Complete $$ {N}_f^2 $$ contributions to four-loop pure-singlet splitting functions

• DOI: 10.1007/jhep01(2024)029
• Publication Date: 2024-01-08T19:02:08Z
• Authors: Thomas Gehrmann; Andreas von Mante...; Vasily Sotnikov; Tong-Zhi Yang
• Keywords: High Energy Physics - Theory; Nuclear Theory (nucl-th); High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); Nuclear Theory; High Energy Physics - Theory (hep-th); 530 Physics; FOS: Physical sciences; 10192 Physics Institute; 3106 Nuclear and High Energy Physics

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.