Analytic continuation and reciprocity relation for collinear splitting in QCD  

作　　者：Hao Chen Tong-Zhi Yang Hua-Xing Zhu Yu-Jiao Zhu 陈豪;杨通智;朱华星;朱雨蛟(Zhejiang Institute of Modern Physics,Department of Physics,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]Zhejiang Institute of Modern Physics,Department of Physics,Zhejiang University,Hangzhou 310027,China

出　　处：《Chinese Physics C》2021年第4期61-69,共9页中国物理C（英文版）

基　　金：Supported in part by National Natural Science Foundation of China (11975200);the Zhejiang University Fundamental Research Funds for the Central Universities (2019QNA3005)。

摘　　要：It is well-known that direct analytic continuation of the 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 due to splitting functions not being analytic functions of external momenta.However,splitting functions can be constructed from the squares of(generalized)splitting amplitudes.We establish the rules 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.

关 键 词：splitting functions next-to-next-to-leading order analytic continuation RECIPROCITY 

分 类 号：O572.243[理学—粒子物理与原子核物理]