CITATION

The analytic results on which this implementation is based were obtained in
the references listed below, which should be cited when using these results
directly or indirectly.

BibTeX entries for the references can be found in the file CITATION.bib.


If you use the unpolarised operator matrix elements please cite:

%-------------------------------------------------------------------------------
%[1] AqqQPS3, AqgQ3 (and O(NF) terms of all unpolarised OMEs)
\bibitem{Ablinger:2010ty}
  J.~Ablinger, J.~Bl\"umlein, S.~Klein, C.~Schneider and F.~Wi\ss{}brock,
  \textit{The $O(\alpha_s^3)$ Massive Operator Matrix Elements of $O(N_F)$ for
  the Structure Function $F_2(x,Q^2)$ and Transversity},
  Nucl.\ Phys.\ B \textbf{844} (2011) 26--54
  [arXiv:1008.3347 [hep-ph]].
  %%CITATION = doi:10.1016/j.nuclphysb.2010.10.021;%%
%-------------------------------------------------------------------------------
%[2] Logarithmic Terms of all OMEs
\bibitem{Behring:2014eya}
  A.~Behring, I.~Bierenbaum, J.~Bl\"umlein, A.~De Freitas, S.~Klein and
  F.~Wi\ss{}brock,
  \textit{The logarithmic contributions to the $O(\alpha^3_s)$ asymptotic
  massive Wilson coefficients and operator matrix elements in deeply inelastic
  scattering},
  Eur.\ Phys.\ J.\ C \textbf{74} (2014) 9, 3033
  [arXiv:1403.6356 [hep-ph]].
  %%CITATION = ARXIV:1403.6356;%%
%-------------------------------------------------------------------------------
%[3] AgqQ3
\bibitem{Ablinger:2014lka}
  J.~Ablinger, J.~Bl\"umlein, A.~De Freitas, A.~Hasselhuhn, A.~von Manteuffel,
  M.~Round, C.~Schneider and F.~Wi\ss{}brock,
  \textit{The Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor
  Number Scheme at $O(\alpha_s^3)$},
  Nucl.\ Phys.\ B \textbf{882} (2014) 263--288
  [arXiv:1402.0359 [hep-ph]].
  %%CITATION = ARXIV:1402.0359;%%
%-------------------------------------------------------------------------------
%[4] AqqQNS3
\bibitem{Ablinger:2014vwa}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~Hasselhuhn,
  A.~von Manteuffel, M.~Round, C.~Schneider, and F.~Wi\ss{}brock,
  \textit{The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous
  Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity},
  Nucl.\ Phys.\ B \textbf{886} (2014) 733--823
  [arXiv:1406.4654 [hep-ph]].
  %%CITATION = ARXIV:1406.4654;%%
%-------------------------------------------------------------------------------
%[5] AQqPS3
\bibitem{Ablinger:2014nga}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel and
  C.~Schneider,
  \textit{The 3-loop pure singlet heavy flavor contributions to the structure
  function $F_2(x,Q^2)$ and the anomalous dimension},
  Nucl.\ Phys.\ B \textbf{890} (2014) 48--151
  [arXiv:1409.1135 [hep-ph]].
  %%CITATION = ARXIV:1409.1135;%%
%-------------------------------------------------------------------------------
%[6] AggQ3
\bibitem{Ablinger:2022wbb}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~Goedicke,
  A.~von Manteuffel, C.~Schneider and K.~Sch\"onwald,
  \textit{The unpolarized and polarized single-mass three-loop heavy flavor
  operator matrix elements $A_{gg,Q}$ and  $\Delta A_{gg,Q}$},
  JHEP \textbf{12} (2022) 134
  [arXiv:2211.05462 [hep-ph]].
%-------------------------------------------------------------------------------
%[7] AQg3 (first-order-factorisable contributions)
\bibitem{Ablinger:2023ahe}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel,
  C.~Schneider and K.~Sch\"onwald,
  \textit{The first-order factorizable contributions to the three-loop massive
  operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$},
  Nucl. Phys. B \textbf{999} (2024) 116427
  %doi:10.1016/j.nuclphysb.2023.116427
  [arXiv:2311.00644 [hep-ph]].
%-------------------------------------------------------------------------------
%[8] AQg3 (non-first-order-factorisable contributions)
\bibitem{Ablinger:2024xtt} 
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel,
  C.~Schneider and K.~Sch\"onwald,
  \textit{The non-first-order-factorizable contributions to the three-loop
  single-mass operator matrix elements $A_{Qg}^{(3)}$ and
  $\Delta A_{Qg}^{(3)}$.}
  Phys. Lett. B \textbf{854} (2024) 138713
  %doi:10.1016/j.physletb.2024.138713
  [arXiv:2403.00513 [hep-ph]].
%-------------------------------------------------------------------------------
%[9] Implementation
\bibitem{Ablinger:2025joi}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel,
  C.~Schneider and K.~Sch\"onwald,
  \textit{The Single-Mass Variable Flavor Number Scheme at Three-Loop Order},
  arXiv:2510.02175 [hep-ph].
%-------------------------------------------------------------------------------
%[10] AQqPSs
\bibitem{Behring:2025avs}
  A.~Behring, J.~Bl{\"u}mlein, A.~De Freitas, A.~von Manteuffel, C.~Schneider
  and K.~Sch{\"o}nwald,
  \textit{The heavy quark-antiquark asymmetry in the variable flavor number
  scheme},
  arXiv:2512.13508 [hep-ph].



