English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It is well-known that direct analytic continuation of DGLAP evolution kernel(splitting functions) from space-like to time-like kinematics breaks down atthree loops. We identify the origin of this breakdown as splitting functionsare not analytic function of external momenta. However, splitting functions canbe constructed from square of (generalized) splitting amplitudes. We establishthe rule of analytic continuation for splitting amplitudes, and use them todetermine the analytic continuation of certain holomorphic and anti-holomorphicpart of splitting functions and transverse-momentum dependent distributions. Inthis way we derive the time-like splitting functions at three loops withoutambiguity. We also propose a reciprocity relation for singlet splittingfunctions, and provide non-trivial evidence that it holds in QCD at leastthrough three loops.

Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD