Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for arbitrary complex arguments and without any restriction on the weight. We have implemented these algorithms with arbitrary precision arithmetic in C++ within the GiNaC framework.
We present version 4.0 of the symbolic manipulation system FORM. The most
important new features are manipulation of rational polynomials and the
factorization of expressions. Many other new functions and commands are also
added; some of them are very general, while others are designed for building
specific high level packages, such as one for Groebner bases. New is also the
checkpoint facility, that allows for periodic backups during long calculations.
Lastly, FORM 4.0 has become available as open source under the GNU General
Public License version 3.Comment: 26 pages. Uses axodra
We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The number of external legs of the loop integrals is not restricted. All calculations are done within dimensional regularization.
The gluon-gluon induced terms for Higgs production through weak boson fusion (WBF) are computed. Formally, these are of NNLO in the strong coupling constant. This is the lowest order at which non-zero color exchange occurs between the scattering quarks, leading to a color field and thus additional hadronic activity between the outgoing jets. Using a minimal set of cuts, the numerical impact of these terms is at the percent level with respect to the NLO rate for weak boson fusion. Applying the so-called WBF cuts leads to an even stronger suppression, so that we do not expect a significant deterioration of the WBF signal by these color exchange effects.
We give an introduction to the C þþ library GiNaC, which extends the C þþ language by new objects and methods for the representation and manipulation of arbitrary symbolic expressions. r
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