%0 Electronic Article
%A Moch, Sven-Olaf
%A Ruijl, Ben
%A Ueda, Takahiro
%A Vogt, Andreas
%A Vermaseren, Jos
%T Low moments of the four-loop splitting functions in QCD
%N DESY-21-203
%M PUBDB-2021-04837
%M DESY-21-203
%M NIKHEF 21-030
%M LTH 1282
%M arXiv:2111.15561
%Z 11 pages, LaTeX, 2 figures. Analytical results in ancillary FORM file
%X 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 α<sub>s</sub>. 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 α<sub>s</sub>-coefficients of order one and sub-percent effects on the scale derivatives of the quark and gluon distributions at α<sub>s</sub>  <~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.
%K strong interaction: coupling constant (INSPIRE)
%K parton: density (INSPIRE)
%K evolution equation (INSPIRE)
%K DGLAP equation (INSPIRE)
%K splitting function (INSPIRE)
%K operator product expansion (INSPIRE)
%K quantum chromodynamics (INSPIRE)
%K quark (INSPIRE)
%K gluon (INSPIRE)
%K perturbation theory (INSPIRE)
%K higher-order: 4 (INSPIRE)
%K Mellin transformation (INSPIRE)
%F PUB:(DE-HGF)25
%9 Preprint
%U https://bib-pubdb1.desy.de/record/472098