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

Johannes Blümlein·Sven-Olaf Moch
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Abstract

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 $x ε[10^{-6},0.98]$.

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Johannes Blümlein, Sven-Olaf Moch. 2005-03-18. Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions. https://doi.org/10.1016/j.physletb.2005.03.073

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