Analytical and unitary approach in mesons electromagnetic form factor applications

In the dissertation thesis we address several topics related to the domain of particle physics. All of them represent interesting open problems that can be connected to the elastic or transition electromagnetic form factors of mesons, the form factors being the main objects of our interest. Our ambition is to contribute to the solution of these problems and use for that purpose known analytic properties of the form factors and the unitarity condition. These two tools are very powerful in the low energy domain (such as bound states of partons), where the perturbative QCD looses its validity. This is the motivation for construction of the unitary and analytic (U and A) models of studied form factors, that enable us to get the majority of our results. We use the U and A model to evaluate the contribution of the processes e⁺e^- → Pγ, P = π⁰, η, η to the muon magnetic anomaly a_μ in the lowest order of the hadronic vacuum polarization. For the contribution a_μ^had,LO (π⁺π^-) we demonstrate, that the use of the model leads to a dramatic error reduction with respect to the results of other authors. We also get a shift in the central value in the 'correct' direction, that brings the theoretical value closer to the experimental one. This results encourages us to use the model also for the evaluation of a_μ^had,LO (P_γ). These contributions are smaller, however the precision of the experiment makes their evaluation necessary. We further use the U and A model of the transition form factors of π⁰, η and η^' mesons to predict the partial decay widths of these particles Γ_π⁰→γγ and Γ_η→γγ and Γ_η^'→γγ. In this way we make an independent cross check of the PDG table values. We find an agreement in the case of Γ_η→γγ and Γ_η^'→γγ, even a smaller uncertainty for Γ_η^'→γγ. In the case of Γ_π⁰→γγ we find a disagreement that points to an interesting problem. We wonder whether it could be related to a very different type of experiment, a direct lifetime measurement, that was predominantly used to get the Γ_π⁰→γγ value (unlike in the case of our evaluation or in the case of the PDG values for Γ_η→γγ and Γ_η^'→γγ. We are looking forward to analyze this issue and contribute to the solution. We finally study the behavior of the elastic pion EM form factor in the space-like domain. In this case we aimed to minimize the model dependence and based our approach only on the analytic properties of the form factor and the precise data in the time-like region. Our motivation was the data in the space-like region that, we believe, cannot be fully trusted. Further, we wanted to compare our prediction to other QCD inspired model. We have shown, that the prediction we obtain has only small model dependence. By making a prediction in the time-like region we have also shown that our approach is self-consistent, the prediction describes well the data points that were initially used to get it. Eventually we observed that our prediction is close tho the most recent result obtained in the framework of the AdS/CFT theory. The obtained results allow us to conclude that the unitary and analytic model and approach as such are correct tools to study meson form factors and we have shown, that they have big potential to give important results in several domains of particle physics. (author)