium. Such broadening is studied within a path integral description of the evolution of the Wigner distribution for a propagating parton in medium. Going beyond the eikonal approximation of multiple scattering, the evolution operator in the transverse direction can be expressed as the functional integration over all classical trajectories of a massive particle with the light-cone momentum $ω$ as its mass. With a dipole approximation of the Wilson line correlation function, evolution with the light-cone time $t$ is determined by the jet transport coefficient $\hat q$ that can vary with space and time. In a uniform medium with a constant $\hat q_0$, the analytical solution to the Wigner distribution becomes a typical drifted Gaussian in both transverse momentum and coordinate with the diffusion width $\sqrt{\hat q_0t}$ and $\sqrt{\hat q_0t^3/3ω^2}$, respectively. In the case of a simple Gaussian-like transverse inhomogeneity with a spatial width $σ$ on top of a uniform medium, the final asymmetrical momentum distribution can be calculated semi-analytically. The transverse asymmetry defined for jet gradient tomography that characterizes the asymmetrical distribution is found to linearly correlate with the initial transverse position of the propagating parton within the domain of the inhomogeneity. It decreases with the parton energy $ω$, increases with the propagation time initially and saturates when the diffusion distance is much larger than the size of the inhomogeneity or $t^3\gg 3ω^2σ^2/\hat q_0$. The transverse momentum broadening due to the inhomogeneity also saturates at late time in contrast to the continued increase with time if the drifted diffusion in space is ignored.
