Abstract
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.
Highlights
Parton Distributions Functions (PDFs) and Fragmentation Functions (FFs) provide essential input for accurate determination of various quantities of QCD and the Standard Model [1,2,3] within the framework of QCD factorization [4]
We identify the origin of the breakdown of direct analytic continuation for splitting functions and TMD distributions, as they are computed from square of splitting amplitudes, and not analytic
In order to understand the analytic continuation for TMD PDFs and FFs, we start with LSZ reduction on the space-like splitting amplitudes: SpSXnq∗←i = ddx e−iPr·x Xn|T{χn(0)JPi l (x)}|0, (7)
Summary
Hao Chen,1, ∗ Tong-Zhi Yang,1, † Hua Xing Zhu,1, ‡ and Yu Jiao Zhu1, § 1Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, 310027, China 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 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 transversemomentum dependent distributions. In this way we derive the time-like splitting functions at three loops without ambiguity. We propose a reciprocity relation for singlet splitting functions, and provide non-trivial evidence that it holds in QCD at least through three loops
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
