论文标题
天体上的软碎片化
Soft Fragmentation on the Celestial Sphere
论文作者
论文摘要
我们开发了两种方法，解决了高能量过程的量规理论中hadron的软片段化问题。第一种方法直接使用$ k_t $ - factorization和bfkl理论，将Parton分布函数的异常尺寸（Twist-Two本地操作员的异常尺寸（Twist-Two本地操作员）的标准重新调整为碎片函数，通过利用横向线的动力学之间的映射在横向线上的动力学之间的映射。至关重要的是，为了正确恢复该映射下碎片函数的异常维度，尽管BFKL方程的明显界线或红外有限性，但必须仔细注意正则化的作用。由于位置和角度之间的维度不匹配而引起的对能量的异常依赖性驱动了Parton密度的空间样和类似时间样的异常维度之间的差异，即使是在共形理论中。第二种方法适应了一个角度的进化方程，但在4-2 $ε$尺寸上工作。这两种方法是通过要求Parton分布功能4-2 $ε$尺寸的异常维度团结在一起的。
We develop two approaches to the problem of soft fragmentation of hadrons in a gauge theory for high energy processes. The first approach directly adapts the standard resummation of the parton distribution function's anomalous dimension (that of twist-two local operators) in the forward scattering regime, using $k_T$-factorization and BFKL theory, to the case of the fragmentation function by exploiting the mapping between the dynamics of eikonal lines on transverse-plane to the celestial-sphere. Critically, to correctly resum the anomalous dimension of the fragmentation function under this mapping, one must pay careful attention to the role of regularization, despite the manifest collinear or infra-red finiteness of the BFKL equation. The anomalous dependence on energy in the celestial case, arising due to the mismatch of dimensionality between positions and angles, drives the differences between the space-like and time-like anomalous dimension of parton densities, even in a conformal theory. The second approach adapts an angular-ordered evolution equation, but working in 4-2$ε$ dimensions at all angles. The two approaches are united by demanding that the anomalous dimension in 4-2$ε$ dimensions for the parton distribution function determines the kernel for the angular-ordered evolution to all orders.
