The eta-eta' system in large-Nc chiral perturbation theory
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Abstract
This thesis is concerned with calculations of processes involving the η-η' system in the framework of large-Nc chiral perturbation theory (LNcChPT). The calculations are performed at the one-loop level up to and including next-to-next-to-leading order (NNLO) in the simultaneous expansion in external momenta, quark masses, and 1/Nc.
First, a general expression for the η-η' mixing at NNLO is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the η-η' system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. The influence of one-loop corrections as well as OZI-rule-violating parameters is studied.
The second part of the thesis deals with quantum corrections to the chiral anomaly accounted for by the Wess-Zumino-Witten action. The anomalous and normal Ward identities are explicitly confirmed at the one-loop level, both in SU(3) ChPT and LNcChPT. To that end, the three-point Green function involving one axial-vector current and two vector currents (AVV) with all three legs off shell is calculated.
The anomalous decays η(')→γ(*)γ(*) and η(')→π^+π^-γ(*) are calculated at the one-loop level up to NNLO in LNcChPT. Both the decays to real photons and the decays involving virtual photons, providing access to the substructure of the mesons, are discussed. The results are numerically evaluated successively at LO, NLO, and NNLO. The appearing low-energy constants are determined through fits to the available experimental data. In the case of η(')→γ(*)γ(*), we investigate the decay widths to real photons, the widths of η(')→γl^+l^-, where l=e, µ, and the single-virtual transition form factors. The considered observables of the decays η(')→π^+π^-γ(*) are the spectra of the decays involving a real photon, η(')→π^+π^-γ, as well as the spectra of η(')→π^+π^-l^+l^-, where l=e, µ, with respect to the invariant masses of the π^+π^- and l^+l^- systems.