相关论文: Difference Equations in Massive Higher Order Calcu…
In recent three--loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short $S$-sums) arise. They are characterized by…
We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, $A_{gg,Q}(x,\mu^2)$ and $\Delta A_{gg,Q}(x,\mu^2)$, at three-loop order for a single mass. These quantities contribute to the matching of the…
The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function $F_2(x,Q^2)$ and the corresponding transition matrix element $A_{Qq}^{(3), \sf PS}$ in the variable flavor number…
We calculate the two-mass QCD contributions to the massive operator matrix element $A_{gg,Q}$ at $\mathcal{O} (\alpha_s^3)$ in analytic form in Mellin $N$- and $z$-space, maintaining the complete dependence on the heavy quark mass ratio.…
We compute Mellin moments of the heavy-quark structure functions in deep-inelastic scattering at next-to-leading order in quantum chromodynamics, retaining their full dependence on the heavy-quark mass. Using the optical theorem and the…
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically…
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 $Q^2 \gg m^2$.
The general structure of infrared divergences in the scattering of massive particles is captured by the soft anomalous dimension matrix. The latter can be computed from a correlation function of multiple Wilson lines. The state-of-the-art…
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…
This thesis is concerned with the calculation of fixed moments of the O(a_s^3) heavy flavor contributions to the Wilson coefficients of the structure function F_2(x,Q^2) in the limit Q^2 >> m^2, neglecting power corrections. The massive…
We derive the structural relations between the Mellin transforms of weighted Nielsen integrals emerging in the calculation of massless or massive single--scale quantities in QED and QCD, such as anomalous dimensions and Wilson coefficients,…
The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities $Q^2$.…
We provide a fast and precise Mellin-space implementation of the $O(\alpha_s)$ heavy flavor Wilson coefficients for charged current deep inelastic scattering processes. They are of importance for the extraction of the strange quark…
The analytic continuation of the Mellin transforms to complex values of N for the basic functions $g_i(x)$ of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index…
We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
We report on recent results on the two-mass corrections for massive operator matrix elements at 2- and 3-loop orders in QCD. These corrections form the building blocks of the variable flavor number scheme. Due to the similar values of the…
Massive on-shell operator matrix elements and self-energy diagrams with outer gluon lines are calculated analytically at $O(\alpha_s^2)$, using Mellin-Barnes integrals and representations through generalized hypergeometric functions. This…