If you use the polarised operator matrix elements please cite:

%-------------------------------------------------------------------------------
%[1] Logarithmic terms of all polarised OMEs
\bibitem{Blumlein:2021xlc}
  J.~Bl\"umlein, A.~De Freitas, M.~Saragnese, C.~Schneider and K.~Sch\"onwald,
  \textit{Logarithmic contributions to the polarized $O(\alpha_s^3)$ asymptotic
  massive Wilson coefficients and operator matrix elements in deeply inelastic
  scattering},
  Phys. Rev. D \textbf{104} (2021) no.3, 034030
  [arXiv:2105.09572 [hep-ph]].
%-------------------------------------------------------------------------------
%[2] polAqqQNS3
\bibitem{Ablinger:2014vwa}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~Hasselhuhn,
  A.~von Manteuffel, M.~Round, C.~Schneider, and F.~Wi\ss{}brock,
  \textit{The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous
  Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity},
  Nucl.\ Phys.\ B {\bf 886} (2014) 733--823
  [arXiv:1406.4654 [hep-ph]].
  %%CITATION = ARXIV:1406.4654;%%
%------------------------------------------------------------------------------
%[3] polAQqPS3
\bibitem{Ablinger:2019etw}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel,
  C.~Schneider and K.~Sch\"onwald,
  \textit{The three-loop single mass polarized pure singlet operator matrix
  element},
  Nucl. Phys. B \textbf{953} (2020) 114945
  [arXiv:1912.02536 [hep-ph]].
%-------------------------------------------------------------------------------
%[4] polAgqQ3
\bibitem{Behring:2021asx}
  A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel, K.~Sch\"onwald
  and C.~Schneider,
  \textit{The polarized transition matrix element $A_{gq}(N)$ of the variable
  flavor number scheme at $O(\alpha^3_s)$},
  Nucl. Phys. B \textbf{964} (2021) 115331
  [arXiv:2101.05733 [hep-ph]].
%-------------------------------------------------------------------------------
%[5] polAggQ3
\bibitem{Ablinger:2022wbb}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~Goedicke,
  A.~von Manteuffel, C.~Schneider and K.~Sch\"onwald,
  \textit{The unpolarized and polarized single-mass three-loop heavy flavor
  operator matrix elements $A_{gg,Q}$ and  $\Delta A_{gg,Q}$},
  JHEP \textbf{12} (2022) 134
  [arXiv:2211.05462 [hep-ph]].
%-------------------------------------------------------------------------------
%[6] polAQg3 (first-order-factorisable contributions)
\bibitem{Ablinger:2023ahe}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel,
  C.~Schneider and K.~Sch\"onwald, 
  \textit{The first-order factorizable contributions to the three-loop massive
  operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$},
  Nucl. Phys. B \textbf{999} (2024) 116427
  [arXiv:2311.00644 [hep-ph]].
%-------------------------------------------------------------------------------
%[7] polAQg3 (non-first-order-factorisable contributions)
\bibitem{Ablinger:2024xtt} 
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel,
  C.~Schneider and K.~Sch\"onwald,
  \textit{The non-first-order-factorizable contributions to the three-loop
  single-mass operator matrix elements $A_{Qg}^{(3)}$ and
  $\Delta A_{Qg}^{(3)}$.}
  Phys. Lett. B \textbf{854} (2024) 138713
  [arXiv:2403.00513 [hep-ph]].
%-------------------------------------------------------------------------------
%[8] Implementation
\bibitem{Ablinger:2025joi}
  J.~Ablinger, A.~Behring, J.~Bl\"umlein, A.~De Freitas, A.~von Manteuffel,
  C.~Schneider and K.~Sch\"onwald,
  \textit{The Single-Mass Variable Flavor Number Scheme at Three-Loop Order},
  arXiv:2510.02175 [hep-ph].
%-------------------------------------------------------------------------------
%[9] polAQqPSs
\bibitem{Behring:2025avs}
  A.~Behring, J.~Bl{\"u}mlein, A.~De Freitas, A.~von Manteuffel, C.~Schneider
  and K.~Sch{\"o}nwald,
  \textit{The heavy quark-antiquark asymmetry in the variable flavor number
  scheme},
  arXiv:2512.13508 [hep-ph].