Work

The four-loop quark-to-quark splitting function in QCD

Year: 2026

Type: preprint

Abstract: The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop pure-singlet contribution to the quark-to-quark splitting function in perturbative QCD. Together with the known non-singlet contribution, our result completes the quark-to-quark splitting function at this order. We confirm previous partial results and obtain, for the first time, a fully analytic expression valid for all momentum fractions. We examine its behavior at small momentum fractions and provide precise numerical representations suitable for parton evolution.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.37563

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

Institutions: University of Zurich, University of Regensburg, Johannes Gutenberg University Mainz, South China Normal University

Language: English

Topic: Quantum Chromodynamics and Particle Interactions

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: European Commission

Award: G2124226988

OpenAlex ID: W7214918938

Cites: 54

Cited by: 1

Related to: 10