The Large-$n_f$ Limit of the Four-Loop Splitting Functions in QCD

Abstract

These proceedings describe a computation of the large-$n_f$ terms contributing to the QCD splitting functions at the fourth order in the strong coupling constant ${\alpha }_s$. Using the FORCER package for the reduction of four-loop two-point Feynman integrals, Mellin moments of the four-loop splitting functions have been computed. These moments are used to derive analytic Mellin-space expressions, by forming and finding solutions to systems of Diophantine equations. Expressions for the terms proportional to $n_f^3$ of the flavour singlet, and to $n_f^2$ of the flavour non-singlet splitting functions have been determined.

Comments: 6 pages, 0 figures. Contribution to the proceedings of the XXV International Workshop on Deep-Inelastic Scattering and Related Topics (DIS2017), 3-7 April 2017, University of Birmingham, UK