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@ARTICLE{Falcioni:625204,
      author       = {Falcioni, Giulio and Herzog, Franz and Moch, Sven-Olaf and
                      Pelloni, Andrea and Vogt, Andreas},
      title        = {{F}our-loop splitting functions in {QCD} – the
                      gluon-gluon case –},
      reportid     = {PUBDB-2025-01052, arXiv:2410.08089. ZU-TH 47/24.
                      DESY-24-144. LTH 1384},
      year         = {2024},
      note         = {the DFGthrough the Research Unit FOR 2926, project number
                      40824754, and DFG grant MO 1801/4-2,and the ERC Advanced
                      Grant 101095857.},
      abstract     = {We have computed the even-N moments N≤20 of the
                      gluon-gluon splitting function Pgg at the fourth order of
                      perturbative QCD via the renormalization of off-shell
                      operator matrix elements. Our results, derived analytically
                      for a general compact simple gauge group, agree with all
                      results obtained for this function so far, in particular
                      with the lowest five moments obtained via structure
                      functions in deep-inelastic scattering. Using our new
                      moments and all available endpoint constraints, we construct
                      improved approximations for the four-loop Pgg(x) that should
                      be sufficient for a wide range of collider-physics
                      applications. The N3LO contributions to the scale derivative
                      of the gluon distribution, resulting from these and the
                      corresponding quark-to-gluon splitting functions, amount to
                      $1\%$ or less at Image 1 at a standard reference scale with
                      αs=0.2.},
      cin          = {UNI/TH},
      ddc          = {530},
      cid          = {$I:(DE-H253)UNI_TH-20120731$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / DFG
                      project G:(GEPRIS)409651613 - FOR 2926: Next Generation
                      Perturbative QCD for Hadron Structure: Preparing for the
                      Electron-Ion Collider (409651613)},
      pid          = {G:(DE-HGF)POF4-611 / G:(GEPRIS)409651613},
      experiment   = {EXP:(DE-H253)LHC-Exp-ATLAS-20150101 /
                      EXP:(DE-H253)LHC-Exp-CMS-20150101 /
                      EXP:(DE-H253)LHC-Exp-other-20150101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2410.08089},
      howpublished = {arXiv:2410.08089},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2410.08089;\%\%$},
      doi          = {10.3204/PUBDB-2025-01052},
      url          = {https://bib-pubdb1.desy.de/record/625204},
}