Structural Relations between Nested Harmonic Sums
arXiv:0807.0700 · doi:10.1016/j.nuclphysbps.2008.09.109
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.
arXiv comment6 pages, to appear in the Proceedings "Loops and Legs in Quantum Field Theory 2008", Sondershausen, Germany
References in corpus (14)
- The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
- Harmonic Polylogarithms
- Harmonic sums, Mellin transforms and Integrals
- The third-order QCD corrections to deep-inelastic scattering by photon exchange
- Harmonic Sums and Mellin Transforms up to two-loop Order
- Algebraic Relations Between Harmonic Sums and Associated Quantities
- Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
- Analytic Continuation of Mellin Transforms up to two-loop Order
- On the Twist 2 and Twist 3 Contributions to the Spin-dependent Electroweak Structure Functions
- The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
- Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions
- Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson Production
- Mellin Representation for the Heavy Flavor Contributions to Deep Inelastic Structure Functions
- Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space