Analysis tools for precision studies of hadronic three-body decays and transition form factors

Abstract

Due to the running coupling constant of Quantum Chromodynamics one of the pillars of the Standard Model, the strong interactions, is still insufficiently understood at low energies. In order to describe the interactions of hadrons that form in this physical regime, one has to devise methods that are non-perturbative in the strong coupling constant. In particular hadronic three-body decays and transition form factors present a great challenge due to the complex analytic structure ensued by strong final-state interactions. In this thesis we present two approaches to tackle these processes.<br /> In the first part we use a modified version of non-relativistic effective field theory to analyze the decay η→ 3π. This perturbative low-energy expansion is ideally suited to study the effects of ππ rescattering and contributes greatly to the understanding of the slope parameter of the η→ 3π⁰ Dalitz plot, a quantity that is strongly influenced by final-state interactions and has presented a long-standing puzzle for theoretical approaches.<br /> In the second part we present dispersion relations as a non-perturbative means to study three-particle decays. Using the example of η'→ ηππ we give a detailed introduction to the framework and its numerical implementation. We confront our findings with recent experimental data from the BES-III and VES collaborations and discuss whether the extraction of πη scattering parameters, one of the prime motives to study this decay channel, is feasible in such an approach.<br /> A more clear-cut application will be given in our study of the decays ω/ϕ→3π due to the relative simplicity of this decay channel: our results are solely dependent on the ππ P-wave scattering phase shift. We give predictions for the Dalitz plot distributions and compare our findings to very precise data on ϕ→3π by the KLOE and CMD-2 collaborations. We also predict Dalitz plot parameters that may be determined in future high-precision measurements of ω→3π and present a calculation of the ππ P-wave inelasticity from ωπ intermediate states.<br /> Finally, we extend the framework and discuss the ω/ϕ→π⁰γ^* transition form factor. For that we use the previously determined ω/ϕ→3π partial-wave amplitude and the well-known pion vector form factor as input. Our findings are compared to recent measurements of ω→π⁰μ⁺μ^- by the NA60 collaboration. We also suggest that a precise measurement of the Okubo—Zweig—Iizuka-forbidden ϕ→π⁰ℓ⁺ℓ^- decay may help to understand the strong deviations found between recent theoretical determinations and transition form factor data.