Structural Relations between Harmonic Sums up to w=6

Abstract

Multiply nested finite harmonic sums $S_{a_1...a_n}(N)$ occur in many single scale higher order calculations in Quantum Field Theory. We discuss their algebraic and structural relations to weight {\sf w=6}. As an example, we consider the application of these relations to the soft and virtual corrections for Bhabha-scattering to $O({\alpha }^2)$.

1 latex + 1 style file, to appear in the proceedings of 15th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2007), Munich, Germany, 16-20 Apr 2007

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• Two-loop QED corrections to Bhabha scattering
• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson Production
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• Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra
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• $O({\alpha }_s)$ Heavy Flavor Corrections to Charged Current Deep-Inelastic Scattering in Mellin Space
• 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines
• New Heavy Flavor Contributions to the DIS Structure Function $F_2(x,Q^2)$ at $O(α_s^3)
• Difference Equations in Massive Higher Order Calculations
• Heavy Flavour Production in Deep--Inelastic Scattering - Two--Loop Massive Operator Matrix Elements and Beyond
• Status of Deeply Inelastic Parton Distributions