On the Generalized Harmonic Polylogarithms of One Complex Variable

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.

25 pages, 1 figure

References in corpus (8)

• NLO Electroweak Corrections to Higgs Boson Production at Hadron Colliders
• Algorithm FIRE -- Feynman Integral REduction
• Feynman Diagrams and Differential Equations
• Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Two-Loop Heavy-Flavor Contribution to Bhabha Scattering
• Two-loop electroweak corrections to Higgs production in proton-proton collisions
• Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering

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