Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results

We present recent analytic results for the 3-loop corrections to the massive operator matrix element $A_{Qg}^{(3)}$for further color factors. These results have been obtained using the method of arbitrarily large moments. We also give an overview on the results which were obtained solving all difference and differential equations for the corresponding master integrals that factorize at first order.Comment: 11 pages Latex, To appear in the Proceedings of: QCDEV2017, JLAB, Newport News, VA, USA, May 22-26, 2017; Po

The O(\alpha_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer

We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure function $xF_3^{W^+}(x,Q^2)+xF_3^{W^-}(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics (QCD) at general values of the Mellin variable $N$ and the momentum fraction $x$. Besides the heavy quark pair production also the single heavy flavor excitation $s \rightarrow c$ contributes. Numerical results are presented for the charm quark contributions and consequences on the Gross-Llewellyn Smith sum rule are discussed.Comment: 30 pages, 6 figures. arXiv admin note: text overlap with arXiv:1504.0821

The Heavy Quark Form Factors at Two Loops

We compute the two-loop QCD corrections to the heavy quark form factors in case of the vector, axial-vector, scalar and pseudo-scalar currents up to second order in the dimensional parameter $\epsilon = (4-D)/2$. These terms are required in the renormalization of the higher order corrections to these form factors.Comment: 131 pages, 3 figure

Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra

Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable $N$ and the dimensional parameter $\varepsilon$. Given these representations, the desired Laurent series expansions in $\varepsilon$ can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of $N$ are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of $V$-topologies.Comment: 110 pages Latex, 4 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

Heavy quark form factors at two loops in perturbative QCD

We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.Comment: 13 pages Latex, Proceedings of XLI International Conference of Theoretical Physics "Matter to the Deepest", Podlesice, Poland, September 3-8, 2017 and RADCOR 2017, St.~Gilgen Austria, Sept 24-29, 201

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

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

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples are the anomalous dimensions to 3-loop order, the massless Wilson coefficients and also different massive operator matrix elements. Starting at 3-loop order, however, also other letters appear in the case of massive operator matrix elements, the so called iterative non-iterative integrals, which are related to solutions based on complete elliptic integrals or any other special function with an integral representation that is definite but not a Volterra-type integral. After outlining the formalism leading to iterative non-iterative integrals,we present examples for both of these cases with the 3-loop anomalous dimension $\gamma_{qg}^{(2)}$ and the structure of the principle solution in the iterative non-interative case of the 3-loop QCD corrections to the $\rho$-parameter.Comment: 13 pages LATEX, 2 Figure