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

TL;DR

This paper computes the large-$n_f$ contributions to four-loop QCD splitting functions, providing analytic Mellin-space expressions that enhance the precision of parton distribution evolution in high-energy physics.

Contribution

It introduces a novel calculation of the large-$n_f$ terms at four loops in QCD splitting functions using Mellin moments and Diophantine equations, advancing theoretical understanding.

Findings

Derived analytic expressions for $n_f^3$ terms in flavor singlet splitting functions.

Computed $n_f^2$ terms in flavor non-singlet splitting functions.

Enhanced the accuracy of QCD evolution equations at four-loop order.

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.