Dispersive analyses of three-body decays and scattering reactions

More than half a century after the discovery of quantum chromodynamics as the quantum-field-theoretical description of the strong interaction, its non-perturbative nature in the low-energy regime still poses a unique challenge. Particularly, the fundamental properties and scattering of light hadrons need to be studied precisely to unravel the structure of the strong interaction. In this thesis, we consider manifold applications of this kind using dispersive techniques that are based on the <em>S</em>-matrix principles of unitarity and analyticity. <br> We perform a study of rescattering effects in 3π final states, which are often described in terms of two-body resonances and a non-interacting spectator particle. Using Khuri–Treiman dispersion relations, we include crossed-channel effects and estimate the rescattering effects beyond the simplest isobar model for a selected set of quantum numbers. This allows for an estimate when rescattering effects become important and more complicated analysis techniques are needed to extract meaningful physical information from experiments. <br> However, Khuri–Treiman equations are limited to low energies as they are built from truncated partial-wave expansions. Therefore, a new parameterization is presented that can fulfill all theoretical expectations and connects the essential physics of hadron scattering both near threshold and in asymptotic limits. In this construction, dynamical information is entirely contained in Regge trajectories that generalize resonance poles in the complex-energy plane to poles in the angular-momentum plane. While the construction and first results are successfully presented in this thesis, this formalism allows for many extensions that can be explored in the future. <br> Properties of kaons are investigated using the kaon electromagnetic form factor and the Primakoff reactions γK→Kπ and γK→γK. These are constructed obeying the constraints of analyticity, which enables the extrapolation to unphysical energies or the pole positions on the second Riemann sheet. Using the kaon form factor allows for a calculation of the electromagnetic charge radius from a fit to experimental data in timelike and spacelike regions, while the Primakoff reactions can be used in the future to extract the chiral anomaly, radiative K^*(892) couplings, and kaon polarizabilities. Additionally, there are several different applications for these results, e.g., the anomalous magnetic moment of the muon and corrections to Dashen's theorem.