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@ARTICLE{Falcioni:615336,
      author       = {Falcioni, G. and Herzog, F. and Moch, S. and Pelloni, A.
                      and Vogt, A.},
      title        = {{F}our-loop splitting functions in {QCD} – the
                      gluon-gluon case –},
      journal      = {Physics letters / B},
      volume       = {860},
      issn         = {0031-9163},
      address      = {Amsterdam},
      publisher    = {North-Holland Publ.},
      reportid     = {PUBDB-2024-06094, DESY-24-144. arXiv:2410.08089. ZU-TH
                      47/24. LTH 1384},
      pages        = {139194},
      year         = {2025},
      note         = {the DFG through the Research Unit FOR 2926, project number
                      40824754, and DFG grant MO 1801/4-2, and the ERC Advanced
                      Grant 101095857.},
      abstract     = {We present the even-$N$ moments $N\le 20$ of the
                      fourth-order (N$^3$LO) contribution $P_{\rm gg}^{\,(3)}(x)$
                      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 $N\le 10$ derived before from structure functions in
                      deep-inelastic scattering. Using the new moments and the
                      available endpoint constraints, we construct approximations
                      for $P_{\rm gg}^{\,(3)}(x)$ 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 of$P_{\rm gg}$ at N$^3$LO with a
                      typical gluon distribution are small at $x \gtrsim 10^{-3}$
                      and exceed 1\\% only at $x \lesssim 10^{-4}$ for a strong
                      coupling $\alpha_s = 0.2$. The present results for $P_{\rm
                      gg}^{\,(3)}(x)$ should thus be sufficient for most
                      collider-physics applications.},
      cin          = {UNI/TH},
      ddc          = {530},
      cid          = {$I:(DE-H253)UNI_TH-20120731$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) /
                      QCDchallenge - QCD challenges in precision physics at the
                      LHC (101104792) / 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:(EU-Grant)101104792 /
                      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)16},
      eprint       = {2410.08089},
      howpublished = {arXiv:2410.08089},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2410.08089;\%\%$},
      UT           = {WOS:001394711600001},
      doi          = {10.1016/j.physletb.2024.139194},
      url          = {https://bib-pubdb1.desy.de/record/615336},
}