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Additional moments and x-space approximations of four-loop splitting functions in QCD

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arxiv 2310.05744 v1 pith:NEAMF74C submitted 2023-10-09 hep-ph

Additional moments and x-space approximations of four-loop splitting functions in QCD

S. Moch (Hamburg U. , Inst. Theor. Phys. II) , B. Ruijl (ETH , Zurich) , T. Ueda (Juntendo U.) , J. Vermaseren (Nikhef , Amsterdam) , A. Vogt (Liverpool U.
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Dept. Math.)
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classification hep-ph
keywords functionssplittingapproximationsmomentscasefour-loopgluon-gluonomes
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We have extended our previous computations of the even-N moments of the flavour-singlet four-loop splitting functions to N = 12 for the pure-singlet quark case and N = 10 for all other cases. These results, obtained using physical quantities in inclusive deep-inelastic scattering, have been and will be used to validate conceptionally much more challenging determinations of these splitting functions from off-shell operator matrix elements (OMEs). For the quark-gluon and gluon-gluon splitting functions, which have yet to be computed to higher N using OMEs, we construct approximations based on our moments and endpoint constraints, where we present new large-x results for the gluon-gluon case. These approximations facilitate an approximate N^3LO evolution of parton distributions which are sufficiently accurate outside the region of small momentum fractions x.

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Cited by 4 Pith papers

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  1. 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

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  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

    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.

  3. 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 ...

  4. 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...