Properties and implications of the four-loop non-singlet splitting functions in QCD

TL;DR

This paper analyzes the four-loop non-singlet splitting functions in QCD, providing new analytic expressions, confirming their consistency, and exploring their implications for high-energy particle collision processes.

Contribution

It presents the complete analytic all-N expressions for four-loop anomalous dimensions in non-singlet quark distributions, extending previous fixed-N results and analyzing their theoretical properties.

Findings

Results agree with previously published fixed-N values.

Structural consistency with theoretical requirements is confirmed.

New insights into small-x logarithms and quartic-Casimir contributions are provided.

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.