Factorization and non-local 1/m b corrections in the decay B X s gamma

In this thesis, a systematic analysis of the bar B to X_sgamma photon spectrum in the endpoint region is presented. The endpoint region refers to a kinematic configuration of the final state, in which the photon has a large energy m_b-2E_gamma = O(Lambda_QCD), while the jet has a large energy but small invariant mass. Using methods of soft-collinear effective theory and heavy-quark effective theory, it is shown that the spectrum can be factorized into hard, jet, and soft functions, each encoding the dynamics at a certain scale. The relevant scales in the endpoint region are the heavy-quark mass m_b, the hadronic energy scale Lambda_QCD and an intermediate scale sqrt{Lambda_QCD m_b} associated with the invariant mass of the jet. It is found that the factorization formula contains two different types of contributions, distinguishable by the space-time structure of the underlying diagrams. On the one hand, there are the direct photon contributions which correspond to diagrams with the photon emitted directly from the weak vertex. The resolved photon contributions on the other hand arise at O(1/m_b) whenever the photon couples to light partons. In this work, these contributions will be explicitly defined in terms of convolutions of jet functions with subleading shape functions. While the direct photon contributions can be expressed in terms of a local operator product expansion, when the photon spectrum is integrated over a range larger than the endpoint region, the resolved photon contributions always remain non-local. Thus, they are responsible for a non-perturbative uncertainty on the partonic predictions. In this thesis, the effect of these uncertainties is estimated in two different phenomenological contexts. First, the hadronic uncertainties in the bar B to X_sgamma branching fraction, defined with a cut E_gamma > 1.6 GeV are discussed. It is found, that the resolved photon contributions give rise to an irreducible theory uncertainty of approximately 5 %. As a second application of the formalism, the influence of the long-distance effects on the direct CP asymmetry will be considered. It will be shown that these effects are dominant in the Standard Model and that a range of -0.6 < A_CP^SM < 2.8 % is possible for the asymmetry, if resolved photon contributions are taken into account.

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.

Risikomaße in der Finanzmathematik

„Risikomaße in der Finanzmathematik“ Der Value-at -Risk (VaR) ist ein Risikomaß, dessen Verwendung von der Bankenaufsicht gefordert wird. Der Vorteil des VaR liegt – als Quantil der Ertrags- oder Verlustverteilung - vor allem in seiner einfachen Interpretierbarkeit. Nachteilig ist, dass der linke Rand der Wahrscheinlichkeitsverteilung nicht beachtet wird. Darüber hinaus ist die Berechnung des VaR schwierig, da Quantile nicht additiv sind. Der größte Nachteil des VaR ist in der fehlenden Subadditivität zu sehen. Deswegen werden Alternativen wie Expected Shortfall untersucht. In dieser Arbeit werden zunächst finanzielle Risikomaße eingeführt und einige ihre grundlegenden Eigenschaften festgehalten. Wir beschäftigen uns mit verschiedenen parametrischen und nichtparametrischen Methoden zur Ermittlung des VaR, unter anderen mit ihren Vorteilen und Nachteilen. Des Weiteren beschäftigen wir uns mit parametrischen und nichtparametrischen Schätzern vom VaR in diskreter Zeit. Wir stellen Portfoliooptimierungsprobleme im Black Scholes Modell mit beschränktem VaR und mit beschränkter Varianz vor. Der Vorteil des erstens Ansatzes gegenüber dem zweiten wird hier erläutert. Wir lösen Nutzenoptimierungsprobleme in Bezug auf das Endvermögen mit beschränktem VaR und mit beschränkter Varianz. VaR sagt nichts über den darüber hinausgehenden Verlust aus, während dieser von Expected Shortfall berücksichtigt wird. Deswegen verwenden wir hier den Expected Shortfall anstelle des von Emmer, Korn und Klüppelberg (2001) betrachteten Risikomaßes VaR für die Optimierung des Portfolios im Black Scholes Modell.

