## 12.15.-y Electroweak interactions; Extensions of gauge or Higgs sector, see 12.60.Cn or 12.60.Fr

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The top quark plays an important role in current particle physics, from a theoretical point of view because of its uniquely large mass, but also experimentally because of the large number of top events recorded by the LHC experiments ATLAS and CMS, which makes it possible to directly measure the properties of this particle, for example its couplings to the other particles of the standard model (SM), with previously unknown precision. In this thesis, an effective field theory approach is employed to introduce a minimal and consistent parametrization of all anomalous top couplings to the SM gauge bosons and fermions which are compatible with the SM symmetries. In addition, several aspects and consequences of the underlying effective operator relations for these couplings are discussed. The resulting set of couplings has been implemented in the parton level Monte Carlo event generator WHIZARD in order to provide a tool for the quantitative assessment of the phenomenological implications at present and future colliders such as the LHC or a planned international linear collider. The phenomenological part of this thesis is focused on the charged current couplings of the top quark, namely anomalous contributions to the trilinear tbW coupling as well as quartic four-fermion contact interactions of the form tbff, both affecting single top production as well as top decays at the LHC. The study includes various aspects of inclusive cross section measurements as well as differential distributions of single tops produced in the t channel, bq → tq', and in the s channel, ud → tb. We discuss the parton level modelling of these processes as well as detector effects, and finally present the prospected LHC reach for setting limits on these couplings with 10 resp. 100 fb−1 of data recorded at √s = 14 TeV.

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.

Despite its precise agreement with the experiment, the validity of the standard model (SM) of elementary particle physics is ensured only up to a scale of several hundred GeV so far. Even more, the inclusion of gravity into an unifying theory poses a problem which cannot be solved by ordinary quantum field theory (QFT). String theory, which is the most popular ansatz for a unified theory, predicts QFT on noncommutative space-time as a low energy limit. Nevertheless, independently of the motivation given by string theory, the nonlocality inherent to noncommutative QFT opens up the possibility for the inclusion of gravity. There are no theoretical predictions for the energy scale Lambda_NC at which noncommutative effects arise and it can be assumed to lie in the TeV range, which is the energy range probed by the next generation of colliders. Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time relying on this assumption. The motivation for this thesis was given by the gap in the range of phenomenological studies of noncommutative effects in collider experiments, due to the absence in the literature of Large Hadron Collider (LHC) studies regarding noncommutative QFTs. In the first part we thus performed a phenomenological analysis of the hadronic process pp -> Z gamma -> l^+l^- gamma at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl star-product of functions on ordinary space-time and the Seiberg-Witten maps. The latter relate the ordinary fields and parameters to their noncommutative counterparts such that ordinary gauge transformations induce noncommutative gauge transformations. This requirement is expressed by a set of inhomogeneous differential equations (the gauge equivalence equations) which are solved by the Seiberg-Witten maps order by order in the noncommutative parameter Theta. Thus, by means of the Moyal-Weyl star-product and the Seiberg-Witten maps a noncommutative extension of the SM as an effective theory as expansion in powers of Theta can be achieved, providing the framework of our phenomenological studies. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. Thus, the azimuthal dependence of the cross section is a typical signature of noncommutativity and can be used in order to discriminate it against other new physics effects. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale Lambda_NC. By studying pp -> Z gamma -> l^+l^- gamma to first order in the noncommutative parameter Theta, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of Lambda_NC > 1.2 TeV. Our result improved the bounds present in the literature coming from past and present collider experiments by one order of magnitude. In order to explore the whole parameter range of the noncommutativity, ILC studies are required. By means of e^+e^- -> Z gamma -> l^+l^- gamma to first order in Theta we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on Lambda_NC derived from the ILC are significantly higher and reach Lambda_NC > 6 TeV. The second part of this work arose from the necessity to enlarge the range of validity of our model towards higher energies. Thus, we expand the neutral current sector of the noncommutative SM to second order in $\theta$. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by homogeneous solutions of the gauge equivalence equations. The expectation was that the ambiguities correspond to field redefinitions and therefore should vanish in scattering matrix elements. However, we proved that this is not the case, and the ambiguities do affect physical observables. Our conjecture is, that every order in Theta will introduce new parameters to the theory. However, only the experiment can decide to what extent efforts with still higher orders in Theta are reasonable and will also give directions for the development of theoretical models of noncommutative QFTs.