论文标题
QCD中共线分裂的分析延续和互惠关系
Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD
论文作者
论文摘要
众所周知，DGLAP进化核（分裂函数）的直接分析延续从太空样到类似时间样的运动学在三个循环下分解。我们将这种分解的起源确定为分裂函数不是外部动量的分析函数。但是，可以从（广义）拆分幅度的平方构建拆分函数。我们建立了分裂幅度的分析延续规则，并使用它们来确定分裂函数的某些全态和抗塑形的部分的分析延续以及横向巨型依赖分布的分析。通过这种方式，我们在三个循环中得出了时间样的分裂函数，而不会含糊不清。我们还提出了单线分裂函数的互惠关系，并提供了至少通过三个循环在QCD中保留的非平凡证据。
It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not analytic function of external momenta. However, splitting functions can be constructed from square of (generalized) splitting amplitudes. We establish the rule of analytic continuation for splitting amplitudes, and use them to determine the analytic continuation of certain holomorphic and anti-holomorphic part of splitting functions and transverse-momentum dependent distributions. In this way we derive the time-like splitting functions at three loops without ambiguity. We also propose a reciprocity relation for singlet splitting functions, and provide non-trivial evidence that it holds in QCD at least through three loops.