Untergrundstudien zur Messung der Strangeness-Vektorformfaktoren des Protons durch paritätsverletzende Elektronenstreuung unter Rückwärtswinkeln

Im Rahmen des A4-Experiments werden die Beiträge des Strange-Quarks zu den elektromagnetischen Formfaktoren des Protons gemessen. Solche Seequarkeffekte bei Niederenergieobservablen sind für das Verständnis der Hadronenstruktur wichtig, denn sie stellen eine direkte Manifestation der QCD-Freiheitsgrade im nichtperturbativen Bereich dar.rnrnLinearkombinationen der Strangeness-Vektorformfaktoren des Protons $G_E^s$ und $G_M^s$ sind experimentell über die Messung der paritätsverletzenden Asymmetrie im Wirkungsquerschnitt der elastischen Streuung longitudinal polarisierter Elektronen an unpolarisierten Nukleonen zugänglich. Vor dieser Arbeit hatte die A4-Kollaboration zwei solche Messungen unter Vorwärtsstreuwinkeln bei den Viererimpulsübertägen $Q^2$ von jeweils 0.23 und 0.10 (GeV/c)$^2$ veröffentlicht. Um die Separation von $G_E^s$ und $G_M^s$ beim höheren $Q^2$-Wert zu erhalten, wurde eine Messung unter Rückwärtswinkeln mit der Strahlenergie von 315 MeV durchgeführt.rnrnIm A4-Experiment werden die an einem Flüssigwasserstoff-Target gestreuten Elektronen eines longitudinal polarisierten Strahls mit einem Cherenkov-Kalorimeter einzeln gezählt. Durch die kalorimetrische Energiemessung erfolgt die Trennung der elastischen von den inelastischen Ereignissen. Bei Rückwärtswinkeln wurde dieses Apparat mit einem Szintillator als Elektronentagger erweitert, um den $\gamma$-Untergrund aus dem $\pi^0$-Zerfall zu unterdrücken.rnrnUm die Auswertung dieser Messung zu ermöglichen, wurden im Rahmen dieser Arbeit die gemessenen Energiespektren anhand von ausführlichen Simulationen der Streuprozesse und des Antwortverhaltens der Detektoren untersucht, und eine Methode zur Behandlung des restlichen Untergrunds aus der $\gamma$-Konversionrnvor dem Szintillator entwickelt. Die Simulationergebnisse sind auf dem 5%-Niveau mit den Messungen verträglich, und es wurde bewiesen, dass die Methode der Untergrundbehandlung anwendbar ist.rnrnDie Asymmetriemessung bei Rückwärtswinkeln, die man nach Anwendung der hier erarbeiteten Untergrundbehandlung erhält, wurde für die Separation von $G_E^s$ und $G_M^s$ bei $Q^2$=0.22 (GeV/c)^2 mit der Vorwärtswinkelmessung beim selbenrn$Q^2$ kombiniert. Es ergeben sich die Werte:rnrn$G_M^s$= -0.14 ± 0.11_{exp} ± 0.11_{theo} undrn$G_E^s$= 0.050 ± 0.038_{exp} ± 0.019_{theo}, rnrnwobei die systematische Unsicherheit wegen der Untergrundbehandlung im experimentellen Fehler enthalten ist. Am Ende der Arbeit werden die aus diesen Resultaten folgenden Rückschlüsse auf den Einfluss der Strangeness auf die statischen elektromagnetischen Eigenschaften des Protons diskutiert.rn

Measurement of the elastic electron-proton cross section and separation of the electric and magnetic form factor in the Q 2 range from 0.004 to 1 (GeV/c) 2

