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Effective description of resonances at low energy region
Kadavý, Tomáš ; Kampf, Karol (advisor) ; Hořejší, Jiří (referee) ; Trnka, Jaroslav (referee)
In this doctoral thesis, we study all the relevant two- and three-point Green functions of the chiral currents and densities. Specifically, in the first part of the thesis, we present the leading-order contributions of the QCD condensates up to dimension six to these Green functions, obtained within the framework of the Operator product expansion. These consist of the perturbative contribution followed by the contributions of the quark, gluon, quark-gluon and four-quark condensates. In the second part, we restrict ourselves to the order parameters of the chiral symmetry breaking in the chiral limit. We investigate them within the Chiral perturbation theory and Resonance chiral theory and, in order to obtain constraints on the parameters of the effective Lagrangians, we require their high-energy behaviour to match OPE. As it turns out, the duplication of the lowest vector, axial-vector, scalar and pseudoscalar resonance multiplets in the corresponding Lagrangians is necessary. As a special case, we study the ⟨V V P⟩ Green function with three vector and three pseudoscalar resonance multiplets taken into account - needless to say, this investigation is performed on an algebraic level only. We also study the correlation of the pion-pole contribution to the muon g − 2 factor and the effective parameter χ(r) . 1
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Dimensional transmutation in quantum theory
Ebr, Jan ; Hořejší, Jiří (advisor) ; Novotný, Jiří (referee)
This work deals with two models - from the quantum eld theory it is the massless scalar electrodynamics (the so-called Coleman-Weinberg model) and from quantum mechanics it is the contact (-function) potential (in two dimensions) - that are apparently invariant under some sort of scale transformations and thus they, in suitably chosen units, contain only dimensionless parameters. It turns out that even in the quantum-mechanical case one has to add an additional procedure to the formal denition of the model and that the use of dierent physical regulators leads to the same results, that furthermore agree with the predictions of the mathematically rigorous method of self-adjoint operator extensions. In this work, we present detailed calculations supporting this result. Contrary to the common literature, we do so in a straightforward manner, which can be followed step by step (with all the necessary elements of functional analysis summarised in the Appendix). In quantum eld theory we apply a similar approach, when we "rediscover" the results of the abstract functional methods in the ordinary perturbation theory. In its framework, we further show how to obtain predictions also for other quantities than particle masses.
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Search for Axion-Like Particles at the NA62 experiment
Jerhot, Jan ; Kampf, Karol (advisor) ; Hořejší, Jiří (referee)
The thesis instructively presents axions and axion-like particles as a plau- sible extension of the Standard Model of particle physics and discusses also the cosmological implications in the case of their existence as they present one of the most favourable dark matter candidates at given circumstances. The main part of the thesis is concerned with a search for axion-like particles at the NA62 experiment at CERN and a study of the gathered data and its impact on the data analysis.
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Electroweak symmetry breaking by dynamically generated masses of quarks and leptons
Smetana, Adam ; Hošek, Jiří (advisor) ; Hořejší, Jiří (referee) ; Olejník, Štefan (referee)
Title: Electroweak symmetry breaking by dynamically generated masses of quarks and leptons Author: Adam Smetana Department: Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University Supervisor: Ing. Jiří Hošek, DrSc., Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic Abstract: The aim of the thesis is to study models of the electroweak symmetry breaking caused by dynamically generated masses of quarks and lep- tons. (1) We perform the basic analysis whether the main underlying idea, that the masses of only known fermions can provide the elec- troweak symmetry breaking, is actually feasible. For that we elaborate a two-composite-Higgs-doublet model of the top-quark and neutrino condensation. The model suggests rather large number, O(100), of right-handed neutrinos. (2) We analyze the model of strong Yukawa dynamics where the dynamical fermion mass generation is provided by exchanges of new elementary massive complex doublet scalar fields. We focus on solving the coupled Schwinger-Dyson equations for fermion and scalar self-energies by means of approximative methods. We doc- ument that strongly hierarchical mass spectra can be reproduced. (3) We elaborate the flavor gauge model where the dynamical fermion mass...
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Scattering of the electroweak vector bosons
Morávek, Petr ; Hořejší, Jiří (advisor) ; Novotný, Jiří (referee)
In the present work we study the scattering of vector gauge bosons in the framework of higher dimensional theory of Kaluza-Klein type. This work provides an instructive introduction to the given problematics with all technical details of the relevant calculations. The basic ideas of the theory are demonstrated on a set of simple models. Particular attention is paid to the selection of consistent boundary conditions using the variational principle of least action, gauge invariance and tree-level unitarity of longitudinal gauge bosons scattering.
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Dynamical symmetry breaking in models with strong Yukawa interactions
Beneš, Petr ; Hošek, Jiří (advisor) ; Hořejší, Jiří (referee) ; Olejník, Štefan (referee)
Title: Dynamical symmetry breaking in models with strong Yukawa in- teractions Author: Petr Beneš Department: Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University Supervisor: Ing. Jiří Hošek, DrSc., Department of Theoretical Physics, Nu- clear Physics Institute, Academy of Sciences of the Czech Repub- lic Abstract: The primary aim of the thesis is to explore the possibility of spon- taneous symmetry breaking by strong Yukawa dynamics. Tech- nically, the symmetry is assumed to be broken by formation of symmetry-breaking parts of both the scalar and the fermion prop- agators, rather than by the scalar vacuum expectation values. The idea is first introduced on an example of a toy model with the underlying symmetry being an Abelian one and later applied to a realistic model of electroweak interaction. In addition, the thesis also deals with some more general, model-independent is- sues, applicable not only to the discussed model of strong Yukawa dynamics, but to a wider class of models with dynamical mass generation. First of these issues is the problem of fermion flavor mixing in the presence of fermion self-energies with a general mo- mentum dependence. It is in particular shown how to define the CKM matrix in such models and argued that it can come out in principle...
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