PreprintCC BY 4.0arXiv
The four-loop quark-to-quark splitting function in QCD
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.
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BibTeX
@misc{gehrmann2026fourloop,
title = {{The four-loop quark-to-quark splitting function in QCD}},
author = {Thomas Gehrmann and Andreas von Manteuffel and Vasily Sotnikov and Tong-Zhi Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37563},
eprint = {2609.37563},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37563},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The four-loop quark-to-quark splitting function in QCD
AU - Thomas Gehrmann
AU - Andreas von Manteuffel
AU - Vasily Sotnikov
AU - Tong-Zhi Yang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37563
UR - https://arxiv.org/abs/2609.37563
AB - 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.
ER -