Structural Relations between Nested Harmonic Sums

Details Structural Relations between Nested Harmonic Sums Structural Relations between Nested Harmonic Sums

2008-07-04

arxiv.org/abs/0807.0700v1

Nucl.Phys.Proc.Suppl.183:232-237,2008

Physics

Mathematical Physics

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

Scientific paper

10.1016/j.nuclphysbps.2008.09.10

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.

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