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Structural Relations between Nested Harmonic Sums

✍ Scribed by Johannes Blümlein

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
206 KB
Volume
183
Category
Article
ISSN
0920-5632

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✦ Synopsis

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 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. * This paper was supported in part by SFB-TR-9: Computergestütze Theoretische Teilchenphysik. w N basis ¬{-1} (w) = 2 w d|w µ w d N ¬{-1} (d) , (2) with µ(d) the Möbius function. This leads to the following reduction

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