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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{moch2026properties,
  title = {{Properties and implications of the four-loop non-singlet splitting functions in QCD}},
  author = {S. Moch and A. Vogt},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.03889},
  eprint = {2605.03889},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.03889},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Properties and implications of the four-loop non-singlet splitting functions in QCD
AU  - S. Moch
AU  - A. Vogt
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2605.03889
UR  - https://arxiv.org/abs/2605.03889
AB  - 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.
ER  -