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arXiv · 2605.03889

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

S. Moch·A. Vogt
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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.

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S. Moch, A. Vogt. 2026-05-05. Properties and implications of the four-loop non-singlet splitting functions in QCD. https://arxiv.org/abs/2605.03889

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