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Low moments of the four-loop splitting functions in QCD

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arxiv 2111.15561 v1 pith:4PGVQEZS submitted 2021-11-30 hep-ph

Low moments of the four-loop splitting functions in QCD

S. Moch (Hamburg U. , Inst. Theor. Phys. II) , B. Ruijl (Zurich , ETH) , T. Ueda (Seikei U.) , J.A. M. Vermaseren (Nikhef , Amsterdam) , A. Vogt (Liverpool U.
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Dept. Math)
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classification hep-ph
keywords alphafunctionsmomentssplittingexpansionfourorderanalyses
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We have computed the four lowest even-N moments of all four splitting functions for the evolution of flavour-singlet parton densities of hadrons at the fourth order in the strong coupling constant alpha_s. The perturbative expansion of these moments, and hence of the splitting functions for momentum fractions x >~ 0.1, is found to be well behaved with relative alpha_s-coefficients of order one and sub-percent effects on the scale derivatives of the quark and gluon distributions at alpha_s ~< 0.2. More intricate computations, including other approaches such as the operator-product expansion, are required to cover the full x-range relevant to LHC analyses. Our results are presented analytically for a general gauge group for detailed checks and validations of such future calculations.

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Forward citations

Cited by 5 Pith papers

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

  1. The four-loop non-singlet splitting functions in QCD

    hep-ph 2026-04 unverdicted novelty 8.0

    Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.

  2. Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

    hep-ph 2026-05 unverdicted novelty 7.0

    Closed-form expression for the ζ(3) term of the four-loop non-singlet twist-two quark anomalous dimension for arbitrary N, extracted via analytic reconstruction from Mellin moments.

  3. Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

    hep-ph 2026-05 unverdicted novelty 7.0

    Presents the zeta(3)-proportional term of the four-loop non-singlet twist-two quark anomalous dimension for general N in closed form, extracted via analytic reconstruction from published Mellin moments.

  4. Properties and implications of the four-loop non-singlet splitting functions in QCD

    hep-ph 2026-05 unverdicted novelty 7.0

    Four-loop non-singlet QCD splitting functions are verified for consistency and used to finalize analytical forms for the gluon virtual anomalous dimension and N^4LL threshold resummation coefficients, revealing a new ...

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

    hep-ph 2026-07 conditional novelty 5.0

    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...