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.

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.

The role of scalar mesons in radiative vector meson decays is investigated. The effects of scalar-isoscalar f_{0}(980) and scalar-isovector a_{0}(980) mesons are studied in the mechanism of the radiative Phi-&gt / pi{+}pi{-}gamma and phi-&gt / pi{0}eta gamma decays, respectively. A phenomenological approach is used to study the radiative phi-&gt / pi{+}p{-}gamma decay by considering the contributions of sigma-meson, rho-meson and f_{0}-meson. The interference effects between different contributions are analyzed and the branching ratio for this decay is calculated. The radiative phi-&gt / pi{0}eta gamma decay is studied within the framework of a phenomenological approach in which the contributions of rho-meson, chiral loop and a_{0}-meson are considered. The interference effects between different contributions are examined and the coupling constants g_{phi a_{0} gamma} and g_{a_{0}K{+}K{-}} are estimated using the experimental branching ratio for the phi-&gt / pi{0}eta gamma decay. Furthermore, the radiative rho{0}pi{+}pi{-}gamma$ and rho{0}-&gt / pi{0}pi{0}gamma decays are studied to investigate the role of scalar-isoscalar sigma-meson. The branching ratios of the rho{0}-&gt / pi{+}pi{-}gamma and rho{0}-&gt / pi{0}pi{0}gamma decays are calculated using a phenomenological approach by adding to the amplitude calculated within the framework of chiral perturbation theory and vector meson dominance the amplitude of sigma-meson intermediate state. In all the decays studied the scalar meson intermediate states make important contributions to the overall amplitude.

In this master’s thesis the width of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> meson is studied as a function of temperature. We consider a background medium consisting of a pion gas and assume a vanishing net baryon chemical potential. The width is obtained in the framework of large <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N_%7Bc%7D" /> chiral perturbation theory and we consider terms up to next-to-leading order in the effective Lagrangian. We use a low-density approximation to calculate the width increase due to scattering with pions from the heat bath. The results suggest that the in-medium width for the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> may become of considerable size: at a temperature <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?T%5Capprox%2075" /> MeV we find a width increase of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%5CGamma%5Capprox%203-4" /> MeV, comparable to the inverse lifetime of the fireball created in a heavy-ion collision. The <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> is of particular interested since it is intimately connected to the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?U(1)_%7BA%7D" /> anomaly of Quantum Chromodynamics (QCD). It has been speculated that <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?U(1)_%7BA%7D" /> may become a symmetry of QCD at high temperatures and studies of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> could indicate if that is the case. Depending on for how large temperatures the results from large <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?N_%7Bc%7D" /> can be trusted, they indicate that the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Ceta'" /> may be possible to study experimentally in heavy-ion collisions due to its sizable in-medium width.