Abstract
The scale evolution of parton distributions is determined by universal splitting functions. As a milestone towards the computation of these functions to four-loop order in QCD, we compute all contributions to the pure-singlet quark-quark splitting functions that involve two closed fermion loops. The splitting functions are extracted from the pole terms of off-shell operator matrix elements, and the workflow for their calculation is outlined. We reproduce known results for the non-singlet four-loop splitting functions and validate our new pure-singlet results against fixed Mellin moments.
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Acknowledgments
We would like to thank Giulio Falcioni, Franz Herzog, Sven-Olaf Moch and Andreas Vogt for constructive discussions. We acknowledge the European Research Council (ERC) for funding of this work under the European Union’s Horizon 2020 research and innovation programme grant agreement 101019620 (ERC Advanced Grant TOPUP) and the National Science Foundation (NSF) for support under grant number 2013859.
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Gehrmann, T., von Manteuffel, A., Sotnikov, V. et al. Complete \( {N}_f^2 \) contributions to four-loop pure-singlet splitting functions. J. High Energ. Phys. 2024, 29 (2024). https://doi.org/10.1007/JHEP01(2024)029
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DOI: https://doi.org/10.1007/JHEP01(2024)029