Structural Relations between Nested Harmonic Sums

Abstract

We describe the structural relations between nested harmonic sums emerging in the description of physical single scale quantities up to the 3--loop level in renormalizable gauge field theories. These are weight {\sf w=6} harmonic sums. We identify universal basic functions which allow to describe a large class of physical quantities and derive their complex analysis. For the 3--loop QCD Wilson coefficients 35 basic functions are required, whereas a subset of 15 describes the 3--loop anomalous dimensions.

6 pages, to appear in the Proceedings "Loops and Legs in Quantum Field Theory 2008", Sondershausen, Germany

References in corpus (3)

• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
• $O({\alpha }_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space