The electromagnetic form factors of the proton are fundamental quantities sensitive to the distribution of charge and magnetization inside the proton. Precise knowledge of the form factors, in particular of the charge and magnetization radii provide strong tests for theory in the non-perturbative regime of QCD. However, the existing data at Q^2 below 1 (GeV/c)^2 are not precise enough for a hard test of theoretical predictions.rnrnFor a more precise determination of the form factors, within this work more than 1400 cross sections of the reaction H(e,e′)p were measured at the Mainz Microtron MAMI using the 3-spectrometer-facility of the A1-collaboration. The data were taken in three periods in the years 2006 and 2007 using beam energies of 180, 315, 450, 585, 720 and 855 MeV. They cover the Q^2 region from 0.004 to 1 (GeV/c)^2 with counting rate uncertainties below 0.2% for most of the data points. The relative luminosity of the measurements was determined using one of the spectrometers as a luminosity monitor. The overlapping acceptances of the measurements maximize the internal redundancy of the data and allow, together with several additions to the standard experimental setup, for tight control of systematic uncertainties.rnTo account for the radiative processes, an event generator was developed and implemented in the simulation package of the analysis software which works without peaking approximation by explicitly calculating the Bethe-Heitler and Born Feynman diagrams for each event.rnTo separate the form factors and to determine the radii, the data were analyzed by fitting a wide selection of form factor models directly to the measured cross sections. These fits also determined the absolute normalization of the different data subsets. The validity of this method was tested with extensive simulations. The results were compared to an extraction via the standard Rosenbluth technique.rnrnThe dip structure in G_E that was seen in the analysis of the previous world data shows up in a modified form. When compared to the standard-dipole form factor as a smooth curve, the extracted G_E exhibits a strong change of the slope around 0.1 (GeV/c)^2, and in the magnetic form factor a dip around 0.2 (GeV/c)^2 is found. This may be taken as indications for a pion cloud. For higher Q^2, the fits yield larger values for G_M than previous measurements, in agreement with form factor ratios from recent precise polarized measurements in the Q2 region up to 0.6 (GeV/c)^2.rnrnThe charge and magnetic rms radii are determined as rn⟨r_e⟩=0.879 ± 0.005(stat.) ± 0.004(syst.) ± 0.002(model) ± 0.004(group) fm,rn⟨r_m⟩=0.777 ± 0.013(stat.) ± 0.009(syst.) ± 0.005(model) ± 0.002(group) fm.rnThis charge radius is significantly larger than theoretical predictions and than the radius of the standard dipole. However, it is in agreement with earlier results measured at the Mainz linear accelerator and with determinations from Hydrogen Lamb shift measurements. The extracted magnetic radius is smaller than previous determinations and than the standard-dipole value.

A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Measurement of the inclusive jet cross section in proton-proton collisions at root out s = 7 TeV with the ATLAS detector

The dominant process in hard proton-proton collisions is the production of hadronic jets.rnThese sprays of particles are produced by colored partons, which are struck out of their confinement within the proton.rnPrevious measurements of inclusive jet cross sections have provided valuable information for the determination of parton density functions and allow for stringent tests of perturbative QCD at the highest accessible energies.rnrnThis thesis will present a measurement of inclusive jet cross sections in proton-proton collisions using the ATLAS detector at the LHC at a center-of-mass energy of 7 TeV.rnJets are identified using the anti-kt algorithm and jet radii of R=0.6 and R=0.4.rnThey are calibrated using a dedicated pT and eta dependent jet calibration scheme.rnThe cross sections are measured for 40 GeV < pT <= 1 TeV and |y| < 2.8 in four bins of absolute rapidity, using data recorded in 2010 corresponding to an integrated luminosity of 3 pb^-1.rnThe data is fully corrected for detector effects and compared to theoretical predictions calculated at next-to-leading order including non-perturbative effects.rnThe theoretical predictions are found to agree with data within the experimental and theoretic uncertainties.rnrnThe ratio of cross sections for R=0.4 and R=0.6 is measured, exploiting the significant correlations of the systematic uncertainties, and is compared to recently developed theoretical predictions.rnThe underlying event can be characterized by the amount of transverse momentum per unit rapidity and azimuth, called rhoue.rnUsing analytical approaches to the calculation of non-perturbative corrections to jets, rhoue at the LHC is estimated using the ratio measurement.rnA feasibility study of a combined measurement of rhoue and the average strong coupling in the non-perturbative regime alpha_0 is presented and proposals for future jet measurements at the LHC are made.

