Structural Relations between Nested Harmonic Sums
Mathematical Physics
2008-12-18 v1 High Energy Physics - Phenomenology
Algebraic Geometry
math.MP
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.
Cite
@article{arxiv.0807.0700,
title = {Structural Relations between Nested Harmonic Sums},
author = {Johannes Bluemlein},
journal= {arXiv preprint arXiv:0807.0700},
year = {2008}
}
Comments
6 pages, to appear in the Proceedings "Loops and Legs in Quantum Field Theory 2008", Sondershausen, Germany