%0 Journal Article
%A Falcioni, G.
%A Herzog, F.
%A Moch, S.
%A Pelloni, A.
%A Vogt, A.
%T Four-loop splitting functions in QCD – the gluon-gluon case –
%J Physics letters / B
%V 860
%N DESY-24-144
%@ 0031-9163
%C Amsterdam
%I North-Holland Publ.
%M PUBDB-2024-06094
%M DESY-24-144
%M arXiv:2410.08089
%M ZU-TH 47/24
%M LTH 1384
%P 139194
%D 2025
%Z  the DFG through the Research Unit FOR 2926, project number 40824754, and DFG grant MO 1801/4-2, and the ERC Advanced Grant 101095857.
%X We present the even-N moments N ≤ 20 of the fourth-order (N<sup>3</sup>LO) contribution P<sub>gg</sub><sup> (3)</sup>(x) to the quark-to-gluon splitting function in perturbative QCD. These moments, obtained by analyticallycomputing off-shell operator matrix elements for a general gauge group, agree with all known results, in particular with the moments N ≤ 10 derived before from structure functions in deep-inelastic scattering.  Using the new moments and the available endpoint constraints, we construct approximations for P<sub>gg</sub><sup> (3)</sup>(x) which improve upon those obtained from the lowest five even moments. The remaining uncertainties of this function are now practically irrelevant at momentum fractions x  >  0.1. The resulting errors of the convolution ofP<sub>gg</sub> at N<sup>3</sup>LO with a typical gluon distribution are small at x  >~10<sup>−3</sup> and exceed 1% only at x  <~10<sup>−4</sup> for a strong coupling α<sub>s</sub> = 0.2. The present results for P<sub>gg</sub><sup> (3)</sup>(x) should thus be sufficient for most collider-physics applications.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:001394711600001
%R 10.1016/j.physletb.2024.139194
%U https://bib-pubdb1.desy.de/record/615336