[en] We report on recent results obtained for the massive operator matrix elements which contribute to the massive Wilson coefficients in deep-inelastic scattering for Q² >> m_i² in case of sub-processes with two fermion lines and different mass assignment. (orig.)

[en] The contributions ∝n_f to the O(α³_s) massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit Q²>>m² are computed for the structure function F₂(x,Q²) and transversity for general values of the Mellin variable N. Here, for two matrix elements, A^PS_qq,Q(N) and A_qg,Q(N), the complete result is obtained. A first independent computation of the contributions to the 3-loop anomalous dimensions γ_qg(N), γ^PS_qq(N), and γ^NS,(TR)_qq(N) is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only. (orig.)

[en] We report on recent results obtained for the massive Wilson coefficients which contribute to the structure function F₂(x,Q²) at O(α_s³) in the region Q²/m²>or similar 10. In the calculation new species of harmonic sums and harmonic polylogarithms generated by cyclotomic polynomials arise in intermediary results which are briefly discussed. (orig.)

[en] We report on results for the heavy flavor contributions to F₂(x,Q²) in the limit Q²>>m² at NNLO. By calculating the massive 3-loop operator matrix elements, we account for all but the power suppressed terms in m²/Q². Recently, the calculation of fixed Mellin moments of all 3-loop massive operator matrix elements has been finished. We present new all-N results for the O(n_f)-terms, thereby confirming the corresponding parts of the 3-loop anomalous dimensions. Additionally, we report on first genuine 3-loop results of the ladder-type diagrams for general values of the Mellin variable N. (orig.)

[en] Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=m"2_c/m"2_b∝1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived earlier (I. Bierenbaum, J: Bluemlein, S. Klein, 2009). We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A"("3")_g_q. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A_g_g. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.

[en] We report on recent progress in the calculation of the 3-loop massive Wilson coefficients in deep-inelastic scattering at general values of N for neutral and charged current reactions in the asymptotic region Q²>>m².

[en] We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q² >> m² to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given both in Mellin-N space and z-space.

[en] We present our most recent results on the calculation of the heavy flavor contributions to deep-inelastic scattering at 3-loop order in the large Q² limit, where the heavy flavor Wilson coefficients are known to factorize into light flavor Wilson coefficients and massive operator matrix elements. We describe the different techniques employed for the calculation and show the results in the case of the heavy flavor non-singlet and pure singlet contributions to the structure function F₂(x,Q²).

[en] We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q² >> m² to 3-loop order in the fixed flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given in Mellin N-space. (orig.)

[en] We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function F₂(x,Q²) in the asymptotic region Q²>>m² and the associated operator matrix element A^(3),NS_qq,Q (N) to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N. This matrix element is associated to the vector current and axial vector current for the even and the odd moments N, respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to O(N_F) and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in N space and harmonic polylogarithms in x-space. Numerical results are presented for the non-singlet charm quark contribution to F₂(x,Q²).