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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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The derivation of dispersion relations for anisotropic thick plates in system Maple
Červená, Olga ; Hora, Petr
The dispersion relations for cubic and orthotropic thick plates, which were derived in system MAPLE, are summarized in the report. The report contains listings of two programs in Maple. The form of Christoffel equation, forms of its roots and polarizations of partial waves for cubic and orthotropic thick plates are derived in first of them. The forms of dispersion relations of symmetric, anti-symmetric, SH-modes and Mindlin’s uncoupled modes for cubic and orthotropic plates are derived in second program. The report is deal with interpretation of the false roots, which are occurred at computing the dispersion relations. The outcome dispersion curves computing by MATLAB are displayed in the conclusion.
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