New Tools for Automatic Cross Section Calculation

In this contribution the matrix element generator AMEGIC++ will be presented. It automatically generates Feynman diagrams, helicity amplitudes, and suitable phase space mappings for processes involving multi-particle final states within the Standard Model and some of its popular extensions. Due to the rising energy frontier in high-energy collider experiments, potential signals and their backgrounds for interesting or new phenomena involve an increasing number of final state particles and their correlations. To describe the production process of a number of particles, in a quantum mechanically correct treatment, at least at leading order, the corresponding amplitudes have to be constructed. This usually results in a potentially very large number of terms, such that their automated construction and evaluation becomes mandatory. Apart from handling the sheer number of amplitudes, which grows factorially or worse with the number of final state particles, the integration over the multidimensional phase space of the final state represents a formidable task. In the past years various solutions, implemented as different codes, to surmount these problems, have been found. Codes, which incorporate the full Standard Model, are: CompHEP [1], which relies on the traditional method of constructing and summing Feynman diagrams, where completeness relations are used to square the total amplitude. The integration is achieved through one phase space mapping selected by the user. MadGraph/MadEvent [2], which constructs Feynman diagrams and employs the method of helicity amplitudes through the HELAS library [3] for their evaluation. The phase space integration is achieved through a single-diagram enhanced mapping.There, each diagram gives rise to one parametrisation of phase space, their interplay is steered dynamically in order to minimise the overall variance. Alpgen [4] uses the (extended) α-formalism [5] to construct the amplitudes. This formalism is based on the Schwinger-Dyson method to recursively define one-particle off-shell Greens functions, which are then numerically evaluated through a specific representation of their ingredients. This approach significantly tames the factorial growth of the number of terms to be calculated with the number of final state particles. In Alpgen a huge number of processes at hadron colliders is implemented ready to use, the amplitudes are supplemented with suitable, predefined phase space mappings. The HELAC/PHEGAS package [6] also employs the Schwinger-Dyson method, however, in a slightly different fashion. The phase space mappings are constructed automatically after Feynman diagram-like topologies underlying