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arXiv · 2609.37563

The four-loop quark-to-quark splitting function in QCD

Thomas Gehrmann·Andreas von Manteuffel·Vasily Sotnikov·Tong-Zhi Yang
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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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Thomas Gehrmann, Andreas von Manteuffel, Vasily Sotnikov, Tong-Zhi Yang. 2026-09-29. The four-loop quark-to-quark splitting function in QCD. https://arxiv.org/abs/2609.37563

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