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@ARTICLE{Ablinger:604020,
      author       = {Ablinger, J. and Behring, A. and Blümlein, J. and De
                      Freitas, A. and von Manteuffel, A. and Schneider, Carsten
                      and Schönwald, K.},
      title        = {{T}he non-first-order-factorizable contributions to the
                      three-loop single-mass operator matrix elements
                      ${A}_{{Q}g}^{(3)}$ and $\Delta {A}_{{Q}g}^{(3)}$},
      reportid     = {PUBDB-2024-00985, DESY-24-027. arXiv:2403.00513. RISC
                      Report series 24-02. ZU-TH 13/24. CERN-TH-2024-30. DO-TH
                      23/15},
      year         = {2024},
      abstract     = {The non-first-order-factorizable contributions (The terms
                      'first-order-factorizable contributions' and
                      'non-first-order-factorizable contributions' have been
                      introduced and discussed in Refs.
                      $\cite{Behring:2023rlq,Ablinger:2023ahe}.$ They describe the
                      factorization behaviour of the difference- or differential
                      equations for a subset of master integrals of a given
                      problem.) to the unpolarized and polarized massive operator
                      matrix elements to three-loop order, $A_{Qg}^{(3)}$ and
                      $\Delta A_{Qg}^{(3)}$, are calculated in the single-mass
                      case. For the $_2F_1$-related master integrals of the
                      problem, we use a semi-analytic method based on series
                      expansions and utilize the first-order differential
                      equations for the master integrals which does not need a
                      special basis of the master integrals. Due to the
                      singularity structure of this basis a part of the integrals
                      has to be computed to $O(\varepsilon^5)$ in the dimensional
                      parameter. The solutions have to be matched at a series of
                      thresholds and pseudo-thresholds in the region of the
                      Bjorken variable $x \in ]0,\infty[$ using highly precise
                      series expansions to obtain the imaginary part of the
                      physical amplitude for $x \in ]0,1]$ at a high relative
                      accuracy. We compare the present results both with previous
                      analytic results, the results for fixed Mellin moments, and
                      a prediction in the small-$x$ region. We also derive
                      expansions in the region of small and large values of $x$.
                      With this paper, all three-loop single-mass unpolarized and
                      polarized operator matrix elements are calculated.},
      keywords     = {master integral (INSPIRE) / differential equations
                      (INSPIRE) / factorization (INSPIRE) / Bjorken (INSPIRE) /
                      singularity (INSPIRE) / structure (INSPIRE)},
      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       = {2403.00513},
      howpublished = {arXiv:2403.00513},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2403.00513;\%\%$},
      doi          = {10.3204/PUBDB-2024-00985},
      url          = {https://bib-pubdb1.desy.de/record/604020},
}