Automating methods to improve precision in Monte-Carlo event generation for particle colliders

The subject of this thesis was the development of tools for the automated calculation of exact matrix elements, which are a key for the systematic improvement of precision and confidence for theoretical predictions. Part I of this thesis concentrates on the calculations of cross sections at tree level. A number of extensions have been implemented in the matrix element generator AMEGIC++, namely new interaction models such as effective loop-induced couplings of the Higgs boson with massless gauge bosons, required for a number of channels for the Higgs boson search at LHC and anomalous gauge couplings, parameterizing a number of models beyond th SM. Further a special treatment to deal with complicated decay chains of heavy particles has been constructed. A significant effort went into the implementation of methods to push the limits on particle multiplicities. Two recursive methods have been implemented, the Cachazo-Svrcek-Witten recursion and the colour dressed Berends-Giele recursion. For the latter the new module COMIX has been added to the SHERPA framework. The Monte-Carlo phase space integration techniques have been completely revised, which led to significantly reduced statistical error estimates when calculating cross sections and a greatly improved unweighting efficiency for the event generation. Special integration methods have been developed to cope with the newly accessible final states. The event generation framework SHERPA directly benefits from those new developments, improving the precision and the efficiency. Part II was addressed to the automation of QCD calculations at next-to-leading order. A code has been developed, that, for the first time fully automates the real correction part of a NLO calculation. To calculate the correction for a m-parton process obeying the Catani-Seymour dipole subtraction method the following components are provided: 1. the corresponding m+1-parton tree level matrix elements, 2. a number dipole subtraction terms to remove the soft and collinear divergencies 3. the finite part of the integrated subtraction terms, added back to make the full real correction term independent of the regularization method. Furthermore, integrators for all necessary phase space integrals are provided. The new implementation is based on the matrix element generator AMEGIC++. For one-loop calculations this tool can provide a significant facilitation: The main difficulties arise for the evaluation of n-point one-loop integrals for n>4. Most promising candidates to resolve this obstacle are semi-numerical approaches to integrate over the loop momentum. Such a technique has been explored. A new decomposition of loop integrals into phase-space integrals is proposed and semi-numerical strategies to evaluate the new integrals were developed. (orig.)