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@ARTICLE{Blmlein:472021,
      author       = {Blümlein, J. and Marquard, Peter and Schneider, Carsten
                      and Schönwald, Kay},
      title        = {{T}he three-loop polarized singlet anomalous dimensions
                      from off-shell operator matrix elements},
      reportid     = {PUBDB-2021-04788, arXiv:2111.12401. DESY-21-192. DO-TH
                      21/31},
      year         = {2021},
      note         = {28 pages Latex, 1 figure},
      abstract     = {Future high luminosity polarized deep-inelastic scattering
                      experiments will improve both the knowledge of the spin
                      sub-structure of the nucleons and contribute further to the
                      precision determination of the strong coupling constant, as
                      well as, reveal currently yet unknown higher twist
                      contributions in the polarized sector. For all these tasks
                      to be performed, it is necessary to know the QCD leading
                      twist scaling violations of the measured structure
                      functions. Here an important ingredient consists in the
                      polarized singlet anomalous dimensions and splitting
                      functions in QCD. We recalculate these quantities to
                      three-loop order in the M-scheme by using the traditional
                      method of space-like off-shell massless operator matrix
                      elements, being a gauge-dependent framework. Here one
                      obtains the anomalous dimensions without referring to
                      gravitational currents, needed when calculating them using
                      the forward Compton amplitude. We also calculate the
                      non-singlet splitting function $ \Delta
                      {P}_{\mathrm{qq}}^{(2),\mathrm{s},\mathrm{NS}} $ and compare
                      the final results to the literature, also including
                      predictions for the region of small values of Bjorken x.},
      keywords     = {structure function: spin (INSPIRE) / deep inelastic
                      scattering (INSPIRE) / luminosity: high (INSPIRE) / scaling:
                      violation (INSPIRE) / strong interaction: coupling constant
                      (INSPIRE) / anomalous dimension (INSPIRE) / polarization
                      (INSPIRE) / quantum chromodynamics (INSPIRE) / splitting
                      function (INSPIRE) / singlet (INSPIRE) / small-x (INSPIRE) /
                      nucleon: structure function (INSPIRE) / twist (INSPIRE) /
                      off-shell (INSPIRE) / higher-twist (INSPIRE) / loop integral
                      (INSPIRE) / higher-order (INSPIRE) / Perturbative QCD
                      (autogen) / Renormalization Group (autogen)},
      cin          = {$Z_ZPPT$},
      cid          = {$I:(DE-H253)Z_ZPPT-20210408$},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611)},
      pid          = {G:(DE-HGF)POF4-611},
      experiment   = {EXP:(DE-588)4276505-5},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2111.12401},
      howpublished = {arXiv:2111.12401},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2111.12401;\%\%$},
      url          = {https://bib-pubdb1.desy.de/record/472021},
}