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Decays of η to three pions
Povišer, Martin ; Zdráhal, Martin (advisor) ; Kolesár, Marián (referee)
In this work, we summarize a method established in the published literature of dispersive construc- tion of amplitude for the ! decay process. We outline Chiral Perturbation Theory (ChPT) as an effective field theory for the description of low-energy hadron dynamics, and then introduce dispersive methods with the objective of constructing process amplitudes (up to the two-loop order) similar in form to ChPT predictions. The original contribution of the present work is a software library implementing the reconstruction procedure that forms the basis for the dispersive construction of mesonic process amplitudes. This library can be used to construct amplitudes in a computer algebra system (CAS) environment, making those forms of amplitude available to fitting of experimental data and theoretical studies, especially those focusing on the extraction of the up/down quark mass difference. 1
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Construction of pseudoscalar meson amplitudes in chiral perturbation theory using a dispersive approach
Zdráhal, Martin ; Novotný, Jiří (advisor) ; Bijnens, Johan (referee) ; Ecker, Gerhard (referee)
Title: Construction of pseudoscalar meson amplitudes in chiral perturbation theory using a dispersive approach Author: Martin Zdráhal Department: Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University in Prague Supervisor: RNDr. Jiří Novotný, CSc. Abstract: We have developed a method enabling a construction of two-loop 2 → 2 scatter- ing amplitudes of pseudoscalar mesons based on the dispersion and the unitarity relations. This method is illustrated on the construction of the amplitudes of all such processes in chiral perturbation theory in isospin limit taking into account strong interactions only. Then it was used for the construction of ππ scattering amplitudes and of K → 3π and η → 3π decay amplitudes including isospin breaking effects induced by different masses of the particles belonging to the same isomultiplet. These parametrizations are prepared for various phenomenological analyses of the ππ scattering lengths and of the isospin breaking effects, both of which could pro- vide us important information for the understanding of quantum chromody- namics at low energies. Finally, we have performed the phenomenological study of η → 3π decay and obtained a value of the quark mass ratio 1/R = (md − mu)/(ms − ˆm). Our conservative estimate is R = 39.6+2.5 −5.1....
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Construction of pseudoscalar meson amplitudes in chiral perturbation theory using a dispersive approach
Zdráhal, Martin ; Novotný, Jiří (advisor) ; Bijnens, Johan (referee) ; Ecker, Gerhard (referee)
Title: Construction of pseudoscalar meson amplitudes in chiral perturbation theory using a dispersive approach Author: Martin Zdráhal Department: Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University in Prague Supervisor: RNDr. Jiří Novotný, CSc. Abstract: We have developed a method enabling a construction of two-loop 2 → 2 scatter- ing amplitudes of pseudoscalar mesons based on the dispersion and the unitarity relations. This method is illustrated on the construction of the amplitudes of all such processes in chiral perturbation theory in isospin limit taking into account strong interactions only. Then it was used for the construction of ππ scattering amplitudes and of K → 3π and η → 3π decay amplitudes including isospin breaking effects induced by different masses of the particles belonging to the same isomultiplet. These parametrizations are prepared for various phenomenological analyses of the ππ scattering lengths and of the isospin breaking effects, both of which could pro- vide us important information for the understanding of quantum chromody- namics at low energies. Finally, we have performed the phenomenological study of η → 3π decay and obtained a value of the quark mass ratio 1/R = (md − mu)/(ms − ˆm). Our conservative estimate is R = 39.6+2.5 −5.1....
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