Baryons in the chiral regime

Quantum Chromodynamics (QCD) is the theory of strong interactions, one of the four fundamental forces in our Universe. It describes the interaction of gluons and quarks which build up hadrons like protons and neutrons. Most of the visible matter in our universe is made of protons and neutrons. Hence, we are interested in their fundamental properties like their masses, their distribution of charge and their shape. \\rnThe only known theoretical, non-perturbative and {\it ab initio} method to investigate hadron properties at low energies is lattice Quantum Chromodynamics (lattice QCD). However, up-to-date simulations (especially for baryonic quantities) do not achieve the accuracy of experiments. In fact, current simulations do not even reproduce the experimental values for the form factors. The question arises wether these deviations can be explained by systematic effects in lattice QCD simulations.rnrnThis thesis is about the computation of nucleon form factors and other hadronic quantities from lattice QCD. So called Wilson fermions are used and the u- and d-quarks are treated fully dynamically. The simulations were performed using gauge ensembles with a range of lattice spacings, volumes and pion masses.\\rnFirst of all, the lattice spacing was set to be able to make contact between the lattice results and their experimental complement and to be able to perform a continuum extrapolation. The light quark mass has been computed and found to be $m_{ud}^{\overline{\text{MS}}}(2\text{ GeV}) = 3.03(17)(38)\text{ MeV}$. This value is in good agreement with values from experiments and other lattice determinations.\\rnElectro-magnetic and axial form factors of the nucleon have been calculated. From these form factors the nucleon radii and the coupling constants were computed. The different ensembles enabled us to investigate systematically the dependence of these quantities on the volume, the lattice spacing and the pion mass.\newpage Finally we perform a continuum extrapolation and chiral extrapolations to the physical point.\\rnIn addition, we investigated so called excited state contributions to these observables. A technique was used, the summation method, which reduces these effects significantly and a much better agreement with experimental data was achieved. On the lattice, the Dirac radius and the axial charge are usually found to be much smaller than the experimental values. However, due to the carefully investigation of all the afore-mentioned systematic effects we get $\langle r_1^2\rangle_{u-d}=0.627(54)\text{ fm}^2$ and $g_A=1.218(92)$, which is in agreement with the experimental values within the errors.rnrnThe first three chapters introduce the theoretical background of form factors of the nucleon and lattice QCD in general. In chapter four the lattice spacing is determined. The computation of nucleon form factors is described in chapter five where systematic effects are investigated. All results are presented in chapter six. The thesis ends with a summary of the results and identifies options to complement and extend the calculations presented. rn

Feasibility studies for accessing nucleon structure observables with the PANDA experiment at the future FAIR facility

The availability of a high-intensity antiproton beam with momentum up to 15,GeV/c at the future FAIR will open a unique opportunity to investigate wide areas of nuclear physics with the $overline{P}$ANDA (anti{$overline{P}$}roton ANnihilations at DArmstadt) detector. Part of these investigations concern the Electromagnetic Form Factors of the proton in the time-like region and the study of the Transition Distribution Amplitudes, for which feasibility studies have been performed in this Thesis. rnMoreover, simulations to study the efficiency and the energy resolution of the backward endcap of the electromagnetic calorimeter of $overline{P}$ANDA are presented. This detector is crucial especially for the reconstruction of processes like $bar pprightarrow e^+ e^- pi^0$, investigated in this work. Different arrangements of dead material were studied. The results show that both, the efficiency and the energy resolution of the backward endcap of the electromagnetic calorimeter fullfill the requirements for the detection of backward particles, and that this detector is necessary for the reconstruction of the channels of interest. rnrnThe study of the annihilation channel $bar pprightarrow e^+ e^-$ will improve the knowledge of the Electromagnetic Form Factors in the time-like region, and will help to understand their connection with the Electromagnetic Form Factors in the space-like region. In this Thesis the feasibility of a measurement of the $bar pprightarrow e^+ e^-$ cross section with $overline{P}$ANDA is studied using Monte-Carlo simulations. The major background channel $bar pprightarrow pi^+ pi^-$ is taken into account. The results show a $10^9$ background suppression factor, which assure a sufficiently clean signal with less than 0.1% background contamination. The signal can be measured with an efficiency greater than 30% up to $s=14$,(GeV/c)$^2$. The Electromagnetic Form Factors are extracted from the reconstructed signal and corrected angular distribution. Above this $s$ limit, the low cross section will not allow the direct extraction of the Electromagnetic Form Factors. However, the total cross section can still be measured and an extraction of the Electromagnetic Form Factors is possible considering certain assumptions on the ratio between the electric and magnetic contributions.rnrnThe Transition Distribution Amplitudes are new non-perturbative objects describing the transition between a baryon and a meson. They are accessible in hard exclusive processes like $bar pprightarrow e^+ e^- pi^0$. The study of this process with $overline{P}$ANDA will test the Transition Distribution Amplitudes approach. This work includes a feasibility study for measuring this channel with $overline{P}$ANDA. The main background reaction is here $bar pprightarrow pi^+ pi^- pi^0$. A background suppression factor of $10^8$ has been achieved while keeping a signal efficiency above 20%.rnrnrnPart of this work has been published in the European Physics Journal A 44, 373-384 (2010).rn

