Chiral properties of two-flavour QCD at zero and non-zero temperature

Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.

The Euler number of OGradys 10-dimensional symplectic manifold

Wir berechnen die Eulerzahl der 10-dimensionalen exzeptionellen irreduziblen symplektischen Mannigfaltigkeit, die von O Grady konstruiert wurde. Die Idee besteht darin, zunächst eine Lagrangefaserung zu konstruieren und dann die Eulerzahlen der Fasern zu berechnen. Es stellt sich heraus, dass fast alle Fasern die Eulerzahl 0 haben, und deswegen reduziert sich das Problem auf die Berechnung der Eulerzahlen der übrigen Fasern. Diese Fasern sind Modulräume von halbstabilen Garben auf singulären Kurven. Der Hauptteil dieser Dissertation ist der Berechnung der Eulerzahlen dieser Modulräume gewidmet. Diese Resultate sind von unabhängigem Interesse.

Nuclear charge radius determination of 7,10 Be and the one-neutron halo nucleus 11 Be

The only nuclear model independent method for the determination of nuclear charge radii of short-lived radioactive isotopes is the measurement of the isotope shift. For light elements (Z < 10) extremely high accuracy in experiment and theory is required and was only reached for He and Li so far. The nuclear charge radii of the lightest elements are of great interest because they have isotopes which exhibit so-called halo nuclei. Those nuclei are characterized by a a very exotic nuclear structure: They have a compact core and an area of less dense nuclear matter that extends far from this core. Examples for halo nuclei are 6^He, 8^He, 11^Li and 11^Be that is investigated in this thesis. Furthermore these isotopes are of interest because up to now only for such systems with a few nucleons the nuclear structure can be calculated ab-initio. In the Institut für Kernchemie at the Johannes Gutenberg-Universität Mainz two approaches with different accuracy were developed. The goal of these approaches was the measurement of the isotope shifts between (7,10,11)^Be^+ and 9^Be^+ in the D1 line. The …first approach is laser spectroscopy on laser cooled Be^+ ions that are trapped in a linear Paul trap. The accessible accuracy should be in the order of some 100 kHz. In this thesis two types of linear Paul traps were developed for this purpose. Moreover, the peripheral experimental setup was simulated and constructed. It allows the efficient deceleration of fast ions with an initial energy of 60 keV down to some eV and an effcient transport into the ion trap. For one of the Paul traps the ion trapping could already be demonstrated, while the optical detection of captured 9^Be^+ ions could not be completed, because the development work was delayed by the second approach. The second approach uses the technique of collinear laser spectroscopy that was already applied in the last 30 years for measuring isotope shifts of plenty of heavier isotopes. For light elements (Z < 10), it was so far not possible to reach the accuracy that is required to extract information about nuclear charge radii. The combination of collinear laser spectroscopy with the most modern methods of frequency metrology …finally permitted the …first-time determination of the nuclear charge radii of (7,10)^Be and the one neutron halo nucleus 11^Be at the COLLAPS experiment at ISOLDE/ CERN. In the course of the work reported in this thesis it was possible to measure the absolute transition frequencies and the isotope shifts in the D1 line for the Be isotopes mentioned above with an accuracy of better than 2 MHz. Combination with the most recent calculations of the mass effect allowed the extraction of the nuclear charge radii of (7,10,11)^Be with an relative accuracy better than 1%. The nuclear charge radius decreases from 7^Be continuously to 10^Be and increases again for 11^Be. This result is compared with predictions of ab-initio nuclear models which reproduce the observed trend. Particularly the "Greens Function Monte Carlo" and the "Fermionic Molecular Dynamic" model show very good agreement.

