On the Generalized Harmonic Polylogarithms of One Complex Variable
R. Bonciani, G. Degrassi, A. Vicini
TL;DR
This paper presents a numerical method for computing Generalized Harmonic Polylogarithms with complex weights, demonstrating its application to electroweak corrections in Higgs boson production.
Contribution
It introduces a numerical approach to evaluate GHPLs with square roots in weights using C++/GiNaC routines, applied to complex mass scenarios.
Findings
Successfully computed NLO electroweak corrections for Higgs production
Validated the numerical method for complex W and Z masses
Provides a practical tool for complex polylogarithm calculations
Abstract
We describe how to compute numerically in the complex plain a set of Generalized Harmonic Polylogarithms (GHPLs) with square roots in the weights, using the C++/GiNaC numerical routines of Vollinga and Weinzierl. As an example, we provide the numerical values of the NLO electroweak light-fermion corrections to the Higgs boson production in gluon fusion in the case of complex W and Z masses.
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