Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions

Author:

Thomas Gehrmann, Andreas von Manteuffel, Vasily Sotnikov, Tong-Zhi Yang

Keyword:

High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Nuclear Theory (nucl-th)

journal:

MSUHEP-23-024, ZU-TH 43/23

date:

2023-08-14 16:00:00

Abstract

The scale evolution of parton distributions is determined by universal splitting functions. As a milestone towards the computation of these functions to four-loop order in QCD, we compute all contributions to the pure-singlet quark-quark splitting functions that involve two closed fermion loops. The splitting functions are extracted from the pole terms of off-shell operator matrix elements, and the workflow for their calculation is outlined. We reproduce known results for the non-singlet four-loop splitting functions and validate our new pure-singlet results against fixed Mellin moments.

PDF: Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions.pdf