Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions

Details Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions

2005-03-18

arxiv.org/abs/hep-ph/0503188v1

Phys.Lett. B614 (2005) 53-61

Physics

High Energy Physics

High Energy Physics - Phenomenology

9 pages latex, 1 style file

Scientific paper

10.1016/j.physletb.2005.03.073

We present for numerical use the analytic continuations to complex arguments of those basic Mellin transforms, which build the harmonic sums contributing to the 3--loop anomalous dimensions. Eight new basic functions contribute in addition to the analytic continuations for the 2--loop massless Wilson coefficients calculated previously. The representations derived have a relative accuracy of better than $10^{-7}$ in the range $x \epsilon [10^{-6},0.98]$.

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