Konstrukce pseudoskalárních mezonových amplitud v chirální poruchové teorii za použití disperzních metod

Zdráhal, Martin

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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