The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

We report on our latest results in the calculation of the two--mass contributions to 3--loop operator matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inealstic scattering structure functions and to generalize the variable flavor number scheme by including both charm and bottom quarks. We present the results for the non-singlet and $A_{gq,Q}$ OMEs, and compare the size of their contribution relative to the single mass case. Results for the gluonic OME $A_{gg,Q}$ are given in the physical case, going beyond those presented in a previous publication where scalar diagrams were computed. We also discuss our recently published two--mass contribution to the pure singlet OME, and present an alternative method of calculating the corresponding diagrams.Comment: 20 pages Latex, 5 Figures, different style file

3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines

We consider gluonic contributions to the heavy flavor Wilson coefficients at 3-loop order in QCD with two heavy quark lines in the asymptotic region $Q^2 \gg m_{1(2)}^2$. Here we report on the complete result in the case of two equal masses $m_1 = m_2$ for the massive operator matrix element $A_{gg,Q}^{(3)}$, which contributes to the corresponding heavy flavor transition matrix element in the variable flavor number scheme. Nested finite binomial sums and iterated integrals over square-root valued alphabets emerge in the result for this quantity in $N$ and $x$-space, respectively. We also present results for the case of two unequal masses for the flavor non-singlet OMEs and on the scalar integrals ic case of $A_{gg,Q}^{(3)}$, which were calculated without a further approximation. The graphs can be expressed by finite nested binomial sums over generalized harmonic sums, the alphabet of which contains rational letters in the ratio $\eta = m_1^2/m_2^2$.Comment: 10 pages LATEX, 1 Figure, Proceedings of Loops and Legs in Quantum Field Theory, Weimar April 201

The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function F2(x,Q2)F_2(x,Q^2) and Transversity

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function $F_2(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ and the associated operator matrix element $A_{qq,Q}^{(3), \rm NS}(N)$ 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 $F_2(x,Q^2)$.Comment: 82 pages, 3 style files, 33 Figure

Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering

We report on our latest results in the calculation of the three-loop heavy flavor contributions to the Wilson coefficients in deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$. We discuss the different methods used to compute the required operator matrix elements and the corresponding Feynman integrals. These methods very recently allowed us to obtain a series of new operator matrix elements and Wilson coefficients like the flavor non-singlet and pure singlet Wilson coefficients.Comment: 11 pages Latex, 2 Figures, Proc. of Loops and Legs in Quantum Field Theory, April 2014, Weimar, German

New Results on Massive 3-Loop Wilson Coefficients in Deep-Inelastic Scattering

We present recent results on newly calculated 2- and 3-loop contributions to the heavy quark parts of the structure functions in deep-inelastic scattering due to charm and bottom.Comment: Contribution to the Proc. of Loops and Legs 2016, PoS, in prin

3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

A survey is given on the status of 3-loop heavy flavor corrections to deep-inelastic structure functions at large enough virtualities $Q^2$.Comment: 13 pages Latex, 8 Figures, Contribution to the Proceedings of EPS 2015 Wie

3-loop heavy flavor Wilson coefficients in deep-inelastic scattering

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 $Q^2$ 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 $F_2(x,Q^2)$.Comment: 4 pages Latex, 2 style files, 4 Figures, Contribution to the Proceedings of QCD '14, Montpellier, Jult 201