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By the end of the year 2011, both the CMS and ATLAS experiments at the Large Hadron Collider have recorded around 5 inverse femtobarns of data at an energy of 7 TeV. There are only vague hints from the already analysed data towards new physics at the TeV scale. However, one knows that around this scale, new physics should show up so that theoretical issues of the standard model of particle physics can be cured. During the last decades, extensions to the standard model that are supposed to solve its problems have been constructed, and the corresponding phenomenology has been worked out. As soon as new physics is discovered, one has to deal with the problem of determining the nature of the underlying model. A first hint is of course given by the mass spectrum and quantum numbers such as electric and colour charges of the new particles. However, there are two popular model classes, supersymmetric models and extradimensional models, which can exhibit almost equal properties at the accessible energy range. Both introduce partners to the standard model particles with the same charges and thus one needs an extended discrimination method. From the origin of these partners arises a relevant difference: The partners constructed in extradimensional models have the same spin as their standard model partners while in Supersymmetry they differ by spin 1/2.\\ These different spins have an impact on the phenomenology of the two models. For example, one can exploit the fact that the total cross sections are affected, but this requires a very good knowledge of the couplings and masses involved. Another approach uses angular distributions depending on the particle spins. A prevailing method based on this idea uses the invariant mass distribution of the visible particles in decay chains. One can relate these distributions to the spin of the particle mediating the decay since it reflects itself in the highest power of the invariant mass $\sff$ of the adjacent particles. In this thesis we first study the influence of higher than dimension 4 operators on spin determination in such decay chains. We write down the relevant dimension 5 and 6 operators and calculate their contributions to the invariant mass distribution. We discuss how they affect the determination of spin and couplings.\\ We then address two scenarios which do not involve decay chains in the usual sense. In three body decays, the method pointed out above cannot be applied since it can only be used if the mediating particle is produced on-shell. For off-shell decays, which are important e.g. in split-Supersymmetry or split-Universal Extra Dimensions, the narrow width approximation cannot be made which previously led to the simple relation between spin and the highest power of $\sff$. We work out a strategy for these three body decays that can distinguish between the different spin scenarios. The method relies on the fact that the differential decay width $d\Gamma /d\sff$ can be rewritten in this limit as a global phase space function and a polynomial in $\sff$. The coefficients in this polynomial are functions of masses and couplings and we show that they have distinct signs or ratios depending on the spins involved in the decay. We test the strategy in a series of Monte Carlo studies and discuss the influence of the intermediate particle's mass. In the last part we consider a topology with very short decay chains. Again one cannot use the relation between spin and invariant mass. We investigate one variable that has been invented for the discrimination of Supersymmetry and Universal Extra Dimensions in the high energy limit which reduces the problem to the underlying production process. We show how this variable can also be used in new physics scenarios where the high energy limit is not a viable approximation. We include all possible spin scenarios with renormalizable interactions and study in detail the influence of the involved masses and couplings on the discrimination power of this variable. We find for example that the scenario containing the supersymmetric case is well distinguishable from most other spin scenarios.
During the last decades the standard model of particle physics has evolved to one of the most precise theories in physics, describing the properties and interactions of fundamental particles in various experiments with a high accuracy. However it lacks on some shortcomings from experimental as well as from theoretical point of view: There is no approved mechanism for the generation of masses of the fundamental particles, in particular also not for the light, but massive neutrinos. In addition the standard model does not provide an explanation for the observance of dark matter in the universe. Moreover the gauge couplings of the three forces in the standard model do not unify, implying that a fundamental theory combining all forces can not be formulated. Within this thesis we address supersymmetric models as answers to these various questions, but instead of focusing on the most simple supersymmetrization of the standard model, we consider basic extensions, namely the next-to-minimal supersymmetric standard model (NMSSM), which contains an additional singlet field, and R-parity violating models. R-parity is a discrete symmetry introduced to guarantee the stability of the proton. Using lepton number violating terms in the context of bilinear R-parity violation and the munuSSM we are able to explain neutrino physics intrinsically supersymmetric, since those terms induce a mixing between the neutralinos and the neutrinos. Since 2009 the Large Hadron Collider (LHC) at CERN explores the new energy regime of Tera-electronvolt, allowing the production of potentially existing heavy particles by the collision of protons. Thus the near future might provide answers to the open questions of mass generation in the standard model and show hints towards physics beyond the standard model. Therefore this thesis works out the phenomenology of the supersymmetric models under consideration and tries to point out differences to the well-known features of the simplest supersymmetric realization of the standard model. In case of the R-parity violating models the decays of the light neutralinos can result in displaced vertices. In combination with a light singlet state these displaced vertices might offer a rich phenomenology like non-standard Higgs decays into a pair of singlinos decaying with displaced vertices. Within this thesis we present some calculations at next order of perturbation theory, since one-loop corrections provide possibly large contributions to the tree-level masses and decay widths. We are using an on-shell renormalization scheme to calculate the masses of neutralinos and charginos including the neutrinos and leptons in case of the R-parity violating models at one-loop level. The discussion shows the similarities and differences to existing calculations in another renormalization scheme, namely the DRbar scheme. Moreover we consider two-body decays of the form chi_j^0 -> chi_l^\pm W^\mp involving a heavy gauge boson in the final state at one-loop level. Corrections are found to be large in case of small or vanishing tree-level decay widths and also for the R-parity violating decay of the lightest neutralino chi_1^0 -> l^\pm W^\mp. An interesting feature of the models based on bilinear R-parity violation is the correlation between the branching ratios of the lightest neutralino decays and the neutrino mixing angles. We discuss these relations at tree-level and for two-body decays chi_1^0 -> l^\pm W^\mp also at one-loop level, since only the full one-loop corrections result in the tree-level expected behavior. The appendix describes the two programs MaCoR and CNNDecays being developed for the analysis carried out in this thesis. MaCoR allows for the calculation of mass matrices and couplings in the models under consideration and CNNDecays is used for the one-loop calculations of neutralino and chargino mass matrices and the two-body decay widths.