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arXiv · 2604.09534

The four-loop non-singlet splitting functions 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 splitting functions in perturbative QCD that control the evolution of quark non-singlet distributions. We confirm previous partial results and obtain, for the first time, fully analytic expressions for all non-singlet contributions at this order. These allow us to extract the analytic form of the four-loop virtual and rapidity anomalous dimensions entering logarithmic resummation. We provide precise numerical representations of the splitting functions suitable for parton evolution.

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Thomas Gehrmann, Andreas von Manteuffel, Vasily Sotnikov, Tong-Zhi Yang. 2026-04-10. The four-loop non-singlet splitting functions in QCD. https://arxiv.org/abs/2604.09534

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