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arXiv · 2310.05744

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

S. Moch·B. Ruijl·T. Ueda·J. Vermaseren·A. Vogt
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Abstract

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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S. Moch, B. Ruijl, T. Ueda, J. Vermaseren, A. Vogt. 2023-10-09. Additional moments and x-space approximations of four-loop splitting functions in QCD. https://arxiv.org/abs/2310.05744

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