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Properties of minimally doubled fermions

Most quark actions in lattice QCD encounter difficulties with chiral sym-rnmetry and its spontaneous breakdown. Minimally doubled fermions (MDF)rnare a category of strictly local chiral lattice fermions, whose continuum limitrnreproduces two degenerate quark flavours. The two poles of their Dirac ope-rnrator are aligned such that symmetries under charge conjugation or reflectionrnof one particular direction are explictly broken at finite lattice spacing. Pro-rnperties of MDF are scrutinised with regard to broken symmetry and mesonrnspectrum to discern their suitability for numerical studies of QCD.rnrnInteractions induce anisotropic operator mixing for MDF. Hence, resto-rnration of broken symmetries in the continuum limit requires three coun-rnterterms, one of which is power-law divergent. Counterterms and operatorrnmixing are studied perturbatively for two variants of MDF. Two indepen-rndent non-perturbative procedures for removal of the power-law divergencernare developed by means of a numerical study of hadronic observables forrnone variant of MDF in quenched approximation. Though three out of fourrnpseudoscalar mesons are affected by lattice artefacts, the spectrum’s conti-rnnuum limit is consistent with two-flavour QCD. Thus, suitability of MDF forrnnumerical studies of QCD in the quenched approximation is demonstrated.

Study of the interactions of Neptunium with humic substances and the clay mineral montmorillonite by direct and non direct speciation methods

For the safety assessment of radioactive waste, the possibility of radionuclide migration has to be considered. Since Np (and also Th due to the long-lived 232-Th) will be responsible for the greatest amount of radioactivity one million years after discharge from the reactor, its (im)-mobilization in the geosphere is of great importance. Furthermore, the chemistry of Np(V) is quite similar (but not identical) to the chemistry of Pu(V). Three species of neptunium may be found in the near field of the waste disposal, but pentavalent neptunium is the most abundant species under a wide range of natural conditions. Within this work, the interaction of Np(V) with the clay mineral montmorillonite and melanodins (as model substances for humic acids) was studied. The sorption of neptunium onto gibbsite, a model clay for montmorillonite, was also investigated. The sorption of neptunium onto γ-alumina and montmorillonite was studied in a parallel doctoral work by S. Dierking. Neptunium is only found in ultra trace amounts in the environment. Therefore, sensitive and specific methods are needed for its determination. The sorption was determined by γ spectroscopy and LSC for the whole concentration range studied. In addition the combination of these techniques with ultrafiltration allowed the study of Np(V) complexation with melanoidins. Regrettably, the available speciation methods (e.g. CE-ICP-MS and EXAFS) are not capable to detect the environmentally relevant neptunium concentrations. Therefore, a combination of batch experiments and speciation analyses was performed. Further, the preparation of hybrid clay-based materials (HCM) montmorillonitemelanoidins for sorption studies was achieved. The formation of hybrid materials begins in the interlayers of the montmorillonite, and then the organic material spreads over the surface of the mineral. The sorption of Np onto HCM was studied at the environmentally relevant concentrations and the results obtained were compared with those predicted by the linear additive model by Samadfam. The sorption of neptunium onto gibbsite was studied in batch experiments and the sorption maximum determined at pH~8.5. The sorption isotherm pointed to the presence of strong and weak sorption sites in gibbsite. The Np speciation was studied by using EXAFS, which showed that the sorbed species was Np(V). The influence of M42 type melanodins on the sorption of Np(V) onto montmorillonite was also investigated at pH 7. The sorption of the melanoidins was affected by the order in which the components were added and by ionic strength. The sorption of Np was affected by ionic strength, pointing to outer sphere sorption, whereas the presence of increasing amounts of melanoidins had little influence on Np sorption.