Green functions of currents allow us to study resonances in the low- energy limit of QCD. Using them, we can construct amplitudes or decay widths of processes. By a comparison of the theoretical predictions with experimental measurements we can determine the values of parameters of the theory and obtain a more comprehensive understanding about the be- haviour of QCD processes. In our investigated topic, an odd-parity sector of QCD, exist five nontriv- ial three-point Green functions, also referred to as correlators. Correlators V V P and V AS have already been studied in [1], whilst a calculation of AAP was provided in [2]. In this thesis we therefore deal with the Green functions V V A and AAA that have not yet been studied before. We present a complete calculation of the contributing Feynman diagrams in the anti- symmetric tensor formalism that satisfies high-energy behaviour within the OPE framework, as was shown also in [2]. The obtained results are submit- ted to phenomenological studies. Further, we also present an introduction to our calculations of the four- point Green functions V V PP and V V V V . The calculations were carried out both in the antisymmetric tensor and vector formalism but due to the complicated tensor structure of the results, the calculations can not be shown here in their...

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Not so long ago, the value of the branching ratio of a neutral pion decay to an electron-positron pair (π0 → e− e+ ) has been updated and became more accurate thanks to the fact, that new measurements were performed at KTeV experiment at Fermilab. In this context it has been showed, that the Standard Model theoretical prediction is not precise enough. The resulting discrepancy was not explained yet. In presented work, there are summarized preceding results, al- ready computed correction were taken into account and newly the Bremsstrahlung contribution was thoroughly calculated. Besides, the contribution of π-loop cor- rections in terms of double-logarithms is estimated. In the end, because of the persisting disagreement of the accepted theory with the experiment, an additional contribution is suggested from beyond the Standard Model on the basis of models describing the dark matter. The latter mentioned is a hot candidate to explain many phenomena, for example the mysterious source of a great amount of γ-rays coming from the center of our galaxy and having the origin in the annihilation of electron-positron pairs. 1

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This thesis familiarizes the reader with the process behind the construction of ππ scattering amplitudes. Several representations and transformations nec- essary to pass from one to another are introduced. Then known solutions of Roy equations are employed to extract values of subthreshold parameters αππ and βππ from recent experimental data. As a second goal three-flavour chiral perturbation theory(χPT), which is a low energy effective field theory of quan- tum chromodynamics, is used to obtain theoretical predictions for αππ and βππ by applying a technique called resummed approach. A large statistical ensemble of predictions is numerically generated. Subsequently, Bayesian statistics is uti- lized to get more information about spontaneous symmetry breaking parameters X(3), Y (3), Z(3), which are related to the leading order low energy coupling constants of three-flavour χPT. These results are then compared to several other recent determinations. Significant shifts in probability distributions compared to Descotes-Genon et al. [2004] are observed. The new results are more consistent with theoretical expectations. 1 Bibliography S. Descotes-Genon, N. H. Fuchs, L. Girlanda, and J. Stern. Resumming qcd vac- uum fluctuations in three-flavor chiral perturbation theory. The European Phys- ical Journal C,...

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Effective field theories (EFTs) provide frameworks to systematically improve perturbation expansions in quantum field theory. This improvement is essential in quantum chromodynamics (QCD) predictions, both at low energy in the description of low momentum hadron-hadron scattering and at high energy in the description of electron-positron, proton-proton, proton-electron collisions. It is also important in quantum electrodynamics (QED), when electrons interact with a high-intensity, long-wavelength classical field. I introduce the principles and methods of effective field theory and describe my work in three EFTs: First, in the perturbative QCD region, I use soft collinear effective theory (SCET) to prove that strong interaction soft radiation is universal and to increase the QCD accuracy to next-to-next-to-next-to leading logarithm order for new particle searches in hadron colliders. I also compute a new class of non-perturbative, large logarithmic enhancement arising near the elastic limits of deep inelastic scattering and Drell-Yan processes. Second, in the QCD confinement region, I use heavy hadron chiral perturbation theory to study near-threshold enhancements in the scattering of 𝐷 and 𝜋 mesons near the threshold for the excited 𝐷-meson state, 𝐷*, as well as in the scattering of 𝐷 and 𝐷* mesons near the threshold for the exotic hadron X(3872). This work provides a clear picture of the hadronic molecule X(3872) and more profound understanding of the nuclear force between hadrons. Finally, inspired by SCET, I construct a new electron-laser effective field theory to describe highly-relativistic electrons traveling in strong laser fields, extract the universal distribution of electrons in strong electromagnetic backgrounds and its evolution in energy from the separated momentum scales of emitted photons and classical radiation, and predict the rate of wide angle photon emission. I conclude with limitations of EFT methods and some perspectives on what new work may be achieved with these EFTs.

