Search

In the current LHC era, a vast number of models for BSM physics are being tested. For predictions accurate enough to match experimental errors, theoretical calculations have to go beyond LO estimates. However, calculating one-loop corrections in BSM models involves many new particles with specific model dependent properties. Therefore, they are done largely by hand, or in partially–automated ways. I present a fully automated tool for the calculation of generic massive one-loop Feynman diagrams with four external particles, implemented as a module within the fully automated MadGolem framework. With this one can compute the NLO–QCD corrections to generic BSM heavy resonance production processes, for example in the context of supersymmetric theories.

The Standard Model scalar potential contains a minimum at the Electroweak scale, responsible for the masses of the weak gauge bosons through the Higgs mechanism. However, if the Electroweak minimum is only a local minimum, and there exists a global minimum at a higher energy in the Higgs potential, then in a su ciently old universe we would expect the vacuum expectation value to be at the global minimum. The absence of a global minimum at higher energy is related to the condition that the Higgs self coupling is greater than or equal to zero for all energies. For any model that fails this, we expect new physics to enter before the energy at which the coupling becomes negative. We developed tools to automate the derivation of beta functions for renormalisable gauge theories, and used these to carry out evolution of the renormalisation group equations for the Standard Model and three extensions to the Standard Model | the Standard Model with a fourth generation, the Standard Model with right-handed neutrinos and a Left-Right Symmetric Model. We conclude that of these four models, the Standard Model is the only one in which all the couplings remain perturbative, and in which the Electroweak minimum is a global minimum.

The LHC has begun collecting data and the first results have now been published. This is truly an exciting time in the field as we wait for the experimental data to exclude or verify new physics beyond the Standard Model. In order to make a precise prediction for the LHC one must go beyond the leading order of our perturbation series. In this thesis I present the extension of tools for the automation of one loop calculations for supersymmetric models. The second part of the thesis contains the application of these tools to neutralino pair production in the Minimal Supersymmetric Model.

Feynman graphs in perturbative quantum field theory are replete with infrared divergences caused by the presence of massless particles, how-ever these divergences are known to cancel order-by-order when all virtual and real contributions to a given cross section are summed and smeared against an experimental resolution. In this thesis we treat the infrared problem formally in the language of distribution theory so that we can remove the divergences with local momentum space subtractions using Hadamard's procedure. This is analogous with the BPHZ mechanism for removing UV divergences. Our aim is to show how it is possible to make both the real and virtual subtractions analytically such that we are left with manifestly finite integrands. For the virtual graphs we present a new decomposition of the integrand in momentum space and remove those terms that are divergent. For the real graphs we show how the Taylor expansion of the momentum conserving delta function allows the explicit removal of the divergent part; furthermore we show that the homogeneous properties of the soft structure greatly simplifies this procedure.

In the very near future the first data from LHC will be available. The searches for the Higgs boson and for new physics will require precise predictions both for the signal and the background processes. Tree level calculations typically suffer from large renormalization scale uncertainties. I present an efficient implementation of an algorithm for the automated, Feynman diagram based calculation of one-loop corrections to processes with many external particles. This algorithm has been successfully applied to compute the virtual corrections of the process u¯u -> b¯bb¯b in massless QCD and can easily be adapted for other processes which are required for the LHC.