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@ARTICLE{Moch:472098,
      author       = {Moch, Sven-Olaf and Ruijl, Ben and Ueda, Takahiro and Vogt,
                      Andreas and Vermaseren, Jos},
      title        = {{L}ow moments of the four-loop splitting functions in
                      {QCD}},
      reportid     = {PUBDB-2021-04837, DESY-21-203. NIKHEF 21-030. LTH 1282.
                      arXiv:2111.15561},
      note         = {11 pages, LaTeX, 2 figures. Analytical results in ancillary
                      FORM file},
      abstract     = {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 $\alpha_s$. The perturbative
                      expansion of these moments, and hence of the splitting
                      functions for momentum fractions $x \gtrsim 0.1$, is found
                      to be well behaved with relative $\alpha_s$-coefficients of
                      order one and sub-percent effects on the scale derivatives
                      of the quark and gluon distributions at $\alpha_s \lesssim
                      0.2$. 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.},
      keywords     = {strong interaction: coupling constant (INSPIRE) / parton:
                      density (INSPIRE) / evolution equation (INSPIRE) / DGLAP
                      equation (INSPIRE) / splitting function (INSPIRE) / operator
                      product expansion (INSPIRE) / quantum chromodynamics
                      (INSPIRE) / quark (INSPIRE) / gluon (INSPIRE) / perturbation
                      theory (INSPIRE) / higher-order: 4 (INSPIRE) / Mellin
                      transformation (INSPIRE)},
      cin          = {UNI/TH},
      ddc          = {530},
      cid          = {$I:(DE-H253)UNI_TH-20120731$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611)},
      pid          = {G:(DE-HGF)POF4-611},
      experiment   = {EXP:(DE-H253)LHC-Exp-ATLAS-20150101 /
                      EXP:(DE-H253)LHC-Exp-CMS-20150101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2111.15561},
      howpublished = {arXiv:2111.15561},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2111.15561;\%\%$},
      url          = {https://bib-pubdb1.desy.de/record/472098},
}