Das Ziel dieser Dissertation besteht darin, die Realisierbarkeit der Berechnungen der Niederenergie-Konstanten der chiralen Lagrangedichte zur Gewinnung physikalischer Informationen im epsilon--Regime der quenched QCD zu erforschen. Wir haben der Neuberger Operator und Overlap Hyperkubus Operator eingesetzt. Ein Hauptergebniss dieser Arbeit ist der Vergleich der Wahrscheinlichkeitsverteilungen einzelner Eigenwerte des Neuberger Operators in der QCD mit den analytischen Vorhersagen der Theorie der Zufallsmatritzen. Wir beobachten eine gute Übereinstimmung solange jede Seite des physikalischen Volumens größ er als etwa 1.12 fm ist. Dabei kann auch das chirale Kondensat Sigma abgeschätzt werden. Es ergab sich, daß diese untere Schranke von L allgemein gilt und die Größ e des physikalischen Volumens, auf dem der Axialkorrelator den Vorhersagen des chiralen Störungstheorie folgt, festlegt. Damit koennen wir die Pionzerfallskonstante bestimmen. Unsere Simulationen zeigen, daß wegen der groß en Wahrscheinlichkeit niedriger Eigenwerte die Messung des Axialkorrelators im topologischen neutralen Sektor extrem aufwändig ist. Doch reicht die Empfindlichkeit der Vorhersagen der chiralen Störungstheorie in höheren topologischen Sektoren bei der gegebenen Statistik nicht zur Bestimmung von Sigma aus. Als alternative Methode, gehen wir dazu über, allein den Beitrag der Nullmoden zu betrachten. Hier koennen wir Abschätzungen für die Pionzerfallskonstante und alpha gewinnen. Wir berechnen die topologische Suszeptibilität für den Neuberger und Overlap Hyperkubus Operator. Im letzten Fall ist der berechnete Wert näher beim Kontinuumslimes. Die Lokalisierung für den Overlap Hyperkubus Operator ist auch besser als für den Neuberger Operator. Unser anderes Ziel ist die Erforschung einer topologieerhaltenden Eichwirkung. / This thesis is dedicated to explore the feasibility of extraction of the low energy constants of the chiral Lagrangian in the epsilon--regime of quenched QCD. We apply two formulations of the Ginsparg-Wilson fermions, namely, the Neuberger operator and the hypercube overlap operator to compute the observables of interest. As a main result we present the comparison of the distributions of the leading individual eigenvalues of the Neuberger operator in QCD and the analytical predictions of chiral random matrix theory. We observe a good agreement as long as each side of the physical volume exceeds about 1.12 fm. At the same time the chiral condensate Sigma can also be estimated. It turns out that this bound for L is generic and sets the size of the physical volume where the axial correlator behaves according to chiral perturbation theory. This allows us to compute a value for the pion decay constant. The simulations also show that due to the high probability of the near-zero modes it is prohibitively difficult to sample the axial correlator in the neutral topological sector. In the higher sectors, however, we observe that the sensitivity of the analytical predictions for the axial correlator to extract Sigma is lost to a large extent. As an alternative procedure we only consider the contribution from the zero modes. Here we are able to obtain an estimate for the pion decay constant and alpha, where alpha is a low energy constant peculiar to quenching. We calculate the topological susceptibility, both for the Neuberger operator and for the overlap hypercube operator. It turns out that the result with the overlap hypercube operator is closer to the continuum limit. Also the locality properties are superior to those of the Neuberger fermions. As a theoretical development the Lüscher topology conserving gauge action is investigated. This enables us to sample the observables of interest in the epsilon--regime without recomputing the index.

Eine zusammenfassende Übersicht über die Formulierung der chiralen Störungstheorie (ChPT) für die Gitter Quantenchromodynamik (QCD) ist gegeben. Wir beginnen mit kurzen Zusammenfassungen der chiralen Störungstheorie für die Kontinuum-QCD sowie Symanziks effektiver Theorie für die Gitter-QCD. Anschließend wird die Formulierung der ChPT für die Gitter-QCD behandelt. Nach einem weiteren Kapitel über partial quenching und Theorien mit gemischten Wirkungen werden konkrete Anwendungen diskutiert: Wilson ChPT, staggered ChPT sowie Wilson ChPT mit einem chiral verdrehten Massenterm. Die folgenden Kapitel behandeln das Epsilonregime mit Wilsonfermionen sowie ausgewählte Resultate für ChPT mit gemischten Wirkungen. Den Abschluß bildet die Formulierung der chiralen Störungstheorie für schwere Vektormesonen mit Wilsonfermionen. / The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed.

The electroweak hierarchy problem is one of the most important puzzles of particle physics that remains without conclusive answer nowadays. One of the most recent new class of solutions to this problem is presented in this thesis, i.e., the cosmological relaxation of the electroweak scale. In this framework, we postulate the existence of a new particle, the relaxion, which drives the Higgs mass to values much smaller than the cutoff of the theory during inflation. As tools to develop this subject, this work presents a resume of chiral perturbation theory, the strong CP problem, axions and the eta prime particle. Finally, we will describe the most simple model of cosmological relaxation of the electroweak scale and the non-QCD model, where a new strong group SU(N) forms a condensate that interacts with the relaxion. / O problema da hierarquia eletrofraco é um dos enigmas mais importantes da física de partículas que continua sem uma solução conclusiva hoje em dia. Uma nova classe de soluções, dentre as mais recentes, para este problema é apresentado nessa dissertação, i.e., o relaxamento cosmológico da escala eletrofraca. Neste quadro, nós postulamos a existência de uma nova partícula, o relaxion, que conduz a massa do bóson de Higgs para valores muito menores que o cutoff da teoria durante a inflação. Como ferramentas para desenvolver este assunto, este trabalho apresenta um resumo de teoria de perturbação quiral, o problema CP forte, axions e a partícula eta prime. Finalmente, iremos descrever o modelo mais simples de relaxamento cosmológico da escala eletrofraca e o modelo sem-QCD, onde um novo grupo de interação forte SU(N) forma um condensado que interage com o relaxion.