TY - EJOUR AU - Moch, Sven-Olaf AU - Ruijl, Ben AU - Ueda, Takahiro AU - Vogt, Andreas AU - Vermaseren, Jos TI - Low moments of the four-loop splitting functions in QCD IS - DESY-21-203 M1 - PUBDB-2021-04837 M1 - DESY-21-203 M1 - NIKHEF 21-030 M1 - LTH 1282 M1 - arXiv:2111.15561 N1 - 11 pages, LaTeX, 2 figures. Analytical results in ancillary FORM file AB - 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. KW - strong interaction: coupling constant (INSPIRE) KW - parton: density (INSPIRE) KW - evolution equation (INSPIRE) KW - DGLAP equation (INSPIRE) KW - splitting function (INSPIRE) KW - operator product expansion (INSPIRE) KW - quantum chromodynamics (INSPIRE) KW - quark (INSPIRE) KW - gluon (INSPIRE) KW - perturbation theory (INSPIRE) KW - higher-order: 4 (INSPIRE) KW - Mellin transformation (INSPIRE) LB - PUB:(DE-HGF)25 UR - https://bib-pubdb1.desy.de/record/472098 ER -