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Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions

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arxiv 2308.07958 v3 pith:DXOY3TM6 submitted 2023-08-15 hep-ph hep-thnucl-th

Thomas Gehrmann , Andreas von Manteuffel , Vasily Sotnikov , Tong-Zhi Yang This is my paper · ORCID
classification hep-phhep-thnucl-th
keywords functionssplittingfour-looppure-singletcontributionsresultscalculationclosed
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 5 Pith papers

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    A closed-form all-order expression for the qg anomalous dimension, plus new all-order results for the LL gluon anomalous dimension and the finite qg/gg Green functions, derived and implemented in HELL 4.0.

  2. Anomalous dimensions at small spins

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  3. Candia-v2: Logarithmic expansions for DGLAP evolution in $x$-space

    hep-ph 2026-07 conditional novelty 5.0 of 10

    Candia-v2 implements (approximate) N3LO x-space DGLAP evolution — exact four-loop non-singlet splitting functions, envelope-approximated singlet inputs, three-loop heavy-quark matching — as a public C++ package with G...

  4. Alien operators for PDF evolution

    hep-ph 2025-09 unverdicted novelty 2.0 of 10

    This proceedings paper summarizes earlier results on all-spin couplings and Feynman rules for gauge-variant alien operators needed for four-loop QCD splitting functions.

  5. Energy Correlators: A Journey From Theory to Experiment

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