Exploring the function of IL-10, BTLA and DCs as regulators of immune responses

This thesis focuses on different aspects of immune regulation, both at the cellular and molecular levels. More specifically, this work concentrates on the importance of Interleukin-10, B and T Lymphocyte Attenuator (BTLA), and dendritic cells in respect to immune regulation, with special emphasis on autoimmunity. In this thesis, we show that the cellular source of IL10 production can dramatically influence the outcome of an autoimmune response. We show that T cell-derived IL10 plays an important role in controlling the viability of recently activated T cells, allowing them to become fully functional T effector cells. T cell-specific IL10-deficient mice failed to induce EAE when immunized with MOG peptide. Furthermore, when re-challenged with MOG or other stimuli, these T cells exhibited increased apoptosis rates. Here we report for the first time the generation of a novel mouse model that allows the conditional over-expression of BTLA. We show that BTLA can negatively regulate CD4+ T cells responses, when expressed by the T cells themselves. BTLA over-expression by CD8+ T cells or dendritic cells, however, resulted in enhanced viral clearance. In this study, we show that depletion of DCs, either early on from birth or later in adulthood, does not prevent EAE induction, but instead leads to a lower state of tolerance and stronger immune response. We also show that DCs are responsible for the upregulation of PD-1 on antigen-specific T cells and subsequently induce the formation of Tregs during immune responses.

Lentivirus-mediated knockdown of Galectin-10 and Foxp3 in human immune cells

Die Suppression von autoreaktiven T-Zellen ist eine Funktion von CD4+CD25+ regulatorischen T-Zellen (CD4+CD25+ Tregs). CD4+CD25+ Tregs unterdrücken autoaggressive Immunantworten. Galectin-10 und Foxp3 sind wichtige Proteine, die an dem supprimierenden Mechanismus der Tregs beteiligt sind. Galectin-10 ist eines der ältesten bekannten humanen Proteine, die nicht in anderen Spezies gefunden worden sind. Foxp3 ist ein Transkriptionsfaktor, der in menschlichen CD4+CD25+ Tregs und in CD4+CD25- T-Effektor-Zellen nach Aktivierung exprimiert wird. Ein siRNA-vermittelter Knockdown dieses intrazellulären löslichen Proteins hebt die supprimierende Funktion der humanen CD4+CD25+ Tregs auf.rnDiese Arbeit beinhaltet in vitro durchgeführte Untersuchungen zur Ermöglichung eines Knockdown von Galectin-10 und/oder Foxp3 in humanisierten Mäusen. Es war möglich, ein Verfahren für die Produktion von lentiviralen Partikeln zu etablierten, die sich als effizientes Vehikel für den Gentransfer in humane Stammzellen und verschiedene Tumor- und Immunzellen erwiesen. Nach der Transduktion von AML14.3D10 Tumorzellen mit GFP-codierenden lentiviralen Partikeln konnte eine langfristige Expression von GFP erreicht werden. Außerdem war es möglich lentivirale Partikel zu erzeugen, die mit shRNA gegen Galectin-10 codiert waren. Die erzeugten Partikel erwiesen sich als funktionell, indem sie eine deutliche Herunterregulation von Galectin-10 in konstitutiv Galectin-10 exprimierenden AML14.3D10 Tumorzellen bewirkten. Unsere Studie präsentierte außerdem eine erstmalige Untersuchung zum Nachweis von Galectin-10-Protein in Eosinophilen aus humanen CD34+ hämatopoetischen Stammzellen (HSC). Diese stabile in vitro Galectin-10-Expression bietet ein alternatives Untersuchungsmodell zu CD4+CD25+ Tregs, die nicht aus CD34+ HSC differenziert werden können. Der zusätzliche Einbau des GFP-Gens in die mit shRNA gegen Galectin-10 codierende lentivirale Partikel war ein wichtiger Schritt zur Markierung von Zellen, die einen Galectin-10-Knockdown aufwiesen. Die neuen bicistronischen lentiviralen Partikel erwiesen sich sowohl in aus CD34+ HSC differenzierten Eosinophilen als auch in AML14.3D10 Zellen, die einen eosinophilen Phänotyp aufweisen, als funktionell. Schließlich konnte mit den bicistronischen lentiviralen Partikeln, die mit GFP und shRNA gegen Foxp3 codiert waren, eine Herunterregulation von Foxp3 in CD4+CD25- T-Effektor-Zellen erreicht werden, was erneut die erfolgreiche Herstellung von funktionellen lentiviralen Partikeln bewies.rn