Properties and implications of the four-loop non-singlet splitting functions in QCD
Abstract
We have studied the recently completed analytic all-N expressions for the four-loop anomalous dimensions corresponding to the next-to-next-to-next-to-leading order splitting functions for the non-singlet quark distribution in perturbative QCD. The results agree with fixed-N values beyond those published so far. Their structural consistency with theoretical requirements is established. They are used to cast the four-loop gluon virtual anomalous dimension and the next-to-next-to-next-to-next-to-leading logarithmic threshold-resummation coefficients for lepton-pair and Higgs production in hadron-hadron collisions and deep-inelastic scattering into their final analytical forms. Further properties and consequences of the new results are addressed, in particular a new structure seen most clearly in the small-x logarithms occurring in a quartic-Casimir contribution.
Keywords
Cite
@article{arxiv.2605.03889,
title = {Properties and implications of the four-loop non-singlet splitting functions in QCD},
author = {S. Moch and A. Vogt},
journal= {arXiv preprint arXiv:2605.03889},
year = {2026}
}
Comments
37 pages, LaTeX, 6 ancillary FORM files with results and useful relations