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The $N_f \,C_F^3$ contribution to the non-singlet splitting function at four-loop order

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arxiv 2310.12240 v2 pith:DYX7GBQC submitted 2023-10-18 hep-ph

classification hep-ph
keywords contributionfour-loopnon-singletresultallowedanalyticanomalousarbitrary
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We report a new result for the $N_f \,C_F^3$ contribution to the four-loop anomalous dimensions of non-singlet, twist-two operators in Quantum Chromodynamics. This result is obtained through computations of off-shell operator matrix elements. Employing integration-by-parts reductions and differential equations with respect to a tracing parameter allowed us to derive analytic results valid for arbitrary Mellin moment $n$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. New results on small-x resummation for splitting functions

    hep-ph 2026-03 conditional novelty 8.0 of 10

    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

    hep-th 2025-06 accept novelty 6.0 of 10

    The quadratic mass-correction combination of twist-two anomalous dimensions stays finite at small spin in the O(N) phi^4, phi^3, and Gross-Neveu-Yukawa models at the computed loop orders, enabling explicit resummations.

  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...

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