Mass spectrum prediction in non-minimal supersymmetric models

Supersymmetry is an attractive extension of the Standard Model (SM) of particle physics. The minimal supersymmetric extension (MSSM) provides gauge coupling unification, a dark matter candidate particle and can explain the breaking of the electroweak symmetry dynamically. However, it suffers from the little hierarchy and the mu-problem. Non-minimal supersymmetric extensions of the SM with a larger particle content or a higher symmetry can evade the problems of the MSSM. Such models may be well-motivated by Grand Unified Theories (GUTs) and can provide a rich new phenomenology with an extended Higgs sector, exotic particles, additional interactions and a close connection to String Theory. Interesting examples are the Next-to Minimal Supersymmetric Standard Model (NMSSM), which is motivated by the mu-problem, and the Exceptional Supersymmetric Standard Model (E6SSM), which is inspired by E6 GUTs. For phenomenological investigations of supersymmetric (SUSY) models the pole mass spectrum must be calculated from the fundamental model parameters. This task, however, is non-trivial as the spectrum must be consistent with measured low-energy observables (fine-structure constant, Z boson pole mass, muon decay etc.) as well as electroweak symmetry breaking and potential universality conditions on the soft supersymmetry breaking parameters at the GUT scale. Programs, which calculate the SUSY mass spectrum consistent with constraints of this kind are called spectrum generators. In this thesis four different contributions to the prediction of mass spectra and model parameters in non-minimal SUSY models are presented. (i) One-loop matching corrections of the E6SSM gauge and Yukawa couplings to the SM are calculated to increase the precision of the mass spectrum prediction in the constrained E6SSM. (ii) The beta-functions of vacuum expectation values (VEVs) are calculated in a general and supersymmetric gauge theory at the one- and two-loop level. The results enable an accurate calculation of the renormalization group running of the VEVs in non-minimal SUSY models. (iii) An NMSSM extension of Softsusy, a spectrum generator for the MSSM, is implemented. It represents a precise alternative to the already existing spectrum generator NMSPEC. (iv) FlexibleSUSY is presented, a general framework which creates a fast, modular and precise spectrum generator for any user-defined SUSY model. It represents a generalization of the hand-written SUSY spectrum generators and allows the study of a large variety of new SUSY models easily with high precision