Bonn 2010 – scientific programme

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T: Fachverband Teilchenphysik

T 12: QCD (Theorie) III / Quantenfeldtheorie I

T 12.5: Talk

Wednesday, March 17, 2010, 15:00–15:15, HG XVI

A Toolbox for Harmonic Sums and their Analytic Continuations — •Jakob Ablinger¹, Johannes Bluemlein², and Carsten Schneider¹ — ¹RISC, J. Kepler University, Linz, Austria — ²DESY, Zeuthen, Germany

The package HarmonicSums implemented in the computer algebra system Mathematica is presented. It supports higher loop calculations in QCD and QED to represent single-scale quantities like anomalous dimensions and Wilson coefficients. The package allows to reduce general harmonic sums due to their algebraic and different structural relations. We provide a general framework for these reductions and the explicit representations up to weight w=8. For the use in experimental analyzes we also provide an analytic formalism to continue the harmonic sums form their integer arguments into the complex plane, which includes their recursions and asymptotic representations. The main ideas are illustrated by specific examples.