Numerical evaluation of two-dimensional harmonic polylogarithms

By Ettore Remiddi, Thomas Gehrmann. 2001

177 citations recorded by the source corpus.

The two-dimensional harmonic polylogarithms G(a→(z);y), a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of two-dimensional harmonic polylogarithms, with the two arguments y,z varying in the triangle 0⩽y⩽1, 0⩽z⩽1, 0⩽(y+z)⩽1. This algorithm is implemented into a FORTRAN subroutine tdhpl to compute two-dimensional harmonic polylogarithms up to weight 4.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/5f7b3611baef7a7305dcd7b0608db4ec96ba89af

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Soft triple-real radiation for Higgs production at N3LO (2013, methodology): “This rational number can easily be determined by evaluating Ai1 numerically at a single point using any of the standard libraries to evaluate multiple polylogarithms [84,126–131], and running for”
Event shapes and jet rates in electron-positron annihilation at NNLO (2009, background): “It should be mentioned that the results of this paper rely heavily on research carried out in the past years: Integration techniques for two-loop amplitudes [13–16], the calculation of the relevant tree-, one- and two-loop-amplitudes [17–29], routines for the numerical evaluation of polylogarithms [”
Feynman integrals and hyperlogarithms (2015, background): “This notation was fixed in [90], were one also finds explicit formulas that express these functions for weight less than four in terms of Nielsen’s generalized polylogarithms (3.”
Mathematical aspects of scattering amplitudes (2014, methodology): “ ai ∈ {0,1,−y,−1− y}, for y ∈ C. They appear in the computation of four-point functions with three on-shell and one oﬀ shell leg [15–17], and can be evaluated numerically using the techniques of ref. [13, 18]. (3) Generalized harmonic polylogarithms (GHPLs) [19]: GHPLs are deﬁned as iterated integra”