We present a program for the numerical evaluation of scalar integrals and
tensor form factors entering the calculation of one-loop amplitudes which
supports the use of complex masses in the loop integrals. The program is built
on an earlier version of the golem95 library, which performs the reduction to a
certain set of basis integrals using a formalism where inverse Gram
determinants can be avoided. It can be used to calculate one-loop amplitudes
with arbitrary masses in an algebraic approach as well as in the context of a
unitarity-inspired numerical reconstruction of the integrand.Comment: 22 pages, 3 figure
We report on the current status of the Golem project which aims at the
construction of a general one-loop evaluator for matrix elements. We construct
the one-loop matrix elements from Feynman diagrams in a highly automated way
and provide a library for the reduction and numerically stable evaluation of
the tensor integrals involved in this approach. Furthermore, we present
applications to physics processes relevant for the LHC.Comment: 7 pages, 4 figures, contrib. to proceedings of "Loops and Legs in
Quantum Field Theory", 10th DESY Workshop on Elementary Particle Theory,
25-30 April 2010, Woerlitz, German
In this article we provide representations for the one-loop three point functions in 4 and 6 dimensions in the general case with complex masses. The latter are part of the GOLEM library used for the computation of one-loop multileg amplitudes. These representations are one-dimensional integrals designed to be free of instabilites induced by inverse powers of Gram determinants, therefore suitable for stable numerical implementations.
In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an applica-tion of our approach we report on the status of the calculation of the amplitude for the process pp → bbbb + X.
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