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Testing Models with Higher Dimensional Effective Interactions at the LHC and Dark Matter Experiments
(2013)
Dark matter and non-zero neutrino masses are possible hints for new physics beyond the Standard Model of particle physics. Such potential consequences of new physics can be described by effective field theories in a model independent way. It is possible that the dominant contribution to low-energy effects of new physics is generated by operators of dimension d>5, e.g., due to an additional symmetry. Since these are more suppressed than the usually discussed lower dimensional operators, they can lead to extremly weak interactions even if new physics appears at comparatively low scales. Thus neutrino mass models can be connected to TeV scale physics, for instance. The possible existence of TeV scale particles is interesting, since they can be potentially observed at collider experiments, such as the Large Hadron Collider. Hence, we first recapitulate the generation of neutrino masses by higher dimensional effective operators in a supersymmetric framework. In addition, we discuss processes that can be used to test these models at the Large Hadron Collider. The introduction of new particles can affect the running of gauge couplings. Hence, we study the compatibilty of these models with Grand Unified Theories. The required extension of these models can imply the existence of new heavy quarks, which requires the consideration of cosmological constraints. Finally, higher dimensional effective operators can not only generate small neutrino masses. They also can be used to discuss the interactions relevant for dark matter detection experiments. Thus we apply the methods established for the study of neutrino mass models to the systematic discussion of higher dimensional effective operators generating dark matter interactions.
In this thesis I present results concerning realistic calculations of correlated fermionic many-body systems. One of the main objectives of this work was the implementation of a hybridization expansion continuous-time quantum Monte Carlo (CT-HYB) algorithm and of a flexible self-consistency loop based on the dynamical mean-field theory (DMFT). DMFT enables us to treat strongly correlated electron systems numerically. After the implementation and extensive testing of the program we investigated different problems to answer open questions concerning correlated systems and their numerical treatment.
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.
In this thesis we study various aspects of chaos synchronization of time-delayed coupled chaotic maps. A network of identical nonlinear units interacting by time-delayed couplings can synchronize to a common chaotic trajectory. Even for large delay times the system can completely synchronize without any time shift. In the first part we study chaotic systems with multiple time delays that range over several orders of magnitude. We show that these time scales emerge in the Lyapunov spectrum: Different parts of the spectrum scale with the different delays. We define various types of chaos depending on the scaling of the maximum exponent. The type of chaos determines the synchronization ability of coupled networks. This is, in particular, relevant for the synchronization properties of networks of networks where time delays within a subnetwork are shorter than the corresponding time delays between the different subnetworks. If the maximum Lyapunov exponent scales with the short intra-network delay, only the elements within a subnetwork can synchronize. If, however, the maximum Lyapunov exponent scales with the long inter-network connection, complete synchronization of all elements is possible. The results are illustrated analytically for Bernoulli maps and numerically for tent maps. In the second part the attractor dimension at the transition to complete chaos synchronization is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks of Bernoulli units as a function of the network size. Furthermore the scaling of the Kaplan-Yorke dimension as well as of the Kolmogorov entropy with system size and time delay is investigated. Finally, we study the change in the attractor dimension for systems with parameter mismatch. In the third and last part the linear response of synchronized chaotic systems to small external perturbations is studied. The distribution of the distances from the synchronization manifold, i.e., the deviations between two synchronized chaotic units due to external perturbations on the transmitted signal, is used as a measure of the linear response. It is calculated numerically and, for some special cases, analytically. Depending on the model parameters this distribution has power law tails in the region of synchronization leading to diverging moments. The linear response is also quantified by means of the bit error rate of a transmitted binary message which perturbs the synchronized system. The bit error rate is given by an integral over the distribution of distances and is studied numerically for Bernoulli, tent and logistic maps. It displays a complex nonmonotonic behavior in the region of synchronization. For special cases the distribution of distances has a fractal structure leading to a devil's staircase for the bit error rate as a function of coupling strength. The response to small harmonic perturbations shows resonances related to coupling and feedback delay times. A bi-directionally coupled chain of three units can completely filter out the perturbation. Thus the second moment and the bit error rate become zero.