Renormalization of fermion mixing

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories.

Effect of mixing, particle interaction, and spatial dimension on the glass transition

In this thesis, the influence of composition changes on the glass transition behavior of binary liquids in two and three spatial dimensions (2D/3D) is studied in the framework of mode-coupling theory (MCT).The well-established MCT equations are generalized to isotropic and homogeneous multicomponent liquids in arbitrary spatial dimensions. Furthermore, a new method is introduced which allows a fast and precise determination of special properties of glass transition lines. The new equations are then applied to the following model systems: binary mixtures of hard disks/spheres in 2D/3D, binary mixtures of dipolar point particles in 2D, and binary mixtures of dipolar hard disks in 2D. Some general features of the glass transition lines are also discussed. The direct comparison of the binary hard disk/sphere models in 2D/3D shows similar qualitative behavior. Particularly, for binary mixtures of hard disks in 2D the same four so-called mixing effects are identified as have been found before by Götze and Voigtmann for binary hard spheres in 3D [Phys. Rev. E 67, 021502 (2003)]. For instance, depending on the size disparity, adding a second component to a one-component liquid may lead to a stabilization of either the liquid or the glassy state. The MCT results for the 2D system are on a qualitative level in agreement with available computer simulation data. Furthermore, the glass transition diagram found for binary hard disks in 2D strongly resembles the corresponding random close packing diagram. Concerning dipolar systems, it is demonstrated that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by binary point dipoles in 2D through a comparison between the experimental partial structure factors and those from computer simulations. For such mixtures of point particles it is demonstrated that MCT predicts always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks in 2D or binary hard spheres in 3D. It is demonstrated that the predicted plasticization effect is in qualitative agreement with experimental results. Finally, a glass transition diagram for binary mixtures of dipolar hard disks in 2D is calculated. These results demonstrate that at higher packing fractions there is a competition between the mixing effects occurring for binary hard disks in 2D and those for binary point dipoles in 2D.

Host race formation in Hyalesthes obsoletus (Signoret 1865)

Die Winden-Glasflügelzikade Hyalesthes obsoletus (Cixiidae, Glasflügelzikaden) nutzte in Deutschland ursprünglich die Ackerwinde Convolvulus arvensis als Wirtspflanze, allerdings nahm in den letzten zwei Dekaden die Abundanz auf der Großen Brennnessel Urtica dioica stark zu, zusammen mit der Inzidenz der Schwarzholzkrankheit Bois noir auf Weinreben. Bois noir wird durch ein Phytoplasma verursacht, das durch H. obsoletus von C. arvensis und U. dioica auf Weinreben übertragen wird. Es stellte sich daher die Frage, ob H. obsoletus Wirtsrassen entwickelt hat, die möglicherweise die Bois noir-Epidemiologie beeinflussen. In der vorliegenden Studie wurden folgende Fragestellungen bearbeitet: rn(1) Gibt es in Deutschland und Europa genetisch unterscheidbare Wirtsrassen von H. obsoletus auf den beiden Wirtspflanzen C. arvensis und U. dioica? Es wurden sieben Mikrosatellitenmarker entwickelt und etabliert, um H. obsoletus Populationen aus Deutschland und Europa genetisch zu analysieren. Es zeigte sich eine deutliche Differenzierung zwischen Populationen von beiden Wirtspflanzen in Deutschland, jedoch nicht in den historischen Ursprungsgebieten der deutschen Populationen, in der Schweiz, Italien oder Slovenien.rn(2) Wo sind die deutschen Wirtsrassen von H. obsoletus entstanden? Eine Einwanderung von südlichen, bereits an U. dioica angepassten Individuen stand einer lokalen Wirtsrassenevolution gegenüber. Die engere genetische Verwandtschaft der deutschen Population auf U. dioica zu denen auf C. arvensis, im Vergleich zu den übrigen Populationen auf U. dioica, impliziert einen lokalen Prozess im nördlichen Verbreitungsgebiet. Eine Immigration südlicher Tiere scheint nicht zur Diversifizierung beigetragen zu haben, führte aber möglicherweise einen U. dioica-spezifischen Phytoplasma-Stamm ein. Durch Wirtsrassenevolution entwickelten sich spezifische, vektorbasierte epidemiologische Kreisläufe der Schwarzholzkrankheit Bois noir. rn(3) Welche Präferenzen zeigen die beiden Wirtsrassen von H. obsoletus für die Wirtspflanzen C. arvensis und U. dioica und unterscheiden sich diese? Die Präferenz von H. obsoletus aus beiden deutschen Wirtsrassen in Bezug auf den Geruch der Wirtspflanzen wurde in einem Y-Olfaktometer untersucht, zusätzlich wurden beide Pflanzen direkt zur Wahl gestellt. Bei beiden Untersuchungen zeigte die Population von C. arvensis eine signifikante Präferenz für ihre native Wirtspflanze. Die Population von U. dioica wies dagegen keine Präferenz für den Geruch einer Wirtspflanze auf, bevorzugte im direkten Test jedoch signifikant ihre native Wirtspflanze. Dies weist darauf hin, dass die Anpassung an den „neuen“ Wirt noch nicht vollständig ist.rn