$O(\alpha_s^3 T_F^2 N_F)$ Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function $F_2(x,Q^2)$ at $Q^2 \gg m^2$

The massive 3-loop fermion-loop corrections $\propto C_{A} N_{f} T_{F}^{2}$ and $C_F N_f T_F^2 $t o t h e m a s s i v e o p e r a t o r m a t r i x e l e m e n t s$ A_{Qg} $,$ A_{Qq}^{\rm{PS}} $,$ A_{qq,Q}^{\rm{PS}} $,$ A_{qq,Q}^{\rm{NS}} $a n d$ A_{qq,Q}^{\rm{NS,TR}} have been obtained for general values of $N$ . Thereby the corresponding contributions to the asymptotic heavy flavor Wilson coefficients of the structure function $F_{2} (x, Q^{2})$ and of transversity in the region $Q^{2} \geq 10 \cdot m^{2}$ are known. Our method is based on direct integration, avoiding the integration-by-parts technique, which is advantageous due to the compactness of the intermediate and final results. We also obtain the corresponding contributions to the 3-loop anomalous dimensions and confirm results in the literature.

$O (α_{s}^{3} T_{F}^{2} N_{F})$ Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function $F_{2} (x, Q^{2})$ at $Q^{2} ≫ m^{2}$

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$O (α_{s}^{3} T_{F}^{2} N_{F})$ Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function $F_{2} (x, Q^{2})$ at $Q^{2} ≫ m^{2}$

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O(αs3TF2NF)O(αs3​TF2​NF​) Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function F2(x,Q2)F2​(x,Q2) at Q2≫m2Q2≫m2

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O(αs3TF2NF)O(αs3​TF2​NF​) Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function F2(x,Q2)F2​(x,Q2) at Q2≫m2Q2≫m2

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$O (α_{s}^{3} T_{F}^{2} N_{F})$ Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function $F_{2} (x, Q^{2})$ at $Q^{2} ≫ m^{2}$

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$O (α_{s}^{3} T_{F}^{2} N_{F})$ Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function $F_{2} (x, Q^{2})$ at $Q^{2} ≫ m^{2}$

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